Preface
Three of the major challenges that mankind will come across in the coming decades are increasing energy demand...
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Preface
Three of the major challenges that mankind will come across in the coming decades are increasing energy demand, threatening water shortage, and so far inscrutable climate warming. World climate has been always undergoing significant changes in the past, which were represented by irregular interchanging of colder and warmer cycles of varying duration. At present, however, we witness a pronounced global warming, which seems even to accelerate. Air temperature is rising rapidly as does increase in the weather variability producing frequent extreme events. Six of the 10 warmest years of the twentieth century occurred in the 1990s. Temperatures predicted for the twenty-first century ranges well above the present-day value. If such trend is to continue in the future, serious environmental consequences may be unavoidable. The time period of the last 100-200 years covered by the direct meteorological observations is too short and does not provide material to reliable assess what may happen over the next hundred(s) years. A faithful prediction of the future requires understanding how climate system works, i.e. to reconstruct past climate much further into the past. The estimates of climate variability prior to the existence of an instrumental record of surface temperature are derived from climate proxies. The need to better understand the temperature component of climate models and to extent it into the past inspired the development of a new direct climate reconstruction method (which we call here Borehole Climatology) based on tracing the subsurface "climate fingerprint" left by the past climatic changes. Borehole climatology enables climate reconstruction of the past several millennia, unlike proxy methods provides a direct past temperature assessment and can extend the areal range to the remote regions poorly covered with meteorological observations. The global warming is manifested by increasing mean surface air temperature. Surface temperature changes then propagate downward and impart certain temperature "signature" to the rock strata in the shallow subsurface that can be analyzed to yield direct information on the past climate history. The Earth's subsurface represents, thus, a unique archive of the past climate data, which can be gained by inversion of the present-day temperature-depth profiles measured in boreholes. While the instrumental air temperature records cover only a relatively short period of one or two centuries, the alternative "geothermal" method provides useful research tool to infer paleoclimate variations on the long timescale. Significant progress that has occurred in the borehole climatology in the last two decades was the major motivation for the proposed book. Our book represents the state-of-art of "Borehole Climatology". It explains the principles of the "geothermal" method, gives an account on various techniques of the ground surface temperature reconstruction and summarizes the major results to reveal the climate scenario spanning from Holocene to Recent. On the borehole temperature data taken in various locations all over the world we demonstrate examples of the interaction between the subsurface temperature response to time changes in the ground surface, vegetation
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cover, land-use, and urbanization. An incorporation of the geothermal data into a multiproxy reconstruction provides an independent estimate of the long-term temperature trends. Thus, the worldwide results of the borehole data analyses indicate, for example, that observed increase in the mean air temperature in the twentieth century is likely to be the largest of any preceding century of the past 1000 years. The final goal is to assess the magnitude of the present-day warming and to distinguish between the natural climate variability and the potential human contribution due to environmental pollution. Precise temperature-time monitoring in shallow subsurface can further provide the magnitude of the present-day warming within relatively short time intervals. We are grateful to have found a forum for Borehole Climatology research in this book, and we hope that it will contribute to the continuation and advance of the research work in this area in the future.
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CHAPTER 1
Background and History of the Problem
Weather substantially influences our day-by-day life. The most simple explanation of weather: “It is all that happens outside”. Weather includes the changes of hot and cold or wet and dry. It may be calm or stormy, and clear or cloudy. Weather is a variety of events that occur in the atmosphere all over the world. Broadly speaking, weather is the placeby-place and the day-by-day and/or season-by-season feeling of the state of the atmosphere, when the events take place on relatively small scales both spatially and temporally. Meteorologists record the weather every day. Continuous recording of various weather indices helps to determine the climate of an area. In the every day life people grasp mainly the short-term weather fluctuations, while human perception of climatic changes is rather limited. Climate is a powerful tool for dealing with the weather and represents the average of weather on some spatial scale over a long period of time. It puts somewhat wild, unpredictable everyday weather into long-term perspective. If one knows the climate of some region, he possesses information about what the weather may occur today, a week later, or next year. Climate is the time integral of weather over a period of decades or longer. It accumulates the totality of weather events, thus, may be broadly defined as the long-term behavior of the environmental system. 1.1 The Climate of the Holocene The fact is that Earth’s climate is perpetually changing. Widespread climatologic investigations have shown that climate varies on all timescales from decades to millions of years. The past changes have ranged from slow and gradual to fast and even abrupt. An impact of climate fluctuations on the mankind is extremely significant, sometimes dramatic. Even in relatively recent fifteenth to eighteenth centuries the decrease of the mean annual surface air temperature (SAT) by one or two degrees produced the so-called “Little Ice Age” that had strongly altered many social and economic sectors in Europe. That time the populations died from the crop failure and famine. According to Lamb (1969) “… climatic history must be central to our understanding of human history …”
1
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Fig. 1. Climate for the last 420 000 years: Temperature anomalies are based on Vostok ice core data, Antarctica (adopted from Petit et al., 1999). Reference baseline corresponds to the present global mean air temperature.
Climate can be usually described in terms of normals,1 means and extremes of a variety of weather elements. SAT is typically of interest in any discussions of the large-scale climate variability. It is also a major driving factor in various investigations of the climate impact on many natural and managed systems as well as determining variable for different climatic models. Climate may vary on a large range of temporal and/or spatial scales. Spatial scales may be local (⬍105 km2), regional, continental (10–100 million km2), or global. Temporal scales may vary from relatively short duration (annual/decadal) to long scales comparable with the characteristic times of the geological processes (hundreds of millions of years). On the longer timescale the Earth’s climate roughly represents the alternating of ice ages and interglacials, when the former are characterized by major extension of the polar ice sheets and growth of the mountain glaciers. Figure 1 shows the existing temperature deviations from the long-term temperature average over approximately the past half million years. The temperature anomalies were deduced from the measurements of the isotopic fractionation of oxygen in the ice core from Vostok, the Russian base in Antarctica (Petit et al., 1999; see also the web site of the National Climatic Data Center
1
Climate normals or averages are used to summarize or describe the average climate conditions of a particular location.
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Fig. 2. Climate of the last 50 000 years: Temperature reported for central Greenland (adopted from Alley, 2000). Climate pattern in central Greenland is characterized by a pronounced rapid termination of the ice age about 15 000 years ago, followed by an irregular transient cooling period known as the Younger Dryas, and by abrupt return to the warm interglacial conditions (warming of approximately 0.8 K/yr).
www.ncdc.noaa.gov/paleo/data.html). Temperature anomalies varied between ⫹2 and ⫺8°C reflecting the oscillations in global ice volume with a period of about 100 000 years, although the time pattern is not perfectly regular. Multiple shorter time excursions were superimposed on the long-term cycles. It is obvious that the ice age conditions were characteristic for the most of the last 420 000 years. The short warmer periods (the interglacials) typically continued not longer than few thousands to maximum 15⫺20 thousand years. Figure 2 shows the Greenland ice core data for the last 50 000 years (Alley, 2000). Temperature interpretation is based on stable isotope analysis and ice accumulation data from the GISP2 ice core (central Greenland). Table 1 summarizes the estimated durations of the main events shown in Figure 2. As seen, the peak of the last glacial period occurred 21 000 years ago (the Last Glacial Maximum). That time the continental ice sheet reached to mid-latitudes of Europe and North America (Bradley, 1999; Ruddiman, 2001). This glacial period was somewhat abruptly transformed into the present interglacial not later than 12 000⫺7000 years B.P. Until the 1990s, the general view of climate change was that the Earth’s climate system changes gradually in response to the natural as well as human-induced forcing. However, recent evidences gained from various fields of climatology show that climate may change more rapidly, even abruptly. Greenland ice core record provides a clear picture of such abrupt climate change. One of the best-known and well-studied widespread abrupt temperature decreases is the Younger Dryas cold interval,
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Borehole Climatology: A New Method on How to Reconstruct Climate Table 1. Main paleoclimatic events of the last 125 000 years (guide to terminology) Event Last interglacial peak Last glacial maximum Last glacial Younger Dryas Last deglaciation Holocene “Climatic Optimum” Holocene maximum warming
Estimated age (ka B.P.) ⬃124 ⬃25 to 18 ⬃74 to 14 ⬃12.7 to 11.5 ⬃18 to 10 ⬃10 to present ⬃4.5 to 6 (Europe) ⬃10 to 6 (Southern hemisphere)
when the last warming trend was shortly interrupted by a sudden cooling at about 12 700 years ago. This cooling event was ended even more suddenly about 11 500 years ago (Figure 2). Climate records proved that much of the Northern hemisphere was affected by extremely cold, dry, windy conditions. This event is important because it demonstrates that rapid temperature drops can still occur even during relatively stable and continuous interglacial conditions. The warming was restored at 11 600–10 500 B.P., and this most recent glacial retreat is still going on. The Holocene is the name given to the last approximately 10 000 years of the Earth history, the time since the end of the last major glacial epoch. The unusual, “flat” nature of the last 11 000–12 000 years of the Greenland record represents striking contrast to the periods of cold that had preceded it. Temperature variations over the Holocene period (0.01 Ma to the present) show significantly smaller range in comparison with the early ice age oscillations. However, even such small variations might have significant impact on human civilizations. The Climatic Optimum was the most noticeable period of the mid Holocene. In Europe its maximum was centered around 6000–4500 years B.P., higher SAT by 1 to 2°C existed in some parts of the Earth (particularly in the extra-tropics of the Northern hemisphere). This period coincides with time when the great ancient civilizations were born and flourished. Temperature records of the last two millennia for the Northern and Southern hemispheres and on the global scale are presented in Figure 3 (Mann and Jones, 2003). For more information see also the link of Goddard Institute for Space Studies, New York, (www.giss.nasa.gov/research/paleo). As seen, SATs have changed rather differently in the two hemispheres, and a sharp recent temperature increase in the Northern hemisphere does not bear a resemblance to more gradual increase in the Southern hemisphere. From the review of paleoclimatic data covering the last two millennia (late Holocene) Williams and Wigley (1983), Jones and Mann (2004; see also the references therein) have identified three main climatic excursions. As has been recently demonstrated, the timing of these cold and warm excursions of climate varies geographically over the globe (Crowley and Lowery, 2000). The comparison on the global scale has a trouble in doing because the direct evidence for temperature changes in past few centuries for the Southern hemisphere is sparse. Thus, the timing of the main climatic changes is generally tied on the conventionally-defined European region and/or the Northern hemisphere.
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Fig. 3. Last two millennia multiproxy temperature reconstructions for the Northern and Southern hemispheres and for the global scale (drawn from Mann and Jones, 2003). Temperature anomalies are based on 1961–1990 instrumental reference period. Smoothed course corresponds to 50-year running mean.
The first of the mentioned epochs was a cold period around eighth century, which caused, e.g. renewed ice growth in alpine glaciers and 1–2 m sea level drop below presentday level. This period later changed back and restored warmer conditions between ninth to thirteenth century, the so-called Little Climatic Optimum or Medieval Warm Period (from eleventh to fourteenth centuries) that represented the warmest climate since the Climatic Optimum that occurred at 6000⫺5000 years B.P. At the Medieval Warm Period the warming, however, was not as intensive as under the earlier Climatic Optimum. During this period, global average annual temperature was approximately 1 K (or less) warmer
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than in 1900. That time, for example, the Vikings established a colony in Greenland and the wheat was grown in Norway (64°N latitude). However, the regional evidence of this period is variable, sometimes even unclear. For example, Crowley and Lowery (2000) did not find evidence for warmth in the tropics. The twelfth and fourteenth centuries appeared mainly cold in China (Wang and Gong, 2000). The restricted reconstructions from the Southern hemisphere, such as tree-ring record from Tasmania (Cook et al., 2000), did not confirm any distinct warmer time during the Medieval Warm Period. Generally, this period appeared more evident in areas near and around the North Atlantic. Keigwin and Pickart (1999) hypothesized that the corresponding temperature changes were associated with changes in ocean currents in the North Atlantic, the fact that maintains the role of ocean circulation-related climate variability. On the contrary to the Medieval Warm Period, the position of the Little Ice Age appears to have been much clearer. This time interval represents the greatest glacial advance of the Holocene that have continued from 1300–1450 until 1850–1900 A.D. While the geographic pattern of the Holocene climate fluctuations remains murky, the Little Ice Age and the subsequent warming were really global in their extent. The evidence from mountain glaciers suggests glacier advances in a number of widespread regions, in Europe prior to the twentieth century, as well as in Alaska, New Zealand, and Patagonia (Grove and Switsur, 1994). During the Little Ice Age, average annual air temperatures of the Northern hemisphere were about 1–2 K lower than today, and unusually cold and dry winters prevailed in Europe. That time agricultural productivity dropped significantly, even farming became unmanageable in vast regions in northern Europe. The freezing of the canals in Holland for three months straight as recorded by famous Dutch and Flemish painters can be mentioned in this connection. The Little Ice Age cooling did not represent a one-way story and was sometimes interrupted by several provisional returns of warmth. The regional variability of cold conditions played a significant role. While the hemispherical averages of temperatures for the seventeenth century generally reflect the cold conditions in Eurasia, the nineteenth century cold is mainly associated with the cold climate in North America (Mann and Jones, 2003). Even the timing of peak coldness may depend on the particular season. Since 1850 A.D. the climate is dominated by a clear steady warming trend, which has become known as global warming. Figure 4 shows that the twentieth century SAT has increased by 0.7 K, with about half of that increase occurring since 1978. This warming is particularly noteworthy because the rate of temperature increase is enormously high. In addition, the recent 50–100 years have been the time of unprecedented growth of human activities, accompanied by industrialization, massive deforestation, and other human interferences with the nature with a thoughtful (harmful) effect on the environment. The natural agents, exerting their influence upon climate has been thus “recruiting” with a new powerful mean to produce sizeable changes in the climate. One of the essential problems of the present days is to answer the question to what degree the mankind may be responsible for the present-day climate warming. Is the observed global warming just of natural origin, or does it have certain anthropogenic component? Is the fact that the climate is getting warmer the result of human insensitive approach to its habitat? Is this warming to continue in the future and how serious are the potential environmental consequences? If so, the problem of the worldwide increasing air temperature comes to an end as the strictly scientific discipline, but became the uneasy task for everybody on this planet.
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Fig. 4. Global warming of the twentieth century documented by the mean SAT anomaly (relative to the base period 1961–1990). Figure adopts data from www.cru.uea.ac.uk.
It is true, that some skeptical researchers have debated whether the observed temperature trend is reliable (see Chapter 3) and how the present knowledge is to be extrapolated into future. However, certain evidence of a sizeable warming was reported even after removing data from the urban areas where the “city heat-island effect” could have affected the long-term meteorological temperature data. In most cases, however, the SAT data are consistent with other evidence of warming, e.g. increase of ocean temperatures, shrinking mountain glaciers, decreasing polar ice cover, etc. During this period, the energy reaching the Earth’s surface from the Sun had been measured precisely enough to confirm the conclusion that the reported recent warming has not been occurring just due to solar radiation changes. Although the reason for detected warming is not completely understood, the most of the climatologists interpret it as the result of the increasing concentrations of CO2, CH4, and other greenhouse gases into the atmosphere caused by anthropogenic activity. Greenhouse gases have increased significantly since the Industrial Revolution,2 mostly from burning fossil fuels for energy, industrial activities, and also by transportation (Figure 5, see also Figure 99, Chapter 3). Now the greenhouse gases are at their highest concentration levels in the last 400 000 years and continue to rise. Even when the global 2
Term Industrial Revolution implies a period of rapid industrial growth beginning in the second half of the eighteenth century. It originated in England when the steam engine was invented and later has spread over Europe and the world. It means the beginning of intense use of the fossil fuels with the corresponding emission of carbon dioxide and other numerous anthropogenic influences on the climate system.
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Fig. 5. The comparison of the increase of the greenhouse gases concentration in the atmosphere (bottom panel: CO2 and CH4 data by the Carbon Dioxide Information Analysis Center, CDIAC; http://cdiac.esd.ornl.gov) with the mean annual SAT (top panel).
warming is expedient in some parts of world bringing, e.g. milder winters and longer growing seasons, it may have fatal consequences in others, and globally the expected losses are to outweigh the potential benefits. The Intergovernmental Panel on Climate Change (IPCC; www.ipcc.ch/index.htm) that involves hundreds of scientists and was established to assess scientific, technical, and socio-economic information relevant for the understanding of climate change, predicted that by year 2100 the average global temperature will rise by 1.4 to 5.8 K above 1990 level. The uncertain broad range of possible temperature increase is due to different assumptions considered in the variety of model simulations. Lower boundary indicates that even low climate sensitivity and low economic growth will lead (if no measures are undertaken) to a mean global warming of above 1K, thus surmounting the warmest phase of the Holocene. The IPCC predicted that combined effects of melting ice and seawater expansion from ocean warming may cause the global average sea level rise of approximately 0.1 to 0.9 m between 1990 and 2100. Such rise may bring devastating consequences to coastal communities who will likely experience the loss of their land, increasing flooding due to sea level rise, and more severe storms and surges. Uncertainties remain only about the exact magnitude, rate, and impact of future changes as well as how climate change will afflict different regions. They are stipulated mainly by the lack of sufficient knowledge of how climate could be affected by so-called climate feedbacks (for details see Section 3.4, Chapter 3) and by the difficulty to predict future actions of the society, particularly in the countries of future economic growth and highenergy demands.
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Another important question is how abrupt the future changes will be. Abrupt climate change generally refers to a large shift of climate that takes place so rapidly and unexpectedly (sometimes in the mere span of a decade) that human and/or natural ecosystems have difficulty to adapt. Further definition of “abrupt” or “rapid” climate change is subjective and depends on the long-term temporal pattern of the climate change within which the sudden shift is embedded and/or the sample interval used in a particular study. The shifts from dominantly glacial to interglacial conditions were the most distinct abrupt change over the past half million years. These sudden transitions support the hypothesis that the relatively minor changes in climatic forcing may lead to dramatic response of climate system (e.g. Mikolajewicz et al., 1990). Studying the climate evolution over the last 100 000 years the researchers have discovered repeated examples of abrupt changes like, e.g. the Younger Dryas – the fast slide into and jump out of the last ice age. The termination of the Younger Dryas cold event, for example, is manifested in ice core records from Central Greenland as a near doubling of snow accumulation rate and a temperature shift of approximately 10 K occurring within a decade (Alley, 2000). One of the more recent abrupt climate changes was the Dust Bowl drought, windblown dust, and agricultural decline of the 1930s that displaced hundreds of thousands of people in the American Great Plains. Numerous sudden changes over widespread areas are preserved in paleoclimatic archives and therefore could happen again in future. The likely hypothesis to explain abrupt climatic transitions is that the ocean thermohaline3 circulation switches between different stable modes. Warm climate intervals reflect, e.g. strong deep water formation in the northern North Atlantic and vice versa (Stocker, 2000). It has been suggested that oscillations on such timescale represent an intrinsic feature of the climate system and have persisted throughout the Holocene. If it proves to be the case, any prediction of future climate changes in the North Atlantic region would require accounting for this process. Other forcing can also join in the rapid climate changes. Some short-term, abrupt climate changes, for example, clearly reflect the impact of major volcanic eruptions (Briffa and Osborn, 2002). Growing attention is now to be paid to the possibility of anthropogenic influence on climate that may induce rapid climate changes that are far beyond the range of variability on which the social operating and planning schemes are based. One of the theories, for example, states that the global warming could trigger off the mechanism of abrupt cooling in northern Europe. It has been hypothesized that the melting ice caps will “freshen” the water in the North Atlantic, shutting down the natural ocean circulation that brings warmer Gulf Stream waters to the north. The actual regional drop in temperature may be as high as 6 to 8 K. Such change in the ocean circulation could occur over relatively short period, perhaps within 50 to 100 years. As the present scientists do not know enough about exact mechanisms and details of abrupt climate changes to be able to accurately predict them. The larger and faster the climate change may be more difficult will be the human and natural systems adaptation and stronger expected adversity effects can be expected. Thus, more precise descriptions of the processes causing such changes should be developed. This is especially the case in relation to changes in the magnitude and frequency of extreme events (Knox, 2000). 3 There are three basic processes that make the ocean water circulate, namely tidal forces, winds stress, and density differences. The latter occur due to the temperature (thermo-) and salinity (-haline) differences, thus, the density driven circulation is called the thermohaline circulation.
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Comparing present and past climatic conditions one can conclude that we are indeed fortunate because we are living in one of the warmest and “quiet” periods of the past million years under the milder temperatures that the Earth could provide for human life to flourish. Thus, any significant change of existing climate should be met with an apprehension, and the investigation of past climatic variations holds not only academic interest. This is true especially for the last century when the natural variability of the climate is amplified by the anthropogenic disturbances arising from the drastic transformation of the planetary environment induced by an unimaginable explosion of human activity. Investigations of the past climate may be useful both to understand the present-day climate and its possible future changes, and to test the hypotheses about the causes of the climate change. More climate information from the distant past could be greatly valuable to strengthen our understanding of climate changes and to improve existing models of climate development. In particular, an enhanced effort is needed to expand the geographic coverage, temporal resolution, and variety of the paleoclimatic data. The borehole climatology represents a useful addition to the available array of existing paleoclimate information. Because of numerous boreholes the method is applicable over most continents including polar ice caps. Subsurface temperature records measured in boreholes may represent a useful tool for the past temperature reconstructions in areas less covered by traditional climatic investigations. Borehole geothermometry could also provide data for other purposes, like the atmosphere and land “couplings”. 1.2 Principal Sources of Data on the Earth’s Climate System 1.2.1 Background Climate is variable on all timescales. Its variations represent the complex product of the interaction of Sun and all components of the Earth including atmosphere, oceans, landmasses, snow and ice cover, life, and other structural elements. Geologically, short-term climate changes (⬍120 000 years) occur because of external forcings as well as due to internal factors, both natural and human-induced changes (www.ace.mmu.ac.uk). External causes of climatic changes include changes in the solar radiation and the Milankovitch cycles. Solar radiation is the radiation emitted by the Sun. Its spectral range is determined by the temperature of the Sun. About half of the radiation falls into visible short-wave part of the spectrum, while the other half is mostly in the near-infrared part with a small part in ultraviolet part. The output of energy from the Sun slightly varies over time, changing the total amount of energy absorbed by the Earth atmosphere and thus affecting the climate. The solar activity is linked to the sunspot cycle that occurs with a 22-year periodicity. Quasi-periodic oscillations of the sunspot number with the period of approximately180 years also appear to exist. Figure 6 illustrates the correlation of the global solar irradiance4 reconstructed by Bard et al. (2000) for the last 1200 years and the global temperature anomalies (Figure 3, bottom). The well-known solar minima are centered about 1900, 1810 (Dalton), and 1690 A.D. (Maunder) and correlate with the corresponding temperature falls.
4
Irradiance is the term for the power of electromagnetic radiation that is incident on the surface per unit area. The SI unit for irradiance is W/m2.
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Fig. 6. Correlation between global solar irradiance and global temperature anomalies for the last 1200 years (adopted from data by Bard et al., 2000 and Mann and Jones, 2003).
Appeared near 1200 A.D. maximum is characterized by the irradiance that is comparable or even slightly higher than the present-day level. It can be connected with the Medieval Warm Period, while the Little Ice Age can be attributed to a rather long period of low irradiance between 1450 and 1750 A.D. Notwithstanding that solar activity is recognized as undoubted cause of variations in the climate system (Blackford and Chambers, 1995; van Loon and Labitzke, 1998), its exact role in climate variations on the decadal/centennial timescale is a topic of continuing debate. Crowley and Kim (1996) investigated the correlation of several Northern hemisphere temperature proxy records with solar variability indices and concluded that solar forcing may explain as much as 30–55% of the climate variations on these timescales. The hypothesized source for the rest part of the climate change is internal climate dynamics. Recently van der Schrier and Versteegh (2001) applied new technique to separate solar activity and internal climate dynamics. Based on the 250 years long sunspot record and series of summer temperatures, these authors concluded that for low values of sunspot number the internal climate mechanics dominates, while at high sunspot number internal climate dynamics does not seem so important. Details on how sunspots affect the Earth climate and further references can be found on the web site ⬍www.das.uwyo.edu/⬃geerts/cwx/notes/chap02/sunspots.htm⬎. The Milankovitch theory relates climate variations to the changes of the parameters of the Earth orbit around the Sun, namely to the changes in eccentricity (the shape of the Earth’s orbit), obliquity (the tilt of the Earth’s axis), and in orbital precession (the shifting of the equinoxes). Each variation has its specific time period. For example, the orbit may be more elliptical and/or more circular completing period in about 110 000 years, and the mean annual flux varies as a function of actual eccentricity. These three components of
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the orbital variations affect the total amount of energy received by the Earth, and its seasonal distribution at different latitudes. Fluctuations in solar energy input measured in tens of thousands of years are generally regarded as the cause of major climate fluctuations, and much evidence from paleoclimatic records has been found to support this theory. There is a good correlation between the glacials and periods of low eccentricity. The distribution of the interglacials also shows the evidence of the 41 000 (obliquity) and 21 000 (orbital precession) years cycles. Now scientists have recognized, however, that such orbital variations alone are not enough to account for the whole oscillations in the global climate between ice ages and interglacials (Berger and Loutre, 2002). While external variations may indeed act as a pacemaker for glacial–interglacial transitions, additional climate forcing has been invoked to explain the significant changes in global average temperature up to several degrees. The internal forcing factors include variability of the coupled ocean–atmosphere system, volcanism, producing large eruptions of particulates (dust) and gases into the atmosphere, cryosphere,5 and the land surface. The ocean–atmosphere system represents one of the main constituents of the climate. The atmosphere is involved in practically every physical process of potential importance for climate change. Atmospheric temperature, composition, humidity, cloudiness, and winds determine the global energy fluxes. The atmospheric circulation provides the possibility of rapid propagation of any climate forcing from one part of the Earth to another. The bulk of the energy absorbed by climatic system, much more than absorbed by the atmosphere, is stored at the ocean surface. Because of its huge thermal capacity as well as of its ability to circulate this energy over long timescales, the role of the ocean as the climate forcing factor is extremely important and complex. Warm water moves pole ward whilst cold water returns toward the equator. Energy is also transferred by moisture. The water evaporating from the ocean surface stores heat that is then released when the moisture condenses to clouds and rain. Heat moves also vertically within the oceans. Similarly to the currents in the atmosphere the surface and deep-water currents in the world’s oceans are inter-linked forming the global ocean circulation. Changes in ocean circulation and especially the thermohaline circulation in the North Atlantic have been implicated in abrupt climate changes occurred in the past such as the Younger Dryas. Volcanism can increase the Earth’s albedo (reflectivity) and induces cooling the climate. The cryosphere is the portion of the globe covered by ice and snow. It greatly affects temperature. The sea ice masses increase the reflective capacity of the Earth surface, thus, enhancing cooling. They also insulate the atmosphere from the relatively warm ocean causing steep decline of the winter air temperatures and reducing the supply of moisture to the atmosphere. The water frozen in the glaciers and snow cover on land can melt during warming events with consequent effects on sea level and atmospheric circulation patterns. Snow-covered lands promote cold conditions because of their high reflectivity and because land surface temperatures cannot rise above freezing until the snow melts. The reflectivity of the land surface strongly depends on its cover. While fresh snow reflects more than 90% of the sunlight, the dense forests similarly absorb more than 90% of striking energy. The land surface coverage can also affect cloud formation, precipitation, and the surface water flow, thus, feeding back on climate. 5
Term cryosphere implies the component of the climate system including snow, ice, and permafrost both on and beneath the land and/or ocean surface.
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The main anthropogenic causes of climate change include the emissions of greenhouse gases (carbon dioxide (CO2) and methane (CH4) production), changes in land-use, and the depletion of stratospheric ozone. Greenhouse gases such as carbon dioxide are accumulating in the atmosphere resulting in the increase of air and ocean temperatures. Increased concentration of greenhouse gases in the atmosphere is well documented and its climatic consequences are widely reported in climatic modeling literature (McGuffie and Henderson-Sellers, 2005; Figure 5). The anthropogenic land-use changes include reand deforestation, urbanization, changes in the agricultural practice, desertification, major rivers, and other water masses engineering. The importance of these factors was captured by numerous climate modelers. And finally, the discovery of the Antarctic ozone hole6 in 1985, and more recently, less intensive, but observable ozone depletion over the Arctic (stratospheric ozone represents Earth’s natural protection for all life forms, shielding our planet from harmful ultraviolet radiation) has focused the attention on including the twentieth century ozone destruction in the global climate models. The striking complexity of the temperature records in Figures 1 and 2 probably reflects the complex interactions of all feedback mechanisms.7 Our ability to predict future climate strongly depends on the degree of understanding of the climate system operating mode. Such knowledge can be achieved from the study of the past climate variations and their modeling with appropriate forcing. Comparison of the climate models and simulations of their development with climatic reconstructions can provide constraints on the sensitivity of climate to different forcing (van der Schrier and Versteegh, 2001; Bauer et al., 2003). Complete spatial–temporal pattern of the past climate is thus the clue to successive climate modeling and prediction of possible future climatic changes. It is especially a case in the recent decades when the Earth’s temperature has been increased. Is observed warming an ordinary climatic fluctuation or it is stimulated by intensified anthropogenic activity? How extraordinary is this warming relative to the variations occurred in the pre-industrial times? For understanding of the post-industrial impact to the climate and development of effective adaptation/mitigation strategies as precise as possible knowledge of the early climatic fluctuations is indispensable. Generally, all methods for past climate reconstruction can be classified according to the timescale on which they consider climatic influence:
• short-term (1–1000 years), • medium-term (up to 10 000 years), and • long-term (periods of 100 000 to 1–10 millions years). Paleoclimatologists employ a wide variety of methodological approaches to reveal past climate changes. Except the direct measurements of climatic variables, there are three principal techniques to reconstruct past temperature variations, namely proxy methods, 6 The Antarctic ozone hole is a part of the Antarctic stratosphere where ozone level has dropped to as low as 33% of their pre-1975 value. The ozone hole occurs during September to early December, when strong westerly winds start to circulate around Antarctica and create somewhat similar to an atmospheric container. Over 50% of the lower stratospheric ozone is destroyed in this container. 7 Climate feedback implies such mode of interaction between climate forming processes, when the influence of an initial process triggers changes in other process that return back to the initial process and either intensify (positive feedback) or reduce it (negative feedback).
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inversion of the temperature–depth profiles measured in boreholes, and modeling. Most traditional technique is based on the proxy sources that represent the fingerprint of climate changes on surrounding environment. The nature has provided a lot of indirect recording mechanisms. By analyzing records taken from numerous proxy sources, scientists can extend our understanding of climate far beyond of the approximately 200 years long instrumental recording. All methods possess their own timescale and temporal resolution, their summary is presented in Figure 7. We have a general picture of how climate has changed over the last 150 000 years (through the last glacial–interglacial cycle), but only in terms of very large-scale and of low-frequency changes. The knowledge of climatic changes at higher frequencies, say, variations on the decade to century scale, is very poor, while it is this timescale that is the most important to the current environmental concerns. Contemporary climatic variations must be viewed in the context of changes that have occurred before the global scale potential anthropogenic influence on the environment has started. Paleoclimatic reconstruction over the last millennium requires careful retrieval of all available climatic archives. Even when none of the available approaches to climate reconstruction is free from certain uncertainties, confidence of obtained results can only be provided by comparing several independent sources of information and thus support or verify the reconstruction model.
Fig. 7. Sources of paleoclimatic data and their timescales and temporal resolutions.
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1.2.2 Short-term climate changes Short-term temperature changes can be suitably detected on the base of the instrumental measurements and historical documents. Both sources possess high-resolution up to exact moment of occurrence. Instrumental surface temperature data sets are of primary interest for the recent global warming and for the detection of the 100 year long global temperature trends. The reconstruction is based on the compilation of SAT measured at land stations and ship-based marine sea surface temperature (SST) measurements. The overall characteristic of the instrumental sources is that they present vast volume of data rapidly decreasing in amount and geographical coverage when going back in time. Table 2 presents the evolution of the global instrumental observing system in time. It can suitably be divided into five periods. The first covers the time up to around the second half of the eighteenth century. This period, with a very few exceptions, is covered only by proxy data. The longest instrumental SAT series are available for some locations in Europe and North America back to the mid seventeenth century. Methodical thermometer-based records began at approximately 1850. The second period covers the times, say, from 1760 to 1880 and is characterized by a gradual built-up of surface synoptic network covering the inhabited parts of the globe as well as marine observations along the well-traveled routes. The reasonably coherent surface synoptic network was created in the third period from 1880 to the mid of the twentieth century. However, data sources over tropical regions and the oceans were still generally rare. During the fourth period (1946–1979) meteorologists have had a network of radiosonde stations reasonably covering most of the Northern hemisphere. Finally, the fifth period since 1979 is the only period where there has been a global observing network including the full depth of the atmosphere. Obviously, the instrumental observation window is too short to provide real insight in the longer scale climate variability. Although meteorological records represent the principal and the most reliable data source for the climate change study, they possess numerous shortcomings. Because of the changes in the observing techniques and schedules over the years (e.g. different time of the day for measurements), changes in local exposure due to, e.g. urban development around the site and the re-location of meteorological stations, without overlapping of the record to calibrate new station, the integration of measured quantities into the homogeneous time series is not an easy task even for a single station. Because of significant spatial–temporal variability of the surface temperature, the compiling of the homogeneous records for more or less extensive regions represents a difficult problem and can significantly lower the accuracy of compound SAT series especially when measurements are performed over a century or longer period of time. The compilation of recently homogenized long European SAT series was presented by Table 2. Development of meteorological observing systems Time ⬍1760 1760–1880 1880–1946 1946–1979 ⬎1979
Characteristic observing system Essentially proxy data Built-up of a surface synoptic system(mainly Europe and North America) Basic surface synoptic system ⫹Upper air radiosonde network(mainly Northern hemisphere) Comprehensive global observing system
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Camuffo and Jones (2002). This massif is probably the most reliable volume of shortterm climatologic data. However, even this careful reconstruction is a subject of some uncertainty in its earlier part. Examples of estimates of SAT anomalies extended back to approximately1650 are presented in Figure 8. Smoothed values were calculated from the data by Jones and Moberg (2003). Comparison shows clear differences between the illustrated regions. Besides the limitations imposed by temporal inconsistencies in a single weather station record, the space averaging of single site observations over large territories for global and hemispheric analysis may present certain problem. The most straightforward way to obtain average global surface temperature is to calculate the weighted average of thermometer measurements from the weather stations distributed over the Earth. Weighting procedure is indispensable because the stations are not regularly and/or optimally arranged. Restriction of the observation sites to land and island stations, still large land areas without coverage, the varying number of stations and areas of coverage over the observational period, wide ocean spaces without fixed meteorological stations at all times put difficulties in the way of extracting large-area temperature changes from measurements (Jones et al., 2001). Figure 8 (bottom) shows the result of recent hemispheric averaging of combined land and marine temperature anomalies (model HadCRUT2v; data by Hadley Centre of the UK Meteorological Office, www.cru.uea.ac.uk). According this reconstruction the Northern hemispheric means vary by up to 1K for the recent 150 years. Data indicates colder temperatures in comparison with the base period 1961–1990 in the second half of the
Fig. 8. SAT (relative to base period 1961–90) and their 10-year running means for Central England, Central Europe, Fennoscandia (data by Jones and Moberg, 2003), and Northern hemisphere (see text).
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nineteenth and in the beginning of twentieth century, warmed between 1910 and 1940. Slight oscillations around zero occurred between the years 1940–1975 and then climate has warmed again through 2000. Limited agreement between the Northern hemisphere and the European temperatures is obvious and proves that averages for such extensive units cannot be inferred from a single region series. Using these data, Jones et al. (2001) concluded that average temperature increased 0.6 ⫾ 0.2 K during twentieth century. The uncertainty given for this average reflects the statistical uncertainty in the meteorological station measurements and does not contain such systematic biases, e.g. ocean temperature measurements, urban heat-island effect, etc. The temperature increase is spatially unequal; Arctic regions show the greatest degree of warming, while a little or no warming corresponds to some low latitude areas. Historical data are an important source of detailed information on the millennium scale, particularly for the period from about 1000 A.D. to the beginning of the era of instrumental meteorology. Of course, they are not equivalent in the reliability to the meteorological instrumental measurements. These sources contain generally written records of environmental indicators of climate (parameteorological phenomena) including myths and legends, annals, chronicles and scientific writings, records of social administration and government, commercial and private estate data (crop yields, harvests, and prices), maritime books, early journalism, private papers (diaries, correspondence), etc. Some pictorial documents also can be used as evidence of past climate, e.g. in the work by Camuffo et al. (2003) who studied the increase in the sea level and in flooding tide frequency at Venice on the base of early photographs and the “photographic” paintings by Canaletto and Bellotto. Sometimes climatic information can be extracted from unusual sources, e.g. the cherry tree blossom dates that were recorded at Kyoto, the old capital of Japan, since 812 A.D. (Lamb, 1977). In some cases documentary sources may also be completed by archeological evidence of climate change. Generally, the information fixed in documents does not represent systematic series nor can be readily expressed in terms of standard meteorological variables. Data vary widely in quality. While, for example, the note from the collection by Réthly (1962) on the winter of 1528/29 – “… Suleiman Turkish Emperor came near to occupy Vienna and only extremely cold winter drove his army away” can probably be accepted without limitations, the description of the Italian winter 1132/33 – “… the Po river was frozen to the bottom in its total length. The wine was benumbed with cold even in the deepest cellars” should be interpreted with caution. Historic information often contains exaggerations like “the coldest winter from the beginning of the mankind”. Significant problem represents also that our knowledge of the intellectual and social parameters at which text was written is insufficient. Exact meaning of the words and forms of expression is interpreted in terms of the present scientific knowledge. Initial expressions may be distorted in translated, paraphrased, or summarized sources. Definite shortcoming represents also the fact that significant amounts of historical data can be found only in the regions with well-developed cultural tradition, thus, spatial distribution of this information is generally irregular, when vast areas or even continents can appear as “white spots”. Another limitation of the documentary data is that they require independent calibration to the climatic variables and thus are not comparable in their reliability to instrumental meteorological measurements. However properly evaluated, historical data can yield both qualitative and quantitative information about past climate.
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A wealth of historical data is available for Europe that represents one of the few regions of the world where it may be possible to reconstruct regional climatic variations for the last millennium in season-by-season scale. Outstanding examples of reasonably accurate climatic series obtained from documentary sources are the collection of climatic notes for Hungary and surrounding territories from second to eighteenth centuries by Réthly (1962, 1970), the reconstruction of temperatures prevailing in England and Wales since 800 A.D. (Lamb, 1977), the work by Le Roy Ladurie and Baulant (1980) and Chuine et al. (2004) based on wine-harvest dates in France from fourteenth to fifteenth centuries to the present. The most recent comprehensive review of the documentary data archive was published by Brázdil et al. (2005). Figure 9 demonstrates how historical grape-harvest dates in Burgundy (France) were used to reconstruct summer (April–August) temperature (Chuine et al., 2004). Results reveal generally warm conditions before up to the 1650s and somewhat colder climate since then. Temperatures as high as those reached in the 1990s have occurred several times during reconstructed period. China is another area rich in the documentary climate evidence. The regional instrumental temperature series in China have been extended back over much of the past millennium using documentary data combined with inferences from ice cores and treerings (Wang and Gong, 2000).
Fig. 9. Spring/summer temperature reconstruction based on grape-harvest data in Burgundy (France) from 1370 to 2003 (data by Chuine et al., 2004). Temperatures are given as anomalies with respect to the mean April–August temperature at Dijon for the base period 1960⫺1989, smoothed course corresponds to the 10-year running average.
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1.2.3 Medium- and long-term climate changes The relatively short length of most instrumental records and historical sources restricts the study of climate variability. These data indicate warming trend occurred during twentieth century, however, cannot answer the question whether this warming was unusual and/or extraordinary in the whole Earth’s history. The essential need to prolong directly measured climatic series back into the past inspired the development of various methods for the past climate reconstruction from the traces left by climatic changes in the world. The reconstruction of the past temperature variations on the global/hemispheric scales can be performed by three principal approaches: (1) proxy methods, (2) inversion of borehole temperature logs, and (3) modeling. Different proxy techniques are the oldest and traditional, while the “borehole” method and simulations of the past climate with the state-of-art General Circulation Models (GCM)8 represent recent developments. Threedimensional climate models produce internally consistent simulations that in many features coincide with observed climate and are realistic enough to constitute a surrogate complex for the testing of different reconstruction methods and their basic assumptions (see Section 2.4.4, Chapter 2). The “Simulating the Planet Earth” represents probably the most well known such project. It is connected with the world’s fastest supercomputer developed in Japan. Located at the Earth Simulator Center (ESC) at Yokohama (Japan) it can simulate the complex interactions between the Earth’s atmosphere, ocean, and land for deeper understanding of our planet’s climate, ocean currents, and earthquakes. All global environmental changes can be presented in a one thousand times more detailed grid pattern than that provided by previous supercomputers. This means more precise weather simulations as well as the ability to predict cyclone and typhoon paths. Current GCM simulations can be seen directly in the website www.nec.com/global/features/ index9/index.html. Measurements of borehole temperature profiles are the only direct measurements of the long-term past temperatures in contrast to the proxy indicators that must be interpreted in terms of climate changes using different transfer procedures. Anyhow, it is the proxy reconstructions that provided the most abundant paleoclimatologic database. The essence of the proxy method is the next. Temperature variations cause many changes in the biological and physical environment. Some of these changes are regular enough to be used as quantitative indicators of varying temperature. The “proxy” data is the term used to denote any material that contains indirect signatures of climate. A proxy climate indicator is a local record that is interpreted using physical or biophysical principles to represent some combination of climate-related variations back in time. Paleoclimate proxy indicators have the potential to provide evidence for long-term climatic variations prior to the period of existence of instrumental and documentary records. Generally, proxy methods are classified according the scientific branch that provides the data, e.g. biological, chemical, geological, and/or physical climate-related phenomena. For example, numerous evidence of past climate is interpreted by biological sciences: tree-rings, pollen remains,
8 General Circulation is a term that denotes large-scale motions of the atmosphere and the ocean occurring in response to the differential heating of rotating Earth. The GC computer models are based on numerical solution of fundamental equations for the conservation of mass, momentum, and energy. They also consider the physical processes including sources and sinks of these quantities.
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insect faunas, marine micro-fauna, etc. The family of the existing proxies is continuously growing. Except of well-known records some of them are still under development. For example, according to Weidman and Jones (1994) isotopes from mollusks can help to reconstruct bottom temperatures on the continental shelves of the North Atlantic. Daux et al. (2005) described the possibility to reveal past seasonal distribution of precipitation via oxygen isotope compositions of phosphate that were measured in human tooth enamel. Techniques for obtaining proxy temperature information from all the sources except of boreholes are described in the book by Bradley (1999; see also www.ncdc.noaa.gov/paleo/ proxies.html) and in the web site of the Johns Hopkins University (www.jhu.edu/⬃eps/ paleoguide/archive.html). The comprehensive review is presented in the work by Jones and Mann (2004; see also the references therein). Proxy indicators possess different temporal coverage and resolution. Key aspects of a proxy data source are the minimum sampling interval and date resolution. These factors determine the degree of detail that can be extracted from the record. Some of them keep year-by-year patterns of the past climate, while others because of certain factors, e.g. uncertain radiometric dating, simplified “temporal model” assumptions, etc., cannot provide high-resolution data. Common property of the majority of proxy records is also the diminishing of the resolution into the past. For example, datable stratified systems (tree-rings, varves, ice cores, etc.) can provide time resolution of minimum one year. However, seasonal/annual layers in these records appear clearly within only recent periods and are biased to the past by numerous unrelated to climate factors. The properties of the most commonly used proxy measures are illustrated in Figure 7. High-resolution subgroup includes data resolved on the annual/seasonal or at least on decadal scales (tree-rings, corals, laminated ocean and lake sediment cores, high-resolution ice cores, speleothems,9 etc.). Example of the high-resolution data is presented in Figure 10 that shows five regional reconstructions of summer half-year (April–September) mean temperature anomalies for western North America for the period 1600–1982 by Briffa et al. (1992). Tree-ring data are available from much of the continental land area, they can be accurately dated to an individual year, thus, represent primarily high-resolution source, and by reasonable cross-dating can provide continuous records of up to several thousand years in duration. The essence of the method is that in trees each year’s growth creates a well definite ring. Because tree growth tends to hasten in warm conditions compared to cold weather, the width and density of tree-rings may serve as proxies for average temperature. Tree growth measurements can be made both by taking cores out of living trees and by investigation of cut, dead, and/or fossilized examples. On the other hand, Bradley (1999) has pointed out that the tree growth rarely owes to one climatic variable and generally embraces the full range of such factors as temperature, sunshine, precipitation, humidity, and wind intensity. Temperature and precipitation effects, for example, can be separated only if more than one measure of tree growth is available. Tree-ring characteristics also depend on the climate independent variables including the tree species and age (young trees
9
A speleothem is a term denoting various cave deposits that occur as a complex interaction among rocks, water, and air during cave formation. Samples taken from speleothems can be used as a proxy record of past climate changes.
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Fig. 10. Tree-ring reconstruction of summer temperatures across western North America for the period 1600–1982 and their 10-year running means (based on data by Briffa et al., 1992, 2001).
grow faster that older ones), nutrients in the soil, CO2 concentration, etc. The calibration of tree-ring measurements against climate variables represents heavy problem, since the biological response to climate forcing may change over time. The typical situation is that the calibration is performed using recent, in many cases less than century long meteorological data, and obtained information is then extrapolated on the remaining remote sections of measured tree-ring variables. Generally, average values from the multiple samples per tree and/or multiple trees in the study are calculated. Both procedures
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result in the damping or even loss of the long-term variability. As about tree-ring reconstructions presented in Figure 10, Briffa et al. (1992) have demonstrated that time series possess a good significance over the area 35–55°N, but have a large uncertainty north of the latitude 55°N, especially prior to 1750. All data series exhibit high short-term variability. Temperature anomalies averaged on decadal timescale revealed significant inter-decadal changes. However, centennial trends are expressed very weakly. The range of the temperature variations remains approximately the same during all reconstructed period. As was mentioned above, it is a specific feature of the tree-ring proxy. For these reasons, the tree-ring information appears to be more useful when it is supplemented by other types of proxy information in the “multiproxy” estimates of past climate change (see Figure 11). “Coarser” group of proxies includes past pollen and spore records, earlier tree line position, lake level reconstructions, glacial moraine evidence, most sediment cores, and accumulation ice cores. They are useful to reveal the long-term climate variations on centennial and longer timescales. Typical example of such reconstruction was presented in Section 1.1 (Figure 2). The ice sheets that cover Antarctica, Greenland, the northern archipelagos of Canada and Russia, and the summits of some mountain systems reflect the accumulation of the long year snowfall and can provide several climate-related indicators. In cold dry regions, such as Antarctica and the interior of Greenland, because of
Fig. 11. “Multiproxy” temperature reconstructions for Northern hemisphere by Mann et al. (1998), Crowley and Lowery (2000), and Briffa et al. (2001). All series are anomalies for the 1961–1990 instrumental reference period, and smoothed with a 40-year low-pass filter (www.ncdc.noaa.gov/ paleo/recons.html). Multiproxy reconstruction by Huang (2004) is shown for comparison. As seen, temperature reconstructions based on the borehole data inversion suggest colder conditions in the past.
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insignificant year-by-year evaporation and melt, snow compresses into annual layers of ice. The polar ice caps, for example, have 100 000 of these layers or more. Ice core, cylinder of ice drilled out of glaciers, and polar ice sheets can provide several indicators of climate. Recorded there, stable isotopes of oxygen and deuterium are of primary use for the paleoclimatic reconstructions. The isotopic fractionation of oxygen in ice can then provide a proxy for temperature. The physical rationale for such reconstruction is the next. Almost all water is H216O, but two heavier forms, i.e. HDO (D ⫽ 2H is deuterium) and H218O present in the quantities sufficient to provide measurable basis for the proxy temperature record. In most respects these water molecules are the same as regular water except that because they are heavier, they do not evaporate as readily and condense a bit more easily than H216O water. Generally, the colder the air when the snow fell the richer the concentration of the 16O in the record. The isotope content in ice is determined primarily by the air temperature during snow storms. Warmer air contains a larger fraction of D and O18. When incorporated into a stratified deposit, the (18O/16O) ratio remains frozen. This ratio can be measured very accurately using a mass spectrometer. Over short timescales the change in temperature from summer to winter produces a clear oscillation in the (18O/16O) ratio. This oscillation is used to determine the age of the core at different depths, simply by counting the oscillations. Over longer time periods, this ratio indicates the average temperature in the investigated region between the evaporation site and the coring site. The ratio of 1H / 2H (hydrogen to deuterium) can provide even finer details about source temperature and condensation history. Generally, ice cores can store climate information over more than 105 years. However, significant shortcoming of this kind of proxies is that: (1) they are not good representation of average annual temperature conditions because snow accumulation is seasonal, (2) a change in storm tracks direction could change the isotope signature without temperature change at the given site, (3) the chronology of ice cores is disturbed in depth by horizontal and vertical sinking of the ice, which thins the deep layers to a small fraction of their original thickness, and also by the summer melting of the ice. The resolving power originated from counting of the annual layers, may appear two–three orders poorer in the lower sections of the ice cores (Johnsen et al., 1992). And (4) they are available only from a very small fraction of the Earth. Important characteristic of various proxy data is the degree of their sensitivity to abrupt changes in climate. Pollen method, for example, allows to estimate the total amount of plant growth of given year by the pollen count, and thus, provides valuable information about dominant climatic conditions and their variations. However, plants have very long reaction to climatic “jumps”, thus they are practically insensitive to abrupt changes. On the contrary, many insect populations are extremely temperature-sensitive. Discussion of the details of the specific proxy sources is far over the purpose of this section. Independently of the kind of proxy data the common problems in their using are the dating, lag and response time, degree of stationarity in the nature of the proxy’s response to the climate, and mainly their climatologic interpretation. Since the proxies are indirect traces of climate and only a part of measured variations can be attributed to the climatic changes, they need thorough calibration and validation against independent quantitative climatic information, e.g. with instrumental measurements in the vicinity of proxy site in the intervals of temporal overlapping. Because any single source of paleoclimate information has its limitations, sometimes it is more effective to reconstruct
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large-scale (regional, hemispheric) climate patterns applying multivariate statistical approaches to the combined proxy indicator network (Jones et al., 2001; Mann et al., 1998, 1999, 2003). Such approach is motivated by the fact that each proxy has its specific not overlapping strengths and limitations, and in principle they could assist each other. It is the reason for using a “multiproxy” reconstruction that summarizes advantages of different proxy information and reduces shortcomings of existing methods. Typical “two-proxy” example represents the merging of information from ice cores and deep-sea sediments. Deep-sea sediments accumulate very slowly relative to snow on the ice sheet. This results in much longer records from sediment cores, but with significantly reduced ability to resolve short-term changes. While the ice cores provide the annual and/or even seasonal resolution, the intervals of hundreds to thousands of years might be resolved in a sediment core. On the other hand, ice cores can provide only several hundred thousand years records compared with as long as several million years archived in the sediment cores. Because of this differences ice and sediment cores provide complimentary climate information. In the recent decade, there have been several attempts to combine various types of proxy indicators to create long-scale paleoclimate series. Reliable regional proxy based temperature reconstructions of the past millennium and their comparison with GCM were performed by Crowley and Lowery (2000), Briffa et al. (2001), Mann et al. (1998, 1999), and Mann and Jones (2003), who presented reconstructions of Northern and Southern hemisphere as well as global mean surface temperatures over the past two millennia or so based on high-resolution proxy data, namely historical, tree-rings, ice cores, and sediment records (Figure 3). The latter reconstruction is possibly the most often cited one. It was performed using tree-ring, ice core, coral, and historical records of climate (merged with the recent instrumental observations) and shows temperature variations in the Northern hemisphere over the past millennium (from 1000 A.D. to 1980). Comparison of above mentioned reconstructions is presented in Figure 11 (see also Mann et al., 2000; www.ngdc.noaa.gov/paleo/ei/ei_cover.html). Differences between above three climate histories are evident during the sixteenth and seventeenth, and early nineteenth centuries, where series by Crowley and Lowery (2000) and Briffa et al. (2001) fall outside the uncertainties estimated by Mann and Jones (2003). However, really noticeable feature of all records is so significant recent warming that Mann and Jones (2003) have concluded that indicated by their results late twentieth century warming is unprecedented for the Northern hemisphere at least during the investigated period. Conclusions by Mann et al. (1998, 1999) and Mann and Jones (2003) were supported by similar result by Jones et al. (1998) based on the independent data and methodology. Borehole data by Pollack et al. (1998) independently support this finding for the past 500 years. On the other hand, borehole temperature reconstructions alone as well as including of this source in the multiproxy reconstructions always give a colder past than that suggested by tree-ring and/or by multiproxy data sets. On the integrated (multiproxy ⫹ borehole) reconstruction by Huang (2004) presented for comparison in Figure 11, recent warming clearly appears as a simple continuation of the recovery from the cold conditions prevailed in the sixteenth century (this topic is discussed in more detail in Section 3.3, Chapter 3). Similar conclusions for the Southern hemisphere and on the global scale are less significant because of the sparseness of available proxy data.
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The course of the last millennium temperatures proposed by Mann et al. (1998, 1999) was so unusual (nothing in the first 900 years and dramatic temperature rise in the last 100 years), that it was accepted with caution by some climatologists and induced so trenchant debates that the Mann et al.’s curve was even called the “hockey stick”. The controversy about “hockey stick” can be found at the internet sites by the Marshall’s Institute (www.marshall.org and www.realclimate.org/index.php?m=200502), the World Climate Report (www.worldclimatereport.com), and numerical publications. Independently of the debates on the “hockey stick” this graph has been accepted as a fact by such international communities, e.g. IPCC (www.ipcc.ch) and played an important role in the study of the recent climate change and its consequences (up to Kyoto Protocol). The final point in the “hockey stick” story was placed only recently in the works by von Storch et al. (2004), Moberg et al. (2005), and Hegerl et al. (2007). The authors of the former work were interested in how well the multiproxy temperature reconstruction methodology applied in the creation of the “hockey stick” actually works, especially at multi-decadal and centennial timescales. They have used a coupled atmosphere–ocean model simulation forced with historical changes in solar output and volcanic eruptions and have simulated the surrogate climate for the past 1000 years. Calculated synthetic record was realistic enough and accurately reproduced main climatic episodes of the last millennium. Further, the authors have applied a technique similar to Mann et al.’s, using “proxy” data derived from the surrogate climate record to check how well the Mann et al.’s (1998) methodology could reproduce the actual data from which it was obtained. According to von Storch et al. (2004), the techniques used to construct the “hockey stick” significantly underestimated the real level of variability in the modeled temperature record and the real past climate variations may have been at least two times stronger than that indicated by the reconstructions. It is thus reasonable to conclude that the same techniques applied to the real field data would similarly underestimate the true level of natural variability that will result in too flat course of the past climate history. Even more severe argument against the “hockey stick” was presented in the work by Moberg et al. (2005). These authors have performed two thousands past Northern hemisphere temperature reconstructions using a variety of low- and high-resolution proxy data. Taking it for granted that different kinds of proxy temperature records may be more appropriately related to climatic variations at different timescales, Moberg et al. (2005) have applied a wavelet transform technique that can systematically overcome possible non-stationarities in the data and allows each proxy to explain temperature variations on a timescale that it was most sensitive to. For example, as discussed above, tree-rings capture weakly long-term variations, but are quite powerful for investigation annual-to-decadal scale variability. Low temporal resolution proxies are useful for capturing long-term, multi-century climate variations. By combining information of high-resolution and lowresolution proxies, Moberg et al. (2005) have inferred long temperature reconstruction for the Northern hemisphere (Figure 12). As can be seen, their reconstruction shows larger multi-centennial variability than most of previous multiproxy reconstructions, including, e.g. strong Medieval Warm Period and the Little Ice Age. The natural variation of temperatures in the Moberg et al.’s (2005) reconstruction is two to three times larger than that of the “hockey stick”. On the other hand, it agrees well with the ground surface temperature (GST) reconstructions from borehole data by Huang et al. (2000) (see also Section 3.2 and Figure 94, Chapter 3).
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Fig. 12. Low-frequency component of the Northern hemisphere temperature anomalies (Moberg et al., 2005) compared with the reconstruction by Mann et al. (1998) and borehole ground surface temperature reconstruction by Huang et al. (2000).
Recently Hegerl et al. (2007) have suggested a new calibration method that avoids the loss of low-frequency component in the multiproxy reconstructions. On the basis of updated proxy time series, these authors have reconstructed 1500 years long past temperature variations for the Northern hemisphere on decadal scale of aggregation. Obtained record shows substantial variability over the whole reconstructed period that is very similar to the Moberg et al.’s results. Hegerl et al. (2007) have tested their record with independent temperature reconstructions and with the climate model estimates. Good coincidence was found in both cases. The comparison of the reconstructed by Hegerl et al. (2007) temperature course with borehole estimates by Pollack and Huang (2000) and Pollack and Smerdon (2004) (for details see Section 3.2, Chapter 3) that revealed good agreement of both reconstructions appears to be most important for the borehole climatology. Using a conductive forward model and their SAT estimate as a surface forcing function (for details of calculus see Section 2.5, Chapter 2), Hegerl et al. (2007) have also calculated corresponding subsurface temperature anomaly. Its comparison with the average observed anomaly determined by Harris and Chapman (2001) has shown that the two temperature–depth profiles are almost identical. All above cited works mean probably the end of the “hockey stick” representation and have inspired numerous responses in climatologic community, like “Is the hockey stick broken?” www.tcsdaily.com/article.aspx?id=102704F and www.worldclimatereport.com/ index.php/2005/03/03/hockey-stick-2005-rip. As it is described in Section 3.2 (Chapter 3) (see also Figures 11, 12), borehole temperature reconstructions generally reveal more colder past and the warming that is more gradually distributed over past five centuries.
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Being quite different from the “flat” curve accepted by the “mainstream” of the climatologic community, these results were met with caution. Almost perfect coincidence of the GST reconstructions with the SAT changes presented in the works by Moberg et al. (2005) and Hegerl et al. (2007) represents also powerful verification of the “borehole climatology” with independent method and once more corroborates that borehole temperature reconstruction is a good indicator for the land annual SAT change. In summary we can only mention that considerable scientific efforts have been done to reconstruct past climate from the biological and physical proxy sources. This task is a challenging one and its results represent the subject to many complications and potential uncertainties and confidence can only be gained after comparison of more and more independent sources of proxy data. It is clear that the fundamental limitations (both temporally and spatially) of large-scale proxy-based reconstruction for past centuries arise from increasing sparseness of proxy database available to provide reliable climate information back in time. This database can be completed in space and time to such state when significant improvements will be possible in proxy-based reconstruction of the global climate only through joint efforts of large number of paleoclimate researchers. The compilation of many proxies can somewhat extenuate this problem, however, even a “multiproxy” reconstructions can only give a general understanding of what the climate was like and identify large-scale changes which may be related to climatic forcing of hemispheric or global significance. The “multiproxy” reconstructions are best to indicate climate tendencies or trends rather than exact temperature changes. On the other hand, numerous proxy results indicating similar climatic trends represent a powerful evidence that these tendencies are significant and really occurred, even if the magnitude of the change cannot be quantified.
1.3 Borehole Climatology Geothermics is the sub-branch of geophysics that studies terrestrial heat flow (Kappelmeyer and Haenel, 1974; Haenel et al., 1988; Jessop, 1990). Heat flow is the quantity of heat (generally expressed in mW/m2) transferred from the Earth’s interior to the surface. The major source of the interior heat is the decay of radioactive elements in the Earth’s crust and upper mantle. Up to 70% of continental heat flow may be generated within the upper 10–20 km of the crust; while 96% of the oceanic heat flow comes from below the oceanic crust where the concentration of the radioactive elements is significantly poorer (Kearey and Vine, 1990). The distribution of heat flow is related to tectonic processes in the lithosphere. The average heat flow density is inversely correlated with the geologic age of a given tectonic unit or oceanic crust (Sclater et al., 1980; Condie, 1989). On a regional scale heat flow pattern depends on numerous factors, such as regional differences in crustal radioactivity, fault distribution, hydrogeology, and hydrothermal activity (Cermak, 1983). Knowledge of the subsurface temperature field is central for understanding of practically all geophysical processes. The variation of temperature with depth and amount of heat leaving the Earth’s interior through its surface can be easily measured. Heat flow determinations in boreholes are made by combining sets of temperature–depth profiles and thermal conductivity data by the expression Q ⫽ K (dT/dz), where Q is heat flow, K the thermal conductivity, and T the temperature at depth z. The present
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global heat flow data set was compiled under aegis of the International Heat Flow Commission (IHFC; home-page www.geo.lsa.umich/IHFC) and contains more than 24000 measurements. Its description and analysis can be found in the work by Pollack et al. (1993). Temperatures obtained in boreholes, both the single values from maximumreading instruments and/or continuous temperature surveys (temperature logs), are essential to many areas of scientific research and engineering. Present book is devoted to the so-called ‘geothermal’ or ‘borehole’ method of the climate reconstruction which represents the reconstruction of the past temperature changes from the temperature–depth profiles measured in boreholes. This method principally differs from conventional proxies since it provides direct estimates of the GST histories. Ground surface temperature itself represents one of the important climatic variables, thus, reconstructed GST histories do not require calibration against independent climatologic data. The physics of the phenomenon is the next. At the constant surface conditions the underground temperature is governed by the outflow of heat from the Earth’s interior. For the homogeneous stratum it increases steadily with depth. Temperature changes at the surface slowly propagate downward and appear superimposed on this background geotherm. Figure 13 illustrates the ideal case of the penetration of sudden 1 K increase in the surface temperature into the subsurface with zero temperature gradient. As seen, it creates noticeable curvature of the undisturbed geotherm (sometimes called “U-shape”).
Fig. 13. Subsurface temperature distribution corresponding to a sudden 1 K increase in the surface temperature: 100, 300, and 500-years after its occurrence.
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Surface warming manifests itself as a positive disturbance in the subsurface; cooling shows up as a negative disturbance. The perturbation has the maximum amplitude at the surface, and the subsurface effect is limited to progressively shallower depth ranges as the surface change duration is shortened. The velocity of perturbation is a function of the thermal diffusivity of the medium. For typical Earth’s rocks with diffusivity of ⬃10–6 m2/s perturbation can propagate approximately 20 m in one year and 650 m in thousand years (see examples in Section 2.2, Chapter 2). Thus, 500–650 m deep hole archives climatic information for the last millennium or so. Whereas the depth of a subsurface temperature perturbation is related to the timing of the GST changes, its shape reflects details of the GST history. In other words, the borehole temperature log represents the transformation of the surface climatic events from the time into space coordinates. This transformation is performed by the nature and not by mathematics. Thus, the borehole temperature logging can replace the long-term surface temperature measurements. Well-pronounced “U-shapes” occur only in the ideal case of a single powerful climatic event. Arising sequentially several changes in the surface temperature create more complex and/or less expressed patterns than the strong “U-shapes” presented in Figure 13. Example of the temperature–depth profile simulated for the real GST changes is shown in Figure 19 (Chapter 2). Temperature changes at the Earth’s surface occur at several temporal scales. The oscillations are more regular on diurnal, seasonal, and annual scales. The strongest of these changes are the daily and seasonal variations with the amplitude of approximately10°C and the annual GST oscillations with typical amplitude of 20–30°C. Interannual and long-term temperature change patterns are generally irregular. As the surface temperature signal propagates downward, its amplitude decreases exponentially with depth due to the diffusive process of heat conduction. Each variation vanishes over a vertical distance related to the period of change and to the thermal diffusivity of the ground. Shorter period fluctuations attenuate more rapidly. Thus, the Earth selectively filters out high-frequency component of the surface temperature oscillations, and deeper we go, the more distant past can be inverted (unfortunately also more diffused and less credible). Figure 14 illustrates the amplitude attenuation of the temperature signal when propagating downwards and the delay of its phase by showing the results of the 12-year temperature monitoring at several shallow depths in the experimental borehole Sporilov (Prague, the Czech Republic) (Cermak et al., 2000). The daily temperature wave is practically not observable below 1 m depth. On the other hand, the temperature at 1 m represents integrated average of the daily signal of the previous day. Similarly, annual GST oscillations vanish near approximately 10–15 m depth and are not measurable below this depth. However, temperature measured above this depth is a proper index of the averaged temperature wave of the previous year. The temperature field below the 20–30 m depth is free of any response to the annual and/or shorter temperature variations and contains exclusively the fingerprints of longer scale climatic events with characteristic time of at least several years. Such signal may well characterize the pattern of the long-term climate change. Figure 15 illustrates the amplitude decrement and phase shift of the annual temperature wave with depth in more details. It shows the 1998-year interval of the long-term temperature time series from Sporilov presented in the previous figure. Temperature was monitored at several shallow depths from the surface to 7.5 m. As the
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Fig. 14. Results of 12-year precise temperature monitoring at several shallow depth levels in the Sporilov hole (the Czech Republic; 50.04°N, 14.48°E, 274 m asl.) clearly demonstrate the propagation of the surface temperature signal to the depth.
surface temperature signal propagates downward, it is delayed in time and its amplitude decreases exponentially with depth due to the diffusive process of heat conduction. Each variation vanishes over a vertical distance related to the period of change and to the thermal diffusivity of the ground. Thus, the amplitude of the annual wave decreases to 50% of its surface value at ⬃2 m depth with time delay of about 40 days. It decreases to ⬃15% of its surface value at 5 m depth where it arrives with approximately three months delay. Repeated measurements of borehole temperature logs, e.g. the temperature loggings performed in borehole GC-1 (northwestern Utah) over a span of 14 years by Chapman and Harris (1993) have shown a slowly varying temperature field with remarkable similarity of the measured signals and the replication of their main details, remaining evidently coherent in space and time (Figure 16). Bottom panel (c) of Figure 16 shows the temperature differences between the individual logs (data points) together with the synthetic temperature-difference profile (solid line) computed from the 100 years long meteorological record of SATs in the nearby weather station. The deviations between three temperature logs do not exceed 0.1 K. Synthetic temperature profiles exhibit high correlation with the measured temperature logs. In the case of above mentioned borehole GC-1 synthetic profile represented well systematic negative anomaly and significant curvature in the uppermost 60 m of borehole. This fact indicates that “U-shapes”
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Fig. 15. Results of one-year temperature monitoring at several shallow depths in Sporilov hole. The profiles well illustrate the amplitude decrement and phase delay of the temperature change with depth.
are not occasional variations and really represent the result of the long-term processes of changing climate. This conclusion is supported by repeated temperature logging of borehole Hearst (Canada) that embraces even longer period of time. Three holes together with Hearst site were drilled in northeastern Ontario in 1968 as a part of the heat flow project of the Dominion Observatory. The sites were carefully selected in a relatively flat terrain and in geologically uniform strata. The 600 m deep borehole Hearst is located in a slightly elevated, bushed area at the boundary of large forested and cleared fields. A small nearby lake and swampy area affect the temperatures insignificantly. The first incremental log was measured in 1969 (Cermak and Jessop, 1971). Further virtually continuous loggings were performed in 1985 and in 2000. Temperature measurements are highly precise with absolute accuracy of less than 20 mK for the incremental logs and as small as 10 mK for the continuous logs (for further details see Section 2.4.3). Figure 17 compiles the results of these measurements. As seen, all temperature logs are quite coherent with weak, but clear positive “U-shape” curvature in their uppermost parts. Figure 17 and all similar
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Fig. 16. Measured (a) and reduced (b) temperature profiles for borehole GC-1, NW Utah, USA. Temperature logging was repeatedly performed in years 1978, 1990, and 1992 (data by Chapman and Harris, 1993). Bottom panel (c) shows the temperature differences between the individual logs (data points) together with the synthetic temperature-difference profile (solid line) computed from the 100-year meteorological record of SATs recorded in the nearby weather station.
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Fig. 17. Repeated measured temperature logs (together with the reduced temperatures) performed in the Hearst hole, NE Ontario, Canada (personal communication by W.D. Gosnold and A.M. Jessop, see text).
diagrams below present the temperature log not only on the measured, but also on a reduced scale obtained by subtracting from the measured temperatures, a temperature value ⫽ gradient ⫻ depth (see also Eq. (2.5), Section 2.2). This representation enhances the nonlinearities. The shape of the reduced temperature–depth profiles is more complex than that occurring in the case of the single warming event (Figure 13). The waves of the opposite sign in the reduced temperature profiles hint the presence of the recent warming that may be amplified by the environmental effect of the forest clearing occurred approximately 100 years ago (Wang et al., 1992), subsequent cooling, warming, and cooling again. Examples of the GST history reconstruction for this hole are presented in Section 2.4.3 (Chapter 2). The surface temperature history can be inferred directly from the borehole temperature logs. Earlier the subsurface anomalies were found by forward calculation using appropriate physical models with given surface temperature histories and by selection of those GST history that best explains the measured temperature–depth profile. At present the GST changes are inferred by the more general data inversion techniques. The accuracy of the inversion depends on numerous a priori information, e.g. on the knowledge of conductive properties of the subsurface stratum. This technique is essentially multidecadal and cannot provide information about annual temperature changes or for the times near the present. The advantages of the “geothermal” method are discussed in details in Paragraph 2.2. Here, we would like to point out only the two main advantages: (1) subsurface temperatures are measured directly and on the contrary with the proxy measures their inversion provides a direct evidence of past temperature change at the
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Earth’s surface, (2) because of great number of boreholes the method is applicable over most continents including polar ice caps. From the middle of twentieth century numerous measurements of the temperature profiles in boreholes were performed for the terrestrial heat flow study. The recognition that past climate changes influence the GSTs, penetrate in the subsurface and could be recovered from the temperature–depth profiles measured at boreholes dates back to Lane (1923). The first attempt to infer past climate changes from measured temperature–depth profile dates back to Hotchkiss and Ingersoll (1934) and Birch (1948). More systematic studies of the possibilities of the geothermal method were undertaken only in the early 1970s (Cermak, 1971; Anderssen and Saull, 1973; Beck, 1982). However, even that time climatic perturbations to an otherwise equilibrium geotherm were regarded as “noise”, and it was customary to eliminate them from the temperature profiles measured for the Earth’s heat flow investigations and/or use the lower “undisturbed” sections of the temperature logs for the terrestrial heat flow determination. The real recognition of the method has been gained in the 1980s when the evidence of pronounced last century warming was clearly proved in a number of wells in the Alaskan Arctic (Lachenbruch and Marshall, 1986; Lachenbruch et al., 1988). In the recent two–three decades the geothermal community had undertaken widespread re-examining of existing heat flow data in order to reveal the past GST changes and to construct systematic GST perturbation patterns. The previous “noise” was turned into a valuable signal of the climate change. Further studies of the geothermal method developed in three main directions: 1. Inversion methods – Numerous inverse methods based on different assumptions and used definite a priori knowledge have been developed that time. 2. Climate reconstructions using national borehole database – The ample worldwide geothermal database of temperature logs initially measured and compiled for heat flow studies has proved to be very useful for the GST reconstructions. The intensification of the borehole climate studies was supported by simultaneous significant growth of the global geothermal borehole network. Since the 1990s numerous borehole loggings were performed directly for paleoclimatic reconstructions (for more details visit web sites www.geo.las.umich.edu/climate/index.html and/or www.ncdc.noaa.gov/paleo/borehole/borehole.html). 3. Integration of the obtained GST histories in the traditional paleoclimatic network (Harris and Chapman, 2001; Mann et al., 2003). The first compilation of the studies inferring past climatic changes from underground temperatures has appeared in 1992 (Lewis, 1992). The reconstruction of the GST histories has drawn increasing attention under several international projects in the 1990s. The Project No. 428 carried out in the years 1998–2002 under the UNESCO International Geological Correlation Program “Borehole and Climate” was probably the most important of them. The next after the year 1992 current collection of the borehole climate reconstructions from a number of regions all over the world was compiled by Beltrami and Harris (2001). The analyses of the worldwide borehole data for the large-scale spatial–temporal reconstructions of the Earth’s climate are presented in the works by Pollack et al. (1998), Huang et al. (2000), and Mann et al. (2003). Initially
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the paleoclimatic information was gained from conventional widespread land boreholes. Recently the 50 000 years long GST history was recovered from temperature profiles measured in the ice borehole remained after successfully recovered ice core in the Greenland ice sheet (Dahl-Jensen et al., 1998). The ice borehole logs can provide valuable estimates of past temperature changes in polar environments that are complimentary to proxy reconstructions obtained from ice core oxygen isotopes (for details see Section 2.9). Superdeep boreholes belonging to the International Continental Drilling Program (ICDP; www.icdp-online.de) attracted special attention of the “borehole climatology” community. Geothermal and paleoclimatic investigations are among the most important directions of the ICDP scientific research (Section 3.5). The common merits of the geothermal method are that it is based on a simple physical theory, that the past ground temperature conditions can be derived directly from measured temperature logs and do not need any additional calibration, its ability to recover continuous GST trends over the last millennium or longer, and a rather good terrestrial distribution of boreholes. Among the possible weaknesses is somewhat poor resolution that decreases back in time and non-climatic disturbances that could affect measured temperature–depth profiles. Numerous methods for diminishing of possible biases of the geothermal method are worked out. Obtained GST differs from the SAT that is of general use in meteorology/climatology. This complicates comparison of the GST and SAT based climatic reconstructions. The GST–SAT coupling depends on external factors (e.g. land surface cover and its changes, especially seasonal snow cover variations). Additional studies of this problem include experiments on the monitoring of meteorological and subsurface variables. These experiments were planned to reveal details of the air/ground energy exchange under various surface conditions (Putnam and Chapman, 1996; Beltrami et al., 2000; Cermak et al., 2000; see Chapter 4). Despite the existing sources of bias, the results of the last two decades research confirmed the ability of the method to provide reliable GST history that is consistent with other paleoclimatic information. At present the geothermal method plays a new significant role in the investigations of climate of our planet. Borehole temperature profiles became one of the important sources of climatic information and contributed significantly to our knowledge of the millennial surface temperature changes. Some of the leading scientists give extremely positive evaluation of the geothermal method, e.g. “in my estimation, at least for timescales greater than a century or two, only two proxies can yield temperatures that are accurate to 0.5°C: the reconstruction of temperatures from the elevation of mountain snowlines and borehole thermometry” (Broecker, 2001). Using more modest expressions, one could declare that at present the ‘borehole’ method undoubtedly represents an independent well-developed research tool in the paleoclimatic studies and an important supplement to the climate reconstruction by proxy indicators. The purpose of this book is to present our current best knowledge of the geothermal method for the past climate reconstruction. The book explains the capacity of the subsurface temperature field to “remember” what has happened on the surface and how this memory can be utilized. We therefore describe in details different methods of the GST inversion, make note on the strength and emphasize the potential weaknesses and caveats of the past climate reconstruction from geothermal measurements, particularly with respect to its resolving power, non-climatic disturbances to the measured
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temperature–depth profiles and GST–SAT coupling problems, and discuss the possibilities of further development. Significant part of this work summarizes the major results to reconstruct the climate scenario spanning from Holocene to recent and discusses their role in the improvement of the traditional paleoclimatic patterns. The final goal is to assess the magnitude of the present-day warming and to distinguish between the natural climate variability and the potential human contribution due to environmental pollution. We hope that this book will contribute to advance of the “Borehole Climatology” research in the coming years.
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CHAPTER 2
Climate Change and Subsurface Temperature
While the majority of climatologists are looking up to the sky or plunge themselves in the oceans to understand why and how the climate has changed, an adroit “borehole climatologist” is looking inside deep holes drilled in the ground. The most important research implement of the “Borehole Climatology” is a borehole. Typical borehole site looks like as it is shown in Figure 18. A borehole, usually a small-diameter hole drilled from the land surface to the depth of several tens or hundreds meters, presents a deep narrow shaft in the ground which enables to lower a temperature-measuring device (thermometer) down the hole. The temperature measurements are repeated to progressively greater depths until a long temperature–depth profile is obtained. The thermometer measures the temperature of the borehole filling fluid (usually water), not the surrounding rock, so as to obtain meaningful values of the ambient temperature of the surrounding subsurface strata, the borehole fluid must be in thermal equilibrium with its surroundings. If the hole has been only recently drilled, the fluid may not have time enough to attain thermal equilibrium. Also, any event that subsequently disturbs the bore fluid may cause certain thermal disturbance. The disruption of the thermal equilibriun caused by the drilling process is slowly dissipating; to obtain a reliable precise temperature–depth record a long recovery time (up to several months) is indispensable. Production, i.e. removal of fluid from the borehole, also causes thermal disturbances, so in many cases the oil wells or water-pumping holes are hardly suitable for the borehole climate reconstruction. Temperature logging is actually a part of borehole geophysics, the science that records and analyzes measurements of various physical properties in boreholes. Probes that measure different properties are lowered into the borehole to collect continuous or pointby-point data, so-called geophysical log. These records may be used for various environmental investigations and help better understand the subsurface conditions. Geothermics or geothermal research, the sub-branch of geophysics, is the study of the thermal state of the interior of the solid and of the thermal properties of the Earth material. Knowledge of the subsurface temperature field is central for interpreting and understanding practically all geophysical processes. Temperature log is the temperature record in the borehole and 37
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Fig. 18. The Torun IG-1 (Poland) deep borehole site. Standard measurement technique, when the temperature probe is lowered to the hole with the help of cable on the winch. Temperature data are taken and stored with the pre-selected time interval (usually each 5 s), and depth is simultaneously recorded by computer from the number of revolutions of the pulley.
represents a general tool of geothermics. Examples of the temperature logs measured in boreholes are presented in Figures 16 and 17 (Chapter 1). At the constant surface (temperature) conditions the underground temperature is governed by the outflow of heat from the Earth’s interior. For the homogeneous stratum (constant thermal conductivity of the subsurface rocks) temperature increases steadily with depth, i.e. the geothermal gradient is constant. Temperature changes at the Earth’s surface (as the response to the climate changes) slowly propagate downward into the subsurface and appear as tiny temperature deviations superimposed on the background geotherm. While the part of underground temperature field governed by the heat flow from the Earth’s interior is
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generally steady state, the response to the surface conditions is a transient perturbation. Present precise borehole temperature measurements at depth of up to several hundred meters thus provide an archive of temperature changes that have occurred on the surface in the past. They can be analyzed to yield a ground surface temperature (GST) history over the past few centuries.
2.1 Methods and Technique to Carry Out Borehole Temperature Measurements Temperature data measured in boreholes serve as an input to many fields of the scientific research as well as engineering and exploration, and the techniques and equipment for such measurements are well developed. Among others, Lee and Uyeda (1965) and Jessop (1990) presented detailed review of a history of the geothermal measurement and the interpretation of the heat flow data in terms of the basic geophysical studies. The earliest measurement of the subsurface temperatures started at about 1700s, soon after thermometers had been developed, in mine shafts, tunnels, and/or water wells. Some of the early systematic measurements in boreholes were conducted between 1868 and 1883 under the aegis of the Committee of the British Association for the Advancement of Science (see Bullard, 1965). Initially, these measurements were simply individual readings obtained by the maximum-reading thermometers at shallow depths. The development of the petroleum industry during the second half of the nineteenth century made deep boreholes available for subsurface temperature loggings and, together with the development of electrical-resistance thermometers, significantly improved the accuracy of the measurements. Schlumberger services first introduced the temperature survey, using continuous-recording logging tools, in the late 1930s. Guyod (1946) had presented a series of papers, which discussed the theory and the various current and potential uses of the underground temperature data in the petroleum industry and inspired a widespread application of the temperature logging technique. Haenel et al. (1988) and Jessop (1990) have presented reviews of the methodology and technology of the scientific borehole temperature measurements for the heat flow determination. The most accurate temperature and heat flow data are obtained with high-resolution thermistors sunk into small-diameter, thermally stable boreholes at logging speeds of 10–15 m/min. These data are generally recorded as continuous temperature or temperature gradient logs. The different kinds of the logging tools have a resolution of 1–3 mK with typical accuracy of several hundreds of degree. The borehole GST reconstruction methods deal with very small disturbances to the subsurface temperatures, where even tiny variations of some hundreds of degree are considered significant and accuracy of the measured data is crucial. As mentioned before, the drilling operations disturb the temperature field in the vicinity of the boreholes, while good-quality steady-state data reflecting “formation temperature” are indispensable for proper evaluation of the past climate. The undisturbed borehole temperature can be measured only in the equilibrium conditions after the long period the hole was shut in and drilling mud circulation ceased. The “thermal recovery” time for a borehole may range from a few days for a shallow (100–150 m) well to several months for deeper holes. The main assumptions for the mathematical approximation of the temperature disturbances due to drilling are: (1) drilling was continuous and regular, (2) there is no fluid
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loss, and (3) thermal diffusivity equals that of the surrounding rocks. In this case, the temperature disturbance due to drilling (heat exchange with drilling fluid and frictional heating) Td at a distance r can be approximated by a constant line source (Carslaw and Jaeger, 1962) Td ⫽⫺
r2 Q , Ei ⫺ 4K 4 kt
(1)
where K is the thermal conductivity, k the thermal diffusivity, Q a quantity characterizing the amount of heat released by the heat source, and t the time from the beginning of the disturbing effect. Ei(x) is the exponential integral. If the disturbance lasts from the time th to 0 its value can be expressed as Td ⫽
Q 4K
r 2 r2 ⫹ Ei ⫺Ei ⫺ ⫺ 4 kt . 4 k (t ⫹ t h )
(2)
For the typical small-diameter boreholes both arguments in the exponential integral will be also small. Thus, the integral allows approximation Ei(⫺x) ⫽ ln x ⫹ 0.577 22. The latter number is the Euler gamma constant. Final expression for Td will be Td ⫽
Q t ⫹ th ln . 4K t
(3)
The heat release Q is proportional to the diameter of borehole and the temperature difference between the drilling fluid and surrounding rock. The typical values range in the interval 10 to 20 W/m. In a shallow borehole the temperature of the drilling fluid is close to that on the surface. Additional heating caused by the friction of the drilling bit may slightly increase its value; however, because the temperature in borehole increases with depth, the value of Q may somewhat decrease with depth in case of other conditions being constant. Figure 19 shows the re-establishment of the undisturbed temperature field (having existed prior to the drilling) calculated for different values of the heat released during the drilling process. The magnitude of the borehole temperature disturbance due to drilling decreases almost linearly during the period compared with the drilling time. At t ⫽ th the disturbance falls to approximately 12% of its initial value. For times t ⬎ th the attenuation significantly slows down. The above calculations were performed under assumption of continuous drilling; however, suggested method can be further developed for the case of drilling regime interrupted by several breaks (Štulc, 1995). At a certain stage the above approximation may not be valid (Drury, 1984); this happen when the arguments of the exponential integrals (Eq. (2)) are not small enough due to low circulation time and/or large-diameter boreholes. As shown below, a reliable climate reconstruction using borehole temperature–depth data can be substantially improved by the knowledge of the thermophysical properties
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Fig. 19. Re-establishment of the undisturbed temperature field corresponding to the conditions prior to drilling. Individual curves are marked by the value of heat released by the heat source in W/m.
of the subsurface, namely of the thermal conductivity. Thermal conductivity,1 a basic physical property of rocks, depends on rock/mineral composition. Reliable values of thermal conductivity are helpful for modeling of all kinds of processes of heat transfer in the Earth’s crust. “If the mean conductivity cannot be accurately predicted, even the most sophisticated and appropriate modeling techniques … are not sufficient for accurate temperature predictions” (Blackwell and Steele, 1989). Thermal conductivity determination represents an essential part of the borehole measurements suitably completing the borehole temperature logs. Thermal conductivity is usually determined in laboratory on rock samples collected from the drilled core and worked out in either specific shape or on crushed cuttings using various techniques, e.g. divided bar or needle probe technique (Jessop, 1990). 2.2 Subsurface Temperature Field and its Response to Changing Surface Conditions (Climate) At the first sight, the relation climate change versus subsurface temperature field may be strange. How is it possible that the present-day subsurface temperature measured in the solid surface can reflect a climate change that occurred a long time ago and somewhere high above the Earth’s surface? There is no doubt that the thermal regime 1 Thermal conductivity K is the property of material that indicates its ability to conduct heat. Under pure conductive steady-state conditions, it is defined as a quantity of heat transferred in time t through the layer with thickness L in a normal direction to a surface of area A due to a temperature difference T: K ⫽ QL/AT. Typical conductivity of the Earth’s subsurface rocks is in W/mK.
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at the Earth’s surface and in the near-surface shallow depths is controlled entirely by the solar radiation, and the resultant mean surface temperature depends on the longterm budget of the incoming and reflecting radiation. The average energy density of solar radiation just above the Earth’s atmosphere, in a plane perpendicular to the rays, is about 1367 W/m2, a value called the solar constant (although it fluctuates by a few parts per thousand from day to day). The Earth receives a total amount of radiation determined by its cross-section (R2), but as the planet rotates this energy is distributed across the entire surface area (4R2). Hence, the average incoming solar radiation (known as “insolation”) is 1/4th the solar constant or ⬃342 W/m2. At any given location and time, the amount received at the surface depends primarily on the state of the atmosphere and the latitude. Temperature (as well as precipitation and wind) is the most important variable, which characterizes the climate. When speaking about the temperature, we usually understand temperature of the air. However, air temperature is not constant and at the given location it shows daily and yearly variations, which may amount from a few degrees up to several tens of degrees. To deal with climate and its changes which cover time spans varying from decades to thousands or millions of years, we may better use a mean annual air temperature as the unit to describe the time variations of temperature. Actually, the World Meteorological Organization (WMO; www.wmo.ch) proposes 30-year time interval as the classical period when defining climate as the statistical system in terms of the mean and variability. However, being important for the conditions existing on the Earth’s surface, the incoming solar radiation is of no practical meaning for the state under the surface. From the surface the temperature is increasing with depth with the rate (geothermal gradient) proportional to the outflow of the thermal energy from the Earth’s interior. Typical geothermal (terrestrial) heat flow on continents equals to 50–60 mW/m2, which is negligible in comparison to the solar flux. This, even relatively, low geothermal outflow can provide significant geothermal gradients corresponding to 20–30 K growth per kilometer. This outflow is governed by the geologic timescale processes; thus, for shorter characteristic time of climatic studies this part of the subsurface temperature field can be assumed to be steady state. For the uniform crust and constant surface temperature the subsurface temperature–depth profile is the combination of the linear increase of temperature with depth plus the transient response to the seasonal temperature variations on the surface. In general, the sinusoidal oscillation of the surface temperature, T(t) ⫽ T0 cos(t), propagates downwards in accordance with the damped wave equation T(t)⫽T0 exp(⫺z) cos(t⫺z), where t is time, z the depth, k the thermal diffusivity,2 and ⫽兹苶 苶兾苶2苶k. If P is the period of surface temperature oscillations, then ⫽ 2/P. The wavelength is then ⫽ 2/. For a typical value of diffusivity (k ⫽ 10⫺6 m/s), the wavelength of the diurnal oscillation is about 1 m and that of the annual oscillation is about 20 m. At a depth of one wavelength, the amplitude of the oscillation is reduced by a factor of exp(⫺2) ⫽ 0.002, and is thus negligible for most geophysical purposes. If the (high frequency) daily and annual temperature variations vanish at the depth below this zone of seasonal wave penetration (see Section 1.3, Chapter 3), the (low frequency) long-term climate changes propagate deeper.
2
Thermal diffusivity is the ratio of thermal conductivity to volumetric heat capacity (SI units are m2/s).
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In the idealized case, geothermal gradient can be calculated according to the Fourier3 relation G ⫽ Q/K, where Q is terrestrial heat flow and K the thermal conductivity of the medium. In the real case, geothermal gradient depends on local geological structure, e.g. on the composition of rock strata. Under suitable conditions the geological factors affecting the geothermal gradient can be taken into account, so the climate history can be inferred from small temperature anomalies along the depth of borehole. While part of the subsurface temperature field corresponding to the internal processes is steady state, the response to the surface conditions represents a transient perturbation that appears as a disturbance to the background temperature field. Figure 20 illustrates how borehole temperatures can be related to climate change. A sudden warming of the surface by the value of T will heat up
Fig. 20. The response of the subsurface temperature field to the surface change. Bottom: Typical temperature–depth profile measured in a borehole indicating surface warming/cooling together with the (undisturbed) steady-state geotherm. Top: Disturbances to the geothermal gradient. 3 Jean Baptiste Joseph Fourier (1768–1830) has studied the mathematical theory of heat conduction. He has established the partial differential equation governing heat diffusion and has solved it by means of infinite series of trigonometric functions.
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the near-surface rocks. It creates a temperature profile with curvature like the one shown in Figure 20 (bottom, right) with smaller or even negative thermal gradients. Similarly, cooling produces an opposite effect. It increases geothermal gradient creating temperature profile like the one shown in Figure 20 (top, left). It is the heat conduction that helps to preserve the recollection on the past climate change at depth. The deeper we go, the more remote past history can be studied, even if both the amplitude attenuation and the time delay of the surface event increase with depth. As a simple rule, temperature–depth profiles to depth of 200–300 m record surface temperature trends (climate) over the last two centuries or so; deeper holes may reveal climate history farther back but with sharply decreasing resolution. Under favorable conditions all Holocene climate can be evaluated if the precise temperature log is available to the depth of 1 to 2 km. Perturbations to the conductive thermal regime are generally reasonably noticeable at shallow depth, while deeper temperatures are less affected by climatic variations. Well-developed curvature resembling a “U-shape” occurs only in the ideal case of a sudden relatively pronounced climatic event (see, e.g. temperature logs measured at Cuba, Figure 86, Chapter 3). Gradually changing climate, in reality consisting of several shorter alternating warmer and colder time intervals. creates more complex and less expressed subsurface temperature response than the pattern presented in Figure 20. The magnitude and the shape of the departure of the subsurface temperature from its undisturbed steady-state profile are determined by an amplitude and course of the surface temperature variation (climate). The GST history is recorded in the subsurface. These disturbances can be recollected by solving the ordinary heat conduction equation with appropriate initial and boundary conditions. The heat propagation equation for the source-free laterally homogeneous semi-infinite medium where heat is transferred exclusively by conduction can be written as c
T T ⫽ K , t z z
(4)
where z is depth, t the time, T(z,t) the temperature, and , c the density and the heat capacity of the medium, respectively. If necessary, the radioactive heat generation A, resulting from radioactive decay of U, Th, and K, can be also included in Eq. (4). However, this procedure is relevant only for deep boreholes. The addition of the term A to the right of Eq. (4) will produce a systematic decrease in geothermal gradient with depth. But the departure from a constant temperature gradient will be too small to be observed at shallow to intermediate-depth holes even for high rates of the heat production. For example, at boreholes with the thermal conductivity of 2–3 W/mK, including heat production of 1–3 W/m3 (the latter value is typical for granites) will produce only 0.002–0.008 K disturbance to the otherwise linear geotherm at depth 100 m and 0.007–0.030 K at depth 200 m, respectively. Initial temperature–depth distribution is T(z, t ⫽ 0) ⫽ T0(z). For the homogeneous strata it is simply T0(z) ⫽ T0 ⫹ Gz, while for a layered slab composed of m layers with constant thermophysical properties Kj and kj ⫽ Kj /cj, (z0, z1), (z1, z2), …, (zm⫺1, zm) it can
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be expressed as (Bodri and Cermak, 1995) T j ( z ) ⫽ T0 ⫹
Q ( z ⫺ z j⫺1 ) ⫹ Kj
j⫺1
∑K i⫽1
Q
( zi ⫺ zi⫺1 ).
(5)
i
Expression (5) suggests the continuity of temperature and of heat flow at the interface between layers. Surface temperature is T(z ⫽ 0,t) ⫽ f(t), t ⬎ 0. Forward calculation is very simple when the surface temperature history f(t) is known. Figure 21 shows the disturbances to the otherwise steady geotherms that develop in the case of a stepwise increase of the surface temperature by T ⫽ T *⫺T0. The corresponding solution of Eq. (4) at time t ⫽ t can be expressed as (Carslaw and Jaeger, 1962)
z T ( z, t ) ⫽ T0 ⫹ Gz ⫹ T ⴱ erfc , 2 k t
(6)
Fig. 21. The effect of the duration (t) of a step increase (T ) in surface temperature on the disturbance penetration depth and the shape of the corresponding geotherms (k ⫽ 10⫺6 m2/s, T0 ⫽ 0°C, G ⫽ 20 K/km, T ⫽ 3 K).
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where k ⫽ K/c is the thermal diffusivity and erfc(x) the complementary error function of argument x. As seen in Figure 21, a uniform surface anomaly propagates downward. The departure of the disturbed temperature profile from the steady-state geotherm increases, thus, the curvature of disturbed profile decreases with time. The magnitude of the departure of the ground temperature from its undisturbed state is determined by the amplitude of the surface disturbance T. The velocity of propagation of the surface temperature disturbance depends on the thermal diffusivity of the rocks that is relatively small (⬃10⫺6 m2/s). For such diffusivity a thermal front (i.e. 1% of the surface change) propagates to about 20 m in one year from the beginning of surface warming, 65 m in 10 years, 200 m in 100 years, and 650 m in 1000 years. The real changes in the Earth’s surface temperature occur at different temporal scales. As shown in Section 1.3 (Chapter 1; Figure 14), the most significant and regular of them (daily, seasonal, and annual oscillations) are attenuated at relatively shallow depths of approximately 15–20 m. The longer term variations appear as disturbances to the steadystate temperatures at deeper levels. The combination of the subsequent warming/cooling events on the surface complicates the pattern of disturbances to T⫺z profile. Figure 22 illustrates the disturbances that can occur in the more close to the reality case than that presented in Figure 21. We used in calculations the temperature record for Central England (Chapter 1, Figure 8) as the surface forcing function f(t). This record of annual temperatures exists from the 1659 A.D. The time series is highly variable; the range of temperature oscillations reaches approximately 3 K. Figure 22 shows the departures from the steady-state temperature and geothermal gradients. The shape of the temperature anomaly in this case is more complex in comparison with the profiles shown in Figure 21.
Fig. 22. Steady-state temperature–depth anomaly (left) and geothermal gradient–depth anomaly (right) produced by the climatic temperature forcing corresponding to Central England (Chapter 1, Figure 8). Inset shows the enlarged segment of the gradient anomaly between 50 and 300 m depth.
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Fig. 23. The “thermal memory” of the Earth for the (climate) events on its surface: diffusion of the subsurface temperature perturbation caused by a sudden GST change of duration t (k ⫽ 10⫺6 m2/s, T ⫽ 1 K).
Although high-frequency components of GST changes are suppressed by the heat diffusion, calculated temperature–depth profile contains a robust signal of more than three century long climatic history. Negative temperature anomalies and positive gradient in the depth range 50–300 m indicate generally cold conditions in the seventeenth to nineteenth centuries, while the noticeable curvature in the uppermost part of the calculated temperature–depth profile and negative gradients correspond to the rapid warming of the twentieth century. The temperature disturbances propagate downward and slowly fade away. Figure 23 illustrates the downward propagation of the thermal front (1% of the surface temperature change) corresponding to the step-like surface temperature impulse of duration t. The T ⫽ 1 K amplitude impulse with duration 10 years propagates to the maximum depth of 170 m and fades away in the underground after approximately 240 years since its cancellation on the surface; 50-year long change can penetrate to approximately 400 m depth and is preserved in the Earth’s interior for approximately 1200-year long period. This example illustrates well the possible length of the surface climatic history that can be extracted from borehole temperature logs as well as the resolution capacity of the borehole climate reconstruction method. Past variations of the GST propagate slowly downward and, although attenuated and smoothed, remain recorded in the subsurface as a perturbation to the steady-state temperature field. Because the transient climatic signals have significantly shorter living time than the geologic heat flow variations, these two signals operate in differing frequency domains and do not mix; thus, it is possible to use borehole temperature profiles for the extraction of the past GST variations. Present rock temperatures measured at depths of up to several hundred meters provide an archive of temperature changes that have occurred on the surface in the past. They can be recovered by an appropriate analysis of
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temperature–depth data and provide the possibility to reconstruct past GST history. The main advantages of this geothermal tool for climate reconstruction are (1) The method is based on a direct temperature–temperature relation. The temperature–depth profiles reflect a direct relationship to the continuous GST forcing. The borehole climate reconstructions do not require any calibration against independent temperature data and contrary to most proxies such reconstruction is free of uncertainties of calibration. Inferred from geothermal data the GST histories can be used as themselves and present a powerful complementary source of information for the verification of proxy records and enable complex multiproxy reconstructions. Recently several groups of climatologists have combined the results of the GST reconstructions with high-resolution proxies such as tree-rings and/or ice core data and achieved both more accurate temperature estimates for the proxy methods as well as better resolution for the geothermal GST histories (Beltrami and Taylor, 1995; Harris and Chapman, 2001, 2005; Huang, 2004; for details see Section 3.3, Chapter 3). (2) The process of heat conduction integrates GST changes continuously in the same manner and thus secures data homogeneity (unlike, e.g. the meteorological data that can suffer from inevitable modification of the recording equipment or station reorganization). (3) Extensive time interval that could be recovered. Temperature–depth profiles contain a robust signal of the long-term surface temperature history. Resolution of the geothermal method covers one to two millennia, in some cases up to the last glacial (Bodri and Cermak, 1997b; Safanda and Rajver, 2001). (4) Continuous rather than short-term sensitivity. The resolution of the geothermal method is essentially multi-decadal. (5) Extensive geographical coverage. Once a borehole is available, temperature log can be obtained easily. The necessary equipments (borehole thermometer or data logger) are relatively inexpensive and common. At present thousands of the borehole temperature logs measured all over the world are available even when not all are useful and serious selection criteria must be applied. The ample worldwide catalog of temperature logs represents a valuable database for comprehensive paleoclimatic investigations. In many cases borehole temperature logs represent the only source of the climatic information for the region that otherwise appeared as a “white spot” on the paleoclimatic map. (6) Minimal anthropogenic disturbances. Many existing meteorological stations were actually located in settlements which later grew to huge population centers; their records may suffer from the induced anthropogenic pollution when local climate became significantly warmer than its surroundings (urban heat island) and the observed data can be mistakenly used. On the contrary, boreholes are usually drilled far from the population centers in remote regions. Climate information stored here contains minimum of such anthropogenic influence.
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The main disadvantages are (1) The decrease of the resolution into the past and progressive smoothing of the amplitude of the recovered temperatures when moving back to the past due to smearing of the climatic signal caused by thermal diffusion. (2) Exact knowledge of the thermal properties of rocks at each borehole site is indispensable to determine uniquely the pattern of the past climatic changes, while this information is not always available in full. This disadvantage, however, is similar to the common insufficiency of the field information in many other geophysical branches. (3) Climate change is related to the mean air temperature, but the inversion of the borehole data provides the GST, which is not identical to the air temperature. The soil–air temperature coupling is complex and dependent on the type of surface topography, albedo, type of bedrock, micro-vegetation cover (and its temporal changes), snow cover, precipitation, changes in water table, etc. The time variations in all of these factors and their reaction to climate and terrain changes make the interpretation of borehole data more complicated. In general, ground temperature is always higher than the air temperature; however, both follow in principle the same trend and the basic features of the climate reconstruction can be well substituted by the GST reconstruction.
2.3 Geothermal Method of Climate Reconstruction: Principles, Resolution, Limitations (Forward and Inverse Techniques, Sources of Perturbation) 2.3.1 Background and history The effect of the past climate changes, namely the last Ice Age, on the temperature gradient was actually recognized by the early heat flow workers (Lane, 1923), and a general mathematical formulation was thoroughly discussed by Carslaw and Jaeger (1962). Only much later it was realized that the problem could be reversed, i.e. from the detailed measured T–z data to infer the past climate. The first attempt dates back to Beck and Judge (1969) who speculated on recent surface temperature variations using data from a borehole drilled on the campus of the University of Western Ontario. Cermak (1971) used T–z profiles from three holes in the Kapuskasing area and reconstructed GSTs for the past millennium in northeastern Ontario, Canada, when the Monte Carlo type statistical method was used to alleviate the calculation instability problems. However, it was not before the late 1980s when Lachenbruch and Marshall (1986) presented clear geothermal evidence from a number of boreholes in Alaska for a recent global warming. This work can be considered as the beginning of the worldwide attention paid to the importance of the temperature logs for the paleoclimate studies. Even when the very first attempt to infer past climate changes from measured temperature–depth profile in inverse problem dates back to Hotchkiss and Ingersoll (1934), the application of the modern geophysical inverse theory to the reconstruction of the GST
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changes from the measured temperature–depth profiles has started with the work by Vasseur et al. (1983), using Backus–Gilbert formalism (Backus and Gilbert, 1967). Since then numerous inversion methods have been developed. The first compilation of the research results inferring wide assessment and comparative study of various methods for the past temperature history reconstruction from underground temperatures has appeared in 1992 (Lewis, 1992). Generally, three basic groups of the inversion methods won widespread popularity: (1) ramp and step models, sometimes referred as the one or last event analysis, (2) inversion techniques employing singular value decomposition (SVD) algorithm, and (3) functional space inversions (FSI). All three algorithms are based on the theory of 1-D heat conduction. 2.3.2 Theory of 1-D heat conduction The problem of heat conduction is formulated for a source-free composite medium and is defined over the time interval [t0 ⫽ 0, tn] and depth interval [z0 ⫽ 0, zm]. We assume that within the medium heat is transferred exclusively by conduction; thus, basic heat equation takes the form of Eq. (4). The surface temperature and temperature at the depth zm (great enough not to be affected by the surface conditions) are, respectively T ( z ⫽ 0, t ) ⫽ T0 , T ( z ⫽ zm , t ) ⫽ Tm
(7)
Within the solid Earth the temperature field is governed by the heat flow from the depth and by the distribution of the thermophysical parameters. All responses to the changing surface conditions are superimposed over the steady-state (initial) internal temperature field U(z) as transient thermal perturbation V(z,t). Thus, the solution of Eq. (4) can be represented as a superposition of two functions (Carslaw and Jaeger, 1962) T ( z, t ) ⫽ U ( z ) ⫹ V ( z, t ), z 僆[ z0 , zm ], t 僆 [t0 , tn ]
(8)
The choice of the value for t0 depends on available T⫺z data. Anyhow, it should be moved sufficiently back into the past such that the thermal regime prior to t0 could be regarded as the steady state. Further, we assume that at the depth zm the climatic perturbation vanishes, i.e., it is not measurable. In this case, the bottom boundary condition will be Tm ⫽ U(zm). Strictly speaking, this assumption fulfills exactly only at zm ;-, but this will not make much difference if the depth zm is large. The equilibrium (initial) temperature U(z) is taken as steady-state temperature for boundary conditions U(z⫽0)⫽T0(t⫽0)⫽U0, K⭸U/⭸z ⫽ Qm (z ⫽ zm), where Qm represents the undisturbed steady-state heat flow at depth zm. In the case of the stratified medium with constant thermophysical properties in each layer U(z) takes the form of Eq. (5). Function V(z,t) represents the transient temperature field due to changing surface conditions; in other words, it is extracted climate signal. The surface temperature perturbation is propagated downward with amplitude attenuation and time delay that increases with depth. The heat equation for V(z,t) is identical to Eq. (4) for the modified surface boundary condition V0(z ⫽ z0,t) ⫽ T0(t)⫺U0, and for zero bottom and initial temperatures.
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The parameterization of the problem (model) is defined by the set of five parameters/functions: K(z), c(z), U0, Qm, and V0(t). Assumption of the source-free medium is sufficient in the most practical cases. If necessary, the rate of the heat production per unit volume can be added to the steady-state equation for the initial temperature U(z). After the choice of the model one can solve the equations for quantities U(z) and V(z,t). It is so-called forward problem. Its solution requires discretization procedure that transforms primary partial differential equations into a set of algebraic equations relating the discretized model m to the vector of the GST values G G ⫽ f (m)
(9)
Depending on the discretization, the forward problem can be solved as accurately as desired. Solution takes analytical form in the case of the layered medium with constant known thermophysical parameters of each layer (Bodri and Cermak, 1995). In this case, K(z) and c(z) can be excluded from m, and Eq. (9) can be written as G ⫽ Dm, where matrix D is generally referred to as the data kernel. The Laplace transformation can be used to integrate Eq. (4). Let T *j⫺1 and Q*j⫺1 be the transforms of the temperature and heat flow at the depth z ⫽ zj⫺1, corresponding to the base of the jth layer, and T j*, Q*j be the analogous values at the depth z ⫽ zj. In the case of perfect thermal contact between the layers we have Tmⴱ Qmⴱ
⫽
Am Cm
Bm A1 L Dm C1
B1 T0ⴱ D1 Q0ⴱ
(10)
where
kj ⫽
Kj c j
, q 2j ⫽
p , z j ⫽ z j ⫺ z j ⫺1 , kj
1 A j ⫽ cosh (z j q j ), B j ⫽⫺ sinh (z j q j ) K jqj C j ⫽⫺ K j q j sinh ( z j q j ), D j ⫽ cosh ( z j q j ) A j D j ⫺ B j C j ⫽1
(11)
and p is the Laplace transform variable. Eqs. (10) and (11) give the transforms of the temperature and heat flow at any point z1, z2, …, zm. Values for intermediate points can then be found from
T ⴱ( z, p) ⫽ T jⴱcosh[q j ( z ⫺ z j )] ⫺
Qj K jqj
sinh[q j ( z ⫺ z j )]
(12)
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Exact evaluation of T and Q leads to rather complicated series of expansions; for shortness, below we present the solution for a homogeneous slab only T ( z, t ) ⫽
2k zm2
⬁
⫺kn2 2 t nz x sin z 2 zm m
∑ n exp n⫽1
kn2 2 K exp x 关T0 ( ) ⫺ U 0 兴 d 2 0 zm
∫
t
(13)
2.3.3 Ramp/step method Solution of the inverse problem consists of three general steps: (1) choice of an appropriate physical model, (2) parametrization of the theoretical equations, and (3) estimation of the parameters. Naturally, this procedure cannot be started from zero and requires including as much a priori information as possible. Each underdetermined problem needs certain assumptions. More complex model implies the greater number of assumptions and/or amount of additional information for the successful past climate reconstruction. Because of the common insufficiency of the field information, simpler models in some cases can be more preferable. The ramp and/or step models that are sometimes referred to as the last event analysis (Lachenbruch and Marshall, 1986) represent the most simple, but robust manner of the parametrization. While other modern inversion techniques allow an arbitrary form of the GST history, the step method assumes the GST changes with time according to a threeparameter law
t V0 (t ) ⫽ T0 ⫹ T ⴱ t
nⲐ2
(14)
for 0 ⬍ t ⱕ t* and n ⫽ 0, 1, …. The value t* represents the duration of the GST change of the amplitude T, and the power n determines the shape of this change. At n ⫽ 0 we have a simple step increase/decrease in temperature, n ⫽ 2 represents a linear one, and so on. The solution of this equation for a homogeneous half-space at t ⫽ t* is (Carslaw and Jaeger, 1962) T ( z, t ⴱ ) ⫽ T0 ⫹
z Q0 n z ⫹ T 2 n ⫹ 1 xi n erfc 2 K 2 kt ⴱ
(15)
where (x) is the gamma function of argument x and inerfc is the nth time integral of the error function. Formula (15) thus enables us to calculate the subsurface temperature at the end of the GST change. Expression (15) corresponds to a simple four-parameter model m ⫽ [T, t*, T0, Q0]. In the pioneering work by Lachenbruch and Marshall (1986) quantities T0 and Q0 were defined independently of the parameters T and t* by the linear fitting to the measured temperature–depth profile immediately below the obviously disturbed nearsurface part of the temperature record. In the more recent works unknown parameters T0, T, and t* are estimated together with the background heat flow Q0. Using this form
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of parametrization, the inverse problem can be formulated as: given the data T(zk) measured at various depths zk, k ⫽ 0, 1, …, M, find the temperature history characterized by the vector m. To determine the optimum values of the unknown parameters most of the researchers (e.g. Cermak et al., 1992; Safanda and Kubik, 1992) applied the least squares inversion theory proposed by Tarantola and Valette (1982a, b). In this approach, an M-dimensional vector of temperature–depth measurements T is related to parameter vector m by the equation T ⫽ g(m), where g is an M-dimensional vector-function whose components are determined by Eq. (15). Inversion is performed by using the iterative procedure. The advantage of the method is the possibility of quantifying our confidence in the a priori estimates of T and m in a form of their a priori standard deviations as well as of obtaining estimates of the a posteriori standard deviations of m. The a posteriori to a priori standard deviations ratio (SDR) is generally used to characterize the reduction of the uncertainty of the estimated parameters. The ramp/step problem can be extended: (1) for the case of the stratified medium each with constant known thermophysical parameters in the individual layers, and (2) for the multi-step approach V0 (t ) ⫽ T0 ⫹
∑ i
t Ti ⴱ ti
nⲐ2
(16)
where t *i and Ti represent the epochs and magnitude of temperature change (e.g. Beltrami and Mareschal, 1991). For the series of steps of equal duration expressed as departures of the mean temperature value and starting at time tl in the past, present temperature at depth z is given as
T ( z ) ⫽ Tl erfc
z 2 kt
l⫺1
⫹
∑ T erfc 2 i
i⫽1
z k (l ⫺ i ⫹ 1)t
⫺ erfc
2 k (l ⫺ i )t z
(17)
The single-step approach may be more suitable in the case when for the area under investigation there is no information on the surface temperature history at all, since it relates the calculated surface change to the conditions averaged for a long prior period. The use of the multi-step model may give a better insight into what really happened. As shown by Putnam and Chapman (1996), a series of step changes can approximate any real surface temperature variation. 2.3.4 Singular value decomposition (SVD) algorithm Singular value decomposition method was first presented in the works by Beltrami and Mareschal (1991), Mareschal and Beltrami (1992), and Wang (1992). Later it was improved in the work by Bodri and Cermak (1995) by including into the analysis various kinds of additional information and the special technique of the GST discretization that ensures optimal choice of the estimated GST vector. As in the previous case, the problem is formulated as the pure conductive 1-D heat transfer of the surface temperature
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variations in a layered slab with the constant, known thermophysical parameters in each layer as described in Section 2.2.2. The model vector can be thus formulated as m ⫽ [U0,Qm,V0(t)]. The surface temperature history is approximated by a series of unequal intervals of constant temperature V0 (t ) ⫽ Vi , ti −1 ⱕ t ⱕ ti , i ⫽ 1, 2, K , N
(18)
The mean values of temperature for the individual time intervals Vi are the unknown parameters of the problem. At such assumption the integral in the forward problem like Eq. (13) can be easily transformed into the series 1 a
N
∑ i⫽1
(Vi ⫺ U 0 )(e ati ⫺ e
ati ⫺1
n k ), where a ⫽ zm
2
(19)
Borehole temperature data are generally given at discrete zk points (k ⫽ 1, 2, … M). Thus, the solution can be represented by a set of M linear equations in N unknowns Vi Tk ⫽ Aik Vi
(20)
where Tk is the temperature measured in borehole at depth zk and Aik a matrix formed by the values of series similar to Eq. (13) at depth zk for time interval (ti⫺1,ti). When parameters of initial (equilibrium) temperature field U0 and Qm are estimated simultaneously with the GST history V0(t), the vector Vi will consist of (N ⫹ 2) unknowns, and zthe matrix A will contain 1 in its (N ⫹ 1) first column and the thermal resistance R(z) ⫽ 冮0(dz⬘/k(z⬘)) to the depth zi in the (N ⫹ 2) column. At M ⬎ N this yields an underdetermined system of linear equations that can be solved for the unknown parameters Vi by the SVD (Jackson, 1972; Menke, 1989). This general least squares inversion method minimizes both the sum of the squares of deviations of the measured temperature profile from the theoretical model T and the sum of the squares of estimated parameters V 0T V0 ( ⫽ AV0 ⫺ T). Mathematically, the SVD procedure can be formulated as follows. Two sets of eigenvectors u and v can be found such that Avj ⫽ juj and ATui ⫽ ivi, where i are the eigenvalues of the matrix A. One shall again assume that there are P non-zero eigenvalues common to the sets of eigenvectors u and v. The set of eigenvectors u represent complete massif of the orthonormal vectors in the data space, while the eigenvectors v are similar set in the “model” space. The P-value (P is less than or equal to the minimum of M and N ) may be interpreted as the potential number of degrees of freedom in the data. The matrix A can be decomposed into the product A ⫽ UVT, where U is the M ⫻ P orthonormal matrix whose columns are the eigenvectors ui, V an N ⫻ P matrix with the columns of the eigenvectors vi, and the diagonal matrix of eigenvalues. The solution x can then be written as x ⫽ V⫺1UTT, where x is the estimate of V0 and ⫺1 a diagonal matrix whose elements are ⫺1 i . According to our previous assumption all P eigenvalues are not zero; thus, the inverse matrix ⫺1 never ceases. However, definite problems may arise also if values of i are non-zero but very small.
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The linear combination of model parameters that have weak impact on the data corresponds to the small singular values i. In the inversion, the data are divided by the smallest eigenvalues. Even for the noise- and error-free data numerical instabilities appear when the ratio of the largest to the smallest eigenvalue exceeds a critical limit (say, 10⫺6; see Section 2.4). The presence of noise in the data intensifies the problem. In this case the inverse matrix A⫺1 exists; however, the uncertainties in the estimated x-vector that for statistically independent data can be calculated as 2
N ⫺1 var xi ⫽ Vik k V jk var(T j ) k ⫽1 j ⫽1 N
∑∑
(21)
will be too large because of the reciprocal eigenvalue in the bracket. This variance can be interpreted as the amplification of the measurement errors in the solution. The order of magnitude of the variance is inversely proportional to the smallest eigenvalue. In practice, it is thus indispensable to eliminate the small eigenvalues from the solution. For the elimination of the parameters that have weak impact on the data the “sharp cutoff” approach is generally used (Wiggins, 1972). Under the sharp cutoff approach we select some dimensionless cutoff value and ignore all eigenvalues whose ratio to the largest eigenvalue is less than this limit. The cutoff value is thus the crucial parameter of the SVD method. It will be shown below that the large values of cutoff tend to smooth the reconstructed curve and move their extremes toward the present. At lower cutoff values, parameters that are weakly represented in solution are better resolved, but their errors will simultaneously grow. Too small cutoff values may lead to the unacceptable error level and to the instability of the solution. Some optimum value must be chosen. Wiggins (1972) suggested the procedure to establish the optimum cutoff. According to his approach one should set an upper limit on the standard deviation of the estimated parameters, and search for the largest number of eigenvalues associated with the solution for which each estimated variance is less than this limit. This then determines the number of degrees of freedom associated with the solution. In other words, the SVD naturally eliminates from the inverse all the oscillations of the surface temperature that the data cannot resolve and yields the smoothed course of the surface temperature. The stabilizing and smoothing of the solution can be achieved also by adding a small constant to each singular value
k
2k ⫹ 2 k
(22)
This procedure does not affect the inversion of the larger singular values, but it stabilizes the inversion of smallest singular values by damping them to zero. The value of damping parameter (and thus the GST resolution) is determined by the noise level in the data. This procedure generally gives smoother GST histories than the sharp cutoff technique. In principle, there are no exact arguments that could force the choice of either procedure.
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The discretization of time (values of t1, t2, …, tN, Eq. (18)) is an input of the problem. On contrary to the ramp/step method, no explicit constraint is imposed on the surface temperature history. However, excessive number of time intervals in the trial model can result in the instability of the inversion process. On the other hand, we must find the smallest time intervals that can be determined from the given temperature log. The resolution matrix plays an important role in the parametrization of time. In the case of sharp cutoff, the resolution matrix can be defined as R ⫽ VVT. The jth column of this N ⫻ N matrix is the least squares solution for maximizing the jth parameter. At the proper choice of the discretization of time the resolution matrix exhibits delta-like behavior (compact resolution); the column with the best resolving power is nearly always the column with the maximum diagonal element (Bodri and Cermak, 1995, 1997a). Thus, the diagonal elements of the resolution matrix can be used as the measures of the resolving power. When choosing the preliminary discretization scheme, one has to take into account the “thermal” memory of the ground for the events on its surface (see Section 2.2 and Figure 23). One can choose a preliminary timescale with relatively long time intervals gradually increasing toward the past. Subsequently this scale should be refined with the help of the resolution matrix. For such operation a semi-empirical rule that proved to be very effective in the designing of structural models of the Earth from surface-wave and free oscillation data (Wiggins, 1972) can be applied. If, after computing the resolution matrix, we find that a single time interval is nearly perfectly resolved, this means that we have not selected the time interval short enough in the vicinity of the given instant of time to determine the exact shape of the resolution. In such a case the problem should be recomputed for a shorter time interval. In practice the GST reconstruction problem cannot be solved uniquely unless a priori information is incorporated into the analysis from the very beginning (Jackson, 1979). As a priori information the covariance matrices for both measured data and unknown GST are generally used in the SVD approach. For example, one can assume that the measured data are not statistically independent, but are characterized by a positive definite covariance matrix S. The covariance matrix for the data is symmetric (M ⫻ M) matrix, the elements of which are Sij ⫽ 2 r (z )
(23)
where 2 is the standard deviation of the data, r(z) the autocorrelation function, and z the depth lag. The autocorrelation function characterizes the range (intensity) of the interdependence of the measured signal. Dependence can be either short-range or longrange. The short-range dependence is characterized by correlations that decrease exponentially fast, while long-range dependence occurs when the correlations decrease like a power function. Our calculations have shown that measured borehole temperatures are characterized by a short-range dependence, thus, by the correlation that decreases exponentially fast r(z) ⬃ exp(⫺z /D) (Bodri and Cermak, 1995; Bodri et al., 2001). The decorrelation parameter, D, corresponds to the depth lag at which the autocorrelation falls to (1/e), i.e. defines the distance at which the individual temperature values can be considered statistically independent. This quantity represents an individual characteristic of the given hole. According to the field experience, for the majority of the boreholes the D-value ranges from 50 to 300 m. For boreholes with the fast decorrelation and
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the high number of measured points an advantageous technique of the data thinning (“scarcing”) can be used for inversion. In this case, the original data set of measured temperatures can be divided into subsets, and different parameters of the time discretization of the GST history can be obtained from different sections of the T–z profile. This procedure significantly enhances the reliability of estimated parameters, but requires that the data sets used be statistically independent (Twomey, 1977). Details of application of the data thinning technique are presented in Section 3.1 (Chapter 3) for Finnish boreholes. Another kind of additional information is connected to the interdependence between climatic signals. Highly fluctuating climatic time series exhibit scale invariance or scaling behavior over the wide range of timescales; that is, climatic variations at small scales are related to longer ones by the same scaling law without showing any preferred mode. The investigations of the scaling properties of climatologic data received considerable impetus from the paper by Lovejoy (1982) on the fractal dimension of clouds and rain. By the analysis of meteorological and climatic data using further refined methods, it was concluded that climatic processes exhibit a much more complex structure than previously assumed, where statistical properties at various scales are related through different intensity-dependent dimensions, rather than through a single fractal exponent (Tessier et al., 1993; Lovejoy et al., 2001). The introduction of the multiscaling behavior that may be interpreted as the outcome of a so-called multiplicative cascade process is common to all recent analyses. Generally, such models can be characterized by the range (intensity) of their interdependence, the heaviness of the probability tails, and the degree of nonlinearity. As about the interdependence of the meteorological/climatic signals, the so-called persistence of weather is a well-known phenomenon. If, e.g. given day is sunny and warm, there is high probability that the next day will be similar. Such tendency appears also on the longer scales. Early attempts to quantify this behavior were made in the works by Kutzbach and Bryson (1974) and Hasselmann (1976). Further these investigations were continued in the works by Lovejoy and Schertzer (1986), Ladoy et al. (1991), Bodri (1993), Beran (1994), and Rangarajan and Sant (2004). The common consequence of all research works was the quantitative establishment of the long-range dependence of correlations within different meteorological/climatologic time series that occurs when the correlation decreases like a power function in such a way that the spectrum diverges at low frequencies. Thus, the climate persistence, characterized by the correlation C(t) of temperature variations separated by the interval t, follows a power law, C(t) ⬃ t⫺ . Long-term persistence appears to characterize most climatic phenomena and exists over the spectral range of 1–106 year. Most recent investigations of the weather persistence were performed in the works by Koscielny-Bunde et al. (1998) and Talkner and Weber (2000) using long meteorological temperature records from various climatologic zones in Europe, North America, and Australia. The daily and annual cycles were removed from the data. Investigations with modern detrended fluctuation analysis (DFA) and wavelet techniques that can systematically overcome possible non-stationarities in the data revealed power law correlation decay with roughly the same exponent ⬵ 0.7 (⬇2/3) in the range of time lags between 10 days to at least 25 years. The range of persistence law is limited by the total length of the time series considered. The authors cannot exclude the possibility that it may exceed detected limit. The persistence of the climatic variations can be taken into account by means of the covariance matrix for the
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unknown parameters. The covariance matrix is a symmetric (N ⫻ N ) matrix, the elements of which are
t Wij ⫽ s2
⫺
,
(24)
where s is the a priori standard deviation, t the shift in time, and the characteristic correlation time. Similarly to the introduced above characteristic distance D, the characteristic correlation time corresponds to the practical vanishing of the correlation between climatic events. The values of s and are the input parameters of the problem. As will be shown below, generally, smaller s results in the correspondingly smaller disturbances of the GST, and the longer the time the smoother the obtained solution is. Including an additional information modifies the SVD procedure in such a way that it minimizes both TS⫺1 and V0T W⫺1V0. Further limits may be imposed on the unknown parameters. In most of the inversion problems it is customary to pose some bounds (so-called hard limits) on the values of parameters imposed by the physics of the problem. For example, when determining the Earth’s structure, the densities of the lithospheric rocks may be assumed to vary between 3000 and 4000 kg/m3, and their shear velocities between 4 and 6 km/s. One could treat these statements as pairs of inequality constraints c1 ⱕ bT V0 (t ) ⱕ c2 ,
(25)
where vector b is the moment of solution V0(t) and explores the limits of the solution space. In the case of climatic changes, however, these hard limits tend to be so large that they become irrelevant for practical purposes. The probability distribution of climatic changes may be used to put so-called “soft limits” on the solution. As in the above example with the lithospheric structure, two constants c1 and c2 may be chosen to represent limits on V0(t), but there will be some non-zero probability that V0(t) will violate these bounds. As shown by numerous investigators (e.g. Ladoy et al., 1991; Fraedrich and Lardner, 1993; Olsson, 1995) the cumulative probability distribution (probability that random fluctuation dT exceeds a fixed value T ) of climatic time series generally has a nearly Gaussian shape in the center and a tail (probability of the extreme events) that is “heavier” than would be expected for a normal distribution. The “fat-tailed” probability distributions are general characteristics of climatic time series. When the fluctuations are of this type, the phenomenon is so intermittent that the return times of extreme events are much shorter than those for Gaussian process. We illustrated the difference between Gaussian and the real probability distribution with the use of the two-millennia long homogeneous temperature anomaly time series for Northern Hemisphere developed by Mann and Jones (2003) by using different proxy indicators of climate (Figure 3). The cumulative probability of this data is presented in Figure 24. The difference of the probability tails is clearly visible. For example, the temperature fluctuations corresponding to more than three standard deviations (anomalies of more than ⫺0.016 K or less than ⫺0.504 K) for Gaussian process would have a probability level of 0.0013 that gives the return period for such anomalies of near 770 years.
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Fig. 24. Cumulative probability distributions for annual mean temperature record for Northern Hemisphere presented in Figure 3 (solid line) and for Gaussian process (dashed line). T is expressed in terms of standard units: (T-mean)/s.d. (mean ⫽⫺0.260 K, s.d. ⫽ 0.081 K).
Actually such extreme events occurred eight times in the near 1800-year long Mann and Jones (2003) temperature time series, thus, with much shorter average return period of near 220 years. It should be mentioned that the soft limits result from exact calculations, and not simply from physical plausibility arguments; thus, they seem to be more appropriate than the hard limits. The simplest way to incorporate soft limits in the solution is the examination of the extreme solutions (Jackson, 1979). The maximum (or minimum) value of bTV0(t) is given by Tmax,min ⫽ V0 ⫾ Cb,
(26)
where C ⫽ ATS⫺1A, V0 ⫽ CATS⫺1T, and ⫽ [Qmax ⫺ Q0)/(bTCb)1/2. In the last expression Q0 ⫽ TS⫺1, where ⫽ AV0 ⫺ T, and Qmax is the maximum allowable residual criterion for a model that fits the data in a satisfactory way. The value of Qmax should be chosen so that Tmax,min make values of bTV0 to fall as close as possible into the given soft limits.
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Moment vector of the solution b is usually used with the unit coefficients. Some kind of weighting that is reasoned by the well-known progressive smoothing down into the past of the reconstructed climatic fluctuations (see examples presented in the next section) is also possible. Different kinds of additional information are not equally important in all cases. Thus, they may also be weighted for specific problems. 2.3.5 Least squares inversion in functional space (FSI) This algorithm is based on the theory by Shen and Beck (1983, 1991) and modified by Shen et al. (1995). The problem is conventionally formulated as the 1-D pure heat conduction in a laterally homogeneous subsurface with depth-dependent thermal properties (Eq. (4)), where transient component arises from the surface temperature variations. Initial and boundary conditions are the same as described above for SVD and ramp/step methods. It should be mentioned that the use of the 1-D approach is not inspired by the wish to simplify the inversion problem only. An essence of the fact that all inversion techniques are based on the 1-D equation, which obviously neglects the influences of numerous terrain effects such as medium heterogeneity, topography, and groundwater circulation, is that the 2-D inversions will not necessarily improve the GST histories. The 2-D approach will significantly raise the number of degrees of freedom of the inverse problem (underground structure, thermophysical parameters, and pattern of the steady-state temperature field), which implies the corresponding limitation of a priori parameter range treated. As previously, the subsurface temperatures are divided into steady-state and transient components according to Eq. (8). The model is denoted as a set of parameters m ⫽ [K(z), c(z), U0, Qm, V0(t)]. If necessary, the radioactive heat generation can be also included as the parameter into the model m. However, it is justified only for deep holes in the case of the reconstruction of remote GST changes (see Section 2.2 of this chapter). As can be seen, the thermal properties of the medium are formulated as unknown parameters and, in contrast with two previous methods, should be estimated together with the quantities describing the initial thermal state of the medium and the past climate history. In this way the uncertainties of the knowledge of the physical properties of the medium can be also taken into account. It is assumed that the deviation of the true GST history V0(t) from the a priori version V 苶(t) is a stationary Gaussian process with an assumed exponential autocovariogram ⫺ 具[V0 (t ⫹ ) ⫺ V (t ⫹ )],[V0 (t ⫹ ) ⫺ V (t ⫹ )]典 ⫽ 2 exp , c
(27)
where the standard deviation and the correlation time c characterize a priori constraint imposed on the GST history. An exact shape of the autocovariance function is not a crucial factor of inversion. Thus, in the study by Shen and Beck (1991) the authors used the Hanning window. Wang (1992) applied function 2exp(⫺ 2/ 2c ) at the right side of Eq. (27). The only requirement is that this function should be sufficiently tapered at large . The really important parameters of the autocovariogram are and c. The former
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is responsible for the amplitude of the GST changes, and the latter controls the smoothness of the quantity [V0(t)⫺V 苶 (t)]. As in the case of SVD method, the correct choice of values for and c should be based on the use of the existing climatologic records. In its most recent version the FSI can be accomplished in six general steps: (1) Set the model m and define a priori model m0. The values and variances for K(z) and c(z) have been given. It is assumed that they are uncorrelated. To complete m0 one needs the values for remaining parameters U0, Qm, and V0(t). Generally, these quantities are not well known. It is accepted that V0(t) takes small values close to zero, is bounded, and is rather smooth function of time t. Very large a priori standard deviations are assigned to U0 and Qm values to avoid undue bias. (2) Solve the problems posed by the heat conduction Eq. (4) and by its steady-state analog for the steady-state U(z) and the transient components V(z,t) (Eq. (8)) of the temperature field, respectively. Calculated data can be represented as T(z,t) ⫽ Pu[U(z)] ⫹ P[V(z,t)]. This equation describes the “theory” that projects the data on the model, where P and Pu are corresponding projectors. For the discrete data this equation, similar to the SVD, can be written in the algebraic form. However, the fundamental difference between the FSI formulation and the SVD concept is that the former works with operators, while the latter deals with matrices. (3) Calculate the data residual m ⫽ 1/2[T(z,t)⫺T(zk)]T[T(z,t)⫺T(zk)]. The problem of parameter estimation then becomes one of minimizing the weighted least squares misfit function (Tarantola and Valette, 1982a, b; Menke, 1989) 1 1 (m) ⫽ (T ⫺ T0 )T C⫺d1 (T ⫺ T0 ) ⫹ (m ⫺ m 0 )T C⫺m1 (m ⫺ m 0 ) 2 2
(28)
Cd and Cm are a priori covariances describing uncertainties in T(zk) and m0, respectively. The latter equation highlights the fact that for given T0 and Cd, the deviation of the output model from the a priori model depends critically on Cm. It can be illustrated with the simple example. At large Cm (no confidence in the validity of a priori model m0) the second term in the right hand of Eq. (28) will participate only insignificantly in the minimization of (m), so that the initial model become irrelevant. In other words, the model is well resolved by the data. For a small Cm (strong validity of m0), the data will become irrelevant, so the model appears to be poorly resolved by the data. Thus, the application of the FSI strongly depends on the proper assessment of Cm. (4) The quasi-Newton method is applied for minimizing (m) (Shen and Beck, 1991; Wang, 1992). This method can directly compute (approximate) a posteriori model covariance. Its computationally convenient form for jth iteration is m j⫹1 ⫽ m 0 ⫺ C m MTj [ M j C m MTj ]⫺1 ⫻ [T ⫺ T0 ⫺ M j (m j ⫺ m 0 )]
(29)
where M is the derivative operator that maps the model space into the data space, defined by T ⫽ M m. In a functional space formulation the operators M and its
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Borehole Climatology: A New Method on How to Reconstruct Climate transpose MT are not explicitly computed and stored. Only the results of their mapping are calculated. The process of M mapping is presented in detail in the Sections 6 and 8.2 by Shen and Beck (1991) and the mapping of MT in Sections 8.4–8.6 of that work. During the step (4) one should compute the symmetric, positive definite matrix Ej ⫽ Mj CmM Tj ⫹ Cd and solve the vector algebraic equation Ej (dj) ⫽ (mj) for the weighted data residual (dj). (5) Compute the gradient (gj) ⫽ MjT (dj) and model correction (mcorr) ⫽ Cm (gj).
(6) Update the model mj+1 ⫽ m0– (mcorr). The quantification of the uncertainties in the estimated model parameters can be done with the a posteriori covariance operator Cˆm that is given by (Tarantola and Valette, 1982a; Shen and Beck, 1991) C$ m ⫽ Cm ⫺ Cm MT⬁ [ M ⬁ Cm MT⬁ ⫹ Cd ]⫺1 M ⬁ Cm ,
(30)
where M- denotes the derivative operator M evaluated at m ⫽ m-. Eq. (29) corresponds to one iteration of the quasi-Newton expression (28). Generally, the diagonal of Cˆm is interpreted as the variance of m-, and off-diagonal as its covariance. Because of significant computation time needed to examine the whole a posteriori covariance operator, it is common to compute only diagonal entries (the a posteriori variance of m-). They are usually called the SD ratios. The smaller the SD ratio is, the better the estimated parameter is resolved by the measured data. Physically, it means that the data contain sufficient information about this parameter. On the contrary, close to unity SD ratio hints that the data cannot resolve this parameter. 2.3.6 General comparison of the methods Table 3 summarizes the main characteristics of the parametrization schemes and the data inversion for main three methods of the GST reconstruction described above. All methods are based on the 1-D theory of heat conduction and employ the least squares inversion theory. As mentioned above, the use of the 1-D approach is not certainly shortcoming of the inversion problem. The 1-D inversion techniques obviously neglect the influences of numerous 2- and/or 3-D terrain effects such as lateral medium heterogeneity, topography, and groundwater circulation. On the other hand, the development of the 2-D techniques will not necessarily improve the GST histories. The 2-D approach will significantly raise the number of degrees of freedom of the inverse problem (underground structure, thermophysical parameters, and pattern of the steady-state temperature field), while we may only handle finite amount of the measured data. The application of a 2-D approach means that we use more parameters to describe the unknowns than could be uniquely determined by the data. In practice the use of a 2-D approach implies severe limitation of a priori parameter range treated. In all inversion problems some optimal relation between resolution and variance should be established. In other words, one should
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Table 3. Models/parameterization schemes used in the three main inverse methods Property Temporal discretization Spatial discretization
Ramp/step method
Specific heat capacity, c(z)
Step model Homogeneous medium Constant in the medium Known Constant
Heat production rate, A(z)a
Known Constant
Thermal conductivity, K(z)
Bottom heat flow, Qm Steady-state GST U0 GST history V0(t) Additional information
Constant To be estimated Constant To be estimated Polynomial function To be estimated No
FSI
SVD
Finite-difference Finite-element
Steps model Layered medium
Constant in each element To be estimated Constant in each element To be estimated Constant in each element Constant To be estimated Constant To be estimated Piecewise linear To be estimated Yes
Constant in each layer Known Constant Known Constant in each layer Constant To be estimated Constant To be estimated Piecewise constant To be estimated Yes
a
Relevant only for deep boreholes.
answer the question, what is the effective number of degrees of freedom in the data and what parameters can be independently estimated with an acceptable variance. Every method takes the steady-state GST, the equilibrium surface temperature U0, and the basal heat flow Qm as unknown parameters. Together with the thermal conductivity of the medium these quantities control the steady-state temperature profile, and such formulation permits to estimate the parameters characterizing the steady state even for relatively shallow boreholes where estimation of these quantities from the lowermost undisturbed parts of the measured temperature–depth profiles is problematic. From the point of view of the accuracy of the GST reconstruction the SVD and FSI are more effective since they use more complex temporal discretization and incorporate additional information in the analysis, and thus allow the reconstruction of far more detailed GST histories than the ramp/step method. The parametrization scheme applied in the ramp/step method and in SVD uses analytical expressions for the temperature field T(z,t), while in the FSI it can be expressed only numerically. It should be mentioned, however, that the computational efficiency of the methods does not strongly depend on whether the analytical or numerical approximations are used and represent the complex output of the whole parametrization scheme. The ramp/step method and SVD are limited to the problems when the thermal properties of the medium are known. At a first glance it seems to be serious restriction. General insufficient thermal conductivity data in boreholes is a well-known fact. However, in the most field examples errors in K(z) and c(z) are not systematic. In the SVD approach, their effect can be extenuated by imposing appropriate smoothing constraints on the GST history. Thus, notwithstanding the known thermal properties assumption, SVD technique is applicable to a large number of practical cases. The principal distinction from the ramp method and SVD and/or merit of FSI is that the thermal
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properties of the medium are all formulated as unknown parameters and estimated simultaneously with the quantities describing the initial thermal state of the medium and the past climate history. Thus, this method is preferable when the errors in K(z) and c(z) are significant and expected to be systematic. When the thermophysical properties are included in the model as parameters, the problem becomes nonlinear. However, as shown by Shen and Beck (1991) and Wang (1992), for the cases when these quantities are reasonably well known with small uncertainties, the problem is only mildly nonlinear and permits the application of iterative gradient methods to solve the optimization problem described above. It should be also mentioned that for the field examples with exactly known thermal properties the theory becomes strictly linear. Methods of the inversion of the borehole temperature data are all based on the least squares inverse approach. The problem is ill posed; thus, in the real cases the misfit function itself is insufficient to determine the unique and stable solution. The SVD and FSI put definite constraints on the model and employ the concept of incorporating a priori (additional) information to avoid this problem. As will be shown in the next section, a large part of discrepancies in the inverse results obtained by both methods can be attributed to the kinds of constraints and/or the nature of additional information used in the analyses. Unfortunately, the optimal values for the applied constraints depend on the real GST history. Thus, at least some knowledge of the amplitude and timing of the climatic variations that should be reconstructed is indispensable to obtain consistent inversion results. All described methods are based on the least squares technique. Cooper and Jones (1998) have performed a comparison between the effectiveness of the least squares approach and other popular techniques, namely the minimization of the absolute difference between measured data and estimated parameters for inversion of borehole temperature logs that is performed for the purposes of the GST reconstruction. The authors have found that the latter technique requires approximately half the number of iterations to reach the possible minimum error compared to the least squares procedure. According to the above-cited work, the inversion of borehole temperature data in some cases can be significantly improved by the use of techniques other than the standard least squares approach. According to their calculations, exact choice of the inversion technique depends on the statistics of the data. Anyhow, it was used by Cooper and Jones (1998) during all trial runs the best results were obtained by the latter approach combined with some additions that accelerate the procedure in the damped intervals where the model improves only slowly by subsequent iterations. 2.4 Comparison of Ground Surface Temperature (GST) Reconstruction Methods As many geophysical problems, the GST reconstruction involves the estimation of a number of unknown parameters that bear definite relationship to experimental data. These data are generally contaminated by various kinds of random and/or systematic noise as well as may be inconsistent and insufficient for estimation of the unknown parameters. Thus, generally we have strongly underdetermined system; in other words, we would like to draw out the infinity of the details about unknown function from very limited amounts of data. One of the usual ways to overcome this problem is to calculate a family of the trial inversions, compare the interdependence between resolution and
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variance for each case of inversion, and select the run that appears to be most appropriate for the interpretation of the solution. All three above-described methods of the GST reconstruction have treated this problem in their own manner. Existing methods for the GST reconstruction from subsurface temperature–depth profiles are based on the same theory of 1-D heat conduction in a layered medium; thus, we can expect similarity of obtained results in terms of their general features. On the other hand, the GST reconstruction is an ill-posed inverse problem. Its finer output may be method dependent. The inconsistency between GST histories reconstructed by different inverse methods may arise both from the differences in the mathematical/physical approaches used and from the manner in which different kinds of noise (uncertainties) are treated. For comparison and/or joint use of the GST histories inferred by different methods at first the methods themselves should be compared and evaluated. Such comparison including both synthetic and field results has been widely performed at an early stage of the development of “geothermal” method (Beck et al., 1992; Shen et al., 1992). Below we present some examples to illustrate conclusions obtained in above and similar works. We applied two most powerful methods of the GST reconstruction, namely SVD and FSI, to some standard data sets and field data, to illustrate the effects of various constraints on the inferred GST histories. 2.4.1 Effects of smoothing constraints in different methods and the noise in the data: Synthetic examples The most effective way to compare different inversion techniques is to simulate a series of perturbed subsurface thermal regimes using synthetic GST histories, i.e., the true result is known, and to apply the available techniques on those data. Such attempts have been undertaken in numerous works for the simple case of 1-D forward pure conductive model driven by different variants of GST forcing. An inversion approach has been applied to infer GST histories from the simulated profiles and to compare them with the true surface forcing used. The results of such trial numerical experiments have been widely discussed (Beck et al., 1992; Shen and Beck, 1992; Shen et al., 1992). Below we present some illustrations of this approach. The basic synthetic T⫺z data, with which we would like to assess the most effective methods of the GST reconstruction, SVD and FSI, are calculated with the following parameters: K(z) ⫽ 2.5 W/(m K), c(z) ⫽ 2.5 MJ/(m3 K), Qm ⫽ 0, U0(z) ⫽ 4°C. Constant and known thermophysical parameters are chosen to illustrate the effect of the smoothing constraints and not to digress on other influences. The “gate” model of the GST temperature is used to demonstrate the effect of the smoothing constraints in the case of a sudden temperature change. This model has a shape V0(t) ⫽ {4°C at t ⬎ 1600 A.D.; 3°C at 1600 ⱕ t ⱖ1900 A.D., 4°C at t > 1900 A.D.} and roughly corresponds to the Little Ice Age conditions, followed by subsequent warming. Temperature logs were calculated at 5 m interval to a depth of 500 m. The first generated data set G1 is completely noise free, while other profiles were randomly perturbed by a noise with Gaussian distribution with zero mean and standard deviations of 0.01, 0.03, 0.05, and 0.1 K, respectively. Typical measurement error is 0.03 K. The standard deviations were assumed to be independent of the depth. Simulated in this manner T–z profiles are shown in Figure 25.
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Fig. 25. Temperature–depth profile for the “gate” model free of noise (G1) and two synthetic profiles perturbed with Gaussian noise of zero mean and different s.d. of ⫾0.3 K and/or ⫾1.0 K, respectively added to G1. Typical measurement error is usually about 0.03 K.
The GST histories were approximated by a series of individual intervals of constant temperature, when the mean value of temperature in each time interval is an unknown parameter. It is these temperature values that represent the direct result of the inversion procedure. When demonstrating the results graphically, these values were ascribed to the midpoints of the corresponding time intervals and were found as approximated by cubic spline technique (Bodri and Cermak, 1997a). Figure 26 shows the results of GST reconstruction by SVD and FSI for the noise-free G1 data using different smoothing constraints. A priori null GST hypothesis was assumed in the GST reconstructions by FSI technique (no a priori knowledge of the GST history to be estimated). As seen, the true GST history is reasonably well recovered by both inversion techniques. Clearly, the solution depends critically on the cutoff value for SVD and on the values of and c for FSI. The large values of cutoff tend to smooth the reconstructed curve and move its extremes slightly toward the present (Figure 26a). Too small values may lead to instability of the solution (Figure 26b) with frequent small false extremes. It should be mentioned, however, that these false oscillations do not fog significantly general GST pattern; the long scale course of the GST history is preserved even in the reconstructions calculated with the smallest possible cutoff value. Obviously, some optimum cutoff value
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Fig. 26. The effect of smoothing constraints on the GST histories inferred from G1 temperature–depth profile: (a), (b) SVD, and (c) FSI, respectively. The real GST history is the “gate” model (dashed line). Smoothing constraints are imposed in the form of the cutoff value in SVD and the correlation time c in FSI ( ⫽ 0.5 K). Too small cutoff value may cause the instability of the solution (Panel b).
must be chosen. Wiggins (1972) suggested powerful procedure for its establishment. According to a suggestion of this author that is based on the results of numerous experimental runs, one should set upper limit on the standard deviation of the estimated parameters and search for the largest number of the eigenvalues associated with the solution for which each estimated variance (Eq. (21)) is less than this limit. This then determines the number of degrees of freedom associated with the solution. In FSI method, the constraint imposed on the GST history depends on a priori standard deviation and correlation time c (Eq. (27)). The former is responsible for the amplitude of the detected GST changes. and the latter controls the smoothness of the quantity [V0(t)⫺V 苶(t)] (Eq. (27)). Both constraints operate together. Too large values assigned to may turn the autocovariance function into inoperative regime. As will be
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Fig. 27. Method FSI: Effect of varying parameter (standard deviation characterizing the a priori constraint imposed on the GST history; Eq. (27)) on the noise-free “gate” model (G1) (bottom) and on a sinusoidal model (top). The correlation time c in both cases is 100 years.
shown below, the effect of both parameters on the reconstructed GST history depends on the level of noise in the data. As seen in Figure 26c, the influence of the correlation time c is not so strong when the noise level in the data is low. The influence of the standard deviation is illustrated in Figure 27 (bottom). In the ideal case, when the T–z profile and the values of thermophysical parameters are noise free and inversion procedure does not introduce discretization/roundoff errors, one may set relatively large value for standard deviation without the risk that the instability of the solution will occur. For the G1 temperature profile (Figure 27, bottom) the instability threshold is as high as 500 K. In the real cases the optimal values for should be much lower and can be established experimentally. Numerical trial runs have shown that for usual field temperature logs the optimal value is close to 100 K (see also Shen and Beck, 1991, 1992). However, the solution can be regarded as reliable and/or reasonable over a wide range of values for within this interval. Results of similar calculations for the noise-free “sinusoidal” model are shown in Figures 27 (top) and 28. This model was calculated by the expression V0(t) ⫽ 4°C ⫹ sin(t/400⫺5/2) with period of 800 years; t is the time in the years B.P. The oscillations of the surface temperature roughly correspond to the Medieval Warm Period, the Little Ice Age, and the warming since then. Corresponding temperature–depth profile is shown as the inset to Figure 28. Synthetic T⫺z profile used for the GST inversion is completely noise free. This example illustrates the possibility to reconstruct past harmonic oscillations and demonstrates how the damping of high-frequency climatic signal with depth manifests
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Fig. 28. The effects of smoothing constraints in the case of a surrogate climate expressed by a sinusoidal model of the GST with period of 800 years in SVD (bottom), and FSI methods (top), respectively. The calculation was performed with a standard deviation ⫽ 0.5 K. Estimated GST histories are marked by the applied values of cutoff and correlation time c for SVD and FSI techniques, respectively. The inset shows corresponding noise-free temperature–depth profile.
itself in the reconstructed GST history. Estimations of this more complex GST history show that the T–z profile preserves significant information only about less remote course of the GST. As can be seen, the recent 400–500-year warming trend and the long-term mean temperature (zero-frequency component) can be reliably resolved by both techniques. Calculations show that the acceptable range for the smoothing constraint quantities in both methods depends on the actual GST variations. For the latter more complex GST history the instability of the solution occurs at higher cutoff values for SVD method and correspondingly for lower values of the standard deviation for FSI technique. The interval of acceptable values for both parameters is smaller than in the previous case, e.g. optimal cutoff values lie in the range 10⫺2–10⫺4. The influence of the correlation time c in FSI method is not so significant in this case. It may change within the same range as in the previous example without risk that the instability in the solution will arise. The influence of the noise in the T–z profiles on the GST reconstructions is illustrated by the next set of reconstructed GST histories. Figure 29 shows GST reconstructions inferred from the temperature logs viewed through a noisy filter. Synthetic
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Fig. 29. The effect of Gaussian noise on the inferred GST histories in SVD (bottom), and FSI (top) methods, respectively. The cutoff value for SVD is 10⫺4, and ⫽ 0.5 K, c ⫽ 100 years for FSI. The stationary Gaussian noise with standard deviations varying from 0.01 to 0.1 K and zero mean has been superimposed on the “gate” G1 model (Figure 22). For both methods, the results of inversion are practically independent on the noise level, up to standard deviation of 0.04–0.05 K.
temperature–depth profiles simulated for the “gate” model and included different levels of the Gaussian noise (Figure 25) were used as input data. As seen in Figure 29, both methods recovered the “true” gate model by the inversion reasonably well. The interval of the GST history most affected by the noise in the data appears to be the recent past, some 100–200 years. The noise-induced false temperature oscillations are clearly visible in this section of the GST histories reconstructed by both methods. This fact is an obvious consequence of the above-described physical nature of the heat conduction process, when GST variations are attenuated exponentially and smoothed with both depth and time. At the same time the best resolved recent parts of the reconstructed GST curves contain more noticeable fingerprints of noise. The SVD method appears to be more stable to the noise in the temperature logs and is able to tolerate relatively strong noise contamination. As shown, the inversion results are practically independent of the noise level, up to standard deviations close to 0.1 K. The FSI technique appears to be more sensitive to the presence of noise. The amplitude of the GST change is overestimated by 0.5–0.8 K already for the noise s.d. of 0.05 K. The noise-induced instability of the solution occurs for the noise with s.d. values that are slightly above 0.05 K. In principle, the FSI technique sensitivity to the strong noise contamination could be partly suppressed by an accounting of small value to . However, in this case the amplitudes of the GST variations may be underestimated.
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The role of the correlation time c (one of the constraints of FSI) increases in the case of the presence of noise in the data. Figure 30 shows a set of GST histories reconstructed for different values of and c. The input temperature log was the “gate” model disturbed by the Gaussian noise of zero mean and 0.05 K standard deviation. Small value of effectively suppresses the amplitude of detected GST changes. The longer correlation time c smoothes calculated climatic history and moves extremes of the GST variations to the past, while shorter correlation time enhances the effects of noise up to the instability of the solution and tends to move reconstructed extremes to the present. To reduce the effect of noise that is generally more prominent at short periods, large c value should be chosen. On the other hand, value of the correlation time cannot be too large, because in this case some important shorter period variations in the estimated GST history can vanish. In SVD, the data are assumed to have equal uncertainties. On the contrary, in FSI data are weighted in accordance with their uncertainties. This allows additional effective constraint on the noise-induced instability by employing greater uncertainties to the nearsurface temperature data. Summarizing above conclusions we can affirm that, notwithstanding that both methods vary significantly in their mathematical calculus, they gave generally similar results in a sense of the broad features of the reconstructed GST histories. The discrepancies in
Fig. 30. The effect of bounding constraints governed by a priori standard deviation on the inferred GST history (FSI method). Used T–z data are synthetically generated; “gate” model contains Gaussian noise with zero mean and standard deviation of 0.05 K. Small values of tend to over-smooth GST history, while large values could drive to instability of the solution. The individual curves are marked by the value of the correlation time c.
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the inverse results obtained by both methods are not essential and a large part of them can be attributed to the kinds of constraints and/or the nature of additional information used in the analyses. When the optimal values for constraints are applied, the incoherence between solutions obtained by different methods is minimal. On the other hand, unproved choice of parametrization schemes and a priori constraints can significantly affect both the timing of estimated climatic changes and their amplitude. Unfortunately, the optimal values for essential constraints depend on the real GST history. A priori null GST hypothesis (no a priori knowledge of the GST history to be estimated) was used for the above GST reconstructions. Since the estimated GST models were relatively simple, obtained results reproduced the true climate change sufficiently well. For the real field examples at least some knowledge of the amplitude and timing of the climatic variations that should be reconstructed is indispensable to obtain consistent inversion results. Thus, to achieve optimal results information from other available climatic reconstructions should be incorporated into inversion procedure. More cunning testing of the effectiveness of any technique for the GST reconstruction should include the simulation of the subsurface thermal regimes driven by the state-ofart General Circulation Models (GCM) of surface temperature (Section 2.4.4) and/or perturbed by influences additional to the GST changes and the use of simulated T⫺z profiles to retrieve the real surface forcing. The sensitivity of the inversion techniques to various non-climatic uncertainties is illustrated in the next section.
2.4.2 Effect of systematic errors in thermal conductivity There may be different kinds of the systematic noise in borehole temperature logs; however, one of them is almost common in the geothermal data, namely more or less poor knowledge of the thermal conductivity. Above synthetic examples dealt with the homogeneous strata. As shown in Section 2.2 under pure conductive heat transfer conditions the geothermal gradient is inversely proportional to thermal conductivity; thus, its variations with depth produce corresponding variations from the otherwise linear T⫺z profile (Eq. (4)) that can be misinterpreted in terms of a transient surface temperature. In principle, the GST reconstruction methodology can be readily extended to include thermal conductivity variations. However, most of the temperature logs are accompanied by a few measurements of thermal conductivity and/or the conductivity measurements can be available for some sections of the borehole. Thus, the geophysicists are compelled to treat the subsurface as a homogeneous medium and/or assume its significantly simplified model. For example, erroneous values can be accepted when extrapolating these data on “empty” intervals. The real Earth’s subsurface generally contain significant conductivity variations that can be caused by mineralogy changes and stratigraphic heterogeneity at different crustal levels. Compaction of sedimentary rocks with depth leads to an increase in thermal conductivity through reduction of porosity. Similar changes can be caused by the changes of the fluid saturation of subsurface rocks with depth (low conductivity in unsaturated rock near the surface and higher conductivity in the water-saturated rock below the water table), etc. Poor knowledge of the thermal conductivity of the medium manifests itself as a noise in the interpretation biasing the reconstructed GST history. As shown in the
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previous section random noise does not affect seriously the results of inversion. However, what is about systematic noise? It is clear that the perturbation caused by this kind of disturbance can be removed from the solution only if its exact pattern is known. Of course, in the real field situations such procedure is unreal. Synthetic example below illustrates the influence of the systematic noise on the results of the GST reconstruction. For the simulation below we have assumed three-layer thermal conductivity K(z) ⫽ {2.5 W/mK in the depth interval of 0–100 m; 3.0 W/mK between 100 and 200 m; 2.5 W/mK between 200–500 m depth}. As previously, the noise free T⫺z profile was calculated for the “gate” GST change by 1-D forward heat transfer modeling with 5 m intervals to a depth 500 m. Other parameters remained the same as in the previous examples. The Gaussian noise of zero mean and s.d. of 0.03 K typical for the field temperature measurements was superimposed on the above model. When formulating inverse problem we have taken the medium as homogeneous with constant thermal conductivity of 2.5 W/mK. Figure 31 shows the results obtained from this mistaken assumption. As seen, the systematic bias in temperature conductivity pattern has only a weak impact on the GST histories reconstructed by SVD method. The noise free and contaminated with Gaussian noise T–z profiles gave quite coherent inversion results. Influence of the systematic errors is somewhat stronger in the case of FSI. The GST histories
Fig. 31. The effect of a systematic error in thermal conductivity on the inferred GST history. The true model is 2.5 W/mK except between 100 and 200 m where it is 3 W/mK. A uniform value of 2.5 W/mK was assumed in the inversion: SVD method (bottom) and FSI method (top). Both noise-free T–z profile and a profile contaminated with Gaussian noise with zero mean and s.d. ⫽ 0.03 K were used for the inversion. The GST history for homogeneous medium (grey line) reconstructed by FSI method is included for comparison (top).
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calculated for mistaken one-layer thermal conductivity and using real three-layer model are comparable only for the noise-free data. To avoid instability during FSI of the T⫺z profile contaminated with Gaussian noise, the imposing of stronger bounding and smoothing constraints on the GST history ( ⫽ 0.1 K, c ⫽ 500 years) was indispensable. Resulting GST curve appears to be over-smoothed. On the other hand, FSI method provides the possibility to treat systematic errors in thermal conductivity that is unattainable for SVD technique. Namely, it can formulate thermal conductivity as a parameter with uncertainty that should be estimated together with the GST history. On the contrary, the ramp/step method and SVD are limited to the problems when the thermal properties of the medium are assumed to be known. Synthetic example below illustrates the potential advantage of formulating the thermal properties of the medium as the model parameters to be estimated. The noise-free T–z profile was calculated for the above three-layer model (“real conductivity” in Figure 32). When reconstructing GST history by FSI method (Figure 31, top), a priori constant conductivity of 2.5 W/mK was assigned and the thermal conductivity distribution was formulated as the parameter to be estimated simultaneously with the GST history. Figure 32 shows the results of inversion obtained for the thermal conductivity profile. As seen, estimated course of the thermal conductivity approaches the real variations of this quantity well.
Fig. 32. Real thermal conductivity–depth profile and its estimated modification by the FSI technique.
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Summarizing above results illustrating the use of SVD and FSI approaches, we should mention that as it was expected, both methods gave generally similar GST histories. Applied in the above models systematic uncertainty in the thermal conductivity values was sufficiently small and its effect was to a degree absorbed by the influence of the T–z noise. Including K(z) as a parameter to be estimated can somewhat improve the GST history. The advantages of this approach may appear more obviously, when the systematic noise is stronger. All existing techniques of the GST reconstruction from subsurface T–z profiles are based on the 1-D theory of conductive heat transfer. At given depth the medium is assumed to be horizontally homogeneous, and the variations of the thermophysical parameters are supposed to be only vertical. Deviations from this assumption manifest themselves as noise in interpretation. Lewis and Wang (1992) described effects of spatial and temporal variations of the terrain (upper boundary conditions) and have concluded that potentially such kind of noise can give erroneous GST estimations. According to Lewis and Wang (1992), it is these effects that may be responsible for observed deviations in the GST histories inferred from temperature logs measured in closely spaced boreholes and occurrence of so-called “spaghetti diagrams” – tangling of the superposed GST curves that reflects high regional variability of the results (Figure 33, top; see also Section 3.1.1, Chapter 3). Shen et al. (1995) investigated an influence of possible spatial heterogeneity of the thermal properties of the medium (3-D thermal conductivity structure). The authors performed a set of numerical experiments with synthetic T–z profiles. The 3-D subsurface model was obtained on the cubic 10 ⫻ 10 m grid by perturbing initially homogeneous subsurface by Gaussian noise with zero mean and s.d.⫽ 0.25 W/mK. Synthetic T–z profiles were calculated for above subsurface structure using 3-D heat conduction equation. The first set of profiles (“without signal”) was constructed for zero surface temperature boundary conditions to reveal the properties of noise misinterpreted as signal. These profiles have helped to recognize how strong is the influence of the subsurface heterogeneity on the GST history as well as to reveal most effective constraints (standard deviation of the measured temperatures, uncertainties in a priori values of thermal conductivity, etc.) that can suppress this noise. Numerical trial runs have shown that possibility to obtain “spaghetti diagrams” increases when a priori constraints are too severe; thus, small variations in measured temperatures and thermophysical properties are taken as significant for the reconstructed GST history. The authors have shown that extending constraints on thermal conductivity is a more effective way to suppress the influence of noise arising from the 3-D effects rather than change of constraints on the borehole temperatures. They also determined a range of constraints that appear the best for effective noise suppression. Annual temperatures reconstructed for North America from subsurface data were used as the surface boundary conditions for second set of T–z profiles (“with signal”). This experiment was essential, because too wide a priori constraints may lead to a loss of signal and smoothing of inverted GST history. Numerous inversions of profiles “with signal” under a wide range of values assigned to a priori conditions supported conclusions based on the calculations using “without noise” data and have identified final range of constraints for the reasonable suppression of noise and effective signal recovery. The inversions performed using an appropriate range of constraints significantly attenuated the tangling of the GST histories, although small variations still remain.
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Fig. 33. Transient GST histories of 22 boreholes from central and eastern Canada calculated by the FSI algorithm. Top: The relatively narrow constraints on a priori information resulted in the “spaghetti diagram”. Bottom: Effective attenuation of tangling was achieved by the use of optimal constraints that took into account the possible spatial conductivity heterogeneities. (Redrawn from Shen et al. (1995).)
The authors applied this information for the re-processing of the temperature logs of 22 boreholes from central and eastern Canada. As seen in Figure 33 (top), merged together earlier GST reconstructions by different authors exhibit real chaos and are not easy for comparison and determination of averaged climate history in the area. Shen et al. (1995) suggested that at least a part of the disorder observable in Figure 33 (top) is attributable to the insufficient suppression of the representational noise. Their re-processing with detected optimal constraints provided more consistent results. The higher coherency obtained for closely located boreholes as well as for combined GST histories of all holes (Figure 33, bottom) revealed considerably simpler picture than the previous pattern. Average GST history for central and eastern Canada consists of some 1–4 K warming that began in nineteenth century. Part of this warming may be interpreted as the recovery from the earlier colder period.
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2.4.3 Using additional information: Field example The testing of the inversion procedures using real temperature logs is somewhat difficult because of absence of exact knowledge of the GST history in the borehole site against which inferred results could be calibrated. If inversion methods gave different results, it is quite difficult to define whether a technique has provided better estimation of the GST history. Thus, further field examples will be used not for the testing of the methods, but only for the illustration of the effectiveness of incorporation of different kinds of additional a priori information to stabilize and uniquely determine the solution. Both SVD and FSI methods differ in their theoretical approach, parametrization, and the way of parameter estimation. Common characteristic of both algorithms is that they incorporate a priori (additional) information to achieve optimal results. For a final test of the inverse methods we use a real temperature log measured in borehole Hearst (eastern Canada). This borehole was chosen not only because of the high-quality temperature logs and heat conductivity data available, but also because of its “historical” value. In the 1970s this borehole enabled one of the first practical attempts to assess the past climate history from subsurface temperature data (Cermak, 1971). The GST reconstructions were repeated further in numerous works (Nielsen and Beck, 1989; Shen and Beck, 1992; Cermak et al., 2003). Three holes including Hearst site were drilled in northeastern Ontario in 1968 as a part of the heat flow project of the Dominion Observatory. The sites were carefully selected in a flat terrain and in geologically uniform strata. The 600 m deep borehole Hearst (49.69°N, 83.54°W) is located in a slightly elevated, bushed terrain at the boundary of large forested and cleared fields. A small nearby lake and swampy area affect the temperatures insignificantly. The site is apparently free of the groundwater disturbances. The first incremental log was measured in 1969 (Cermak and Jessop, 1971). Further virtually continuous loggings were performed in 1985 and in 2000 (Nielsen and Beck, 1989). Temperature measurements are highly precise with the absolute accuracy of less than 20mK for the incremental logs and as small as 10 mK for the continuous logs. Figure 17 (Chapter 1) shows results of these measurements (Cermak et al., 2003). As seen, all temperature logs are quite similar with the clear positive “U-shape” curvature in their uppermost parts. Figure 17 and all similar diagrams below present the temperature log not only on the measured, but also on a reduced scale obtained by subtracting from the measured temperatures a temperature value ⫽ gradient ⫻ depth (see also Eq. (5), Section 2.2). This representation enhances the nonlinearities. The shape of the reduced temperature–depth profiles is more complex than that occurring in the case of the single warming event (Figure 13). The waves of the opposite sign in the reduced temperature profiles hint the presence of the recent warming that may be amplified by the environmental effect of the forest clearing that occurred approximately 100 years ago (Wang et al., 1992), subsequent cooling, warming, and cooling again. The 192 measurements for thermal conductivity, rather regularly distributed over the length of the hole, are available. The conductivity is almost constant at 3.23 ⫾ 0.09 W/mK. The specific heat capacity is also relatively constant with an estimated mean value of about 2.5 MJ/(m3 K). The mean rate of the heat production is 0.86 W/m3 (Jessop and Lewis, 1978). For the purpose of the present analysis heat production of this rate has negligible effect on the inversion results.
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Fig. 34. GST histories reconstructed for the temperature log measured in borehole Hearst (SVD method). The use of cutoff values of 10⫺3–10⫺4 resulted to GST histories showing the “Medieval Warm Period” centered near 1200 A.D. and the “Little Ice Age” at about 1650 A.D. Early reconstruction by Cermak (1971) based on the Monte Carlo solution is shown for comparison.
As mentioned above, diffusion process never retains sharp signals; thus, estimated GST histories are relatively smooth with increasing duration and decreasing amplitude of the climatic events into the past. Figure 34 shows GST histories inferred by SVD technique using different cutoff values. For comparison the earliest evaluation of the GST history by the Monte Carlo method (Cermak, 1971) is also shown. Except for the more pronounced appearance of the Medieval Warm Period in the Cermak’s reconstruction, the coherence of results given by both methods is high. The use of cutoff values of 10⫺3–10⫺4 leads to similar GST histories with the “Little Climatic Optimum” centered near 1200 A.D. and the “Little Ice Age” near 1650 A.D. At smaller cutoff values (ⱕ10⫺6) the solution has unreliable amplitude and/or becomes unstable. The coincidence of the measured and a posteriori T–z profiles is quite high. The root mean square (rms) misfit equals to 0.01–0.015K for different cutoff values. It is an essential feature of the GST reconstructions and reflects the underdetermined nature of the inverse problem. In other words, the measured and calculated (a posteriori) T–z profiles fall close to each other even for significantly differing GST histories. Above GST reconstructions were performed without use of a priori additional information. The next calculation illustrates the advantages of including additional independent knowledge in the inversion procedure. As additional information we used the information on the decorrelation of the measured data and on the persistence of the climate changes (Section 2.3.4). As described in this section, the autocorrelation function for the most temperature logs approaches zero exponentially (short-range dependence): r(z) ⫽ exp(⫺z/D) where r(z) is the autocorrelation function, z the depth lag, and d the characteristic correlation distance (Figure 35). Parameter D corresponds to the depth lag at which the autocorrelation decreases to (1/e), i.e., it defines the distance at which the individual temperature values can be considered statistically independent. For the majority of the boreholes the D-value ranges from 100 to 300 m (Bodri and Cermak, 1997a). Longest decorrelation distances are characteristic for boreholes drilled in ultrabasic rocks.
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Fig. 35. Autocorrelation of measured temperatures at borehole Hearst in the depth interval 20–600m and its exponential fitting.
The effect of different factors on the correlation distance was studied in a number of synthetic examples in the work by Bodri and Cermak (1995). Decorrelation distance depends on the distribution of the thermophysical properties of the medium, and also on whether fluid circulation is present or not. Generally, an environment with fluid circulation has a smaller D-value compared with an environment with no circulation (Bodri and Cermak, 2005a). The presence of a strong climatic signal in measured underground temperatures can also significantly affect the D-value. The advantages of treating the additional information are illustrated in Figure 36. As seen, an augmentation with additional information does not significantly change inferred GST history especially in its more recent part; however, it helps to recover less smoothed GST history. Under FSI runs, two sets of values for a priori constraints for and c were assigned (Figure 37). Two GST histories were calculated to reveal the uncertainty about the optimal values for the smoothing parameters. Applied values can be regarded as the upper and lower bounds for possible constraints. The GST reconstruction inferred by SVD technique with cutoff value of 10⫺4 is shown for comparison. Once parameters are appropriately chosen the two methods have provided very similar results. All reconstructions revealed cold conditions prior to 1800 A.D. There is also a slight decrease of temperature since about 1964 and 1976 for SVD and FSI reconstructions, respectively. The difference in the onset time of the recent cooling occurs because of the instability induced by noise. Because of the heat diffusion and the uncertainties of measured temperatures, the time span for which the GST history can be reconstructed is limited. Its length is influenced by the depth and quality of measurements and also by the magnitude of the climatic signal that is to be reconstructed (Clow, 1992). The further we go back to the past, the less detail can be distinguished and a smoother course of the true temperature is obtained. This finding can be illustrated in terms of the resolving power of the SVD inversion
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Fig. 36. Effect of the additional information used in the SVD method. An augmentation with additional information provides less smoothed GST history. (Demonstrated on the Hearst data.)
Fig. 37. The GST histories reconstructed for Hearst data by the FSI method using two sets of a priori constraints. The SVD reconstruction (cutoff ⫽ 10⫺4) is shown for comparison.
method (Section 2.3.4). As described in that the given section, the resolution matrix of the unknown parameters can be defined as R ⫽ VVT, where V is a matrix whose elements are the eigenvectors. The jth column of matrix R represents the least squares solution for maximizing the jth parameter. At proper choice of the discretization of time the resolution matrix exhibits delta-like behavior (compact resolution) when the column with the best resolving power is nearly always the column with the maximum diagonal element. Thus, the diagonal elements of the resolution matrix can be used as the measure of the resolving power. It can vary between 1 (perfect resolution) and 0 (no resolution). The resolution was shown to depend on the shape of the surface temperature history, and is also a complex function of many borehole specific parameters, such as accuracy and vertical spacing of the temperature measurements, distribution of thermal conductivity measurements, and the level of noise in the data (Clow, 1992; Bodri and Cermak, 1995); thus, it should be established for each borehole individually.
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Fig. 38. Top: Resolving power of 100, 500, and 1000 year time intervals versus time (Hearst data). Bottom: Resolving power of 50-year intervals versus time without and with incorporating additional information on the interdependence of temperature measurements and on the climate changes (curves are labeled 1 and 2, respectively).
The diagrams of the variation of resolution back in time calculated for borehole Hearst (Figure 38 (top)) illustrate the most prominent property of resolving power of the geothermal method, namely the general fast decrease in resolution into the past. The variance of the jth parameter can be estimated by Eq. (21). A 100-year long event that occurred 300–500 years ago can be resolved with the relative variance of 10–15%. For as early as 2000–3000 years ago, it is only possible to resolve a 500-year interval with the same reliability, and the corresponding duration of event is 1000 years if it occurred 7000–9000 years ago. In other words, the further back we go into the past the less detail can be resolved and the smoother trend of the real temperature conditions on the Earth’s surface can be obtained. However, as mentioned in Chapter 1, such diminishing of the resolution into the past represents a common property of the majority of proxy methods for the paleoclimatic reconstructions. Compared to the variety of proxy climatic reconstruction methods, the resolving power of the geothermal method is lower for the recent 50–100 years and is comparable with other paleoclimatic reconstructions when detecting more remote climatic events (Figure 7, Chapter 1).
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Generally, the Hearst data permits to assess past climatic changes of one millennium or so. Figure 38 (bottom) illustrates the change of resolving power for 50-year time interval calculated for the Hearst hole, i.e. a rapid decrease in resolution with increasing time. The reliability to determine short GST change is about 10–15% for an event, which occurred 50 years ago; for an event that occurred 200 years ago, it is possible to resolve a 50-year interval with the same reliability, and a 200-year interval for an event that occurred 800 years ago. Incorporation of additional information can improve the resolving power of the SVD method. As demonstrated in Figure 38, the ability to resolve 50-year time intervals after incorporating the information about interdependence of temperature measurements and climate changes exhibits an improvement of almost 10% at a time of 0–50 year B.P., and of 23–35% at the interval of 100–150 year B.P. We have compared two of the most powerful methods for the GST inversion using the subsurface temperature–depth profiles. Methods differ in both their parametrization and the technique of parameter estimation. The incorporation of a priori information to obtain a stable and unique solution is central for both techniques. In spite of the theoretical differences between both approaches, their application to synthetic and field examples gives generally similar results in the case of the appropriate choice of the stabilizing constraints. Summarizing conclusions are the next: (1) Large part of discrepancies in the inverse results can be attributed to different constraints imposed on the GST to smooth and stabilize the inverse solution. In general similar results were obtained by two methods when equivalent assumptions were used. (2) In principle, FSI technique allows incorporation of the thermophysical properties as the parameters to be estimated and weighting of the contribution of the data and a priori model and thus appears possessing potential to give better inversion results. However, exact knowledge of the weights/uncertainties of the data as well as a priori model is indispensable to realize this potential, while researchers generally have no sufficient a priori information in their disposal. (3) The computational advantages when incorporating additional information are obvious. Including additional information can improve the resolution and significantly enlarge the extent of the climatic history that can be recovered by the inversion. The more complete is a priori knowledge about past climatic changes from independent complementary sources, the more reliable GST histories can be inferred from borehole data.
2.4.4 Recent testing of borehole inversion methods in simulated climates The reconstruction of the past temperature variations on the global/hemispheric scales is performed by three principal approaches: proxy methods, inversion of borehole temperature logs, and modeling. Different proxy techniques are the oldest and traditional, while the “borehole” method and simulations of the past climate with the state-of-art GCM represent recent developments. The first attempts to decipher certain information on the GST changes from underground temperatures dates back to the early 1970s, and the
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corresponding inversion methods become generally known in the mid-1980s. The first compilation of the studies inferring past climatic variations from underground temperatures edited by T. Lewis has appeared in 1992 (Lewis, 1992). Together with other topics it gathered numerical comparisons/testing of different GST inversion techniques. The goal of these investigations was to prove the ability of the “borehole” method for reliable reconstruction of the past climate change (e.g. Beck et al., 1992; Shen et al., 1992). The attempts to validate and to refine “borehole” method and/or answer numerous questions arising during further development of the techniques and drawing more and more field data in the processing continued permanently for the recent two–three decades. Simultaneously numerous attempts were undertaken to bring together/compare/combine results of different approaches and to integrate them into the complex multi-dimensional paleoclimatic network. Probably the most recent testing of the possibility of the GST reconstruction from borehole temperature logs was performed in the work by González-Rouco et al. (2006; see also the references therein). This attempt has been inspired by the recent comparative studies of various global/hemispherical paleoclimatic reconstructions and somewhat different magnitudes of the past temperature changes (especially in the earlier parts of the records from the sixteenth to eighteenth centuries) of the averaged GST histories in comparison with climatic trends defined from proxy records (Briffa and Osborn, 2002). The global and/or hemispheric scale temperature histories for the several past centuries based on borehole measurements suggest colder past conditions than the reconstructions based on the multiproxy data. For example, tentative hemispheric GST history by Huang et al. (2000) (Figure 94, Chapter 3) revealed a much colder Little Ice Age of approximately ⫺0.8 to ⫺1.0 K in comparison with ⫺0.2 K given by the Mann et al.’s (1998, 1999) multiproxy compilation (for details see Section 3.3, Chapter 3; Mann et al., 2000; www.ngdc.noaa.gov/paleo/ei/ei_cover.html). Results by Briffa et al. (2001; see also Figure 11, Chapter 1) are somewhat closer to the Huang et al.’s (2000) conclusions and give temperatures of the Little Ice Age by 0.3–0.6 K lower than the present, while Crowley and Lowery (2000) proposed, rather, a warming of ⬃0.2 K from 1000 to 1400 A.D., cold conditions of ⬃⫺0.3 K up to 1900, and rapid warming of 0.4–0.8 K in the twentieth century. Two reconstructions for Europe using independent proxies by Luterbacher et al. (2004) and Guiot et al. (2005) have detected almost similar twentieth century warming of 0.25 and 0.27 K, respectively. Mann et al. (2003) have tried to re-assess the coupling of the borehole and traditional proxy data and have re-calibrated the GST history using the twentieth century SAT data. This procedure somewhat increased possible warming to 0.2–0.4 K. Another distinction of the “borehole” and proxy reconstructions is that the amount of warming obtained by Huang et al. (2000) is more regularly distributed over the past five centuries, while in other works the twentieth century warming appears as a continuation of the trend that started only in the nineteenth century. Similar inconsistency was found also among different proxy series. Figure 39 shows comparison of three multiproxy SAT anomaly series for the Northern Hemisphere. Pattern by Esper et al. (2002) represents tree-ring temperature reconstruction, while the compilation by Mann et al. (1998) is based on multiproxy data (tree-rings, ice cores, corals, historical documents, and instrumental data). Reconstruction by Huang (2004) merges multiproxy and borehole sources (for details see Section 3.3, Chapter 3). It was proposed that the inconsistency in the pre-instrumental period between “geothermal” and
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Fig. 39. Comparison of the annually resolved five-century multiproxy reconstructions for the Northern Hemisphere by Mann et al. (1998), Esper et al. (2002), and Huang (2004). Pattern by Huang (2004) integrates also borehole data. Temperatures are shown as anomalies with respect to the 1961–1980 mean.
multiproxy time series could at least in part arise from the significant role that tree-ring information plays in the former reconstructions (Huang et al., 2000). As known, centennial trends are expressed very weakly in tree-ring series (see Figure 9 and Section 1.2.3, Chapter 1). For that very reason Esper et al. (2002) applied a powerful method for the regional calibration of tree-rings that keeps long-term trends better than the method used by Mann et al. (1998) and thus obtained larger variability in the past temperature time series. The early seventeenth century SAT anomaly estimates of these authors diverge by about 0.7 K from those by Mann et al. (1998). Later re-calibration of the data has reduced these differences to only 0.35 K (Briffa and Osborn, 2002). Even bearing in mind turbid complex of reconstruction uncertainty, the curve by Esper et al. (2002) contains evidence for more pronounced climate oscillations in the past millennium than has been previously accepted by the multiproxy reconstructions. Because the divergence in the amplitude of the temperature variation is an extremely important difference, detection of a fair scatter among various published estimates was followed by lengthy discussions. Their effect can be found in the works by Mann and Hughes (2002), Cook et al. (2004), and Esper et al. (2005). The researchers have exchanged their views at numerous conferences (e.g. Session PP19: Climate Change in the Recent
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Past: Integrating Meteorological, Proxy, Borehole, and Modeled Climate Reconstructions; AGU Fall Meeting, December 2005, San Francisco, CA; www.agu.org/meetings/fm05), as well as on the different web sites of professional climatologists, e.g. the Real Climate (www.realclimate.org./index.php?p⫽253), and/or more descriptive the ClimateAudit (CA) and the European Tribune: www.eurotrib.com/story/2006/2/12/19444/8696). The argument on the subject “Borehole versus proxies” has represented only a part of the above “big discussion” on the reliability of different paleoclimate reconstructions. Mann et al. (2003) have optimized the Huang et al.’s (2000) data and partly corrected them later (Jones and Mann, 2004). However, Pollack and Smerdon (2004) did not accept their optimization (for more details see Section 3.2, Chapter 3). Guiot et al. (2005) on the basis of 222 borehole temperature profiles inferred averaged GST history for Europe that indicated ⬃0.5 K higher temperature rise in comparison with their reconstruction based on multiproxy sources. The average of the multiproxy temperature anomalies for the 1500–1700 A.D. segment is ⫺0.1 ⫾ 0.5 K. The average borehole temperature for this period equals to ⫺0.45 K; thus, it is still within the lower boundary of the confidence interval. The amount of warming calculated for Europe is somewhat smaller than Huang et al.’s (2000) value for the Northern Hemisphere. In spite of the higher coincidence obtained after 1750 A.D., Guiot et al.’s (2005) statement was that “borehole temperature reconstruction is not perfect”. The main benefit of this trenchant discussion was probably that it has impelled the researchers to re-assess the skill of different methods for the past climate reconstruction. The most advantageous testing strategies for the ability of the “borehole” method to draw out past GST changes from T–z profiles were applied in the recent works by Beltrami et al. (2006) and González-Rouco et al. (2006), whose authors used simulated subsurface T⫺z profiles forced by the GCM as a substitute of the real climate and applied inversion technique to reconstruct GST histories from calculated profiles. Modern 1000-years long ECHO-g ocean–atmosphere GCM models were used as a surface forcing to the forward models of heat conduction. These models have included the 1000-years long external forcings (solar irradiance, radiative effects, and volcanic aerosols) as well as the anthropogenic influence (greenhouse gas concentration increase) and were complex enough to provide insight into intrinsic properties/possibilities of the inversion technique and to test the correctness of the GST reconstruction. Control and two trial simulations with the same external forcing and different initial conditions were considered. The 600 m deep T–z profiles were gained from the 898 land terrestrial grid boxes and reflected averaged Northern Hemisphere land conditions. To investigate influence of the spatial distribution and surface coupling of borehole sites similar profile was calculated also on the base of the 177 grid boxes reflecting the real borehole distribution. The SVD inversion was applied to these T–z profiles to infer GST history. Recovered from simulated T–z profiles GST histories were compared with the climate model variations used as a surface forcing. Results have shown that in spite of different disturbing factors (e.g. dating of the temperature logs and non-equal depth) and irregular (somewhere sparse) geographical distribution, GST histories return adequately the filtered version of the real climate change. The numerical experiment described above has proved that the SVD inversion technique is powerful enough to reproduce the main features of the multi-century climatic trends. In the case of satisfactory quality of the borehole temperature logs and the proper
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treatment of possible uncertainties, borehole method itself could detect major climatic excursions of the past. It is extremely important that none of the reconstructions based on different models show any evidence of an overestimation of the magnitude of the past climatic change, while it was this difference that has inspiredthe discussion as well as the additional testing of the “borehole” method mentioned above. For the recent two–three decades boreholes distributed over the entire continents were recognized as a great tantamount source for new information in numerous “white spots” of the global map of the paleoclimatic change. Researchers from many countries mastered routine application of the geothermal method and a sizeable number of results have been published. It appears that the boreholes can provide information previously unavailable in character and spatial distribution. Further investigations, however, have added a grain of salt to initial enthusiasm for the “geothermal” climate reconstruction. No doubt, in many cases different inversion methods gave equally good coherent results. However, in a number of situations inversion techniques gave poor results. These failures were attributed to an impact of numerous non-climatic influences on subsurface temperatures that can disturb the ideal heat conduction regime described by Eq. (4). That time potential environmental disturbances to the subsurface climatic archive were recognized as well as the necessity of the careful analysis of the potential perturbations for each individual temperature log. An influence of terrain on the GST has been discussed in detail by Lewis and Wang (1992), and examples of the effects on ground temperatures of spatial distribution of differing terrains, temporal changes in terrain, and subsurface fluid flow have been presented. Since then numerous investigations have been carried out concerning the influence of different local effects on the subsurface temperatures and the ways to recognize these anomalies and reveal reliable GST histories from disturbed temperature logs. The next sections contain the summary of these efforts.
2.4.5 Interpreting ensembles of borehole temperature logs The above sections were devoted to the techniques of the GST inversion from the temperature–depth profiles measured in individual boreholes. As in all branches of geophysics, an extraction of climatic signal from borehole temperature logs is complicated by the presence of noise in the data. The principal sources of noise are of three types: (1) the measurement errors, (2) the representation errors, i.e. the simplification of the mathematical model and its departure from the conditions existing in the real geophysical systems, and (3) terrain effects causing both secular and provisional changes on the ground–air boundary. Since in most of the field situations detailed information that permits sure correction of measured profiles is not available, the development and application of various techniques for suppression of noise and enhancement of the signal have received special importance. Numerous studies in other geophysical branches have shown that the analysis of multiple observations can be more preferable to suppress the effect of the random noise in the data than the use of single measurements. The basic idea of this approach is that the signal can be enhanced and/or noise can be attenuated by the interpretation of the available data together as an ensemble. This approach is widely employed as simultaneous inversion using weighted staking of seismic reflection data (Fatti et al., 1994; Larsen et al., 1999; Margrave et al., 2001; Ryberg et al., 2005). Results have shown that in the
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presence of random noise the combination of the data volumes provides more accurate results than the techniques using individual data. Joint processing effectively suppresses the noise without unnecessary suppression of the signal. The unknown parameters are better constrained and, in spite of the noise present, are more reliably estimated. The advantage of such approach in borehole climatology can be illustrated as follows. Let us assume that the climate in some wide area is characterized by a secular change in temperature that is archived in the underground. It is this signal that should be recovered by the GST reconstruction procedure. Generally, borehole site represents a variety of environmental conditions. Boreholes are drilled into different rock types, on the heights or valleys, embracing a variety of hydrologic regime and surface conditions from bare soil to the dense vegetation. Thus, temperature–depth profiles from different boreholes may contain local non-climatic perturbations to the long-term transient climate signal. All boreholes would unlikely have the same topography and vegetation cover, subsurface structure, and hydrologic regime. If different kinds of noise appear randomly in the data ensemble, an analysis of combined T–z profiles would likely result in the common regional signal enhancement and suppression of noise. A signal common to all the boreholes can safely be attributed to the regional climate change. Combined analysis of borehole data can be performed using two different strategies: (1) simultaneous inversion of the temperature logs from several boreholes, and/or (2) averaging of the individual GST histories. Both procedures differ conceptually. Simple averaging of the GST histories inverted from the single-hole logs can be accomplished without limitations, while the simultaneous inversion of several T–z profiles can be performed exclusively under assumption of the presence of common transient climate signal in all jointly analyzed temperature logs. Beltrami and Mareschal (1993) have extended conventional SVD technique and suggested the multi-inversion approach. The method was verified using 21 temperature logs sampled across the whole eastern and central Canada and yielded generalized GST history for this region. Later Clauser and Mareschal (1995) have performed the testing of this method by the simultaneous inversion of borehole temperature logs from Central Europe. Both studies have supported an increase in the resolution under multi-inversion approach, when common climatic signal can be fully unraveled. Beltrami et al. (1997) has presented detailed description of the simultaneous inversion of borehole temperature data for reconstruction of the GST history in the SVD context. Pollack et al. (1996) have extended the simultaneous inversion approach for the FSI technique. Their method was used for the joint processing of the borehole temperature logs in numerous studies. Thus, Majorowicz and Safanda (2001) have constructed composite surface temperature history from simultaneous inversion of T–z profiles from 43 boreholes located at the western Canadian Basin. The field situations favorable for the simultaneous inversion strategy include: (1) repeated temperature logs from a single borehole, (2) a suite of boreholes from a single site, and (3) a suite of boreholes from a wider region with similar climatologic and environmental changes. The mathematical procedure is especially obvious in the case of the SVD inversion. As previously (see Section 2.3.4), an unknown GST history V0(t) is approximated by N intervals of constant temperature (Eq. (18)). In the case of a single borehole the matrix Aik (Eq. (20)) contains M rows and N columns, where M is the number of temperature measurements in the single-hole. For L holes with Mi measurements in each of them, the matrix A will consist of Li⫽1 Mi rows and N columns, containing series
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similar to Eq. (13) calculated for all given depths in each given borehole. When parameters of initial (equilibrium) temperature field for each borehole U0 and Qm are estimated simultaneously with the GST history V0(t), the vector Vi will consist of (N ⫹ 2L) unknowns, and the matrix A will contain two additions (see Section 2.3.4). The first M1 elements of the (N ⫹ 1) column will be equal to 1 and all other to 0, the following M2 elements in (N ⫹ 2) column are 1 and all other elements are 0, and so on. Similar addition can be constructed for the thermal resistances4 to the depths zi in all given boreholes. Further inversion procedure is the same as for the single-hole SVD case. The efficiency of a simultaneous inversion in the noise suppression is clear. Of course, the GST histories obtained by merging data sets that simultaneously combine a number of T–z profiles and conductivity data with different terrain/microclimate effects and noise level, have typically larger data misfits than the individual holes. In the cases when obtained data misfits are too large, it can mean that a common climatic signal may not present in the data. On the other hand, testing of the simultaneous inversion technique conducted in the work by Beltrami et al. (1997) using SVD approach for both synthetic noisy and noise-free data as well as for the field examples containing common climatic signal have shown that staking temperature perturbations from L boreholes can increase the stability of the solution and resolution of the inversion and improve the signal to noise ratio L. Calculations by Beltrami et al. (1997) revealed the dependence of the by a factor 兹苶 resolving power from the noise level. Generally, composite surface temperature history obtained by simultaneous inversion was comparable with the GST curve obtained by inversion of the single log with the lowest noise. A definite problem for the simultaneous inversion represents the fact that not all available borehole temperature logs were measured using the same sampling interval. In this case the composite GST history was not close to anyone of the individual surface temperature histories and was weighted to the temperature logs with the finer sampling. Thus, temperature logs with similar sampling should be used for simultaneous inversion to avoid possible bias. Temperature logs with large sampling intervals can be interpolated for finer distances. On the other hand, the simultaneous use of the temperature logs of different lengths does not represent serious restriction. Such temperature–depth profiles contain the surface climate history of different time spans. Numerical experiments by Beltrami et al. (1997) have shown that because shallow boreholes does not archive an information on remote GST changes, merging of the shallow- and deep-hole data for simultaneous inversion does not improve the course of the past GST history obtained from the deep holes. On the other hand, this procedure can specify better the recent GST history and/or to improve the estimates of the heat flow obtained from the shallow-borehole data. An averaging of the GST histories reconstructed from the individual borehole temperature logs represents another possible kind of the ensemble interpretation and suppression of the random noise in the geothermal data. As mentioned above, the principal difference between simultaneous inversion and averaging of the individual GST histories is that the averaging can be performed without restrictions, whereas the former procedure provides good results only for boreholes that contain common climatic signal. On the other hand, the simultaneous inversion takes into account the data uncertainties 4
Thermal resistance is the ability of a material to resist the flow of heat. It represents the reciprocal of thermal conductivity and is measured in km/W.
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and the borehole sampling and depth. These effects cannot be easily captured in the simple averaging of the single GST histories. Comparing both techniques, Pollack et al. (1996) have concluded that for the three field situations enumerated above they yield closely identical results. Diverging GST histories were obtained when merging a suite of boreholes from the vast areas that have experienced different surface temperature variations over their different parts. The simultaneous inversion estimate in this case appears to give biased GST history. If both procedures, the GST averaging and simultaneous inversion, exhibit different results it generally notifies that an assumption of a common transient climatic signal in processed boreholes may be invalid. Numerous examples of the application of both procedures to the worldwide database of borehole temperature logs are presented in Section 3.2 (Chapter 3). Recently Chouinard and Mareschal (2006) have compared again different approaches of the GST inversion from ensembles of borehole T–z profiles. They used temperature logs measured in boreholes in two Canadian regions: northwestern Ontario and northern Manitoba/Saskatchewan. Using these data the authors have performed three experiments: (1) simultaneous inversion of all available profiles, (2) screening of the profiles for the possible non-climatic disturbances and simultaneous inversion of the undisturbed profiles, and (3) averaging of the individual inversions. Results of experiments have shown that at least for above two regions the averaging of the individual inversions gives less resolved GST histories than the simultaneous inversion of the same temperature–depth profiles. For example, well resolved by the simultaneous inversion the Little Ice Age appears much weaker in the GST curve calculated by averaging the individual GST reconstructions. Similarly less visible is the fingerprint of the recent warming. On the other hand, the difference between results of the simultaneous inversion of all temperature logs and only selected profiles, which were assumed to be free of the non-climatic influences, was far not so significant than the authors had anticipated. Generally, the most informative results with maximum resolution were obtained from the simultaneous inversion of a few noise-free profiles.
2.5 Ground–Air Temperature Coupling: Pre-Observational Mean Temperature (POM) Borehole temperature measurements contain direct information on the GST history. The GSTs represent important climatic variable; thus, in principle they need no calibration with the independent data. On the other hand, it is the air column temperatures, including the most important surface air temperatures (SAT) taken at screen height (1.5 m above the ground surface), that are typically of interest in discussions of climate variability. The SAT responds to the convective heat transfer in an atmospheric boundary layer, while the GST represents a continuously integrated ground temperature variations in the vicinity of the borehole that occur mainly by conduction process. Thus, both massifs of the data are complementary, but independent data sets that provide measure of the surface temperature and its change through the time in different frequency domains. Once we are sure that we have reliable methods to infer the GST history from borehole logs, further task should be the relation of the GST to the SAT changes. This ensures that the climate change will be tackled with more confidence.
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The problem of coupling of the GST and SAT has arisen from the very beginning of the borehole climatology. The fact of the systematic difference between the GST and SAT, namely that the soil may be warmer than the air has been revealed already in the early work by Chang (1958), who demonstrated that a greater part of the solar radiation is absorbed by the Earth’s surface rather than by the atmosphere. The micrometeorological processes near the Earth’s surface causing higher “thermal capacity” of the ground were investigated in the work by Deacon (1969). Figure 14 (Chapter 1) illustrates the air and ground temperature oscillations measured during 12-year temperature monitoring at several shallow depths in the experimental borehole Prague-Sporilov (the Czech Republic) (Cermak et al., 2000). The annual wave is seen as the most important variation. In addition to an annual cycle, ground temperature exhibit a daily cycle and variations associated with changes in weather. These variations are confined to the near-surface zone. The filtering of the high-frequency components and the lag of the ground response with respect to air temperature variations is apparent in the temperature record presented in Figure 15 (Chapter 1). The daily temperature wave and the weather cycles are practically not observable below about 0.5 m and approximately 1 m depth, respectively. Figure 40 shows monthly averaged GST change in Eilat area (Israel). Ground temperatures were measured at 2 cm, 20 cm, and 1 m depth during the years 1957–1963 (data source: www.fortunecity.com/greenfield/runningbrook/729/id23_m.htm). Temperatures were recorded at 8, 14, and 20 h. This example represents ideal case of the air–ground temperature coupling in warm dry environment without snow cover or freezing. As shown, the coherency of the general course of the near-surface and deeper ground temperatures is practically perfect. On the other hand, deeper ground temperature is higher than the near-surface temperature in winter and is lower in summer. This creates definite attenuation of the total annual range of variation of the GST in comparison with air temperature variations. Due to the fact that the GST is higher than the SAT in winter and is lower in summer, the ground represents potential storage capacity and a source for the heating/cooling. Heat flows out and/or into the ground in the cold and warm seasons, respectively. This phenomenon is referred as the “heat-valve” effect (Gilpin and Wong, 1976). Factors connected to the movements and/or diffusion of air and/or moisture masses (wind, evaporation/transpiration, vertical soaking of soil moisture, and precipitation) tend to equalize air and soil temperatures (Arya, 1988). One of the first empirical long-term relationships between annual mean GST and SAT has been presented by Kukkonen (1987) for the territory of Finland. It is based on the combination of air and ground temperatures measured on the meteorological stations all over the country and borehole temperatures extrapolated to the surface TG ⫽ 0.71 ⫻ TA ⫹ 2.93,
(31)
where TG and TA (°C) are annual mean ground and air temperatures, respectively. As seen on the annual scale ground is warmer than the air. On the other hand, the ground temperature fluctuations are approximately 30% attenuated in respect to the air temperature. The fact that generally the mean annual SAT is lower than the corresponding GST was corroborated by numerous later measurements. Comparison of soil and air temperatures by Chisholm and Chapman (1992) for the Salt Lake City Airport meteorological
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Fig. 40. Monthly averaged ground temperatures measured in Eilat area, Israel. Data are averaged through 1957–1963 period. Ground temperatures were measured at 8, 14, and 20 h at the depths 2, 20, and 100 cm, respectively. (Data source: www.fortunecity.com/greenfield/runningbrook/729/ id23_m.htm.)
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station have shown that the ground is generally warmer than the air by 1–2 K. Similar results was obtained in the work by Schmidt et al. (2001) for Fargo (North Dakota). For the nine-year long record the mean annual average ground temperature was ⬃2 K higher than the air temperature. The same difference was obtained for 1997–1998 years GST–SAT monitoring at the station Pomquet (Nova Scotia). In most of the mentioned locations this difference occurs mainly due to the insulating effect of the snow cover, although such factors as evaporation also play a role. As demonstrated by the regional investigations in Canada, in the regions with insignificant snow cover (e.g. coastal areas) the mean annual GST–SAT difference equals to only 1 K, while in the areas with deep and long duration snow cover (e.g. described below Kapuskasing site) it may reach as much as 5 K. A comparison of mean monthly air and soil temperatures recorded during 1984–1989 period at Salt Lake City Airport has shown that the soil temperatures at all recorded depth (10, 20, 51, and 102 cm) almost perfectly repeat the annual air temperature variations, however, with considerable offset (Chisholm and Chapman, 1992). Repeated model studies have revealed that on the long scale mean annual GST corresponds linearly to the mean annual surface temperature (Baker and Ruschy, 1993; Putnam and Chapman, 1996; Gosnold et al., 1997; Harris and Gosnold, 1999; Majorowicz and Safanda, 2005). This statement can be confirmed by the Granger causality test (see Section 3.4.5, Chapter 3). For this analysis we have used reconstructions of the annual global surface temperature over the last five centuries (1500–1980), based on the multivariate calibration of the high-resolution proxy climate indicators (tree-rings, ice cores, corals, and historical documents) combined with the long-term instrumental records by Mann et al. (1998) (Figure 39 of this chapter) and similarly long GST reconstruction based exclusively on the terrestrial borehole data (Mann et al., 2003; Figure 98, Chapter 3). Application of the Granger causality test to these records have shown that on the long scale the SAT series is the Granger cause of the examined GST, and has thus supported strong long-scale GST–SAT coupling (for details see Section 3.4.5, Chapter 3). All above-mentioned investigations have given the confidence that it seems reasonable to consider borehole temperatures as filtered versions of the surface air temperature (SAT). The complementary nature of the GST and SAT has inspired the idea of coupling of the measured temperature logs and the SAT time series for the joint processing. To estimate the magnitude of recent climate change, specifically the amount of the recent global warming, paleoclimate reconstruction from the temperature–depth records can be suitably completed with a long-term meteorological SAT series monitored at the weather stations. This idea was introduced by Harris and Chapman (1995, 1997) and provided a useful tool for the assessment of the so-called pre-observational mean temperature (POM) that represents the temperature conditions existing before the routine instrumental observations actually started some 100–250 years ago, i.e. the value against which the twentieth century climate warming is usually referenced. Coupling the inverted borehole temperature logs with the SAT series provides a more realistic benchmark than the models based on the inverted borehole data themselves. For the 1-D case of the purely conductive heat transfer POM can be obtained by comparing the temperature log measured in a borehole with synthetic temperature–depth profile, corresponding to the solution of the 1-D heat conduction equation in a horizontally
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layered half-space that describes purely conductive heat transport with no heat sources taken into account (Eq. (4), Section 2.2). The surface boundary conditions corresponding to the observed SAT series are
POM, 0 ⬍ t ⱖ t0 T ( z ⫽ 0, t ) ⫽ , TSAT , t ⱖ t0
(32)
where TSAT is the SAT temperature time series, and t0 the time when the SAT record started. It is assumed that the interval (0, t0) is long enough. Thus, at constant temperature before t0 and for an absence of other effects the initial temperature–depth profile, T–z, at time t0 represents a steady-state temperature field corresponding to the constant heat flow from depth. The approximate duration of t0 can be estimated from the expression for the characteristic time of the thermal relaxation t0⬃L2/4k, where L is the characteristic length and k the thermal diffusivity. When k equals to 10⫺6 m2/s for a 100–200 m deep borehole t0 achieves approximately 100–300 years. As in the previous processing examples, measured temperatures can be converted into reduced temperatures by removing the quasisteady state part from the measured temperature log. The reduced temperatures contain only temperature “disturbances”, ideally in absence of substantial topographic elevation and other disturbing factors the subsurface climate recollection alone. Since the boreholes have different depths, the measurements to the depth z ⫽ 兹4苶kt 苶苶*, where t* is the time from the beginning of the meteorological record to the date of borehole logging, are generally taken for the inversion. This procedure avoids the biasing due to different borehole depths (Harris and Chapman, 1997). To estimate the POM-value, the standard least-square inversion analysis can be used, which minimizes the sum of the squared differences between reduced and synthetic temperature–depth profiles. Inverted data are sensitive to the calculated POM-value; in the absence of non-climatic disturbances the POM-value can be assessed quite accurately, which is otherwise not possible by using the SAT record alone. Below we illustrate the application of the method to the data from Canadian borehole Hearst (49.69°N, 83.54°W), the GST reconstructions for which were presented in the Section 2.4.3. Generally, results of the meteorological temperature measurements are representative of extensive areas; thus, making POM estimates, there is no need to get results of SAT measurements of especially close to investigated boreholes meteorological stations and/or to reject from consideration borehole temperature logs where such data does not exist. According to investigations by Hansen and Lebedeff (1987), the correlation coefficient between the annual mean temperature variations for pairs of stations selected at random from among the station pairs with at least 50 common years in their record is above 0.5 within 750 km distances at latitudes 23.6–44.4°N and within 1250 km distances for latitudes 44.4–64.2°N for each direction defined by 45° intervals. At middle and high latitudes the correlations approach unity as the separation between the stations becomes small. Of course, local specific conditions, such as vegetation cover, slope orientation, presence of large water body, etc., may produce lateral variations in the GST of up to several degrees over a short distance (e.g. Blackwell et al., 1980). In such cases the SAT records from the nearby meteorological station should be used to calculate the POMvalue (Harris and Chapman, 1997).
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Fig. 41. Annual mean SAT record at the meteorological station Kapuskasing (Canada) for the 1918–2001 period. Data are shown as temperature anomalies from the base period 1961–1990. POM – pre-observational mean temperature.
As a representative SAT record we have taken mean annual temperatures measured at meteorological station Kapuskasing (49.42°N, 82.38°W) (Figure 41). The homogeneous SAT series exists there from 1918. The record reveals certain warming with the mean rate of 0.015K/year characteristic for the most of the twentieth century. In the last few decades, the general warming has been accelerated and its rate for the period 1970–2000 was almost triplicate (0.047K/year). Both Kapuskasing and Hearst boreholes are located in a bushed area that was formed after clearing of surrounding forests approximately 100 years ago. Large cleared fields are situated approximately 500m away from Kapuskasing and, according to Wang et al. (1992), may have only small effect of the temperatures. The larger effect from the closer deforestation may be at the Hearst site. The mean temperature anomalies corresponding to the 1918–2000 and 1970–2000 periods equal to 0.52 and 0.76K, respectively. Temperature logging of the Hearst borehole was performed three times (for details see Section 1.3 (Chapter 1). Figure 17 (Chapter 1) compiles the results of these measurements. As shown, all temperature logs are quite similar with a weak but clear positive “U-shape” curvature in their uppermost parts that hints the presence of the recent warming. For inversion we used temperature–depth data only from below 20 m depth to exclude any seasonal temperature variations. The reducing parameters (T0 – surface temperature and G – geothermal gradient) were calculated by the linear regression of the deepest part of the T–z record. Reduced temperature obtained by subtracting background thermal field from the measured temperature log is shown in Figures 42 and 43. It is curved and systematically positive above 100–150 m depth indicating recent climatic warming. Chisholm and Chapman (1992) have demonstrated high sensitivity of the borehole temperature profiles to the POM-values. This statement is illustrated in Figure 42 that shows the observed and synthetic reduced temperatures for the three different POMvalues. The degree of conformity between the real and simulated models is usually characterized by the sum of the squares of deviations between measured and synthetic temperature logs. We have calculated root mean square (rms) misfits for wide spectra of
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Fig. 42. Combined meteorological and geothermal data were used to infer the POM-value for Hearst hole; reduced temperatures compared with synthetic transient temperature–depth profiles calculated for three choices of POM for the time prior to 1918 (see text). The inset shows the rms misfit as a function of POM and illustrates the best fit for POM ⫽⫺1.98 K.
Fig. 43. Left: Reduced temperature profile for Hearst hole compared with synthetic temperature profile computed for the best-fit POM-value. Right: “Left-over” temperature.
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possible POMs to determine the best fit. Generally, preferred value of estimated parameter corresponds to the minimum of rms misfits. As seen in Figure 42, small differences in POM-value cause significantly poorer fit to the observed reduced temperatures. Even 0.5 K difference in the POM-temperature is critical to obtain a good fit with the observed reduced temperatures. For the Hearst hole the best fitting reduced temperature is POM ⫽⫺1.98 ⫾ 0.01 K (rms misfit ⫽ 0.095 K). A sharp extreme in the misfit diagram (Figure 42, inset) indicates the character of the POM as a robust temperature estimate. Obtained POM-value is almost 2.5 K lower than both 1918–2000 and 1970–2000 temperature means, indicating significantly colder pre-1918 conditions. As shown in Figure 43, there is a satisfactory coincidence between both the amplitude of warming and the depth of perturbed temperatures. The “left-over” temperature residuals, calculated as the difference between reduced and the synthetic best-fit POM–SAT temperature, does not exceed ⫾0.1 K below 100 m depth and reach 0.5 K in the uppermost part of the borehole. In most cases POM coupled with the SAT measurements explains 80–90% of the transient borehole temperature signal (Harris and Chapman, 1997; Bodri et al., 2001). Larger “left-overs” were obtained, e.g. during the POM estimations from a suite of Cuban boreholes (Bodri and Cermak, 2001), where coupled POM–SAT data explained not more than 50–60% of the transient borehole temperature signal. This indicates that for definite sites, at least some portion of the borehole temperatures cannot be explained by the SAT origin and reflects also specific terrain effects. Larger magnitude of the “left-overs” in the uppermost part of the borehole Hearst can likely be attributed to the local different impact of deforestation detected by Wang et al. (1992) at the Hearst and Kapuskasing sites. Essential requirements for the correct POM determination are: (1) the pure conductive regime in the subsurface and (2) the persistence of the land–atmosphere boundary layer conditions, thus a “constant” SAT–GST coupling mode. As known, the process of the heat exchange at the land surface is a complex function of the coupled atmospheric–plant–soil interactions; thus, in principle the response of the land surface to the atmospheric forcing may be time-dependent even at the annual and longer scales of aggregation. Drastic changes in the near-surface hydrology (evaporation and transpiration system), albedo,5 and even surface roughness change that accompanies extensive forest clearing, all have significant impact on the ground–air temperature coupling and therefore on the POM estimate. These problems will be discussed in the next section. 2.6 Ground–Air Temperature Coupling: Effect of Various Environmental Changes 2.6.1 Background The above-mentioned investigations by Baker and Ruschy (1993), Putnam and Chapman (1996), Gosnold et al. (1997), and Harris and Gosnold (1999) have given the confidence that it seems reasonable to view borehole temperatures as the filtered versions of the 5 Albedo is an important concept in climatology and represents a dimensionless measure of the surface/body reflectivity. It may be also expressed as a percentage from 0 to 100% and is determined as the ratio of total electromagnetic radiation reflected to the total amount incident upon it. The average albedo of the Earth is about 30%.
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surface air temperature (SAT). Modeling of the GST–SAT coupling by González-Rouco et al. (2003, 2006) using surrogate SAT simulations have shown that at long timescales the GST represents a good SAT indicator, and their variations practically repeat each other (for details see Section 2.4.4). However, observations do not support this conclusion unconditionally and at all timescales. Recent studies have revealed that in certain regions and under certain conditions the GST does not track accurately the SAT changes, especially at the short timescales. In the recent decade, the problem of the GST–SAT coupling represented the target of continuous study by several research groups. Factors affecting ground temperature can be subdivided into three general categories: (1) meteorological, (2) terrain, and (3) subsurface thermophysical properties. Large spatialscale GST differences are determined primarily by meteorological factors: solar radiation, air temperature, and precipitation through the processes of absorption/reflection/emission of solar short-wave and/or thermal infrared radiation and conductive coupling of ground–air temperature. Except for the factors mentioned above, thermal balance in the ground surface can be affected by numerous secondary processes. Basic agreement between reconstructed GST histories and available SAT records has been documented by numerous investigations at different spatial scales all over the world (see the references above). On the other hand, a strong correlation between both signals has been questioned by Majorowicz and Skinner (1997), Majorowicz and Safanda (2005), and Mann et al. (2003), especially for the northern locations with prolonged snow cover in the winter. The latter authors have argued that in such areas ground loses significant part of the information about air cooling in the winter months because snow insulates and reflects the incoming radiation. The GST–SAT decoupling can also arise due to latent heat effects of freezing/thawing processes. The GST–SAT differences at the daily and seasonal timescales are well documented. Except for the influences mentioned above, the oneby-one coupling between the GST and SAT can be also affected by such processes as the partitioning of moisture content between infiltration/evaporation/runoff, the biological processes, e.g. seasonal vegetation changes, chemical weathering and other long-term land surface changes, and other factors that are not directly connected to the climate. The summary of all processes creates the heat flux at the ground surface and thus affects the GST–SAT coupling. The investigations of the ground–air temperature correlation are performed in two main related and/or complementary directions: (1) Empirical site-specific observations of the GST–SAT coupling at specific locations using monitoring of the air/subsurface temperatures and other meteorological conditions. A comparison of soil and air temperatures provides a direct test of details of their coupling at shorter timescales (from daily to annual). (2) Development of numerical models to simulate both short- and long-scale active processes at the level of air–ground interaction and in the subsurface. (3) Collection of high-quality measurement data. The International Heat Flow Commission global geothermal data set (www.geo.lsa.umich.edu/IHFC) contains over 10 000 worldwide measured borehole temperature logs. GST reconstructions inferred from these data can be compared with the SAT measurements as well as with proxy sources available in the same locations during periods of overlap.
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Despite that studies enumerated above represent different spatial and/or temporal scales, they complement each other. Empirical correlations established by comparison of the meteorological and geothermal data provide an experimental basis that could be simulated by numerical models primarily concentrated on the physics of various near-surface processes. The investigations by Zhang et al. (2001) represent typical example of the latter-kind research. The authors have examined records of soil temperature at several depths and have compared them with the main climatic variables (air temperature, precipitation, snowfall, and snow thickness data) at Irkutsk (Russia) over the 100-year long period from 1898 to 1995. The relationship between air temperature and soil temperature was proved to be so complex that, using the words by the authors, “changes in air temperature alone cannot explain the changes in soil temperatures in this region”. This research has captured almost all important sources of uncertainties that subsurface temperatures could contain. One of the surprising observations was, e.g. that summer soil temperatures decreased by up to 4°C while summer air temperatures slightly increased. In other cases, when winter air temperatures have oscillated in the narrow range from 4 to 6°C, the rise of soil temperatures was even higher and reached as much as 9°C. Possible explanations for these phenomena suggested by the authors have included: (1) an increase in summer rainfall and (2) an increase in early winter snowfall coupled with an earlier increase in spring snow melt, respectively. The authors have concluded that the changes in soil temperature represent a combined complex output of the SAT and precipitation variations, especially of the snowfall and snow cover on the ground surface, and have warned that “when changes in soil temperature are used as the evidence of climatic warming, caution is required”. They also emphasized that revealed surface warming of permafrost at high latitudes and subsurface ground warming in wide areas elsewhere in the world may be misleading and/or occasional because air temperature alone cannot explain such ground warming. Similar studies by Baker and Ruschy (1993) and Putnam and Chapman (1996) have detected an air–soil temperature offset, when the ground was generally warmer by 1–3 K as well as the seasonal differences in the detected offset. These and other works on this topic have attracted attention for the possible serious shortcomings that the GST histories inferred from borehole temperature logs may contain. The next sections are devoted to the detailed discussion of this problem. 2.6.2 Snow cover and ground freezing Winter snowfall as well as seasonal freezing and thawing cycles of soil can strongly influence the thermal and hydrological characteristics of the uppermost ground layers. Impact of these processes on the surface energy and moisture balance at least on the short scales may be quite serious. Latent heat exchanges at the ground surface and snow cover insulates it from air temperature variations. Because the thermal conductivity of frozen soil is larger compared to an unfrozen state, freezing significantly increase the soil heat flow.
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Simultaneously it reduces hydraulic conductivity thus decreasing infiltration that can lead both to the more runoff and/or higher uppermost soil moisture content caused by restricted drainage (Williams and Smith, 1989). Traditionally, investigations of seasonal freeze/thaw oscillations are performed by in situ measurements and numerical modeling of the ground–air temperature coupling, and thus reflect mainly site-specific and short timescale features of the process (Beltrami, 2001a; Schmidt et al., 2001). The effort to extend existing results to broader spatial regions and to investigate how precisely the GST and SAT signals track each other on the seasonal scale was undertaken in the work by Gosnold et al. (1997). The authors compared the GST record with the air temperatures along transect of the Northern Plains between southern Manitoba and northern Texas (approximately 33–49°N) and examined the nature of the ground–air coupling. Flat topography and geology of this area ensured favorable conditions for borehole temperature reconstruction free of potential topographic disturbances, microclimate, and groundwater effects. Criteria for the borehole screening also included surfaces as uncultivated grassland, shale bedrock, and sites remote from the regions of intensive anthropogenic activity that could result in transient variations of microclimate. For the first test the set of 29 boreholes was selected. The GST reconstructions were performed using FSI method. All obtained GST histories indicated prominent warming trend over the last century. Its amount depended on the latitude; greater warming was detected for the northernmost boreholes. The comparison of the GST histories and SAT was performed using data from 55 stations of the United States Historical Climatology Network (U.S.HCN; http://cdiac.esd.ornl.gov/r3d/ushcn/ushcn.html) situated in the same region. The HCN SAT data series are approximately century long and extend to at least 1994. The latest dates of borehole logging were 1994 and/or 1995. Similarly to the GST reconstructions the HCN temperature data have shown warming during the past century and strong latitudinal trend of its amount. Comparison of both datasets revealed coincidence between amplitude of GST and SAT warming south of about 45°N. On the other hand, the GST reconstructions have shown much stronger warming north of this latitude. The authors have performed modeling of the GST–SAT coupling by repeated calculations and used more than 100-year long SAT signal as a forcing to the 2-D conduction in the subsurface. The FSI of the generated synthetic T–z profiles has given an amount of GST warming similar to the temperature change determined by regression of the SAT records, and thus corroborated the one-by-one coupling between the ground and air temperatures under pure conductive regime of the heat transfer. To interpret obtained inconsistency of the GST and SAT north of the 45°N latitude Gosnold et al. (1997) have tested the data from a network of automated weather stations situated in the investigated area and the results of continuous monitoring of the SAT and soil temperatures at 10 cm depth at automated weather stations installed at three locations with different latitudes at Texas (33.1°N), South Dakota (43.7°N), and Manitoba (49.6°N). The results of this monitoring experiment have shown that the mean annual soil–air temperature differences arise primarily during the separation of both temperatures in winter. This conclusion can be illustrated with the time series of temperatures recorded during similar monitoring experiment that was carried out by the Research Group of the Geophysical Institute of the Czech Academy of Sciences at the microclimate station Prague-Sporilov, the Czech Republic (50.04°N, 14.48°E, 274 m asl). The monitoring has
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been running continuously since the summer of 2002. Four different surface types were investigated: bare soil, sand, grass, and asphalt. Air temperatures at 5 and 200 cm above the surface as well as the soil temperature at depth levels of 2, 5, 10, 20, and 50 cm were recorded at 5 min intervals. The every 3-year (2003–2005) air temperature averages were surface dependent, but appeared lower than the soil temperature means for all four types of the surface. Thus, the differences between air temperature and soil at 2 cm depth amounted to 1.4–1.6 K, 1.8–2.0 K, 0.2–0.4 K, and 4.1–4.8 K for bare soil, sand, grass, and asphalt, respectively. This result hints that on the annual scale the soil is warmer than the air and corroborates similar observations mentioned above by Baker and Ruschy (1993) and Putnam and Chapman (1996) who have detected that the ground is generally warmer than the air by 1–3 K. The inter-annual variability of measured in Prague microclimatic station difference is also surface type dependent and ranges within the first tenths of degree Kelvin. Figure 44 (See Plate 1 of Colour Plate Section) shows temperature variations for some shallow sensors in the Prague-Sporilov hole during the first quarter of the year 2005. It illustrates well the influence of the snow cover on the GST–SAT coupling. As seen, the magnitude of the GST–SAT difference exhibits significant variations. Subsurface heat conduction as well as the factors connected to the movements and/or diffusion of air and/or moisture masses (wind, evaporation/transpiration, vertical soaking of soil moisture, and precipitation) tend to equalize air and soil temperatures. Thus, soil temperatures generally follow the air temperature course when average SAT is above 0°C. The one-byone GST–SAT coupling violates below zero temperatures in the presence of snow cover, because it insulates the ground surface and reduces heat loss (the condition at the measurement site was not enough cold for the soil freezing). It is noticeable that perfect coupling is restored almost immediately after snow cover was thawed (see, e.g. time interval between February 1 and 15). Similar monitoring experiment was performed at the station Potucky (the Czech Republic 50.43°N, 12.78°E, 864 m asl). It is situated in the Ore Mts. forming the natural border between North Bohemia and Germany. The suite of boreholes is located on small territory in the close vicinity of the forested area of coniferous woods. The subsurface temperature monitoring at several shallow depths began in 2003 (for details see Section 4.2, Chapter 4). Figure 45 shows results obtained during autumn 2003 to spring 2004. Temperature was recorded at 2 cm depth and 5 cm height above ground surface to detect the effect of snow cover on shallow subsurface temperatures. The record completely corroborates the results of the Prague-Sporilov monitoring. The coupling of the temperatures is almost perfect in fall and spring and breaks down during most of the winter. The presence of the snow cover in the 2003–2004 winter and absence of really cold temperatures at Potucky station prevented occurrence of soil freezing. Thus, the winter decoupling of the GST–SAT that is seen in Figures 44 and 45 can be attributed exclusively to an influence of the snow cover. Smerdon et al. (2004, 2006) have generalized results of above-cited and similar monitoring experiments. Except for the Czech records mentioned above, the authors have used temperature time series measured during monitoring experiments at Fargo (North Dakota), Cape Henlopen State Park (Delaware), and Cape Hatteras National Seashore (North Carolina). All sites represent different kinds of subsurface strata and/or climatic settings located within the mid-latitude zone from 35 to 50°N, and thus can be used also for the spatial decisions. Similarly to the Czech records, the North American time series
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Fig. 44. Time series of air (at the height 2 m) and soil temperatures (at 2 cm depth) recorded under different surfaces at Prague-Sporilov station. Soil temperatures follow SAT at temperature above 0°C, but are decoupled when the surface is covered by snow. (See Plate 1 of Colour Plate Section).
Fig. 45. Time series of air (at 5 cm above surface) and soil (at 2 cm depth) temperatures recorded at Potucky microclimatic station during the 2003–2004 winter.
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represent several years of simultaneous air and soil temperature monitoring at different heights/depths, and are particularly suitable to reveal the differences between annual GST and SAT signals. Thorough examination of the records has shown that on the annual scale GST signal (even somewhat attenuated and insignificantly phase shifted) follows well the SAT variations. The slight differences between annual GST and SAT signals may occur in both winter and summer seasons. Their amount depends on the site location and its climate as well as on the terrain characteristics. Thus, the study by Smerdon et al. (2004) has demonstrated that the GST–SAT decoupling at Fargo occurs mainly during the winter, whereas at Capes Henlopen and Hatteras observed attenuation of the GST signal has taken place during the summer season. The seasonal partitioning of the GST–SAT decoupling is caused mainly by the corresponding partition of the summer precipitation and snow. While the Fargo location is characterized by the modest rainfall and significant amount of snow, the Cape Henlopen and Hatteras stations have negligible or no snowfall. Similarly to the Czech monitoring results, the North American stations inferred influence of the snow cover on the GST–SAT coupling. According to the results by Smerdon et al. (2004, 2006), in all investigated locations snow cover has affected heat transfer in the surface in such a manner that mean daily soil temperature under snow cover was warmer relative to the SAT. The experiments described above have also detected finer features of the GST–SAT decoupling during cold season, e.g. dependence of the temperature of the soil covered by snow on the thickness of snow layer, the snow quality, both air and ground temperatures before a snowfall, the presence of the vegetation cover as well as the thermophysical properties of the soil. Effect of the snow cover thickness is only of secondary importance. Numerical modeling by Gosnold et al. (1997) of the GST–SAT tracking in the presence of the snow cover has detected that the winter soil temperatures are more sensitive to the presence or absence of snow rather than to the variations in its thickness. Thus, the exact amount of the winter snowfall is not likely a decisive factor of the GST–SAT coupling during the winter. Snow pack control on the soil–air temperature tracking in other seasons was studied in the work by Grundstein et al. (2005). Annual coupling of the GST and SAT was investigated using the soil–air temperature measurements performed during 1990–2002 at Fargo (North Dakota) as well as numerical simulations based on the snow pack physical model. In accordance with the conclusions of the previously discussed studies, Grundstein et al.’s research has corroborated that the GST–SAT decoupling in the investigated location appears to be visible only during winters when dense, thick snow cover, and its long persistence cause strong insulation of the ground. In the late autumn and/or early spring the snow is thin and has a low density. It gives imperceptible thermal insulation and does not break one-by-one GST–SAT coupling. The Czech monitoring experiments described above have supported the influence of the type of surface on the ground–air temperature tracking. Thus, the grasslands preserve the snow cover longer than the bare surfaces, where the snow is not isolated from the ground heat flow. Combining the snow cover with the grass provides better insulation and the temperature under such surface remains above zero (see Section 2.6.3). The rate of snow melting was proven to be also surface dependent. The thickest snow cover is characteristic for the grass and the thinnest can be found in asphalt. The monitoring results mentioned above are more representative of the mid-latitude seasonal GST–SAT relationships. As at the Prague-Sporilov station, winter temperatures
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at the investigated locations are generally not low enough for the soil freezing. At highlatitude regions where SAT temperature for a long time remains far below 0°C, the effect of freezing may even surpass the influence of the snow cover, Gosnold et al. (1997) have interpreted systematic northward increase of GST–SAT difference in the North America, which is revealed in their work, as the result of the northward increase in the duration of snow cover and often occurrence of the ground freezing. While on frosty days the air temperature may be significantly negative, latent heat released during freezing of soil moisture makes soil temperature remain at 0°C level until the whole moisture content has frozen. This is so-called “zero-curtain effect” that is caused by transfer of latent heat during freezing and thawing of water contained in the rock or soil. The degree of saturation and the thickness of the saturated soil represent the main factors controlling the duration of freezing process. Since near-surface soils often freeze before snow covers the land surface and durable soil freezing (sometimes for weeks to months) is a more often phenomenon than continuous snow cover, the freezing effect appears to be of greater influence on the GST–SAT decoupling. According to the observations by Gosnold et al. (1997), the onset of the strong soil–air temperature decoupling does not always correlate with the variations of snow cover; however, in all cases it coincides with the beginning of the soil moisture freezing. Recent results of the continuous temperature monitoring at the Czech micrometeorological stations confirmed conclusions by Gosnold et al. (1997). Effect of the soil freeze/thaw events on the GST is reflected in the early section of the time series, presented in Figure 46. This diagram displays the air temperatures measured at 5 cm above the surface and the ground temperatures registered at depths of 2, 10, and 50 cm at Potucky station. The end of October and especially the beginning of December were characterized by the absence of snow and by the two episodes of the sharp fall of the air temperature well below 0°C. In the time intervals of strong air temperature decrease ground temperature at shallow depths of 2 and 10 cm have remained almost constant and close to 0°C and 1–1.5°C, respectively, illustrating the above-mentioned “zerocurtain effect” that occurs mainly due to latent heat released from the freezing of soil.
Fig. 46. Time series of air (at 5 cm height) and soil temperature changes at 2, 10, and 50 cm depth at Potucky station during October–December 2003.
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Fig. 47. Behavior of the soil temperature at different depth levels below sand and grass surfaces at Prague-Sporilov station during freezing cycles of February 2006 (See Plate 2 of Colour Plate Section).
The data indicate that the soil freezing at Potucky station during October–December 2003 did not actually achieve even 10 cm depth. The ground temperature at the uppermost “active” layer is a complex result of the heat transfer from the frozen upper and undisturbed lower layer as well as the heat release from advancing freezing front. That time there was no snow cover at the station; thus, time series in Figure 46 reflect pure influence of the freeze/thaw processes on the GST. Irregular monthly air surface temperature variations are significantly attenuated at the depth of 50 cm and occur with time delay of days. Temperatures at that depth are lower than the highest positive air temperatures by approximately 3–4 K and may be higher than the lowest negative air temperatures by 8–10 K. Figure 47 (See Plate 2 of Colour Plate Section) shows the behavior of the ground temperature under sand and grass surfaces during February 2006 at the Prague-Sporilov station. Due to heavy frosts and absence of snow in January, the subsurface temperature below both surfaces has dropped below the freezing point. Temperature at 20 cm depth was quite stable at 0°C and ⫺0.3°C under the grass and the sand, respectively. The higher temperature under the grass occurs due to an insulation effect of the vegetation cover, which is mentioned above. In the first half of February, when the SAT was relatively low slightly oscillating around zero, the GST under both surfaces remained practically constant. Its sharp decrease between 2 and 5 cm depths was observed only between February 14 and 15 and was given by a similar drop of the SAT. During the second half of February, when the air temperature increased above zero, the subsurface temperature change under the sand surface generally repeated the SAT course. However, the phase changes of soil water substantially reduced the GST variations. The surface temperature variations vanished at the interface of the frozen and thawed soil layers that remained at zero temperature. Temperature at 20 cm depth was practically constant, which hints that all heat coming from the surface was spent in melting the soil water between 10 and 20 cm (Figure 47, left). Under the grass, where insulation of the surface and low thermal diffusivity of the soil slowed down the penetration of the surface warming, at all measured depth soil temperature remained close to 0°C. (Figure 47, right).
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It should be emphasized that the effect of soil freeze/thaw cycles on the GST–SAT decoupling is only of seasonal importance. On the longer timescales it probably does not violate the air–ground temperature correlation in such a strong manner as it seems at a first glance. The widespread investigations of the timing, duration, and areal extent of this phenomenon by Zhang and Armstrong (2001) over the contiguous USA territory using passive microwave remote sensing revealed high variability of the freeze/thaw variations. The onset of soil freeze occurred generally in October–November, while its termination was in March–April. However, it does not mean that the near-surface layer was continuously frozen during this period. Measurements by Zhang and Armstrong (2001) have shown that the number of days with real surface soil freezing varied from several days to as long as 5 months. Majority of the regions experienced less than 60 days of the actual freezing and their occurrence was quite sporadic. Because of the combined effects of the snow cover and latent heat released by freezing, the soil moisture significantly changes with time; thus, this kind of disturbance vanishes during averaging over large temporal/spatial scales and probably cannot create a false systematic secular trend in the GST. Some recent critiques of GST reconstructions were presented in the works by Mann and Schmidt (2003) and Mann et al. (2003). These authors have compared the SAT, GST, and snow cover trends simulated for the latter half of the twentieth century for terrestrial regions of the Northern Hemisphere by means of the GISS ModelE kind of the GCM family, similar to the one described in Section 2.4.4 of this chapter, and argued that the interpretations of the past SAT trends using GST reconstructions could be significantly biased by an influence of the snow cover during cold season. According to the calculations of the above authors, air temperatures have a dominant influence on ground temperatures only during warm season, while during cold period snow cover has significantly insulated the ground surface from the SAT changes. This process tends to exaggerate the role of warm season, thus providing a source of possible bias when comparing GST and SAT series (see also examples in Section 3.3, Chapter 3). This conclusion was rejected in the works by Smerdon et al. (2004) and especially by Chapman et al. (2004), who have argued that the statement by Mann and Schmidt (2003) completely contradicts with the results of their monitoring experiments. According to Chapman et al. (2004), the source of discrepancy is an artificial sharp division of the years and corresponding temperatures into cold and warm season performed in the work by Mann and Schmidt (2003), while the nature of the conduction process makes the ground temperatures sensitive to continuous rather than to rapid or even seasonal variations. Separated seasonal anomalies are thus inappropriate for detection of the GST–SAT coupling on the long scales that are used in the climatologic studies. An analysis by Chapman et al. (2004) has proved that the GST–SAT tracking is almost perfect (correlation coefficient equals to 0.97), when temperatures are assessed on at least annual scale and thus summarize/compensate both summer and winter effects. This result is confirmed by the recent millennium long simulation of ground temperatures performed in the works by González-Rouco et al. (2003, 2006), who used simulated subsurface T–z profiles forced by the GCM as a substitute of the real climate and applied inversion technique to reconstruct GST histories from the calculated profiles (for details see Section 2.4.4 of this chapter). Modeling results of these authors have proved the fact that the air and ground temperature variations are practically identical on centennial and longer timescales.
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2.6.3 Effect of precipitation In meteorology, precipitation means any form of water, whether liquid or solid, that falls from the clouds and reaches the ground. Precipitation is a major component of the hydrologic cycle, and is responsible for depositing most of the fresh water on the Earth. It also represents the main component of weather. Precipitation occurs in a variety of forms, however, generally as rain and snow. An influence of the winter snow cover on the GST–SAT tracking has been discussed above. What about an influence of the summer rains? Summer soil temperature is controlled by the combined effect of air temperature variations and soil moisture content. An increase in rainfall during summer season would increase both the surface wetness and the soil moisture. This will result in more energy consumption for evaporation and thus cause cooling of the ground surface and soil. It is so-called soil moisture feedback (Yasunari et al., 1991; Matsuyama and Masuda, 1998). In principle, soil moisture feedback mechanism may explain soil cooling during summer, when air temperatures increase. Zhang et al. (2001) have detected clear negative correlation between monthly precipitation and soil temperature at 40 cm depth (greater monthly precipitation with lower soil temperature, and vice versa) in the 100-year long (1980–1990) meteorological time series measured at Irkutsk, Russia. Existing monitoring experiments as well as the above-described numerical simulation by Mann and Schmidt (2003), Mann et al. (2003) have shown that anyhow the air temperatures have a dominant influence on ground temperatures during the warm season. Thus, revealed by the same monitoring experiments possibility of the GST–SAT decoupling during warm periods of the year likely represents the far weaker effect than the decoupling of both temperatures in the cold season. While winter snowfall as well as seasonal freezing and thawing cycles are the main reasons responsible for the breaking of the one-by-one GST–SAT tracking during cold season, the rainfall can produce definite air–ground temperature differences at warm conditions. Precipitation is one of the main factors determining the subsurface thermal regime because it affects the amount of soil moisture and therefore the amount of energy removed from the soil by latent6 and sensible7 heat fluxes. Figure 48 illustrates the types of energy balance at dry and moist ground surfaces. Expression Q* ⫽ H ⫹ LE ⫹ G combines the components of the total heat balance in the air–ground system, where Q* is available net radiation, H the sensible heat, LE the latent heat, and G the subsurface (ground) heat. The latter three variables represent the major categories of the total energy use. Sensible heat is strongly conditioned by the temperature gradient between ground surface and air, while the ground heat flux depends on a similar gradient between the surface and the subsurface. When the evaporation of the water takes place, the positive latent heat flux (LE⫹) occurs in the ground surface. This means that the surface loses energy to the air above. Thus, evaporation is a cooling process for the ground surface. 6
Latent heat flux is the flux of heat from the Earth’s surface to the atmosphere that is associated with the change of states or phase, e.g. with evaporation of water at the surface. Term “latent” is used because this energy does not increase the temperature of water molecules and is only stored in molecules to be released later during the condensation process. 7 Sensible heat is the heat energy transferred between the Earth’s surface and air when there is a temperature difference between them. According to the direction of the temperature gradient, this flux can warm the ground or air.
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Fig. 48. Types of energy balance at the ground surface during warm period.
Various processes operating in the vicinity of the ground–air boundary influence the heat flux balance that cause corresponding changes in both the SAT and GST. Thus, in some cases the GST may reflect the energy balance at the Earth’s surface, rather than the SAT variations. Two of the diagrams in Figure 48 illustrate the differences between heat fluxes for dry and moist surfaces occurring in the daytime. In both cases equal amounts of incoming heat Q* are conducted down to the subsurface. No latent heat transfer occurs without available moisture content, which means the absence of the latent flux from the dry surface. Most of the energy Q* is transferred by sensible flux (H⫹) that results in warmer air temperatures above dry surface. At moist surface the share of sensible heat is lower, while significant amount of the available radiant energy is used for evaporation of surface water, thus creating relatively cooler air than that above dry soil. It should be mentioned that latent heat flux always has priority. If moisture is available for evaporation, this process (LE⫹) takes preference over warming of the air (H⫹) and /or warming of the ground (G⫹). At night the processes reverse. Because the thermophysical properties of the subsurface rock, such as thermal conductivity and heat capacity, depend on the water content, the rainfall can influence not only the energy balance of the ground surface–air system, but also thermophysical and/or hydrological characteristics of the ground. Regions with low porosity and permeability will likely not be significantly affected, while less consolidated medium will experience more pronounced changes. Primarily influence of the precipitation on the GST–SAT coupling occurs on the very short timescales (directly during and after rain events) through, e.g. advective transport of heat by falling water that may significantly contribute to the development of shallow subsurface temperatures. For example, boreal forest sites in interior Alaska and NW Canada exhibited rapid but short soil warming of several degrees in response to summer precipitation events (Hinkel et al., 1997). Figure 49 displays temperature difference between the ground surface and 2 cm depth measured in dry and rainy periods at Prague-Sporilov. During 10-day interval with no rain the differences have shown quasi-periodic oscillations with maximum positive values in the daytime and negative values at night (compare with Figure 40 of this chapter). The range of variations reached ⬃9 K. The temperature differences were negative after rain events both during
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Fig. 49. Time series of temperature difference between ground surface and 2 cm depth temperature at Prague-Sporilov station; comparison of rainy decade with dry period. Top panel also shows total rainfall amount.
day and at night (air temperature at wet surface is lower than that at 2 cm depth, e.g. June 30–July 2 and/or July 5–6; Figure 49, top). Its variations were significantly reduced and ranged within only ⬃3–4 K. On the other hand, evaporation proceeds relatively quickly; thus, depending on the rain strength the “dry” regime was restored 1–2 days after rainfall. The role of precipitation appears to be far more important on seasonal and/or annual scales because of its possible seasonal persistence. In the mid-latitudes snowfall and soil freezing (especially the latter process) represent generally sporadic events. As mentioned in the previous section, their effect on the GST–SAT decoupling is not perceptible already under decadal averaging. On the contrary, rainfall occurs more regularly during much of the summer and its annual distribution remains preserved for the long periods. The Prague site represents typical example of the seasonal timing of precipitation. Daily precipitation at Prague has no significant linear long-term trend. However, it has revealed a certain seasonal character that was preserved for a longer time (Bodri et al., 2005); the wetter season falls during May–August period and the precipitation minimum occurs in winter. This conclusion is confirmed by the meteorological observations in the nineteenth to twentieth centuries on the monthly scale of aggregation (Figure 50). The increase in precipitation in “wet” years occurs mainly due to its significant growth in summer period, when the actual monthly amounts of precipitation can be a few times higher than the average. Prevalence of summer precipitation is a specific feature of the hydrologic cycle in the Czech Republic and is preserved for at least 180-year long period. Similar persistence of the annual distribution seems to be common feature of the precipitation in many regions. According to Lin et al. (2003), there were no significant changes in the seasonal distribution of precipitation
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Fig. 50. Averaged monthly precipitation at Prague-Ruzyne. The 2214 months between 1805 and 1989 were used for averaging. (Data source: The Global Historical Climatology Network, GHCN 1; www.worldclimate.com.)
in the USA and Canada for at least twentieth century. The influence of the precipitation on the GST–SAT relationship may be even more perceptible in the tropics, where evapotranspiration8 is potentially significant year round. Except for the cold season GST–SAT decoupling, the above-cited studies by Smerdon et al. (2004, 2006), which generalized the results of temperature monitoring at four microclimatic stations, have detected the GST–SAT discrepancies during warm period that occur as a result of the changes in surface energy balance caused by the rainfall. Precipitation spans a wide range of 52–115 cm/year at four investigated locations with significantly different amounts of the rain and snow related parts. Thus, four data sets reflect the local climate conditions that may represent a base for comparison. Figure 51 shows time series of daily averages of air temperature (at 5 cm height) and soil temperatures at 5, 100, 200 and 500 cm depth measured at station Prague-Sporilov during the “rainy” year 2000. The amount of precipitation is presented on the histogram below. Detectable high-frequency oscillations of the air temperature record in summer (Figure 51) are caused mainly by the rains that change the moisture content of the soil and correspondingly both latent and sensible heat flow at the ground surface. General influence of precipitation at short timescales is to increase latent heat flux and to decrease sensible heat flux. As seen, rainfall events are accompanied by corresponding changes of both air and ground temperatures. The main observation about summer GST–SAT interrelation is that the rainfall does not cause total decoupling of both temperat-ures similar to that occurring in the winter due to snow cover and freezing/thawing cycles. The air
8 Evapotranspiration represents the sum of evaporation and plant transpiration. The former process accounts for the movement of water to the air from the surfaces, while the latter process is responsible for the water movement within plants and for its loss through plant leaves. Types of vegetation and land use, percentage of soil cover, level of plant maturity as well as meteorological variables (solar radiation, temperature, humidity, wind) are among the factors that affect evapotranspiration.
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Fig. 51. Time series of daily averages of air temperature (5 cm height) and soil temperatures at the surface and at 5, 100, 200, and 500 cm depth measured at station Prague-Sporilov during year 2000. The histogram below shows precipitation amount.
temperature record at 5 cm height and the GST records at the air–soil interface practically repeat each other. Correlation of both temperatures amounts to 0.96. The ground temperature at 20 cm depth slightly fluctuates around air temperature. Depending on the moisture content, the differences between both temperatures may be positive or negative and reach several degrees of Celsius. It causes some offset and attenuation of the GST variations in comparison with air temperature. However, the correlation of both temperatures still remains high and equals to 0.82. This hints that in summer the GST–SAT decoupling does not appear too serious even in the years with large magnitude and high frequency of the precipitation events. Surface temperature variations are still visible at 1 m depth, where they appear as a muted version of surface temperatures. Correlation between air temperatures and temperatures at 1 m depth is 0.69. At least part of the lower correlation between SAT and ground temperatures at deeper levels can be attributed to the phase lag of the GST and SAT occurring during depth propagation of the surface temperature signal rather than to the precipitation influence. Recently, Rybski et al. (2003) have proposed the powerful method for the phase synchronization in different meteorological records. This method can be applied to complex signals and enables to reveal relations between two records by focusing on the phases of the fluctuations in each record. The application of this method to above time series of the SAT and GST at 1 m depth has shown that (1) non-shifted case does not correspond to the best synchronization and (2) best phase synchronization can be found only for a certain time lag of approximately 7 days. When time series were delayed by this interval obtained correlation increased to
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0.79. An approximate value of phase delay t0 can be estimated from the expression for the characteristic time of the thermal relaxation t0⬃L2/k, where L is the characteristic length and k the thermal diffusivity. When k equals to 10⫺6 m2/s, for a 1 m depth t0 reaches approximately 11–12 days; thus, it is comparable with the best phase calculated by the phase synchronization technique. Surface temperature oscillations in Figure 51 are practically imperceptible at 2 m and deeper levels. Ground temperatures below 1 m depth are steadily lower than air temperatures from May to September and are higher than the air temperatures from November to February. At shallow depths variations of the GST around SAT are more erratic. At the shallow subsurface soil temperatures remain steadily higher than air temperatures only during November–February (Figure 51). During most of the year shallow GST irregularly oscillates above and below air temperature depending on the temporal pattern of the rainfall. These oscillations likely will disappear under long-scale averaging. Investigated in the work by Smerdon et al. (2006) stations Cape Henlopen (Delaware) and/or Cape Hatteras (North Carolina) are considerably warmer sites with over twice as much mean annual precipitation as Prague. They exhibit even larger oscillations of the soil temperatures around the air temperatures than the Prague-Sporilov station (Smerdon et al., 2004, 2006). However, irregular interchange of these differences up and down of the air temperature course can scarcely represent the serious failure of the hypothesis about one-by-one GST–SAT coupling on the long-term scales. Smerdon et al. (2006) performed the quantification of the influence of meteorological conditions on the GST–SAT difference by a multivariate regression technique. The analysis of these authors has shown that (1) the differences between ground and air temperatures can be explained in terms of seasonal changes of meteorological variables and (2) the annual GST–SAT differences (GST–SAT) can be closely estimated by using of the meteorological information alone. The authors suggested the expression including two predictors GST⫺SAT ⫽ ( P ⫻ SATs ) ⫹ (SD ⫻ SATw ) ⫹ ,
(33)
where (, ) are regression coefficients, P the cumulative precipitation in months without snow, SD the total number of days with snow cover of more than 2.5 cm, and SATs and SATw are mean air surface temperatures during June, July, and August (summer) as well as during December, January, and February (winter), respectively. Term is associated with the white noise characteristics. For example, at station Fargo mean annual snowfall and rain precipitation amount as well as the number of days with snow cover equal to 123 cm, 52 cm, and 96 days, respectively. For the 10-year long monitoring series at this station estimations by Smerdon et al. (2006) have given ⫽ 0.39 ⫾ 0.11 and ⫽⫺1.06 ⫾ 0.11 (for standardized values of variables) with significance levels of 1.0 ⫻ 10⫺2 and 3.3 ⫻ 10⫺5, respectively. Common use of two predictors included in Eq. (33) explains 91% of the total variance of annual GST–SAT differences. Values of regression coefficients and depend on the local climatic conditions and thus should be determined for each site separately. For example, at Fargo location, where mean annual snowfall is four times larger than at Prague or at Cape Henlopen, the SD represents more important influence than the rainfall amount. This quantity alone explains 67% of the variance in the GST attenuation. The use of only SD and SATw product can explain 77% of the variance in the GST attenuation.
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Alternative correlation analysis using only P and SATs explains only very little part of the variance in the annual GST–SAT attenuation and does not bear statistical significance. As shown by numerous trial runs, expression (33) is the best possible one. Other combination/separation of the quantities and/or addition of other regression terms do not significantly improve prediction results. Detected GST–SAT amplitude decoupling during summer and/or winter can be used to describe quantitatively their tracking on the annual scale. Summer attenuation will decrease mean annual GST relative to the SAT, while winter attenuation will have an opposite effect. The difference between means of the annual SAT signal and the same signal attenuated and/or strengthened in its maximum or minimum can be expressed as GSTsp ⫺ SATsp GSTwp ⫺ SATwp GSTa ⫺ SATa ⫽ ⫹ , 2 2
(34)
where GSTa and SATa are annual means of the GST and SAT, index “p” means the peak amplitudes, and indices “s” and “w” represent the summer and the winter, respectively. Including in this equation regression coefficients from Eq. (33), one can transform it into GSTa ⫺ SATa ⫽⫺ (SATA ⫻ GST⫺SAT ) ⫹ 冷 冨 (SATA ⫻ GST⫺SAT ),
(35)
where SATA is the year-to-year amplitude of the annual SAT signal. Observations by Smerdon et al. (2006) have revealed 1.5–4.5 K GST–SAT differences at Fargo (North Dakota) in 1981–1989 and 1993–1999 periods. Their variations were erratic and did not exhibit any significant linear trend for approximately two decades of observations. Correlation between differences observed and calculated by expression (35) was 0.86 (significant at the 0.0001 probability level). It was shown that calculated differences explain 73% of the variance in the observed values. The above estimation has supported the hypothesis that meteorological conditions are the dominant causes for the occurrence of the GST–SAT decoupling and that the above empirical regressions represent a useful tool for the investigation of the GST–SAT differences on the longer scales. Application of the long meteorological records to the multivariate expressions (33)–(35) provides the possibility of the GST–SAT calculation on decadal to centennial timescales. This idea was realized in the work by Pollack et al. (2005) (see Section 2.6.4). While most of the relationships between ground temperature and meteorological variables generally represent the multivariate empirical regressions (like abovedescribed Eq. (33)) and are not focused on the underlying physical processes, England et al. (2003) and Lin et al. (2003) have worked out numerical model that captures effects of rainfall on the GST temperature changes and provides controlled reliable simulations based on the quantitative description of the coupled moisture and energy transport through the air–ground interface. Their methodology uses the Land Surface Process (LSP) model that takes into account vertical energy and moisture transport in soil and vegetation. Its extensive discussion is presented in the works by England (1990),
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Liou and England (1996), Judge et al. (2003), and Lin et al. (2003). Extensive calibration and validation of this model was performed through numerical field experiments (Judge et al., 1999, 2001). The LSP comprises relatively complex and detailed description of the microphysical ground–atmosphere processes using multilayered soil and vegetation. The temperature and moisture profiles of the ground and canopy are determined by the coupled energy and moisture transport based on the changes in infiltration, evaporation, transpiration, and recharge fluxes over time. Infiltration is a positive term (water at the ground surface enters the soil) governed by the hydrological properties of the subsurface and by the difference between total precipitation and its share captured by the canopy. Effect of the runoff is generally not taken into account. It occurs when the precipitation rate exceeds the rate of infiltration, while most of the simulations do not include such extreme precipitation events. Because of an absence of runoff and because surface vegetation characteristics remained constant on the multiyear timescale, all changes in infiltration in the LSP model were caused exclusively by the changes in precipitation characteristics. Both evaporation and transpiration are negative terms that remove moisture from the soil and/or surface canopy by transport of vapor into the atmosphere. Finally, recharge fluxes occur due to the fluid flow at the water table boundary. Depending on the flow direction they can be positive or negative. It should be mentioned that the annual sum of recharge fluxes is small; thus, this latter factor is not as significant as the former processes. In the works by England et al. (2003) and Lin et al. (2003) the 1-D model is developed for the multilayered soil with a two-layer vegetative canopy (grass and thatch) at the surface of the hypothetical location characteristic for the prairie grassland in the state of Kansas, belonging to the Great Plains area of the USA. This environment appears to be the most suitable to distinguish the influence of precipitation from other factors, because it is practically not subjected to snowfall and/or freezing and thus can illustrate well the pure effect of rainfall. Other advantages represent a good knowledge of the soil structure and an abundance of the meteorological data for the credible model forcing. Numerical simulations of the microclimatic ground–air interactions were performed over decadal timescales with minute resolution; thus, the authors have investigated both short- and long-term effect of precipitation on the GST changes. Thermophysical and hydrological properties of the subsurface layers in LSP model vary not only with depth, but also with the temperature and moisture content. The model forcing realizes from the surface and includes down-welling radiation, SAT, humidity, wind, cloudiness, and precipitation. An evaluation of the precipitation changes on the GST was a central goal of above researches. The study has concentrated on four primary characteristics of precipitation: its amount, intensity, frequency, and timing that were considered on the wide range of scales from diurnal to decadal. The SAT and precipitation data for model forcing were taken from the database of the U.S. National Climatic Data Center (NCDC; www.ncdc.noaa.gov). Meteorological time series have corresponded to the above-mentioned southern prairies region of Kansas. Results of numerical experiments have proved that independently of other meteorological processes changes in various rainfall characteristics alone in principle can affect the GST temperature. The range for possible changes in precipitation characteristics was chosen in such a manner that simulation results were able to put upper limits on the
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expectable GST changes introduced by precipitation. The study has revealed the next principal influences of the precipitation on the GST change: (1) To investigate the influence of the precipitation amount on the GST the baseline precipitation distribution was multiplied by factors from 0.5 to 2.0. Increase in the amount of daily precipitation manifests itself in the corresponding cooling and wetting of the ground and reduces mean annual GST. The reason is that enhanced precipitation intensity increases the amount of retained moisture and prolongs the time of the water storage in the ground. Both processes cause an increase of the average annual latent heat flux and a corresponding decrease in the sensible flux. Decrease of the precipitation amount and intensity has the reverse effect and causes warming in the ground. The 100% increase in the amount of daily precipitation in comparison with an average baseline value for the Great Plains area may cause annual GST cooling of ⬃0.5K, while its 50% decrease has resulted in the 0.6K warming. (2) To investigate an influence of the precipitation intensity on the GST its distribution was filtered to either decrease rate of occurrence and increase intensity (increasing variance) or to decrease intensity and increase the frequency of rainfall (decreasing variance). The possibilities varied from the constant drizzle all over the year (standard deviation equals to 0 mm) to the weekly precipitation amount that has fallen during one year (s.d. ⫽ 8.2 mm in comparison to the 6.2 mm for baseline). In all cases an amount of annual precipitation remained constant. Decreasing frequency and increasing intensity of the daily precipitation results in the cooling of the ground and increasing of the soil moisture content. On the contrary, increasing frequency and reduced intensity leads to warming and drying of the ground. In addition, when precipitation intensity decreases, significant part of the available moisture remains at the canopy and does not penetrate into the deeper soil. This causes an increase of the latent heat at the air–surface interface, because evaporation of shallow moisture occurs more rapidly than of that stored at deeper levels. Numerical simulations have shown that the 25% increase in the precipitation variance has cooled the ground by only 0.07 K, while a similar decrease has warmed the ground by ⬃0.3 K. The factors described above thus have stronger impact on the GST than the changes in precipitation intensity. (3) Experiments with diurnal precipitation timing (e.g. daytime or nighttime) have shown that it is not significant for the appearance of the GST changes on the longer timescales. On the other hand, precipitation is not equally distributed also over the year. Similar experiments with seasonal precipitation timing revealed more noticeable relationships between annual precipitation peaks (as presented in Figure 50), seasonal changes of the solar radiation, and the SAT. When precipitation maximum coincides with the maxima of the two latter variables (e.g. in Prague occurring in July), it reduces the mean annual GST and increases the annual soil moisture content. In those locations where precipitation peak is close to the radiation minimum in January precipitation causes the warming and drying of the soil with the corresponding reduced role of the latent heat and increased sensible heat. The physics of the process is the next. As known, recharge rates reach their maximum after precipitation events in the winter, when soil moisture is high and latent heat flux is
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low. When precipitation peak occurs in cold season and thus coincides with the maximum positive recharge rates, significant part of the moisture is removed to the phreatic9 zone as positive recharge. Moisture flow to deeper layers dries the uppermost soil. According to the estimates by England et al. (2003) and Lin et al. (2003), seasonal clustering of precipitation can in principle change the GST by 0.4–0.5 K. Detected influence of the seasonal distribution of precipitation on the magnitude of energy and moisture fluxes at the surface hints that the rough modeling of the precipitation influence on the long-term GST–SAT coupling based only on annual averages may not exactly reflect the consequences of seasonal patterns. Above numerical experiments have shown that estimated maximum GST changes, caused by corresponding changes in the main characteristics of precipitation, may reach tenths of degree. Even though such magnitudes are small, potentially they are not insignificant for detection of the real amplitude of the climate signal. Resulting subsurface temperature–depth profiles have a curvature similar to that caused by the climate change (so-called “U-shapes”; see Figure 20, Chapter 2). This opens the possibility of misinterpreting both effects. At a first glance the problem appears quite serious. However, numerical experiments by England et al. (2003) and Lin et al. (2003) have been performed for the extremely wide range of precipitation characteristics to put upper limits on the possible GST changes. Applied range of precipitation changes significantly exceeded really observed characteristics; thus, calculated amount of the GST disturbance can be taken only as acceptable upper limits. Precipitation influence on the GST does not appear so serious in the real nature. Numerical experiments by England et al. (2003) suggest that much less than half of the GST warming detected for the last five centuries could be credibly attributed to the overall changes in precipitation amount or its redistribution within the year. This conclusion was supported by the Lin et al.’s (2003) estimates, who have found that the GST response for really observed precipitation changes on the long scales will be relatively low. For example, during the twentieth century precipitation has increased by only 5–10% at the territory of United States. The Intergovernmental Panel of Climate Change (IPCC; www.ipcc.ch) has reported an increase of 0.5–1% total (including snowfall) decadal increase in the mid and high latitudes of the Northern Hemisphere. Some of subtropical areas have been subjected to only 0.3–0.5% decadal decrease in precipitation. The minimal increase/decrease factor used in model simulations by Lin et al. (2003) was 25% causing approximately ⫾0.2 K GST change. It is more than twice larger than the actual precipitation increase estimated for North America and/or Northern Hemisphere. Extrapolation of the simulated GST change to the observed precipitation trends gives the values of the GST disturbance of only 0.05–0.10 K. This temperature range is approximately an order of magnitude smaller than the amount of the twentieth century warming. Similar estimates have shown that the changes in the occurrence of extreme precipitation events that were also reported by the IPCC will cause very small changes in the annual GST of the order of hundreds of degree. And finally, no significant changes in seasonal timing of precipitation were documented over at least twentieth century; thus their contribution to the long-scale GST changes appears to be negligible.
9
The phreatic zone represents permanently saturated with groundwater layers of soil or rock below the water table.
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Taken together, described monitoring and modeling results help to understand real influence of the various effects of precipitation on the GST–SAT differences on seasonal and annual scales. An extrapolation of conclusions based on short-scale observations over much longer timescales is complicated. While short-scale GST–SAT differences may achieve several degrees of Celsius with significant and irregular inter-annual variations, the amplitude of the long-term trends is typically an order of magnitude lower. Because the amplitude of inter-annual GST–SAT differences will be smoothed on the long-scale averaging, it is obvious that only secular changes in the GST–SAT differences can violate the use of the GST history reconstructions as reliable estimates of long-term SAT variations. However, because of higher magnitude and irregular inter-annual oscillation of the GST–SAT differences their more weak secular variations may be hidden by the high variability of the short-term pattern. Results of numerical modeling by Lin et al. (2003) suggest that actually observed long-scale precipitation trends can only insignificantly break the GST–SAT coupling. Total effect of the precipitation on the GST is likely incomparable with the GST and SAT changes that occurred during twentieth century. 2.6.4 Effect of surface vegetation Vegetation is the ground cover provided by plants. It may be regarded as the skin of the ground. It influences various processes in the biosphere at wide spatial and temporal scales. Besides that the vegetation regulates numerous biochemical processes (e.g. water, carbon,10 and nitrogen cycles),11 it also influences local and global energy balances that are important for the climate. In forested areas, e.g. not more than 5–20% of the shortwave solar radiation reaches the ground surface (Beltrami, 2001a; Nitoiu and Beltrami, 2005). Thus, the ground temperature exhibits weaker fluctuations in the regions with complete dense tree cover. Removing of this protection layer will be accompanied by a corresponding increase in solar radiation that reaches the ground surface and subsequent re-arrangement of all energy balance components (net short wave radiation, net long wave radiation, latent heat, sensible heat, and ground heat). Vegetation also strongly affects soil characteristics (e.g. soil volume, texture, and composition). Both processes can influence the GST–SAT coupling. Investigations of the GST–SAT coupling by Smerdon et al. (2004, 2006) comprising results of the Czech and the North American monitoring experiments have shown that the differences between soil and air temperatures arise in both winter and summer seasons. While the snow cover/soil freezing are responsible for the decoupling of winter temperatures, summer precipitation reduces soil temperatures relative to SAT through evapotranspiration process. Observations have shown that except for the influence of the summer and winter precipitation and soil freezing/thawing on the GST–SAT coupling, it depends also on the type of the land cover. The above-mentioned monitoring experiment at the Prague-Sporilov site was performed under different surface types. Measurements have detected significant influence of the surface type on the GST–SAT difference. Four types of the surface were chosen for the experiment: the bare soil, the sand, the grass, and 10 In the biosphere carbon cycle represents an exchange of carbon between living organisms and the nonliving environment. 11 The nitrogen cycle describes the transformation of nitrogen and its compounds in nature.
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the asphalt. The 3-year temperature averages indicate that the soil is warmer than the air for all surface types, but the soil (at 2 cm depth) and air (at 5 cm height above given surface) temperature difference was surface cover dependent and amounted to 1.5 K, 1.9 K, 0.3 K, and 4.4 K for the bare soil, the sand, the grass, and the asphalt, respectively. This pattern is valid also for the individual year averages. The inter-annual variability of the GST–SAT differences seems to be of the order of the first tenths of degree of Kelvin. New denser grass was seeded in spring 2004 and since that time the temperature above the grass cover appeared to be higher, probably due to decreased air circulation around the sensor that was partially protected by the grass. The highest difference for the asphalt can be explained by an extremely low albedo of this material that makes it very sensitive to incident solar radiation during the year. The GST of the asphalt in the “sunny” year 2003 was by ⬃0.7 K higher than in more “cloudy” year 2004 and 2005, whereas the air temperature was higher by less than 0.3 K. During the winter, vegetation can give a similar insulating effect as a snow cover, protecting the ground from the weather extremes that induce high rates of heat transfer from and to the atmosphere. For example, studies have shown that forest soils do not really freeze in the winter due to the buffering capacity of forests. During January–February 2006, the weather in Prague-Sporilov site was characterized by heavy frosts and absence of the snow cover (see also Section 2.6.2). As a result, temperature under all surfaces has dropped to near the freezing point. Minimum temperatures at the depth 50 cm under the bare soil, the sand, the grass, and the asphalt were ⫺0.29, ⫺0.35, 0.26, and 0.046°C, respectively. The higher temperatures under the grass are given by the insulation of the vegetation cover and those under the asphalt by the above-mentioned low albedo of this material that helped to absorb sunshine during the frosty, but sunny days. When relating the GST and SAT it is customary to assume that the soil–air temperatures coupling mode remained the same over long time intervals. This assumption could be questioned when the borehole sites were subjected to the drastic vegetation/land use changes. The vegetation changes and their causes are manifold. The processes that lead to the vegetation changes can be characterized as gradual or abrupt. Such processes can produce changes of vegetation structure and/or composition very quickly or for long time periods, respectively. Changes in land cover type may be direct, e.g. agriculture, forest clearing; or indirect as a result of altering disturbance processes, e.g. fire events, landslides, floods, etc. They may be either natural, such as germination, growth, death, or human-induced. All processes can operate over various temporal and spatial scales. Changes in the land cover influence all energy balance components. Exact responses to the land cover change are component specific. For example, both sensible and ground heat fluxes are reduced with an increase in tree canopy. On the contrary, conversion of a forest to short vegetation may raise surface temperatures due to increased sensible heat flux in relative to latent heat flux (Eltahir, 1996). In completely forested areas temperature at ground–air interface is lower than at grasslands or bare soils. Annual ground temperature under complete tree cover is also on average lower, while the soil moisture will be on average higher under such areas cover than under complete grassland. The lower ground and air surface temperature will lead to lower evaporation rates and to decrease the latent heat flux from the ground surface. Among all possible land use changes the influence of the deforestation on the GST–SAT coupling represents probably the best-studied process. Deforestation is the removal of trees
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without sufficient reforestation. It may occur naturally as slow forest degradation or sudden extensive forest fires. Anthropogenic influence means conversion of forests to grassland and/or to arable land as well as urbanization and technological uses. Removal of significant tree masses influences all environmental characteristics, changes air–ground boundary as well as the surface hydrological regime, and thus seriously modifies the surface energy balance (Zeng and Neelin, 1999). It generally provokes noticeable changes in climate. Numerous studies have detected an increase in subsurface temperatures following deforestation (Murtha and Williams, 1986; Cermak et al., 1992; Majorowicz and Skinner, 1997; Zhang et al., 2001; Beltrami and Kellman, 2003; Nitoiu and Beltrami, 2005). Except for direct influences caused by the changes in the surface energy balance, climate changes may occur due to indirect feedbacks of altered bio/geo/chemical processes. Climate changes due to deforestation not only are of only local character, but generally embrace global scales as well (e.g. Chase et al., 2000). Betts (2004) and Betts et al. (2004) have compared the radiative forcing caused by the land use changes with the influence of the greenhouse gases, aerosols, and stratospheric ozone (see Section 3.4.2, Chapter 3) and have concluded that these effects have comparable magnitudes. Common effect of deforestation manifests itself as an increase of surface temperature in tropical and temperate regions (Betts, 2004; Betts et al., 2005). Such changes have been detected in numerous borehole temperature logs. Importance of the account for the deforestation disturbances during GST reconstruction from borehole temperature logs was emphasized in the work by Lewis and Wang (1992). These authors have measured temperature–depth profiles in 11 boreholes located at different Canadian environments. Repeated measurements have shown that average GST depends on the vegetation cover. Thus, in forested areas it is generally 4–5 K cooler than at the bare surface. Similar values were measured in Atlantic Canada (Beltrami and Kellman, 2003) and in British Columbia (Plotnikoff et al., 2002). In the regions subjected to deforestation Lewis and Wang (1992) have collected the evidence that these areas have experienced subsequent GST warming. Numerous further studies have corroborated an increase in subsurface temperatures following tree cover removal (Bentkowski and Lewis, 1992; Majorowicz and Skinner, 1997; Skinner and Majorowicz, 1999; Bodri et al., 2001; Cermak and Bodri, 2001; Beltrami and Kellman, 2003; Lewis and Skinner, 2003; Nitoiu and Beltrami, 2005). Beltrami and Kellman (2003) have performed the monitoring of the soil and air temperatures at three locations in Nova Scotia (Canada) to examine how they follow each other in “field” and forested areas. The “field” surfaces included a clay soil and the grass. High-resolution air–soil temperature monitoring over one-year time interval have shown that the maximum positive differences in soil temperatures between “field” and forested locations occur generally in the warm season (spring and summer) mainly because of direct solar heating of the surface at the “field” sites (the direct solar radiation in the forest amounts to only 5% of that detected at the “field” sites). Because of this effect, the spring thawing has occurred some 2 weeks earlier at the grasslands than in the forests. Differences may reach approximately 8 K at the 0–20 cm depth range, and are of ⬃6 K in the 50–100 cm depth interval. During cold seasons differences are significantly smaller. The authors have performed numerical modeling of soil temperatures. Their model has applied the 1-D conductive heat transfer regime and used air temperature as the surface forcing function. Calculations have indicated that during frost-free season (approximately 290 days in the spring-fall period) the soil thermal regime in the forest floor is directly
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coupled to the temperature at lower atmosphere. The discrepancies between measured and modeled data were insignificant. Decoupling of the measured and modeled temperature time series appears to be more noticeable at “field” sites, where assumption of conductive thermal regime driven by air temperature changes was not valid. Detected misfit clearly followed daily periodicity. The measured-modeled data differences were the largest in the daytime. The explanation of this phenomenon lies in the significant increase of the incident solar radiation on the field surface, such that air temperature forcing alone represents only small fraction of the energy driving thermal regime of the subsurface in the daytime. On the contrary, in forested areas, where direct solar radiation was much smaller than at the field sites, the SAT was the main forcing for the ground temperatures and the GST could be accurately simulated by a pure conductive model. In forested areas the shortscale GST–SAT coupling appears to be one by one, while in open fields GST changes are not properly represented by conductive models with SAT forcing. Because deforestation is a widespread anthropogenic activity at all times and all over the world, many drilling sites may contain such kind of disturbance and need correction to separate influence of the non-climatic energy balance changes superimposed on the climate signal. Indeed, numerous temperature logs have been rejected from the GST history reconstruction because boreholes where they were measured were located in the regions of well-documented strong land use changes. The need to correct borehole temperatures for such perturbations was recognized from the very beginning of the borehole climatology. Lewis and Wang (1992) have suggested simple ramp/step model to correct effect of ground warming observed in several boreholes of British Columbia (Canada) after deforestation. This correction should be applied to the temperature log prior to its use for the GST history reconstruction. Obviously, this model was only a first-order approximation, and was not intended to account for all processes occurring in such areas. Recently, Nitoiu and Beltrami (2005) developed a more detailed method for simulation of the effects of the GST changes caused by deforestation. One of the most influential studies in the history of forest ecology was that performed by Covington (1981), who described a pattern in organic matter storage as a function of the date of forest harvest. This so-called Covington’s curve was based on the study of forest floors in series of northern hardwood stands of different ages in New Hampshire (USA). Since the energy balance at the forest floor is affected by the removal of trees and by the variations of the layer of organic matter at the forest flow, Nitoiu and Beltrami (2005) proposed a model based on the Covington’s curve to describe GST variations following deforestation. For the case of total recovery of initial forest the model is formulated as TG ⫽ At B exp (Ct D ) ⫹ TG0 ,
(36)
where TG is GST, t the time after deforestation (in years), and A, B, C, D, TG0 regression coefficients. Figure 52 shows GST variations caused by deforestation that occurred 50 and 100 years B.P., respectively. As seen, the GST sharply increases immediately after deforestation event, when environment is dramatically declined by the biomass removal and by the mixing of the forest flow into mineral soil during harvesting operations. Temperature disturbance reaches its maximum of 2 K at approximately 15 years after harvest. As the forest floor organic matter recovers, temperature slowly returns to its original value TG0. Full recovery may take decades or even century-long periods. Eq. (36) assumes that the
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Fig. 52. Response of the ground surface temperature to deforestation, two events considered which occurred 100 and 50 years B.P. (model by Nitoiu and Beltrami, 2005; A ⫽ 0.221, B ⫽ 1.24, C ⫽⫺0.0649, D ⫽ 1.063, GST0 ⫽ 0 K).
removed forest re-grows to its original state. This model can be improved for the more common cases when the new forest differs from its pre-harvest state or is transformed into bare soil/grassland. In the latter case temperature increase can be much higher than 2 K, which is shown in Figure 52. Subsurface temperature perturbations due to deforestation can then be simulated by 1-D purely conductive equation of heat transfer using synthetic GST histories, as presented in Figure 52, as the surface boundary condition. Correction for deforestation is performed by removal of the simulated T–z profiles from measured temperature logs. Calculations by Nitoiu and Beltrami (2005) have shown that disturbances due to deforestation propagate to some 150–200 m depth. Correction is the largest in the uppermost 100 m depth interval. Its values depend on the harvest timing and for the recent century events can range between 0.1 and 0.6 K. Effect of deforestation is more serious for the more recent events, while the magnitude of the disturbances caused by remote deforestation is significantly attenuated by subsurface heat diffusion process. In the case of remote deforestation at borehole site the GST histories inferred from corrected and uncorrected T–z profiles were practically indistinguishable. This hints that correction for deforestation is unnecessary in regions that experienced older deforestation. Both numerical simulations and analysis of field examples performed by Nitoiu and Beltrami (2005) have shown that the above method very effectively removes disturbances caused by deforestation. The shortcoming of suggested technique is that exact correction is only possible if timing and character of the land use change is known. In the real field situations the harvested and fully re-grown forest case is far not common. More often the deforestation represents a series of events, whose details are generally not well documented. Poor knowledge of the land use history may be a source of significant bias in applied correction. The GST anomalies may affect not only areas that were really subjected to the land use changes, but also their wide surroundings. Ferguson and Beltrami (2006) have studied transient lateral effects of deforestation. Their numerical simulations have indicated that
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the subsurface temperature anomalies caused by deforestation of vast areas may extend far beyond the cleared region. Thus, for 500 m wide deforested area 0.1 K temperature increase reaches approximately 40 m distance beyond the edge of the cleared ground in 50 years after deforestation and ⬃70 m after 100 years, respectively. The authors have proposed effective technique for correction of the T–z profiles measured in boreholes drilled close to the areas affected by the land use change. Unfortunately, this method could not be applied at all locations. Similarly to the above-described correction the latter technique also requires at least some knowledge of the land use changes. Generally, applied models are based on an assumption of a homogeneous deforestation, while real deforestation takes place preferentially near areas that have already been deforested. This creates a mosaic of forested and deforested patches that further complicates the lateral effect of deforestation. An impact of such localized deforestation on the development of shallow temperature anomalies was studied by Bense and Beltrami (2007). The authors have used a suite of the 2-D models to illustrate thermal effect of the patch-like deforestation. Heat transfer can take place by both conduction and advection due to groundwater flow. Modeling results have shown that the patch-like pattern of deforestation can produce significant temperature gradients in the subsurface. Anomalous gradients can be intensified by the horizontal groundwater flow if its rate is above 10⫺8 m/s. While in the case of pure conductive heat transfer maximum extent of the anomaly would not exceed ⬃50 m (Ferguson and Beltrami, 2006), lateral advection of heat can extend the measured disturbance to several hundred of meters away from the deforested area during 100 years after forest clearing. The measured up- and downstream T–z profiles can exhibit contrasting features notwithstanding that both areas had undergone the same GST changes. The vegetation increase can also affect GSTs. In their recent study Kaufmann et al. (2003) have applied statistical techniques to quantify effect of inter-annual variations in vegetation on the surface temperature for different types of land cover over Northern America and Eurasia. The database included satellite measurements of the surface greenness (interpreted as a proxy for photosynthetically active vegetation) and the groundbased meteorological observations for the years 1982 to 1999. Statistical analysis has shown that summer increase in terrestrial vegetation causes corresponding ground temperature decrease. Reductions in the extent of snow cover during the winter compel temperature to rise. Except for the seasonal vegetation increase, its long-term enlargement (e.g. reforestation process) can cause corresponding long-term decrease in the GST. For example, it is the case for many regions of North America over the past century, where subsistence farming was stopped and previous agricultural land was occupied by the forest (Ferguson and Beltrami, 2006). Other local terrain effects causing spatial and/or temporal variations in the land cover, such as forest fires, can also affect surface temperature and influence underground temperature field (Skinner and Majorowicz, 1999; Lewis and Skinner, 2003). Yoshikawa et al. (2003) have investigated an impact of wildfire on the ground temperature in the boreal forests of interior Alaska. Their experiment has detected significant increase of the near-surface temperatures in a short time after ignition. At 2 cm depth temperature has risen to more than 800°C already in about 10 min after ignition. However, the ground temperature has increased only at the shallowest layer (5 km) as the next-generation nuclear waste repositories. The ICDP is a multinational program to further and fund geosciences in the field of the continental scientific drilling. Currently Austria, Canada, China, Czech Republic, Finland, Germany, Iceland, Japan, Mexico, Norway, Poland, South Africa, and the USA are its members through their National Funding Organizations and/or major research institutions. In addition, UNESCO and some international companies are the associated members. From the very beginning, geothermal and paleoclimatic investigations have appeared among the most important directions of the ICDP scientific research. Numerous processes occurring in the continental crust are temperature dependent. Measurements of subsurface temperature distribution and associated quantities (thermal conductivity, heat production, heat flow) are of vital importance to the understanding of these processes. Paleoclimatic directions include the following research fields: (1) the manner in which Earth’s climate has changed in the recent as well as in the remote past and the reasons for these changes, and (2) the subsurface effects of major impacts on climate and mass extinctions. The German KTB continental deep drilling program represents one of the primary and celebrated attempts of climate investigation in the superdeep holes. The drilling site is located at Oberpfalz area in NE Bavaria (Germany). This region is quite suitable for the study of deep-seated crustal processes. The drill site is located at the boundary between two major tectonic units of the Hercynian fold belt in Central Europe: the Saxothuringian and Moldanubian. The region represents a suture zone formed by the closure of an oceanic basin 320 million years ago. This process gave way to a continent–continent collision and the formation of the huge mountain chain comparable to the present extension
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of the Himalayas. Now the high mountain relief is eroded and previously deeply buried rocks are exposed at the surface (Burkhardt et al., 1989). During the KTB project two deep boreholes were drilled: so-called pilot hole (VB, 4 km) and ultra deep main hole (HB, 9.1 km). Both drill holes are located at a distance of only 200 m from each other. It is the unique constellation of two deep boreholes that are very close at one site. Both holes are drilled in the crystalline metamorphic rocks of the Hercynian continental collision zone, where the dominate rock types are paragneisses and metabasites. First studies for the KTB project began in 1978, and official inauguration of the KTB pilot hole occurred in 1987. The project has included collection, compilation, analysis, and interpretion of a high-quality dataset. Geothermal investigations represented significant part of the KTB scientific program. That time this deep-drilling project has produced one of the world’s best collections of the geothermal data and provided a unique opportunity for the study of heat transfer processes in the deep continental crust. Priliminary research on the GST changes on the 0.01 Ma scale using the KTB-hole information has examined the temperature log measured in the 4 km deep pilot hole. The drilling ceased in 1989, and perturbation to the subsurface temperature field caused by drilling had almost entirely dissipated to the moment of the last temperature logging in 1996 (Huenges and Zoth, 1991). Figure 116 shows examples of the temperature logs measured in the KTB-VB hole. Full set of the temperature logs measured in both the KTB-VB and the KTB-HB drillholes can be found on the web site of the ICDP (www.icdp-online.de/sites/ktb). Except for the small-scale temperature oscillations, the most striking feature of the measured T–z profiles is their distinct non-linearity: the curve is concave. Temperature deficit relative to a linear T–z profile is especially pronounced in the depth range 0.5–3.5 km. It was very enticing to attribute observed curvature to the remote climate change, and a number of forward models were simulated to interpret the curvature of the T–z profile from the KTB drilling site in this context (Rybach, 1992; Jobmann and Clauser, 1994; Kohl and Rybach, 1996). Numerical modeling has demonstrated that the subsurface temperature at the VB-hole bears a clear signature of the paleoclimatic temperature change and quantitatively agrees with the reference climatic series of the last 0.1 Ma for Germany reconstructed by Zoth and Haenel (1988) on the basis of the proxy records. Clauser et al. (1997) have inverted temperature log measured in the 4 km deep KTB pilot hole where temperatures probably were close to the original pre-drilling conditions (Figure 116). Even under simplified approach of the half-space with homogeneous thermal properties, the authors obtained reasonable well timing of the post-glacial warming with amplitude of nearly 10 K. It was also shown that concave shape of the KTB-VB could in principle be explained by the paleoclimatic effect alone. Further investigations have revealed several factors contributing to the thermal field. Probably, one of the major findings of the KTB program was the discovery of the presence of free fluids at significant depths. The KTB researchers expected bone-dry deep crystalline rocks. To their surprise, fluid inflow occurred at several depths from open fractures. Numerous experiments/tests were performed to ascertain the properties of the hydrogeological system at the borehole site. Because the thermal regime in the KTB hole is possibly affected by the groundwater flow, several authors (e.g., Kohl and Rybach, 1996; Clauser et al., 1997) have investigated the thermo-hydraulic field near the KTB in 2- and 3-D approaches. All models were based on detailed knowledge of the geological structure in the drilling site and have taken into account vertical contrasts of rocks with
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Fig. 116. Two temperature logs measured in the KTB pilot hole. (Data from the public database www.icdp-online.de/sites/ktb).
significantly different thermal conductivities as well as information on hydraulic properties which was necessary for an interpretation of advective heat transfer process. Forward numerical experiments by Kohl (1998), who used a complex 3-D transient model of the KTB site accounting for advection, topography, lithologic heterogeneities, and paleoclimatic GST variations, confirmed conclusion made by the earlier research that, together with the lithologic effects, the Pleistocene temperature changes induced by the last glaciation represent the most dominant influence on the temperature field in the KTB. The effect of the thermal advection by subsurface fluid movement is traceable but of minor importance. The author has demonstrated that even in the strongly advection-dominated systems that at certain depth ranges can significantly perturb conductive temperature distribution the paleoclimatic signal cannot be completely “washed out”. On the other hand, the estimation of the paleoclimate fingerprints from advectively disturbed environments cannot be performed using pure conductive approach. For certain recovery of the paleoclimate signal the use of improved advection inversion techniques is indispensable (see Section 2.7, Chapter 2). However, in most of the field situations the construction of both realistic forward models and inversion parametrization schemes represents an extremely complex task because of the lack of sufficient field (especially hydrological) information. At present time, geothermal data from advectively disturbed boreholes can be used rather for the investigation of the temperature-dependent processes occurring in the continental crust than for paleoclimate reconstructions. The Kola superdeep project represents similarly well-known deep-drilling effort. The Kola (SG-3) borehole site is located on the northern rim of the Fennoscandian (Baltic) shield near the Norwegian border at about the same latitude as Prudhoe Bay, whose GST
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reconstruction results were described in Section 3.1.2 (Table 7). It was a Russian-funded project to drill deep into the Earth’s crust. As in the case of the KTB, the Kola project planned wide-ranged geophysical/geological studies. The research areas were: (1) the deep structure of the Baltic Shield, the physical and chemical composition of the deep crust, and the hypothetical transition from granite to basalt; (2) lithosphere geophysics; (3) seismic discontinuities; and (4) the thermal regime in the Earth’s crust. The drilling of the main Kola hole began in 1970, and a number of boreholes were made from a central branch. The deepest of them (SG-3) reached its final depth of 12 262 m in 1994. It is currently the deepest borehole in the world and penetrates about a third through the Baltic continental crust. Extensive geophysical studies have been performed at the project site. Geophysical loggings and other measurements in this hole began almost immediately after the drilling was ceased. Undisturbed temperature–depth profile was measured there in 1998 after four years of continuous shut-in time of borehole (Popov et al., 1999). The Kola drill hole exhibits a considerable variation in the vertical component of heat flow density (Kukkonen and Clauser, 1994; Mottaghy et al., 2005). Measurements revealed significant growth of the vertical heat flow across the borehole. It is about 30 mW/m2 in the uppermost 1 km and equals approximately 70 mW/m2 at 4–5 km depth. Observed variation in the vertical component of the heat flow cannot be attributed to the technical disturbances caused by the drilling procedures, but reflects the complex impact of three main natural processes. The SG-3 hole is located at slightly elevated terrain (150–300 m a.s.l.). Similar to the German KTB holes, the presence of free fluids was indicated in the Kola site down to a depth at least of some kilometers (Huenges et al., 1997). Forward 2-D numerical models by Kukkonen and Clauser (1994) were simulated using the vast available data on lithology, hydrogeology, topography, and the thermophysical structure in the area. Modeling results indicated that contrary to the KTB situation that archives significant paleoclimatic information, the main factors affecting the heat flow at Kola site are advective heat transport (especially in upper 2–3 km) and the complicated crustal structure. The area was covered by the Weichselian glaciation. Kukkonen and Clauser (1994) calculated the paleoclimatic influence using the reference late Pleistocene and Holocene climate history as the forcing function. Their simulations have shown that paleoclimate influence appears to be considerably smaller than the advective and structural effects. Paleoclimatic disturbances to the heat flow decrease rapidly with depth from approximately16 mW/m2 to less than 2 mW/m2 at 1.5 km. This conclusion was supported by the recent investigations of 36 shallow boreholes situated in the vicinity of the Kola SG-3 hole (Mottaghy et al., 2005). Except for the temperature logging, detailed studies of thermal conductivity as well as other important geophysical variables (density, specific heat capacity, radioactive heat generation rate, porosity, and permeability) on numerous samples were performed. Obtained data appear to be in good agreement with the corresponding quantities early measured for the superdeep SG-3 borehole. Detected heat flow values fall in the range of 31–45 mW/m2. Moreover almost all boreholes exhibit significant increase of the heat flow with depth similar to that observed early in the SG-3 hole. For simulation and/or interpretation of observed regularities the authors constructed a realistic 3-D numerical model that incorporated wide amount of available data on the crustal structure at the SG-3 surrounding. Results of numerical trial runs have shown that at least in the upper 4 km advection heat
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transport is the main reason for heat flow growth and the crustal heterogeneity is of only secondary importance. On the other hand, the latter study has shown that at the deeper levels at least half of measured temperature disturbances occur due to the paleoclimate influence. The authors have concluded that the advection of heat by groundwater flow and the paleoclimate play significant role in the downward increase of the heat flow. As in the case of the KTB for the reliable reconstruction of the past climate history both effects should be interpreted together. The above-described results of the geothermal investigations in two superdeep holes probably appear somewhat disappointing concerning the possibilities to infer remote climate change. It is clear as to why numerous measurements/investigations did not provide expected results. Borehole sites were chosen for mainly geotectonic reasons. Due to the lack of previous attempts, both the technical experience of drilling to a great depth and the knowledge of the deep crustal conditions were insufficient in the beginning. For example, numerical ingenuities were applied during the Kola drilling experiment. The main innovation was that, instead of turning the drill bit by rotating the stem, in the Kola well the bit alone was turned by the flow of drilling mud. Thus, it became possible to eliminate rotation of the entire drill string above. The researchers expected to find highly compact rocks at the deep crustal levels. On the contrary, deep rocks were strongly fractured and saturated with water. Initially it was planned that the Kola superdeep hole would be 15 000 m deep. However, mainly because of the higher temperatures that reached 180°C instead of expected 100°C, the final depth did not approach even 13 000 m (after 24-year drilling). Further penetration down to 15 000 m would have meant working at approximately 300°C, and the drill bit could no longer work at such conditions. However, the abundance of the potential sites for the superdeep borehole research and the increased experience in the deep hole drilling permanently support the interest in such studies. An international workshop on continental scientific drilling was held at the GeoForschungZentrum, Potsdam, Germany, from March 30 to April 1, 2005. The purposes of the workshop were: (1) to review and summarize the achievements of the last decade of the ICDP, and (2) to define the opportunities for the future drilling projects addressing a broad set of topics in the earth sciences. The potential sites included subduction zones at the Izu Peninsula (Japan) and/or at Crete, the greatest continental collision zone in the Nanga Parbat region of the Himalayas, etc. The “Climate Change and Global Environment” was declared among the most important scientific research priorities in future. Some of the superdeep drilling programs are currently operating. Thus, e.g., since the 1990s the crater Chicxulub on the Yucatan Peninsula, Mexico, represents the area of extended geophysical and geological research (Hildebrand et al., 1991; Steinich and Marin, 1997). It is assumed that this structure resulted from the impact on the Earth of a large (more than 10 km in diameter) asteroid or comet (Dressler et al., 2004). The study of the impact structure with a diameter of 180–200 km and a center at the port of Chicxulub involved drilling of eight cored UNAM (Universidad Nacional Autónoma de México) boreholes inside the crater and in its immediate vicinity (Urrutia-Fucugauchi et al., 1996) with a depth range between near 60 (UNAM 4) and 700 m (UNAM 7) and culminated by drilling the 1.5 km deep borehole Yaxcopoil-1 (YAX-1) of the Chicxulub Scientific Drilling Project that represents a part of the International Continental Deep Drilling Program (Urrutia-Fucugauchi et al., 2004).
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The precise high-resolution temperature logging was repeated nine times in the period March 2002–February 2004 (Wilhelm et al., 2003, 2004; Popov et al., 2004). The long-term GST reconstructions using the temperature–depth profiles measured in the deep-drilled boreholes in Fennoscandia are of special interest. Two-millennia long GST histories reconstructed in Finnish boreholes have been already presented in Section 3.1.1. The study confirmed certain incoherence of the climatic history in Finland with the results obtained for other parts of Europe. The early section of the reconstructed GST histories covers a cold period between approximately 400 and 1000 A.D., followed by a long gradual warming up to 1500–1700 A.D. and a cold period around 1800 A.D. followed by strong subsequent warming. The fifteenth to sixteenth century warming in Finland appears to be different from the Little Ice Age conditions reported, e.g., for central Europe. During the Weichselian period this area was covered by glaciers. The analysis of the depth dependence of the heat flow in the Fennoscandian Shield and the neighboring parts of the East European Platform has shown its systematic variations with depth (Kukkonen and Joeleht, 2003). The authors have attributed these variations to the long-term climate change during the late Pleistocene glaciation and the Holocene. Inversion of the temperature–depth profiles from a suite of boreholes have shown that the lowest temperatures occurred during the last glacial maximum (⬃20 000 years B.P.) and were followed by the average warming of 8.0 ⫾ 4.5 K approximately 10 000 years B.P. Kukkonen et al. (1994) have estimated the 10 000-year long GST history using T–z data measured in approximately 1 km deep borehole in Lavia, SW Finland. Their reconstruction revealed three steps of the long-term GST history in the region: (1) rapid recovery from the previous cold conditions about 9000 years ago that can be attributed to the retreat of the Weichselian ice sheet, when the temperature increased by approximately 4 K, (2) the warm period that continued from 8000 to 5000 years B.P., and (3) approximately 1K further warming that occurred at the beginning of the twentieth century. This GST history coincides well with the climate course after the latest ice age obtained for southern Finland on the basis of the proxy data (Donner, 1974). The Geological Survey of Finland (GTK) is currently running the Outokumpu Deep Drilling project (www.gsf.fi/projects/o_k_deepdrilling). Drilling at Outokumpu (eastern Finland) site began in April 2004 and was successfully completed in January 2005 at the final depth of ⬃2500 m. The site under investigation belongs to the Paleoproterozoic formation that is well known for its polymetallic massive sulfide ore deposits. It is also one of the oldest ophiolitic formations all over the world. The main reason that has motivated this deep drilling project was the investigation of the deep structure of a classical ore province in the stable Precambrian terrain. On the other hand, it is expected that the Outokumpu deep hole will provide a wide range of research possibilities in numerous scientific branches. The Outokumpu hole is expected to be a deep geolaboratory for various in situ experiments. Among other important activities the research program includes carrying out numerous down-hole temperature logging experiments. The main goal of these measurements is inferring the GST history during the Weichselian glaciation and the Holocene from the geothermal data. Except for the possible new paleoclimatic contributions, results of the planned measurements are expected to provide an improved understanding of heat transfer and fluid flow in the crystalline bedrock. It can be believed that geothermal measurements at the Outokumpu deep hole will turn this site into a reference example of the paleoclimate reconstruction and the heat transfer regimes in the Precambrian crystalline crust.
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These two efforts are neither the first nor the last attempts at drilling superdeep boreholes. The potential of the deep/superdeep holes for the borehole climatology is likely not fully revealed. The selection of scientifically useful sites, drilling of superdeep holes, and their investigation are ongoing and may present with unexpected discoveries. The results described above confirm the possibility to extend the GST history back to the last glacial period. Due to their significant depth extension, the deep holes can reveal information about remote climate changes. In spite of somewhat lower resolving power of the geothermal method compared to most of the proxy indicators and its significant reduction on the timescales of 10 000 years and longer, it is evident that obtained during numerous research efforts GST histories contain clear fingerprints of the last Pleistocene glacial/interglacial transition. The latter event possibly represents the most dominant signal archived in the T–z profiles measured at European deep boreholes. The consistency between GST histories obtained from borehole temperature logs by various authors as well as their coherence with existing independent climatologic records gives strong support to the possibility of using the borehole thermometry database to extract information on remote climate changes.
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CHAPTER 4
Subsurface Temperature Monitoring: Present-Day Temperature Change and Its Variability
4.1 Geothermal Observatories and Subsurface Temperature Monitoring In the previous chapters we have described the reconstruction of the past ground surface temperature (GST) changes from the temperature–depth profiles measured in boreholes. Such profiles actually represent an important part of borehole geophysics, the science that records and analyzes measurements of various physical properties in wells or test holes. The geophysical logging system consists of probes, cable and draw works, and power and processing modules as well as data recording units. Modern logging systems are controlled by a computer. Probes (thermometers) that measure temperature–depth distribution are lowered into the borehole to collect continuous or point-by-point data, socalled temperature log, with one pass of the probe (for details see Section 2.1 and Figure 18). These records may be used for various environmental investigations including paleoclimate reconstructions and assist in better understanding of the subsurface conditions. Because of reduction of the resolving power of the “geothermal” method in the past, the GST reconstructions inferred from borehole temperature logs capture only the general course of the climate variations and not the precise variance or periodic signals clearly presented in the time series of meteorological records. Temperature monitoring represents another data collection method. This measurement scheme applies several temperature sensors (thermistors) fixed at various positions along a cable that is then placed into a borehole for long-term recording of temperatures at selected depths. An interval between neighboring measurements may be from minutes to hours. The sampling design depends on the objectives of the research program. Temperature monitoring is frequently accompanied by additional instruments that determine air temperature and other meteorological variables and/or subsurface parameters such as soil moisture, water level change in borehole, etc. This procedure provides finescale and accurate temperature time series over multiyear time intervals. While temperature logs from deeper holes (ⱖ200–300 m) are used for the GST history reconstructions, the monitoring experiments are generally performed in the shallow (⬍100 m depth) holes. 267
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A special kind of underground measurements represents the soil temperature monitoring. Soil temperature monitoring is the recording of the temperature of soil at specific levels just below the surface. For the measurements at or very near the surface, thermometers can be buried directly into the soil. The main processes affecting soil temperature in the upper meters are solar radiation and heat exchange at the surface. They depend on seasons, physical properties of the soil such as soil type, compaction and moisture content, and vegetation cover. Because atmospheric processes are strongly reflected in soil temperatures, soil temperature monitoring can provide valuable data for the climate change analysis, especially for the detection of the recent climate change magnitude and capturing of the high-frequency climate variability. Soil temperature can also be used to give background data for other environmental monitoring programs such as plant phenology,1 soil decay rate, species diversity, invertebrate2 studies, etc. Recent perspective utility of the soil temperature monitoring is the tracking changes in temperature to determine the effectiveness of greenhouse gas emission reduction measures (see below). It should be mentioned that the borehole and/or soil temperature monitoring represents only a part of the general climate monitoring efforts that include an observation, measurement, and analysis of the past and the present states of climate from systematic networks all over the world. Sure conclusions about an extent of the present climate change and the role of the human activities can be achieved only through an understanding the past climate change and its natural variability. To obtain this information, scientists monitor five components of the climate system: atmosphere, oceans hydrology, land surface, and cryosphere. The land temperature monitoring represents an essential part of the net land monitoring. It can be regarded as an indispensable prerequisite of regional and global environmental studies and management activities. Systematic climate monitoring provides valuable data that can assist in developing climate models for prediction of future trends. Tracking changes in temperature can also help to determine the effectiveness of greenhouse gas emission reduction measures. An establishment of the joint air quality and climate monitoring system in the Black Triangle Region represents a typical example of such efforts. The Polish, Czech, and German border area (so-called Black Triangle) has been recognized as the most heavily industrialized and simultaneously the most environmentally degraded region of Europe. It covers an area of 32 400 km2, and has a population of more than 6 million. The region is one of the largest basins of lignite coal in Europe. Significant amount of sulfur dioxide (SO2) is emitted by area power stations, district heating plants, and other industries. This region accounts for about 30% of Europe’s total SO2 emissions. The member states as well as the EU’s actions have been made to reverse the Black Triangle’s air pollution legacy. The latest data provided by the trans-boundary monitoring system have detected that promising results of this efforts are already in evidence (see, e.g., www.energy.rochester.edu/pl/blacktriangle).
1
Phenology is the study of cyclic events of nature – usually the life cycles of plants and animals – in response to seasonal and climatic changes to the environment. 2 Invertebrate is a term for any animal lacking a backbone. The group includes 97% of all animal species.
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Concerning borehole climatology, subsurface temperature monitoring in boreholes is generally performed in three main related and/or complementary investigation directions: (1) Empirical site-specific observations of the GST–SAT coupling at single sites using monitoring of the air/subsurface temperatures and other meteorological variables. A comparison of soil and air temperatures provides a direct test of details of their coupling at shorter timescales (from daily/annual to decadal) and accounts for how air temperature and other meteorological conditions influence the downward propagation of the surface temperature signal. It is expected that continuous monitoring of the ground temperatures and related meteorological variables that is being carried out at numerous locations in the frames of various international programs will significantly extend available climatologic database and improve our present understanding of the GST–SAT linkage. Examples of such monitoring have been described in Section 2.6 of Chapter 2. (2) Monitoring of the ground temperatures at shallow depths where seasonal/annual temperature variations vanish can serve as an alternative useful tool for a direct quantitative assessment of the global warming rate. For the data collected from climate monitoring to be useful, measurements have to be taken at least over a decade or longer. Any gaps in information make it harder to capture trends and changes in climate. Both above-mentioned kinds of research can assist in resolving the differences between the influence of the past climatic effects and the effects of the present-day air–ground temperature coupling and of how this coupling may change through time. Methods for analysis depend on the specific research questions being asked. (3) An investigation of the shallow subsurface temperature time series can significantly advance our knowledge of the temporal and spatial patterns of the recent changes in the climate variability. A special kind of such research represents permafrost monitoring (see, e.g., web site http://gsc.nrcan.gc.ca/permafrost/canpfnetwork; and Section 2.8, Chapter 2). An analysis of the microtemperature time series monitored at depth in boreholes can also be used successfully in other fields of the geophysical research. Thus, they can help to quantify the stochastic heterogeneity of the temperature signal and provide valuable information on the fine scale features of the heat transfer process in different geological environments (see, e.g., Bodri and Cermak, 2005b). However, these applications lie beyond the scope of our book; thus, next sections will be devoted to the above-enumerated three directions of the climatic research using temperature monitoring data. 4.2 Detection of the Present-Day Warming by Temperature Monitoring in Shallow Boreholes As known, temperature changes at the Earth’s surface occur at various temporal scales. The oscillations are more regular on diurnal, seasonal, and annual scales. Interannual and long-term temperature change patterns are generally irregular. As was demonstrated in
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Sections 1.3 (Chapter 1) and 2.1 (Chapter 2), as the surface temperature signal propagates downward, its amplitude decreases exponentially with depth due to the diffusive nature of the heat conduction process. Each variation vanishes over a vertical distance related to the period of change and to the thermal diffusivity of the ground. Shorter period fluctuations attenuate more rapidly. Thus, the Earth selectively filters out high-frequency component of the surface temperature oscillations, and the deeper we go, the more distant past is archived there (unfortunately also more diffused and less credible). As a part of the UNESCO International Geological Correlation “Borehole and Climate” Program of the IGCP 428 project (for details see Section 3.1, Chapter 3), two experimental shallow boreholes were drilled in two different environments to monitor the depth response of the underground temperature field to changes on the ground surface. Both holes were equipped with a measuring chain of temperature sensor elements at a number of selected depths covering the whole 0–40 m interval. It was expected that several years’ temperature records would provide direct evidence of the decade-scale GST warming. This warming that can be related to the present-day global change was already detected in the territory of the Czech Republic by the more traditional inversion of the borehole temperature logs. Figure 14 (Chapter 1) illustrates the amplitude attenuation of the temperature signal when propagating downwards and the delay of its phase by showing the results of the 12-year temperature monitoring at several shallow depths in the experimental borehole Sporilov (Prague, the Czech Republic) (Cermak et al., 2000). The daily temperature wave is practically not observable below 1 m depth. Similarly, annual GST fluctuations vanish near approximately 10–15 m depth and are not measurable below this depth. The temperature from the 20–30 m depth level is free of any response to the annual and/or shorter temperature variations and contains exclusively the fingerprints of the longer scale climatic trends with characteristic time of at least several years. Such signal may characterize well the pattern of the long-term climate change. Figure 117 illustrates the amplitude decrement and phase shift of the annual temperature wave with depth in more details. It shows the 2003-year segment of the long-term temperature time series from Sporilov presented in Figure 14 (Chapter 1). Temperature was monitored at several shallow depths from 2.5 to 38.3 m. As the surface temperature signal propagates downward, it is delayed in time and its amplitude decreases exponentially with depth (see also Figure 15, Chapter 1). Each variation vanishes over a vertical distance related to the period of change and to the thermal diffusivity of the ground. Thus, the amplitude of the annual wave decreases to 50% of its surface value at ⬃2 m depth with time delay of about 40 days. It already decreases to ⬃15% of its surface value at 5 m depth where it arrives with approximately three months’ delay. Higher frequency oscillations vanish more rapidly. Similar attenuation is observable also in statistical characteristics of the records, e.g., in standard deviations of measured temperatures, the parameters of the linear trends, etc. Monitoring results from the depth interval 25–38.3 m contain fingerprints of the long-term linear warming trend only. Figure 118 compares 10 years’ long monitoring time series measured in Sporilov hole at the surface and at 38.3 m depth. The regular almost linear warming trend of 0.029 K/year is clearly visible at 38.3 m depth. It is not difficult to identify trend parameters in the time series where the trend is monotonous (consistently increasing or decreasing). If the time series contains significant variations over observational period,
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Fig. 117. Results of one-year temperature monitoring at several shallow depths in Sporilov hole (Prague, the Czech Republic). Profiles illustrate the amplitude decrement and phase delay of the temperature change versus depth.
the trend identification is more problematic. Because of the strong and irregular oscillations of the surface temperature, detected at 38.3 m depth, warming tendency is practically not visible in the surface data series. Faulty trend estimates can be obtained by simple linear regression procedure. Even the use of more complex techniques (e.g., different kinds of smoothing and data decomposition into significant components, e.g., Grieser et al., 2002) reveals the warming trend with lower reliability. The situation is similar to that described in Section 3.1.2. An inversion of numerous temperature–depth profiles in North America has revealed the presence of unambiguous ground surface warming during the past 100–150 years with the amplitude varying in the order of
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Fig. 118. Ten-year-long (1994–2003) temperature monitoring series in Sporilov hole. Plot shows temperatures that were measured at the surface and at 38.3 m depth. Line superimposed on the surface temperature series represents an estimate of the linear trend.
0.3–4 K, strongly depending on locality. The fact is that this warming was not derived from the SAT records. For example, Karl et al. (1991), after analyzing the meteorological station records for the mid-continent, concluded an absence of statistically significant climatic trends. As shown in Figure 118, the amplitude of the surface temperature variations does not increase with the overall trend. This means that the variance is not correlated with the mean over the segments of the series (see Section 4.3.1). Detected warming trend is illustrated in more detail in Figure 119 that compares temperatures monitored during 1994–2005 in Sporilov hole at 38.3 m depth with annual average warming rates. For the decade, temperature has warmed from 10.63°C in 1994 to 10.89°C in 2003. The monitoring results exhibit closely parallel linear trends for the individual years for the period from 2000 to 2005 and a progressive rise of the warming rate from 0.0296 K/year in 1994 to 0.0402 K/year in 2003. This warming was not one-way story. Warming was stronger in the year 1996 than in the years 1997–1999. The greatest warming rate of the whole 1994–2005 observational period has occurred in the year 2002. Smaller and less significant mean warming rate of only 0.026 K/year reflects more complex course of the temperature increase on decadal scale. Because of attenuation of high frequencies, trends at all depths in the underground have the same or even 2–3% lower relative error than those calculated from the data monitored in the air. In other words, subsurface trends are determined with the same or little bit higher accuracy as the SAT trends. As the subsurface is seeing more remote events, the amounts of the surface and deeper-measured trends and their timing cannot be compared directly. Figure 120 illustrates the penetration of the linear warming trend occurred at the surface to the depth. This process can be described by Eqs. (2.14) and (2.15) (Section 2.3.3, Chapter 2)
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Fig. 119. Top: results of the one-by-one year temperature monitoring at 38.3 m depth in Sporilov hole for the years from 2000 to 2005. Bottom: comparison of the temperature monitoring results at 38.3 m depth with the mean annual warming rates during 1994–2005 period.
with n ⫽ 2. Velocity of penetration depends on the thermophysical properties of the medium and not on the rate of the surface warming. The fingerprint of the surface warming is already measurable at 1 m depth after ⬃20 days from the beginning of the surface warming, after ⬃220 days at 10 m depth, and after 3 and ⬃7 years at 30 and 50 m depth, respectively. In the case of sustained warming, an amount of the linear trend observable, e.g., at 10 m depth achieves 70% of the surface value after 10–14 years from the beginning of warming. At 30 m depth, warming rate will achieve 50% of the surface value after 25–40 years from the beginning of warming. Comparing the trends detected by Sporilov monitoring experiment with the long-term SAT record at meteorological station Prague-Klementinum (Figure 64, Chapter 2), it can be concluded that today’s subsurface likely reflects strong warming trend that began in the area after the relatively cold 1940s (see also Cermak et al., 2000). As was shown by both the GST reconstructions and the analysis of the SAT data in the territory of the Czech Republic, this warming trend is characteristic for the wide territory surrounding Prague (Section 3.1, Figure 82). An independent analysis of the SAT records from 30 Czech meteorological stations (period 1961–1996) has revealed warming trends that fall in the interval from 0 to 0.04 K/year with characteristic regional warming rate of 0.0283 K/year (Cermak et al., 2000). Approximately 60% of the results fall within 0.02–0.03 K/year interval. An analysis of the spatial pattern of this trend has confirmed the conclusion by Bodri and Cermak (1999) that more pronounced recent warming is observed in more populated and generally industrialized areas, while lower values occur in either agricultural or forested areas.
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Fig. 120. Penetration of the linear warming trend into the subsurface. Curves are labeled by the depth level. After 10–14 years the warming at 10 m depth will achieve about 70% of the value of the surface warming (k ⫽ 10⫺6 m2/s).
Because at least a part of the warming observed at Sporilov can be attributed to an anthropogenic contribution to the local climate in a large urban agglomeration (so-called “urban heat island” effect3), similar monitoring experiment was performed in the Kocelovice site, the Czech Republic (49.47°N, 13.84°E, 518 m a.s.l.; Cermak et al., 2000). The locality represents a rural zone. The 40 m deep borehole is situated at the territory of the meteorological station, and monitoring experiment was put in operation in 1998. Thermistor sensors were fixed in depths of 0.02, 0.05, 0.1, 0.2, 0.3, 0.4, 0.5, 0.75, 1, 1.5, 2, 2.5, 3, 4, 5, 7.5, 10, 15, 20, 25, 30, 35, and 40 m. Air temperature was measured at 0.2, 1, and 2 m. In addition to the temperature measurements, the level of underground water, precipitation, snow cover thickness, wind speed and direction, solar radiation, and air moisture were also registered. The rate of registration was once in an hour. Figure 121 shows the year 2003 temperature increase recorded in the Kocelovice borehole. Detected warming rate was 0.0176 K/year in 1999 and thus was only near 70% lower than that
3 An urban heat island effect (UHI) corresponds to significantly warmer urban agglomeration area than its surrounding countryside. The principal reasons for the UHI are the comparatively warm buildings, significantly differing thermophysical properties of the surface materials used in urban areas (like as asphalt; see results of the monitoring experiments described in Section 2.6.2), and the lack of evapotranspiration (Section 2.6.3). The process of the population agglomeration growth is generally accompanied by a corresponding increase in average temperature that in principle can be confused with the warming trend occurring due to global warming phenomenon.
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Fig. 121. One-year temperature monitoring record at 40 m depth (Kocelovice hole).
observed at Sporilov. It had grown to 0.024 K/year in 2003. These rates, lower than those observed in Sporilov station, coincide well with the lower warming trend obtained for the Kocelovice location by the GST reconstructions as well as with SAT trends presented in Figure 82 (Chapter 3). On the other hand, similarly to the Sporilov site, data from the Kocelovice borehole have shown near 40% decadal increase in the warming rate. This hints that the increase of the amount of warming may represent essential feature on the recent climate change in the Czech Republic. Similar to the results of the GST reconstructions mentioned above, monitoring experiments have revealed spatial dependence of observed recent warming rates, when the highest warming has occurred in the industrialized regions. For further examination of this conclusion, the next monitoring experiment was established at the site Potucky, the Czech Republic (50.43°N, 12.78°E, 864 m a.s.l.). The choice was also inspired by the fact that it is this area where noticeable disagreement between warming trends calculated from the GST and SAT data was detected (Figures 82 and 83, Chapter 3). The borehole Potucky is situated in the western portion of the Ore Mts. (German Erzgebirge, Czech Krušné hory) forming the natural border between North Bohemia and Germany. For the long years, the Ore Mts. area has represented one of the most industrialized regions given by the rich mineral resources, especially the lignite coalfields and connected with them the power and chemical industries. Industrial activity was accompanied by extensive discharges of man-made pollutants into the environment. Acid rain resulting from sulfur dioxide emissions has damaged forests. The problem was particularly serious in North Bohemia during the 1980s due to pollution from the large amounts of fossil fuel used by the neighboring industries and brown coal (lignite) burned by power stations in the former East Germany and southern Poland. Only after 1991, emissions were stopped by the collapse of the emitting industries and by legal reductions of emissions from power plants. However, the long-term damages in the forests, caused by the acidification of the soils, are not yet repaired. High rates of the man-made climate warming may be expected in this territory.
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The Potucky boreholes are situated in the highland region that is characterized by extensive forest cover of coniferous woods and mountain meadows with abundant peat bogs. However, natural woods are spoiled very much by emissions from foothill coal basins. Now intensive work on their recovery is being performed. The suite of shallow boreholes was drilled in Potucky site during 2002, and subsurface temperature monitoring at several shallow depths from 2 cm to 50 m began in 2003. Results of the temperature measurements at 40 and 50 m depth in Potucky borehole from October 2003 to June 2004 are shown in Figure 122. Because of the relatively high thermal conductivity of the subsurface strata in Potucky site (3.2 W/(mK)) in comparison with approximately 2 W/(mK) characteristic for the Sporilov and Kocelovice stations, an annual temperature wave penetrates deeper into the subsurface there. This is the reason that the warming trends detected in Potucky hole at both 40 and 50 m depths do not appear as linear as in Sporilov hole and can be inferred with little bit less significance. As shown in Figure 122, the warming rate calculated for the temperatures measured at 50 m depth is quite high and equals to ⬃0.04 K/year. It is still higher at the 40 m depth where detected warming trend is approximately four times larger than that observed at the same depth at forested and less industrialized southwestern slope of the Bohemian Massif (Kocelovice hole) and approximately two times larger than that measured during the same period in the industrial region of Prague (Sporilov hole). Because the characteristic time of the penetration of the surface temperature signal into the subsurface is inversely proportional to the thermal conductivity of the medium, the warming trend detected in Potucky hole likely reflects more recent events. While the Sporilov and the
Fig. 122. Temperature monitoring at the depth of 40 and 50 m (borehole Potucky, the Ore Mts., Czech Republic) from October 2003 to June 2004. Solid lines represent the estimated linear trends.
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Kocelovice trends can be attributed to the strong warming that began in the area after the relatively cold 1940s, trends detected in Potucky site can be connected with climatic changes of the 1970s and the 1980s. An interpretation of the enormous warming trend detected at Potucky site does not represent an easy task because of the still short observational period but mainly because of the complexity of the processes involved in the local climate changes. The high value of detected warming hints that at least part of it may reflect an influence of the human environmental pollution. However, detailed investigation of all possible forcings reveals the possibility of more complex interdependences. The warming trend observed at Potucky hole can be compared with the long-term SAT measurements at the nearby meteorological station at Fichtelberg, Germany (Figure 123). The Fichtelberg is one of the highest mountains in the German part of the Ore Mts. (50.43°N, 12.90°E, 1213 m a.s.l.). This region is characterized by harsh, cloudy weather with significant precipitation including both wet winters and summers. Long-time annual mean temperature on the Fichtelberg is only 3.2°C. The SAT record exists here from 1891. The local climate has experienced insignificant warming with the rate of 0.0077 K/year for the total observational period from 1891 to 2003. Time interval between 1950 and 1980 was relatively cold. Strong sudden temperature rise with more than 0.05 K/year rate began here since the 1980s. The main temperature increase occurred between 1987 and 1991. It was detected over the whole Central Europe and is known as the “Climate Jump II” (in comparison with the “Climate Jump I” that occurred between approximately 1920 and 1935; see, e.g., Figure 64, Chapter 2). During “Climate Jump II” the GST in Central Europe has
Fig. 123. Mean annual SAT recorded at meteorological station Fichtelberg (Germany) during 1891–2004 and its 10-year running average. Solid lines represent the mean warming rates for the whole observation period and for years 1980–2004.
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increased by approximately 1.2–2 K above the average level for 1950–1985 (Borchert, 2005). This temperature course is quantitatively similar to the global temperature change. However, while the twentieth century global warming rate coincides well with the one observed at the Fichtelberg weather station, the rate of the recent warming in the latter location is approximately four times higher (Figure 4, Chapter 1). The supposed cause of the global warming is the combined effect of the anthropogenic activity and the natural forcing (see Section 3.4, Chapter 3), and it is very enticing to represent an increased warming trend in the study area as man-made, caused by extensive industrial activity. On the other hand, investigations by Borchert (2005, 2006) have revealed significant correlation between recent climate warming and air pollution characteristics with increasing Sun activity, which were observed in Central Europe, represented by increasing sunspot number and flare intensities as well as by decreasing cosmic radiation4 (neutron rates) resulting in reduced cloudiness and corresponding increase of intensity and duration of sunshine. On the basis of the detected correlations, the author has proposed extraterrestrial and not anthropogenic causes for the recent temperature increase in Central Europe, when the transportation and concentration of air pollution may also be strongly affected by external effects. Further studies (including prolonged temperature monitoring) can make causal connections of the recent warming clearer. The success of the monitoring experiments performed in the Czech Republic has inspired an establishment of the joint international monitoring project in the Czech Republic, Slovenia, and Portugal (Safanda et al., 2006). For all the three experiments, 100–200 m deep holes were chosen. Because a thorough thermal equilibrium is an essential requirement to obtain an undisturbed temperature time series suitable for the climate study, only old boreholes that have already achieved thermal equilibrium were used for monitoring experiments. Repeatedly measured temperature–depth profiles revealed fingerprints of an appreciable warming in the uppermost parts of all holes. Temperature monitoring began in the years 2002 (the Czech Republic), 2003 (Slovenia), and 2005 (Portugal) in several depths from 2 cm to 40 m. The air temperatures at 2 m and 5 cm above the ground surface were also measured. Preliminary comparative results are expected to be available in the end of the year 2006. All above-described monitoring experiments have proved that the present-day warming corresponding to the last one to several decades can be reasonably well extracted by precise temperature monitoring at shallow boreholes below the depth of penetration of the seasonal variations. Of course, the detection of the linear trends in the monitoring data sets and their interpretation represent only prelude to the precise analysis of this data. The geothermal inverse theory (e.g., ramp/step method, see Eqs. (2.14) and (2.15), Section 2.3.3) can be used to quantify more precisely the amount and the onset time of the warming trend. Anyhow, even preliminary studies have confirmed the applicability of this kind of temperature measurements for the GST reconstruction. The temperature monitoring in shallow boreholes of 30–50 m depths may be an alternative to the temperature log inversion, routine method of detecting local recent climate changes 4
Cosmic radiation (cosmic rays) is a naturally occurring ionizing radiation coming outside the Earth and filtering through atmosphere. A significant amount of these high-energy particles is discharged by the Sun. Scientists have argued that cosmic radiation can cause the changes in weather, e.g., can cause clouds to form in the upper atmosphere. The cosmic radiation shows an inverse relationship with the sunspot cycle. The reason is that the Sun’s magnetic field is stronger during sunspot maximum and shields the Earth from cosmic rays.
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and for the direct assessment of the present warming rate. Evidence obtained in the shallow subsurface by precise temperature monitoring can also satisfactorily complement meteorological observations. Borehole temperature monitoring in the recent decade became one of the building blocks of the borehole research to help us to understand how the Earth’s climate is changing. A heap of the monitoring experiments is performed all over the world. Except for the detection of the recent warming trends, numerous subsurface monitoring experiments were established for specific climatic applications. Of special interest are reports on the data from so far uncovered areas and attempts to separate the potential man-made components of the global warming from the natural climate variability. Below, we mention some of them. 4.2.1 Emigrant Pass Observatory, Utah Over a decade-long ground temperature monitoring has been performed at the Emigrant Pass Observatory (EPO), Utah (Bartlett et al., 2004, 2006; Davis et al., 2006). To better understand the GST–SAT coupling and to document the details of the penetration of the surface signal into the ground, a climate and ground temperature observatory was installed in arid NW Utah in 1994. The EPO (41.50°N, 113.68°W, 1750 m a.s.l.) consists of a standard weather station situated on exposed granitic rock at the top of a 150 m deep borehole (GC-1) drilled in 1978. Results of its repeated temperature logging are presented in Figure 16 (Chapter 1). Inversion of the measured T–z profiles inferred surface temperature changes that are closely coherent with those observed at the nearby meteorological station 40 km to the northeast (Chisholm and Chapman, 1992). The EPO consists of an array of thermistor strings in the subsurface. Ground temperatures are monitored at several shallow depths from 2.5 cm to 1 m. Meteorological and shallow ground variables are recorded simultaneously. All data from the EPO since November 2004 are available and can be found on the web site http://thermal.gg.utah.edu/facilities/ epo/EPO_data. The file is automatically updated daily. The combined database gives an opportunity to observe the GST–SAT dependence in near real time and to test theoretical models of the GST–SAT interactions. It can also be used for the investigation of the energy balance in the Earth’s surface, reconstruction of the climate change from borehole temperatures, and other geothermal studies. Over decade-long continuous temperature monitoring has shown that the subsurface temperatures at all monitored depths are in general agreement with the air temperature (e.g., correlation coefficients are 0.97 and 0.87 for air-10 cm and air-1 m depth temperatures, respectively). Except for the surface air temperature that explains 94% of the GST variance, the GST variations are influenced by incident solar radiation that accounts for 1.3% of the GST variance and by snow cover. Daily averaged GST–SAT differences range between ⫹14 and ⫺10 K. Observed differences occur due to the solar radiation effect in the summer and the insulating effect of snow cover in the winter. They are much lower on the annual scale and vary between only 2.3 and 2.5 K. In this scale of aggregation, ground temperatures are generally warmer than air temperatures. Much of the interannual variations in the GST–SAT difference occur due to the changes in solar radiation. It was shown that incident solar radiation is more important during the summer. On the long scale there is a linear relationship between the GST and SAT difference and solar
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radiation with a slope of 1.21 K/100 W/m and intercept of 2.47 K (Bartlett et al., 2006; Davis et al., 2006). Because of its low thermal diffusivity, snow attenuates surface temperature variations in the winter, but its insulating effect has only minor influence on the annual GST–SAT coupling at the EPO site (accounts for only 0.5% of the annual GST variance). Using EPO monitoring results, Bartlett et al. (2004) have developed twolayered forward numerical model of snow–ground interactions. Model is based on three characteristics of snow cover: (1) the onset time, (2) duration of the snow cover, and (3) its thickness. These parameters are generally available from meteorological and remotely sensed data, and the authors have validated their model using the National Weather Service data from 23 sites over North America. Their calculations have verified the applicability of the developed model for the broad spectrum of snow conditions and have confirmed its suitability for the prediction of the GST changes in different environments. On the whole, the EPO observations have shown that the GST really tracks the air temperature on the timescales relevant to the climate change studies. The GST reconstructions generally assume that the GST–SAT difference is constant over long timescales and thus the transient temperature changes at the ground surface reproduce the transient SAT changes measured at weather stations. The EPO monitoring results have warranted this assumption over the past decade and thus have given a serious experimental support for the use of the GST histories as a valuable addition to the SAT measurements and multiproxy reconstructions in climate change research. 4.2.2 The Sornfelli borehole In numerous regions, e.g., high elevation sites, islands, flat northern environments, etc., the surface air temperature may represent a complex result of an interaction of some climatic variables. The detection of the real warming trends in such areas and their separation from an impact of the short-term changes of other climatic variables may be quite difficult. Climate monitoring in such locations can help to filter out disturbing effects and identify long-term climatic trends. One of such monitoring efforts is being carried out at the Faroe Islands (Denmark). It is a small group of islands that is situated in the stormiest part of the North Atlantic, midway between Scotland and Iceland. The Faroe Islands are located in a key region for understanding land–atmosphere–ocean interaction in the North Atlantic region. Under the influence of the warm ocean current of the Gulf Stream, the climate is relatively mild for the latitude. On the other hand, because these islands lie in the path of the majority of Atlantic depressions, they are cloudy (daily sunshine in the summer months averages only about 4 h), wet (annual precipitations ranges between 1500 and 2500 mm), and windy throughout the year. The air surface temperatures in the region strongly depend on the wind speed and direction as well as on the cloud and snow cover (Cappelen and Laursen 1998; Humlum and Christiansen, 1998). The Climate Research Station was situated at the summit of Sornfelli mountain (799 m a.s.l.) on the main island Streymoy, and the monitoring was started in November 1999. It is expected that this experiment will provide meteorological data on the arctic climate environment on the Faroes that can then be placed in a wider North Atlantic as well as the Northern hemisphere perspective. Traditionally, meteorological stations in the area are located near sea level, which makes studies of the vertical climate change effects problematic. Data from Sornfelli borehole can allow the calculations of climatic altitudinal gradients, which
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can then be used for additional studies such as the interpretation of the vegetational zonation, soil development and present periglacial processes, and their relation to the past climatic conditions. Because of the cold, wet, and windy climate, as well as expected heavy icing problems, the measurements with standard meteorological equipment are difficult on Sornfelli, if not impossible. Thus, a special meteorological station was constructed, using a drum-shaped housing and internal heating. For the subsurface temperature monitoring, an 11.32 m deep borehole was drilled and thermocouples were installed. The station was redesigned in the spring of 2004, and new instruments and data logging equipment were installed in June 2004. Meteorological data are logged each 30 min. Similar to the EPO data, the Sornfelli monitoring results are regularly published in the web site www.metsupport.dk/data/sornfelli. On-line borehole data are updated every hour except at night local time. 4.2.3 Kamchatka Kamchatka is a peninsula in the Russian Far East comparable in size to Japan and surrounded by the Pacific Ocean and the Bering and Okhotskoe Seas. Human intervention to the atmospheric temperature and environment is expected to be small in Kamchatka because of very sparse population and small industrial activities. The recent climatic trends detected there probably reflect natural climate variability characteristic for the Northern Pacific region and not an anthropogenic influence. As a part of the 3-year joint Japanese–Czech–Russian research project “Reconstruction of the climatic changes from borehole temperature profiles and tree rings in the Kamchatka Peninsula” (2000–2002), precise temperature measurements were performed in a number of holes ( Yamano et al., 2002). This project primarily concentrated on obtaining precise temperature–depth profiles in a number of boreholes, drilled more than 15 years ago, and on verification of the previous measurements in the region. Temperature logs were repeatedly measured in 12 boreholes during 2000–2002 at intervals of a few months to one year (for details see Section 3.1.2, Chapter 3). Data were used to propose a climate model of the last 100–150 years (Figure 97, Chapter 3). All temperature logs have shown a general turn to the warmer conditions since approximately 1950. The most detailed GST history was inferred for a suite of boreholes at Malki location (53.33°N, 153.47°E). Climatic history shows warm period with the maximum near 1850, cold conditions culminating between 1920 and 1950 and pronounced warming of 1.2–1.6 K since then. Obtained results are in good agreement with the existing SAT series. Jones et al. (1999) have presented global patterns of the surface temperature change over the past 150 years’ combined land and marine data on the 5° ⫻ 5° grid box basis. Figure 98 (Chapter 3) shows one box of this database, namely, an estimate of the SAT changes for southern part of the Kamchatka Peninsula. The temperature anomaly time series, available back to the beginning of the twentieth century, exhibits high interannual temperature variation that somewhat attenuated between 1960 and 1990. Warming trend of 0.007 K/year calculated for the interval 1890–1998 is insignificant. The slow temperature rise with warming rate of 0.026 K/year occurred after approximately 1960–1963. It was followed by the marked period of warmth during the last 10–15 years of the record. Similar warming trends were obtained for the Pacific Ocean at latitudes 40–60°N and in eastern Siberia (Rogers and Mosley-Thompson, 1995).
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It was this warming that Budyko (1977) and other climatologists have interpreted as the start of a new large-scale climate warming. Except of the numerous temperature loggings, a high-resolution temperature monitoring of 1 mK accuracy was performed at several selected depth levels in four boreholes (Yamano et al., 2002; see also Bodri and Cermak, 2005b and the references therein). Temperatures in two unstable wells in Elizovo (E-1) and Yugozapadnaya (UZ) sites were monitored at 325 and 108 m depth, respectively. Such high depths were chosen because the scatter of data during repeated borehole logging has exceeded any explainable differences due to instrumental incorrectness and/or field of technical problems. Data loggers for temperature monitoring were installed at the depths of maximum temperature gradient. Temperatures have shown high degree of irregularity over all measured periods within up to several hundreds of degree, but because of relatively large monitoring depths they did not exhibit any significant linear trend that could be attributed to the recent warming. However, monitoring was not performed in vain, because an analysis of these deep microtemperature time series has helped to quantify the stochastic heterogeneity of the borehole temperature signal and provided valuable information on the fine-scale features of the heat transfer process in different geological environments (see, e.g., Bodri and Cermak, 2005b). Temperature loggers were also installed at four shallower depths 25, 30, 35, and 40 m in two boreholes with more stable temperature–depth profiles (Malki-2 and Malki-19) for 10–11 months. Similar to monitoring results described above short-term temperature variations observable in the upper 10–20 m depth interval of Malki holes significantly decayed in comparison with the surface temperature variations. On the other hand, recorded temperature time series have not shown any significant linear trend. Temperature has remained almost constant (within 2 m K). The reason is that the most recent warming that began 10–15 years ago still not penetrated to 25–40 m depth and insignificant warming trend characterized for the most of the twentieth century appeared too weak to be archived in the subsurface. For the same period, temperature was monitored at 50 and 100 cm below the ground surface in the close vicinity of Malki-12 and Malki-19 boreholes with lower accuracy of only 0.1 K. Analysis of these time series have shown that heat transfer in the uppermost ground is pure conductive at Malki-12 location, while small non-conductive component was detected at Malki-19 hole during February to May 2002. This non-conductive disturbance can be related to the freezing/thawing of the soil around 50 cm depth. 4.2.4 Livingston Island, Antarctic At the polar and sub-polar environments there are large areas subjected to high energy transfer in the ground surface. To investigate the surface energy balance in such regions for prognostic research of climate change two shallow boreholes (1.1 and 2.4 m) were drilled in the year 2000 in Livingston Island (South Shetlands, Antarctica; 62.65°S, 60.35°W). Temperature monitoring was performed in four depths during 2000 and 2001 (Ramos and Vieira, 2003; www.igme.es/internet/cnda). Temperature data were collected at 4-h intervals in several shallow depths. Because of quartzite bedrock setting, temperature time series were characterized by an absence of any trace of the phase change processes. Measurements have shown that the subsurface temperature regime is almost exclusively controlled by air temperature, which conductively penetrates to the depth
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with usual loss of amplitude and phase delay. The monitoring results at the Livingston Island’s boreholes bottom have shown only seasonal variations. Future international project plans drilling and monitoring of two new 20 m deep boreholes in Livingston and Deception Islands. Although shallow measurements described above can provide information about the surface ground temperature history only for the short time intervals comparable with the length of the time series, they are useful complements to the longer scale but less wellresolved GST histories inferred from the temperature logs measured in deeper holes. Current temperature monitoring experiments are performed in the single borehole sites. Once trends are detected and local characteristics and causes are identified, these results can be integrated into wider spatial scale network. These results can also be incorporated into other research fields or ecological issues, e.g., the environmental management. 4.3 Recent Climate Variability 4.3.1 Climate change and climate variability For a better understanding of the nature of the climate change, attention is to be focused not only on the evolution of mean climate characteristics, but also on the changes in climate variability, and on climate extremes. The necessity of including the variability characteristics in the climate change studies has been demonstrated in several works (Katz and Brown, 1992; Wilks and Riha, 1996; Rebetez, 1996, 2001; Bodri, 2004; and the references therein). It can be demonstrated that the frequency of climatic extremes is more sensitive to the changes in variability rather than to the mean climate state (Katz and Brown, 1992). Increase or decrease in the frequency of extremes can be enormously large even for relatively small mean changes in climate (Katz, 1999). Rebetez (1996) has shown that climate variability is one of the most important characteristics in the human perception of climate. The potential response of the socio-economic fabrics of the global community to the changes in climate variability may be stronger than to the changes in climatic averages (Rebetez, 1996; Wilks and Riha, 1996), while these changes are completely obscured when examining only the evolution of mean characteristics. In the everyday life, climate change and climate variability are often confused. In its exact mean climate (and any other real-valued random variable) variability refers to the spread of a data set. An assessing of variability generally includes two key components: (1) how spread out are the data values near the center, and (2) how spread out are its tails. The common definitions of the central value that best describes data are their mean, median, and mode. The common numerical measures of the spread are variance, standard deviation, range, average absolute deviation, etc. The changes that are greater than 4 standard deviations are generally referred as extreme events. When assessing variability, variations in the central (typical) state and the spread statistics of the climate should be detected on all temporal and spatial scales beyond that of individual weather events. An analysis of the climate and its variability from observed data is especially challenging in the case of a changing climate. An interaction between mean characteristics of climate and its variability and extremes depends on the statistical distribution of given climatic variable (Meehl et al., 2000). Possible influence of the changes in the mean and variability on climate is illustrated in Figure 124. The climatic temperatures
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Fig. 124. Effect of the change in the mean and in the variance for the standard normal distribution of temperature. “Previous climate” curve corresponds to mean⫽0 and variance⫽1. “New climate” is calculated for the next cases: (A) mean temperature increases (mean⫽1), (B) variance of temperature increases (variance⫽2), and (C) both characteristics increase (mean⫽1, variance⫽2).
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often have a normal distribution (“the bell curve”). The non-stationarity of this distribution implies changes in the mean temperature and/or its variance. Increase in the mean temperature gives more warm conditions and less cold weather (Figure 124, panel A). However, it does not produce any change in climate variability. In other words, the range between the warmest and coldest temperatures does not change. The change in extremes occurs only due to a shift in the distribution without a change in its shape. This means that for the real situations prediction of changes in extremes there is no need of additional study of variability. They could be predicted simply from the changes in longer term monthly, seasonal, or annual means that are generally available (e.g., global gridded data by Jones et al., 1999). On the contrary, an increase in variability without change in average temperature (panel B) produces the change in the shape of the probability distribution resulting in the same increase in the probability of both warm and cold extremes as well as increase in the absolute value of these extremes. Prediction of changes in extremes needs detection of changes in meteorological variables (e.g., indices of extremes) such that determination from station data is not a trivial task. Panels A and B illustrate that the global warming is not equivalent to climate change, and significant climate change can occur without any global warming or cooling. Increase in both characteristics of temperature distribution (panel C) results in an asymmetric increase of the probability of extremes producing more frequent warm events with more extreme hot temperatures. Its influence on cold extremes is far less pronounced. Figure 124 illustrates typical case of the global warming. Obviously, other combinations of changes in the mean temperature and its variability would lead to different patterns of the probability of cold and warm events occurrence. For the climatic variables that, like precipitation, are not well approximated by the normal distribution situation may be far more complex. Consequently, even when changes in temperature extremes were detected, their attribution to the changes in the mean or variance (or both) needs specific analysis and/or some kind of “key test” that may provide an idea on the degree of confidence associated with obtained conclusions. The fact is that Earth’s climate is always changing. It varies on a broad range of timescales and over many orders of magnitude. Climate oscillates on the millennial timescales between ice ages and interglacials causing global scale rearrangements of ice cover and ocean circulation. The shorter scales of its variation embrace periods from centuries like the Medieval Warm Period and the Little Ice Age to decades, as indicated by the temperature changes in the twentieth century. Generally the shorter the timescale, the stronger is the impact expected on a local spatial scale and the longer the timescale, the more is impact on the global scale and resulting socio-economic consequences. For example, long-term climate variations may alter agricultural productivity, land and marine ecosystems together with the resources that supply these ecosystems, while seasonal to interannual climate variations can strongly affect agriculture, the abundance of water resources as well as the demand of energy. On the other hand, different-scale climate variability modes cannot be treated separately. Results of the recent investigations increasingly support that short- and long-term climate variability are intrinsically linked. The climate system is quite complex and highly non-linear. Expected modes of its variability are also complex. Variability may be due to natural internal processes within the climate system (internal variability) and/or variations in natural or anthropogenic external forcing (external variability). An overview of the natural climate variability and its causal
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mechanisms was presented in the pioneering work by Mitchell (1976). It was partly this work that inspired the U.S. National Geophysical Data Center (NGDC) to design an interactive web site “Climate Timeline Tool: What is Variability?” that helps to assess the basic processes and causes of climate variability (www.ngdc.noaa.gov/paleo/ctl/about1.html). This graphic demonstrates also the interactions of variability over varying timescales. Significant climate variations are occurring within the diurnal scale to the 100 000 timescale corresponding to orbital forcing. All these variations have occurred before any anthropogenic influence on the climate system could be in operation. The natural variability of the climatic system itself is quite high. Evidence for such intrinsic variability has been found in observations and coupled general circulation models (Delworth and Mann, 2000). The past three to five decades have seen an increasing recognition that human activities may have substantial effect on the climate system. Recent climate variability may be intensified by the human influence. Because this is one of the great, still unresolved problems of climate science, changes in climate variability and in both weather and climate extremes have received increased interest in the recent decades. Numerous research programs, such as the international program “Climate Variability and Predictability” (CLIVAR; www.clivar.org), the Climate Variability and Trends Group of the NOAA (U.S. National Oceanic and Atmospheric Administration) Air Resources Laboratory (www.arl.noaa.gov/ss/climate), Climate Variability Working Group (CVWG; www.ccsm.ucar.edu/working_groups/Variability/index.html) together with the Intergovermental Panel of Climate Change (IPCC; www.ipcc.ch), were put on operation. The general objective of these efforts is to describe and understand the physical processes responsible for climate variability and predictability on various scales through the collection and analysis of observations and the development and application of models of the climate system. This goal can be achieved in wide cooperation with other relevant climate research and observing programs. Questions that could be addressed with the focused study of borehole temperature monitoring data include: 1. How does climate variability varied? 2. Are these changes consistent in the key regions? 3. In cases when reported variability changes appear to be contradictory, it should be examined where detected differences represent real regional variability or simply reflect the differences in quality of data and/or detection methods used. The answers to these questions will come from the development of the monitoring network and the acquisition data having sufficient length and resolution to provide a base for variability studies. Results from intensive local investigations should be combined for the studies of regional variability change patterns. Future valuable outcome of such efforts may be monitoring time series database similar to already existing “Borehole Temperatures and Climate Reconstruction Database” initiated by the Geothermal Laboratory of the University of Michigan (www.geo.lsa.umich.edu/⬃climate). A systematic review and evaluation of existing data can produce a coherent and internally robust data that will serve as a base for the variability studies, revealing potential forcing mechanisms and modeling of not only a warmer but also more variable future world.
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4.3.2 Trends in the recent climate variability The Earth’s climate system consists of a number of subsystems (atmosphere, hydrosphere, lithosphere, cryosphere, and biosphere) with their own characteristic times of operation from days to millennia. Each subsystem has its own internal variability mode, when some of its parameters change intensively over narrow range of timescales, while others remain constant over fairly long time. These ranges may overlap between subsystems. Due to these complex interactions climate varies on all timescales. For simplicity the vast range of the global variability is studied across the hierarchy of frequency domains with different scales of aggregation (such as intra- and interannual, and interdecadal to multimillennial). These studies have revealed specific features of the variability within distinct frequency bands, e.g., day-by-day versus interannual temperature variability. As about temperature variability, there is a vast amount of research works using surface meteorological observations, upper-air temperatures estimated from radiosondes, satellite-inferred tropospheric temperature trends, and other variables to detect its variability trends. Because we would like to connect these efforts with the possibility of the variability detection from the ground temperature monitoring (multiyear time series), further we will describe only results concerning the high-frequency variability detected from the SAT data that can serve as a background for a comparison with the results obtained from the subsurface temperature monitoring data. Considerable insight into empirical climate variability changes over the last century was obtained from the details of the patterns of annual and seasonal surface temperature variations. Recent studies have detected not only the global scale warmth but also changes in the SAT variability. Most recent efforts significantly advanced our knowledge of the temporal and spatial patterns of climate variability. Results of investigations of the local and spatial patterns of the high-frequency climate variability were presented in numerous works (Karl et al., 1993, 1995, 1999; Balling, 1995; Liang et al., 1995; Kelly and Jones, 1999; Moberg et al., 2000; Grieser et al., 2002; Bodri and Cermak, 2003; Bodri, 2004; Braganza et al., 2004; Seidel and Lanzante, 2004). Most of the authors have used only the twentieth century data. This has helped to avoid bias due to progressively increasing number of measurements during the whole observational period. Given the number of techniques for variability detection in different works, results of the earlier studies have shown significant scatter. Thus, Parker et al. (1994) have compared interannual variability for the global data of seasonally accumulated surface air temperatures for two periods 1954–1973 and 1974–1993 and found small global increase of SAT variability. Especially noticeable increase was obtained for central North America. Jones et al. (1999) have worked with global data and have not detected any change in variability. Investigations by Grieser et al. (2002) based on the monthly averaged European temperatures have shown that at least in this region of the world the SAT variance has mainly decreased or remained constant during the last 100 years. Michaels et al. (1998) have examined monthly averaged SAT data for the 5° ⫻ 5° grid boxes around the world and have detected decrease in the intra-annual variability that prevailed over the past 50–100 years. The authors also have found general decrease in monthly temperature variability for the United States, some regions of the former Soviet Union and China. Mixed trends were detected for Australia.
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More uniform results exist for the high-frequency temperature variability. An analysis by Karl et al. (1995) using SAT data of 1910–1990 observational period has revealed that day-by-day to interannual variability has generally decreased in the Northern hemisphere. Balling (1998), analyzing daily and monthly variability of historical temperature records, has found its overall decrease from 1897 to 1996. Collins et al. (2000) have identified reduced day-by-day variability trends for Australia. Karl et al. (1993), Easterling et al. (1997), and New et al. (2000) have shown that the land surface warming observed over the last 50 years has been accompanied by relatively stronger increases in daily minimum temperatures than in daily maximum temperatures (see also www.ncdc.noaa.gov/oa/climate/mxmntr/mxmntr.html). Thus, the difference that is called the diurnal temperature range (DTR) and represents effective measure of the daily temperature variability has decreased in recent years. Easterling et al. (1997) have revealed a decrease of the DTR from 1950 to 1993 for ⬃4100 stations in both the Northern and Southern hemispheres. A study by Karl et al. (1993) states: “Since 1950 all of the increase of temperature across the U.S.A. is due to an increase in the minimum temperature (about 0.75 K/100 years) with no change in the daily maximum temperature. This caused a decrease in the diurnal temperature range”. Subsequently, similar decrease in daily SAT variability has been observed at other locations and as stronger as one goes towards the Polar Regions. A study by Braganza et al. (2004) has detected strong negative trend of ⬃0.4 K in the DTR over global land areas (gridded SAT data) for the last 50 years. The last 50-year period was chosen by most of the researchers because it has the largest and most consistent data coverage. A study by Braganza et al. (2004) detected that the increase in daily minimum temperature over this period was ⬃0.9 K, while the maximum temperature had risen by only ⬃0.6 K. It now appears that most of the observed global surface warming of recent decades is occurring at night. The studies of the correlation between changes in mean SAT value and its variability are sparse and not as unanimous as the results of the DTR change. Braganza et al. (2004) have shown that observed clear DTR decrease is not spatially uniform. The correlation of the DTR with the mean temperature over all observations of the 1901–2000 period is not significant and equals to only ⫺0.24. Griffiths et al. (2005) have revealed significant location-dependent trends in the DTR in the majority of stations across the broad Asia-Pacific region, as well as the correlation between mean temperature and the frequency of extreme temperature events. This correlation appears stronger in the less populated/urbanized regions. Vincent and Mekis (2006) have examined trends in the mean temperature and the DTR for Canada and have shown that at least for the period 1950–2003 there is significant decrease in the DTR as well as a decrease in the variance of the daily mean temperature. Both trends were location dependent. Observed reductions in daily temperature variability over the last century are large; they unlikely occur due to natural climate variability alone. Numerous attempts were undertaken to capture the correlation between changes in the SAT mean and variability through numerical modeling of the effects induced by humans. The majority of the climate model simulations associated with the build-up of greenhouse gases predicts not only climate warming but also a general decrease in the climate variability (e.g., Karl et al., 1999; McGuffie et al., 1999). Dai et al. (2001) and Stone and Weaver (2002, 2003) have shown that anthropogenic forcing by greenhouse gases and sulfate aerosols
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in General Circulation Models (GCMs) caused small but detectable decrease of 0.2 K/100 years in the global DTR over the twentieth century. The 50-years DTR trends of similar amount were simulated by Braganza et al. (2004). Modeling results have also corroborated that expected DTR decrease is not spatially uniform. Possible reasons for the DTR decrease are: (1) urban heat island effect (see previous Section), (2) an increase in cloudiness, and (3) anthropogenic greenhouse gases and sulfate aerosol emissions. Verdecchia et al. (1994), Stone and Weaver (2002), and Braganza et al. (2004) have shown that the main controlling factors for the DTR are clouds and soil moisture. Because of the number of atmospheric and surface boundary conditions affecting the maximum and minimum temperature, the linkages of the observed changes in the DTR to large-scale anthropogenic climate forcings still remain tentative. Further studies for more sure detection of the temperature variability (including measurement of underground temperature) are indispensable. Detection of the temperature variability does not represent an easy task. Notwithstanding that all variability measures are based on the difference from some reference point, e.g., long-term mean or previous discrete value, there are many ways to define temperature variability. It may be calculation of the change of the magnitude of the DTR, frequency of occurrence of temperature extremes, the difference of the mean temperature from one day to the next, change of the standard deviation of temperature between two adjacent time periods, etc. Results are clearly dependent on the statistics chosen. Thus, for example, the latter technique may cause confounding of the high- and low-frequency variability and is insensitive to the position of large positive and negative departures from the mean within given interval (Karl et al., 1995). For example, two time series 0, 0, 0, 1, 1, 1 and 0, 1, 0, 1, 0, 1 have identical standard deviations, but significantly differing variability. The DTR is highly sensitive to small changes in maximum and minimum temperatures, etc. In addition, because all variance statistics are dependent on the reference level, e.g., mean, the uncertainties in the rate of change of the mean may confound detection of the changes in variance. Moberg et al. (2000) have compared the properties of eight statistical measures of the day-by-day variability using European series of daily averaged surface air temperatures for the period 1880–1998. Two techniques were found to be most powerful for the detection of variability in temperature time series: (1) the intramonthly standard deviation of daily temperature anomalies and (2) suggested in the work by Karl et al. (1995) the mean of a series of values defined by the absolute value of the difference in temperature between two adjacent discrete time periods. The quality of observed data is a vital factor for both methods. For example, the latter procedure is very sensitive to the homogeneity of the temperature series; thus, it can be applied as the diagnostic tool for detection of the changes in the measurement techniques or other inhomogeneities in the temperature time series used. Applying both methods, Moberg et al. (2000) have revealed different behavior of daily variability trends in different parts of Europe. Variability has decreased by 5–10% in the northeast of Europe, has shown change of 0% to ⫺5% in the northwest, and has increased by 5% to the southwest. On a longer timescale, day-by-day temperature variability in winter, spring, and autumn in northern Europe has decreased over the last approximately two centuries. The larger variability in northern Europe before twentieth century can be mainly attributed to a higher frequency of winter extremes.
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General analysis of the climatic temperature change/variability includes decomposition of the observed time series into following significant components: 1. linear trend 2. harmonic components 3. extreme events 4. noise (stationary or non-stationary). Robust estimation of each component in the presence of other components is not a trivial task. It can be performed by various statistical methods, from the linear regression and spectral analysis to far more complicated, e.g., the Generalized Additive Model (GAM; Vislocky and Fritsch, 1995; Grieser et al., 2002). Independently of their capacity/performance all these techniques should answer the following questions: 1. Is there significant linear trend in measured records? 2. Are there significant harmonic components? 3. If so, has any observed cycle changed, e.g., how has changed an amplitude of the annual cycle? 4. Are there extreme events that cannot be explained by the statistical properties of the record? While many time series can be described in terms of two basic classes of components: trends and periodicity, climatic time series contain significant intrinsic stochastic component. Thus, the last but not least question should be: 5. When all significant deterministic components were removed, what is the structure of the remainder stochastic noise? To meet these requirements a flexible stepwise strategy has to be used. Below we present an example of the detection of variability changes in the 8-year-long time series of the GST monitored at station Prague-Sporilov. While borehole GST reconstructions capture low-frequency variability only, temperature monitoring data can be complementary to these long-term trends detecting shortterm variability. Details of the monitoring experiment at Prague-Sporilov site are described in the previous section. The site is located on the top of a low hill in the campus of the Geophysical Institute of the Czech Academy of Sciences on the rim of large urban agglomeration. The temperature has been monitored since 1994 (Cermak et al., 2000) at a number of selected depth/elevation levels below/above the surface. Figure 125 shows results of 8-year temperature monitoring. These data refer to the temperature measurements obtained by zero-depth thermistor sensor installed on the top of a few millimeters of the rotten organic relics upon the compact soil ground. The individual measurements were taken at 15-min intervals and then averaged to 6-h regular grid; the precision of the individual readings is better than 0.01 K. The early years suffered by several data gaps; an uninterrupted continuous record exists only for the period 1998–2001. There were no changes on the observational procedure or in the equipment installation
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Fig. 125. Results of 8-year temperature monitoring of the ground surface temperature at PragueSporilov borehole.
during the whole experiment. The estimates of variability are thus not influenced by any data inhomogeneity problems, which otherwise may seriously bias the results (Moberg et al., 2000). The record of the natural internal variability can be reconstructed by removing estimates of the response to the periodic external forcing (Jones and Hegerl, 1998). The actual character of changes in the temperature variability may be distorted by the annual temperature variations when the slope of the annual cycle is steep in the spring and autumn seasons (Karl et al., 1995; Moberg et al., 2000). To minimize the potential influence of the annual cycle, the measured data, before being processed, should be converted into non-periodic temperature anomalies. Figure 126 shows how this pre-processing works. The measured temperatures were expressed as TLY, where Y ⫽ 1, % , 8 corresponds to years from 1994 to 2001, and index L ⫽ 0, 1, % , 1460 means the serial number of the corresponding 6-h long interval within the respective year. The mean annual cycle contained 1461 points from 0 to 365 days at 6-h intervals and was calculated by averaging 8-year values of 苶 TL ⫽ ᎏ18ᎏ8y⫽1TLY. The reference temperature was then obtained from this cycle using the mean value, first four harmonics of the Fourier analysis, and the daily wave (wave number 365). Little, if any, additional variance could be explained when higher order harmonics are used. To obtain the temperature anomaly the reference temperature was removed from measured temperature (Figure 127). As seen, temporal oscillations of obtained signal are erratic and do not exhibit apparent regularity, trend, or cyclic pattern. The first insight in the variability of this record can be gained using its probability distribution. Figure 128 presents the comparison of the probability distribution of the Sporilov temperature anomalies record with the normalized standard distribution. Both distributions generally coincide. Prominent feature of the temperature anomaly record is the prevalence of extremes in warm seasons of the year while extremes are relatively rarer
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Fig. 126. The average annual cycle and its Fourier-smoothed representation (thick line).
Fig. 127. Temperature anomalies calculated from the surface temperature monitored in PragueSporilov during the period 1994–2001.
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Fig. 128. Histogram of occurrences of different temperature anomalies in the time series shown in previous figure. The Gaussian distribution is shown for reference.
in cold seasons. The probability distribution of the temperature anomalies (Figure 128) is skewed5 to the right (moment coefficient of skewness is equal to 1.59). More heavy (“fat”) right tail indicates that warmer extremes are more frequent than colder extremes. This finding agrees well with the knowledge obtained for the larger scales of aggregation. An infrequent occurrence of cold extremes in daily temperatures in the last two decades relative to warmer extremes was reported both for local and for global temperatures (Jones et al., 1999; Rebetez, 2001). Data presented here confirmed this fact for the higher frequency variation up to 6-h aggregation level. Note that the temperature anomaly distribution is also more peaked6 with respect to the normal distribution (kurtosis is equal to 9.55). The appropriateness of the existing numerous variability measures is judged by their power to detect/describe the details of variability pattern. The measure used for the detection of the temporal changes in variability was suggested in the work by Karl et al. (1995) and is defined as the absolute value of the temperature difference between two adjacent periods of time. The measure, which we call N-point change, is calculated as the absolute
5 Skewness is a measure of the asymmetry of the probability distribution. A distribution is right-skewed if the right tail (higher values of variable) is longer, and, on the contrary, is left-skewed if the left tail (lower values) is longer. Symmetric distribution looks the same to the left and right of the center and has zero moment coefficient of skewness. Skewness of the normal distribution is 0. 6 Kurtosis is a measure of the “peakedness” of the data relative to a normal probability distribution. Positive kurtosis means that the distribution has a distinct peak near the mean, declines rather rapidly, and has heavy tails. In other words, it means that more of the variance occurs due to infrequent extremes, as opposed to frequent lower size variations. Negative kurtosis indicates a “flat” distribution. Kurtosis of the normal distribution is equal to 0.
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difference between the average for the N-point long sequence that begins at measured point t and the similar average of N anomalies that begins at point t ⫹ t. Generally, t ⱕ N, which implies the possibility of overlapping. The overlapping is useful for longer intervals when the application of the strictly non-overlapping differences artificially constrains their number, and may lead to noisy seasonal estimates. We have temperature anomalies time series T1, T2, T3, % , Ti, % . The measure of variability TN (N-point change) is defined as the absolute difference between the average of a sequence of temperature anomalies for N points that begins at point I and the average for the N-point long sequence beginning at point (i ⫹ N ⫺ k) TN ⫽abs(Ti ⫺Ti⫹ N ⫺k ),
(53)
where Ti ⫽
1 N
i ⫹ N ⫺1
∑ l ⫽i
Tl ; Ti⫹ N ⫺k ⫽
1 N
i ⫹2 N ⫺ k ⫺1
∑
Tl .
(54)
l ⫽i ⫹ N ⫺ k
For the time lag k ⬎ 0 there are partly overlapping running differences (Karl et al., 1995). The measure of variability was calculated successively for the whole temperature time series to obtain time series of variability measure. The values of N were chosen as 1, 2, 3, 4, and 20, 40 corresponding to the averaging intervals from 6 to 24 h as well as to 5 and 10 days. There are some natural separations of the temporal scales of the climate system variability. Perhaps, the most important of them is that between weather and climate. Mainly in technical reasons, weather refers to variability in the climate system at timescales less than about 10–14 days, while the climate variability refers to the longer timescales. While the multihour timescale data aggregation patterns still reflect variability of the weather fluctuations, the 5- and 10-day aggregation can be attributed exclusively to the short-term climate variability. Daily periodic variability (the daily wave) was removed from the observed temperatures (see above); thus, it cannot have any influence on the calculated variability patterns discussed later. Four upper panels of Figure 129 show variability changes on the 6-h to day-by-day scales of aggregation for 8 years. The variability patterns depend on the length of the averaging interval N, and this dependence reflects essential features of the climate dynamics at different timescales. Variability time series for 6-h intervals do not show any significant linear trend, but they exhibit apparent quasi-seasonal oscillations. In all studied time intervals the variability increases during the spring season (partly also in the summer) and decreases in the autumn–winter seasons. Except for extremely variable year 2000, the spring “explosions” in variability are very short. The 12- and 18-h patterns do not offer any special features and represent only a gradual transition from higher to lower frequency variability pattern. Detected quasi-seasonality is relatively less pronounced in the dayby-day variability, the oscillations of which are more irregular. Day-by-day variability rarely falls to very low values and even it does then only for a short time interval. On the other hand, the 24-h variability exhibits a general decreasing trend of ⫺0.038 ⫾ 0.002 K/year similar to what is predicted by the most of greenhouse warming simulations. Climate model simulations associated with the build-up of greenhouse gases predict not
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only climate warming but also a general decrease in climate variability (e.g., Karl et al., 1999; McGuffie et al., 1999). This trend is absent in the higher frequency variability. Such decreasing trend existing during the second half of the twentieth century was reported also in works cited above dealing with the changes in the diurnal range of the SAT. Two lower panels of Figure 129 show variability changes on the 5- and 10-day scales of aggregation for the same 8 years. Surface temperature variability is somewhat higher than at the daily scale; however, its pattern is comparable with the day-by-day variability oscillations. Quasi-seasonal oscillations characteristic for the short-term scales of aggregation are absent, and decreasing trend of the same order as in the variability time series on 18- and 24-h scales of aggregation is preserved. Probably, part of the variability decrease observed in the Sporilov data may be attributed to the urbanization effect (see, e.g., Jones et al., 1990; Griffiths et al., 2005) characteristic for the intensively developing suburban part of city of Prague. However, its most significant part can be attributed to the NAO forcing. As known, the climate of the European-Atlantic sector exhibits considerable spatial and temporal variability. Recent studies have indicated that the variability of atmospheric circulation patterns in the Northern Hemisphere may be affected by the differences in the sea level pressure between the Atlantic Subtropical High centered near the Azores and its Sub-polar Low near SW Iceland. This phenomenon is referred to as the North Atlantic Oscillation (NAO; for more details see www.ldeo.columbia.edu/NAO). It has roughly decadal pattern with a dominant period of 12 years and, as shown by the recent studies, has a strong impact on weather (both temperature and rainfall regimes) and climate from the eastern coast of the United States to Eurasia and from North Africa and Middle East to the Arctic regions especially in the wintertime (see, e.g., Rodwell et al., 1999; Marshall et al., 2001; and the references therein). As shown in the work by Bodri and Cermak (2003) at all frequencies there is a significant correlation between Sporilov variability and the NAO index. At the investigated location correlation is positive and appears more prominently in winter periods, when the NAO control over the weather is stronger. 4.3.3 Structure of the stochastic component of the short-term climate variability There is little doubt that climate change involves a number of non-linear processes. Thus, except for the deterministic trend components, the climate contains significant stochastic part. A deterministic signal is traditionally defined as anything that is not noise (i.e., an analytic signal, or perfectly predictable part, predictable from measurements over any continuous interval, etc.). Deterministic components have reduced the degree of uncertainty and normally correspond to the main modes of the system behavior. They arise as a result of their own physical mechanisms and a sum of contributions from various forcings. Stochastic component (noise) represents an accumulation of random influences (the day-by-day weather variations, stochastic climate change on longer timescales, etc.) superimposed on the deterministic part on the climatic signal. The unpredictable weather fluctuations represent a permanent source of stochastic noise in the climatic time series. Induced by these fluctuations, noise variability can mask climate changes caused by anthropogenic and other deterministic influences, and its presence causes additional challenges to the climate researcher that deals with climate variability.
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Fig. 129. Variations of differences in average temperature anomalies for 6-, 12-, 18-, 24-h and 5-, 10-day averaging intervals and their linear trends (thick lines). Low-frequency changes are highlighted by a Gaussian filter, roughly corresponding to 10-day moving averages.
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On the other hand, the weather noise cannot be regarded as annoying hindrance. It represents essential part of the climate variability. Characteristic timescales of the deterministic and stochastic variability are matching. Sometimes an addition of the stochastic noise can significantly amplify deterministic signal. This so-called stochastic resonance has become widely recognized as a paradigm for noise-induced effects in driven non-linear dynamic systems. This phenomenon has been propounded as, e.g., a possible explanation for the ice ages and the noise-induced transitions in thermohaline circulation. The early work by Hasselmann (1976) has first introduced the idea of the separation of timescales observed in the climatic records and treating their short-term components as stochastic variables. Further studies have indicated that an application of the ideas of stochastic processes provides a useful insight into the climate physics. Weather-induced climate variability can be studied with stochastic climate models using stochastic processes and stochastic differential equations that are able to capture complex patterns of both signal and noise and their “cooperation”. Modes of the stochastic climate variability can be identified by statistical analysis of the observational data. Various tools of mathematical statistics have found wide application in climatologic research. Fractal dimensional analysis represents a powerful tool for the detection of the stochastic component of climate and/or the construction of stochastic terms of the climate models. This analysis (fractal dimension analysis) consists of an assessment of the invariant quantities that arise from the scaling properties of records and is based on the numerical evaluation of variance (a quadratic measure of variability). Fractal dimensional analysis of geophysical time series is a well-established research tool to investigate their dynamics. It was initiated by a series of papers by Mandelbrot and Van Ness (1968) and Mandelbrot and Wallis (1968, 1969) and has been followed by the application of the fractal/multifractal technique to various geophysical processes (Mandelbrot, 1982; Lovejoy and Mandelbrot, 1985; Ladoy et al., 1991; Turcotte, 1992; Schertzer and Lovejoy, 1995). Fractal dimension analysis is particularly well suited for an assessment of the time series variability (Hastings and Sugihara, 1993). Scale invariance has been found to hold empirically for a number of geophysical processes. The mathematical definition of the “simple scaling” or scaling of the increments is as follows. The function Y(x) is termed scale invariant, if it fulfills the condition: Y (x )⫽ H Y (x ),
(55)
where Y(x)⫽Y(x1)⫺Y(x0), x⫽x1 ⫺x0 and Y(x)⫽Y(x2)⫺Y(x0 ), x2 ⫽x0 ⫹ (x1 ⫺ x0 ) for arbitrary scale ratios and x. Equality in Eq. (55) means equality in probability distributions. The random variables u and v are equal in this sense when Pr(u ⬎ q)⫽Pr(v ⬎ q) for any threshold q (“Pr” means probability). The “simple scaling” means that if we scale the coordinate x by means of an appropriate choice of the exponent H, then we always recover the same function. The parameter H is a constant called the-unique-scaling parameter (0 ⱕ H ⱕ 1). An assessment of scaling properties of the climatic time series starts with the assumption that they can be modeled as a stationary stochastic process. There are many standard methods to assess the scaling structure of {Yi}. A typical (and probably simplest) procedure consists in performing a Fourier (spectral) analysis of the time series.
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Spectral analysis is concerned with the detection of cyclic patterns of the data and expresses the amount of variance in a time series that occurs at different frequencies or timescales. In the case of deterministic time series the purpose of this analysis is to decompose a multicyclic time series into a few sinusoidal functions with particular frequency. If a time series represents a complex output of the stochastic process, distinct periodicities are generally absent and power density is distributed across the entire spectrum. In this case, spectral analysis represents a conventional method of analyzing time series data to determine the power (mean square amplitude) as a function of frequency. A stochastic, or noise, signal is fully described by its power spectral density which gives the expected signal power versus frequency. Assuming that a process can be described by a single dimension, H allows one to use the energy spectrum E( f ), where f is the frequency, of the observed variable Y(x) for scaling investigations. The energy spectrum is scaling when it can be described by a power law relationship according to (e.g., Ladoy et al., 1991): E ( f ) ⬃ f ⫺b ,
(56)
where b ⱖ 0. In the simple scaling case, exponents H and b are related according to b ⫽ 2H ⫹ 1. When E( f ) is of this form over given frequency range, fluctuations occur at all scales with no characteristic time and hence within this range the process is scale invariant. Most geophysical time series and particularly climatic time series obey this behavior. Spectra of climatic time series are characterized by two important features: (1) continuity and (2) so-called “red noise” behavior (slope towards longer timescales in the logarithmic representation of the power spectra). The “redness” can be attributed to stochastic mechanisms where random high-frequency fluctuations (e.g., unpredictable weather variations) are being integrated by the components of the climate system with slower response, e.g., ocean, while the low-frequency fluctuations develop and grow in the amplitude with increasing timescale (Hasselmann, 1976). Different values of b represent the cases of the “colored noise”. For example, white noise has equal power density across the entire spectrum (constant energy at all frequencies) as white light. In the logarithmic power spectral density versus frequency diagrams it appears as flat, with b ⫽ 0. Thus, an exponent b can be interpreted as a measure of departure from the non-correlated random white noise. The scaling spectrum with b " 0 has an “excess” of energy at low frequencies and thus is known as a “red noise” (in the sense of Gilman et al., 1963). It got this name after a connection with red light, which is on the low end of the visible light spectrum. In the logarithmic power spectral density versus frequency diagrams, red noise appears as descending line with the slope b. Figure 130 shows different kinds of the time series of the “red noise”. Brownian noise is a kind of signal noise produced by Brownian motion (one-dimensional random walk).7 It is named in honor of Robert Brown (1773–1858), leading British botanist, the discoverer of the Brownian motion. 7
A continuous process {Y(t)} represents a continuous-time random walk or a Brownian process if, for any time step t, the increments y(t) ⫽ y(t ⫹ T) ⫺ y(t) are: (1) Gaussian, (2) of mean 0, and (3) of variance proportional to t (to t2H in the case of fractional Brownian noise).
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Fig. 130. Synthetically generated kinds of the fractional Brownian noise (“red noise”).
An ordinary Brownian noise has b ⫽ 2 meaning that it has more energy at lower frequencies. For the ordinary Brownian noise, the change, or increment, from one moment to the next is random (non-correlated) and normally distributed. For the simple scaling case the coefficient of correlation r of successive increments is equal to 22H ⫽ 2 ⫹ 2r (r ⫽ 2b⫺2 ⫺ 1), where ⫺1/2 ⬍ r ⬍ 1 is independent of the time step t (Hastings and Sugihara, 1993). In the case b ⫽ 2, this equation gives r ⫽ 0. In other words, successive increments are uncorrelated. Because of the absence of the correlation between amplitude of oscillations corresponding to two successive time intervals, such signal is unpredictable. Brownian noise can be produced by integrating white noise. In the intervals of 2 ⬍ b ⬍ 3 and 1 ⬍ b ⬍ 2 stochastic time series exhibit two distinct types of behavior: persistence or antipersistence. Persistence is a presence in time series of significant dependence between observations a long time span apart. Persistence represents a long-range correlated or long memory process and may be characterized by a correlation function decaying hyperbolically as the lag increases, as opposed to the exponential decay of short memory processes. In this case, even
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sufficiently distant from each other, fluctuations are strongly influenced by the longterm, persistent trends. Such records are qualified as less variable. Visual appearance of persistent noise with spectral exponent 2 ⬍ b ⬍ 3 looks like random fluctuations superposed upon a “background” that performs several quasi-cycles. Because the future trend is more likely to follow an established trend, persistent processes are more predictable. In the case of b ⫽ 3, correlation coefficient between two successive increments is 1, and the function is completely differentiable (deterministic). Beran (1994) has characterized the family of strongly persistent time series. They are well known in geophysical and in particular in climatic time series (for more details see Section 2.3.4). The signals with higher b values obey less erratic or more regular, trend-reinforcing behavior. In the signals with b between 1 and 2 (antipersistent), inversely correlated fluctuations dominat and the signal reveals a more “nervous”, rough appearance with frequent reversals. The upper panel of Figure 130 represents the signal with familiar Kolmogorov8 spectrum with b ⫽ 5/3 characteristic for the turbulent wind fluctuations. In spite of the relative complexity of the antipersistent time series, the predictability again increases below b ⫽ 2. It occurs due to inverse correlation of fluctuations in such series. It means that an increase in the amplitude of the process is more likely to lead to its decrease in the next time interval. The scaling regime describes the random part of climate variability: in the range of timescales where the scale invariant law holds, the climatic system has no characteristic timescale, and the climate changes result from the accumulation of random fluctuations. Possible breaks of scaling that are often observed in climatic time series (e.g., Fraedrich and Larnder, 1993; Olsson, 1995) signify the appearance of the basic characteristic timescales of climate system and identify the boundary between the random and deterministic regimes. Due to strong intermittency, scaling studies require vast amount of the measured data and preferably many independent realizations. Some of the analyses using climatic time series have suffered from the shortness and the low quality of the data. Results of precise, decade(s)-long temperature monitoring appear to be especially suitable for this kind of analysis. Below we illustrate an application of above technique using time series of the temperature anomalies recorded at 0.05 m above the ground and at 1 and 10 m depth at Prague-Sporilov. All data are 6-h averaged, and thus still contain significant part of the weather fluctuations. Data were preprocessed in a similar way as the GSTs, shown in Figure 126. As in Figure 127, the temporal oscillations of calculated temperature anomalies are erratic and do not exhibit apparent regularity, trends, or cyclic pattern. Figure 131 shows examples of the power spectra of temperature anomalies measured at Prague-Sporilov at 0.05 m above the surface and at 1 and 10 m depth. All power spectra are similar. There is no evidence of periodic variations at any particular frequency; the background seems to be quite dominant. All spectra exhibit clear red noise behavior over all normalized frequency domain with spectral exponent b between 1 and 2 signifying antipersistence. The exponent b is the largest for the air temperature
8
A.N. Kolmogorov (1903–1987) is a Russian mathematician who made major advances in the fields of probability theory and topology. He has also worked on turbulence, classical mechanics, and information theory. In 1941, Kolmogorov has published a paper in which he derived a formula for the energy spectrum of turbulence.
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Fig. 131. Power spectra of temperature anomalies monitored at Prague-Sporilov at 0.05 m above ground surface and at 1 and 10 m depth. Frequency dependence of the power spectral density variations are shown in a log–log plot. The values are relative: the frequencies are normalized to the lowest frequency in the spectrum, the power spectral density to that at the lowest frequency. Solid lines represent the least squares fit to the data.
anomalies and progressively decreases with depth. This means that the degree of antipersistence (variability) is the highest for the temperatures recorded in the air and decreases into the subsurface because of the well-known gradual filtering out of the high-frequency oscillations. The antipersistence of the temperature time series reflects, in particular, the turbulent nature of the atmospheric and ocean dynamics responsible for weather fluctuations. As the signal penetrates into the surface its probability distribution comes nearer to the Gaussian. Figure 132 shows the histogram of occurrences of different temperature anomalies measured in Sporilov station at 1 m depth. Its comparison with the Gaussian distribution that is shown for reference, as well as with similar diagram calculated for the SAT temperature anomalies (Figure 128), demonstrates that the former histogram is more close to the Gaussian distribution. The right tail (the prevalence of warm extremes) disappears. The skewness of the distribution (degree of asymmetry) is close to zero characteristic for the normal distribution. The distribution is still more peaked than the Gaussian (kurtosis is equal to 4.75). However, this value is two times lower than that obtained for the air temperature anomalies. The differences from the Gaussian distribution appear in the more damped form in the temperature anomalies measured at deeper levels. Above calculations hint that the underground temperature monitoring could provide reliable information on the short-term variability of stochastic component of the surface temperature signal. The Earth smoothes extremes and filters out high-frequency fluctuations; thus, only the most important time resistant irregularities are preserved in the ground temperatures. More complex stochastic model that reproduces the variability and the long-term correlation observed in climatic time series was suggested in the work by Lavallée and Beltrami (2004). The stochastic model proposed by these authors represents a convolution between the Fourier transform of the random variable (white noise) {Xi}, i ⫽ 1, % , N
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and the function with a power law dependence (Eq. (56)) in the frequency space. Its output {Yi} can be presented as
2(i ⫺1)( j ⫺1) Yi ⬀ ∑ f ⫺b Ⲑ 2 Ff ( Xi ) exp , N j ⫽1 N
(57)
where Ff (Xi) is the discrete Fourier transform of the random variable and j is related to f by f ⫽ 2( j ⫺ 1). In this case, the power spectrum of {Yi} takes the form of Eq. (56). Using this relation, the scaling exponent b of the measured time series can be estimated from observed data. The values of the underlying random variable {Xi} can be calculated from the relationship: Xi ⬀ Fi⫺1 Ff (Yi )⫻ f
bⲐ 2
,
(58)
where Fi⫺1 is the Fourier inverse. While analysis of the Prague-Sporilov data presented above has assumed the Gaussian distribution of the measured data, in the model by Lavallée and Beltrami (2004) the probability distribution, controlling the variability of stochastic model, is unspecified. When it is identified from the analysis of the probability density function of {Xi}, the statistical properties of the stochastic model can be regarded as completely known.
Fig. 132. Histogram of occurrences of different temperature anomalies in time series monitored in Sporilov station at 1 m depths. The Gaussian distribution is shown for reference.
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The authors applied the model outlined above to the 1500–2000 years’ long dendrochronological time series. Obtained exponent b ranged between ⫺0.5 and ⫺0.7, thus, revealed much less departure from the non-correlated random white noise than PragueSporilov time series described above. Lavallée and Beltrami (2004) have also investigated some possible probability laws including the Gaussian, the Cauchy, and the Lévy distributions (three of the few distributions that are stable and that have probability density functions that are analytically expressible) to find the best fitted to their data probability distribution. The authors have compared the cumulative probability distributions (probability that random fluctuation DT⬘ exceeds a fixed value DT) of the three probability density functions mentioned above. The misfit of the theoretical and measured probability density functions is more obvious in such plots. The cumulative probability distribution of climatic time series generally has a nearly Gaussian shape in the center and a tail (probability of the extreme events) that is “heavier” than expected for a normal distribution (see Section 2.3.4 and Figure 24, Chapter 2). Note that the “fat-tailed” probability distributions are general characteristics of the long-term climatic time series. When the fluctuations are of this type, the phenomenon is so intermittent that the return times of extreme events are much shorter than those for Gaussian process. According to the Gaussian law, very strong fluctuations have almost zero probability of being observed. The Lavallée and Beltrami’s analysis has shown that the stochastic model based on Lévy’s law reproduces the climatic variability archived in dendrochronological time series in the most precise manner. Similar cumulative probability plot presented in Figure 133 was calculated for the ground temperature anomalies monitored at 1 m depth in Sporilov borehole. The misfit of the
Fig. 133. The log–log plot of the cumulative probability distribution for the temperature anomalies measured at 1 m depth at Sporilov site. The Gaussian cumulative probability is given for comparison.
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measured data with the Gaussian law is minimal. It hints that this distribution reproduces measured data with enough accuracy. The “fat-tailed” distributions characteristic for longterm climatologic time series (e.g., Lévy’s law that was found for the dendrochronological time series in the above-cited work) means the higher probability of large fluctuations. The Gaussian distribution characteristic for the underground temperatures reflects the main properties of the heat conduction process: progressive smoothing of the surface signal and filtering out of its high-frequency component. The variability of stochastic component of climate can be studied from different viewpoints. The fractal approach presented above provides the simplest non-trivial example of scale invariance, and is appropriate for dealing with extreme and ubiquitous variability of climate. Numerous similar (mono-) fractal studies were performed in different climatic as well as geophysical fields. An assumption of a unique dimension was abandoned in the later works. More sophisticated statistical summaries consider the multifractal theory in combination with the multiplicative processes similar to energy flux cascade in turbulence (Davis et al., 1994; Schertzer and Lovejoy, 1995, 2004; Lovejoy et al., 2001; Schertzer et al., 2002). Except for the single dimension, it involves a moment scaling function that describes the behavior of the statistical moments at different scales and is able to embrace an entire range of complexity of the geophysical signals. An applicability of the multifractal theory has been thoroughly investigated during the last decade. The discrete wavelet transform (DWT) is a powerful signal processing technique that also offers several advantages over traditional spectral analysis techniques. It can be used for the analysis of the non-stationary time series (one of the primary limitations of Fourier analysis). It is scale adaptive and allows to decompose original time series into a collection of new time series, each of which represents the variability in the signal over a characteristic band of scales. Unlike Fourier coefficients that capture variability over the entire time series, the DWT captures variability associated with their local features giving better estimates of the variance attributable to local, intermittent variations in time series. Further developments of the DWT, e.g., the maximum overlapping discrete wavelet transform (MODWT), provides several advantages over the DWT. Other examples of statistical methods specific to climate research are presented in a book by Von Storch and Zwiers (1999). The book describes applications ranging from simple use of sampling distributions to obtain estimates of the uncertainty of a climatological mean to complex statistical methodologies composing the basis for calculations that are capable of revealing the dynamics of the climate system. In the past decade, climate variability research has made considerable progress in understanding and modeling climate changes on timescales of years to decades. In the previous section we looked briefly at several applications of stochastic processes to the detection of the short-term variability that presents in the time series arising from subsurface temperature monitoring. The examples discussed have shown that while GST reconstructions from the borehole temperature logs represent a useful tool for inferring long-term climate trends, time series resulting from borehole temperature monitoring can be of key importance in assessing the patterns of temporal climate variability. This suggests a direction for future research. The investigations of variability likewise the investigations of warming trends can be used for the validation of the simulated models for various scenarios of greenhouse-gas emission and land use. A detailed understanding of climate variability is also important for the prediction of extreme climatic events.
Conclusions and Perspectives of Future Progress Climate provides/controls certain basic conditions of life to all constituents of the living world. The reconstruction of a long past climate record is necessary for an evidence of the past climatic regimes and for the study of the long-term processes controlling climate change. Investigations of the past climate are also indispensable for both to understand present-day climate and its possible future changes, and to test the hypotheses about the causes of the recent climate change. More climate information from the distant past could be highly valuable to strengthen our understanding of the modern climate changes and to improve existing models of climate development. An ultimate utility of paleoclimate reconstructions can be their contribution to the detection of the causes of climate change. In traditional paleoclimatology the reconstruction of the long climate changes is based on a variety of proxy records. Because climatic variables are only indirectly reflected in these data and their evaluation requires an interpretation of physical, chemical, or biologic phenomena, results may contain systematic biases and errors. To compile the most meaningful and complete climatic history, it is necessary to consider the information of many independent records. Measurements of underground temperatures in boreholes performed worldwide at the recent decades represent a valuable source of the paleoclimatic information. Subsurface temperatures respond to an integrated, continuous temperature change at the Earth's surface. Surface temperature changes penetrate deep into the subsurface. Process of heat conduction in rocks smoothes out high-frequency air temperature oscillations; thus, temperature-depth profiles measured in boreholes preserve information on average surface temperatures over a decade to millennium or longer timescales. Like other approaches to the paleoclimate reconstruction, the "borehole" method has its own strengths and weaknesses. Its major advantage is that in contrast to the proxy data representing indirect inferences of climate change, the subsurface temperatures measured in boreholes directly archive past GSTs. In other words, except for the meteorological instrumental records, borehole temperature-depth profiles contain the most quantitative information on the past climate change. Borehole temperature-depth profiles yield robust long-term temperature trends, but because of the nature of heat conduction in the subsurface with decreasing in time resolution. It is these properties (direct measure of temperature, its continuous recording at the same place, low-pass filtering) that make borehole temperature logs so valuable for the family of the climate change detection techniques. Because of the wide geographic availability of this geothermal archive, subsurface temperatures have significant potential to provide spatial paleoclimatic information. Obviously, it exists practically everywhere beneath the land surface. To get this information one should perform only relatively simple and inexpensive procedures of the borehole drilling and logging. An application of this technique is especially important in numerous, still poorly sampled, regions of Asia and the Southern Hemisphere. During the last decades our understanding of the borehole climatology has improved, and it has taken place among the leading methods of the paleoclimate reconstruction. 305
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Inferring of the GST history from borehole temperatures has become a major endeavor of geothermal research. Numerous analyses of the individual boreholes or local suites of boreholes have inferred temporal patterns of the GST change over various time intervals, while the regional and hemispheric to global ensembles of the GST reconstructions have revealed generalized patterns of the temperature change at the Earth's surface. Globally averaged borehole data have indicated a climate warming in the Northern Hemisphere of about 1 K over the past five centuries, half of which has occurred in the twentieth century alone. Results obtained by various research teams using slightly different techniques of the GST reconstruction show general agreement. Detected warming coincides well also with the climatic trend established by various proxies and in its last section by the instrumental record. Similar trend has been detected in the temperature time series monitored in shallow boreholes. Numerous monitoring experiments and field studies performed by multiple research groups also have documented the fidelity of the GST-SAT coupling. Together with the borehole temperature logging, borehole temperature monitoring in the recent decade became one of the building blocks to help us understand how the Earth's climate is changing. Last decades have been characterized by a remarkable progress in different practical efforts to apply borehole temperature measurements in a number of climatologic problems. Much more work was carried out in the borehole temperature logging, in the extension of the temperature monitoring systems, in the data collection and creation of the database with easy access, and in data evaluation than that was anticipated in the beginning of the borehole climatology. This work is progressively continuing, because borehole climatology indubitably cannot be regarded as an accomplished scientific branch. Studies investigating regional GST variations still have relatively large uncertainty because of the high local-scale microclimate variability as well as the lack of exact techniques for screening out boreholes that are not ideally suited for the climate change reconstruction. Substantial progress should be achieved in the widening of existing database to the regions that still appear as the "white spots" on the climatologic maps, in the development of more powerful mathematical procedures reducing uncertainties in the GST inversions, in robust method of merging of the borehole results with other paleoclimatic information, and in the incorporation of this new knowledge into modeling flamework to better understand how climate variables, which are important to human and natural systems, are affected by the changes in the Earth's system resulting from natural processes and anthropogenic activities. All these studies will assist to better understand and predict future climate change. Considerable uncertainty still remains in the interpretation of the borehole data owing to possible non-climatic environmental influences. Discovering the causes of climate change is tied in part to our ability to discern regional variations in GST histories. There are many questions on the physical nature of the GST changes over the last one to two millennia that cannot be quantitatively and conclusively answered on the current level of knowledge. It is expectable that future international borehole research activities will ensure progressive advancement of the GST reconstruction techniques and results. Combined with other climatologic studies they will provide aggregate, broader answers on numerous questions regarding the real significance of various physical factors of the climate change perspective. The borehole climatology is still under development.
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Subject Index a posteriori covariance, 62 a priori information, 33, 52, 56, 76-77, 82 accuracy, 39, 40, 63, 172 additional information, 52-53, 57-58, 60, 63-64, 72, 77-82, 189, 225,240 adiabatic lapse rate, 130 advection, 121,129, 133-134, 136, 138, 140-141,144, 147, 149, 153, 158, 262-264 Alaska, 6, 49, 107, 121, 150-156, 163-164, 166, 176, 197, 199-200 albedo, 12, 49, 96, 117, 150 amplitude, 29-31, 42, 44, 46-47, 49-50, 52, 61, 64, 67, 70-72, 78, 84, 96, 99, 112, 115-116, 123, 126-127, 129, 140, 150, 154, 179, 189, 192, 199, 203, 214, 224, 239, 241-243, 255,259, 261,270-272, 283, 290, 298-300 amplitude decrement, 29, 31,270-271 annual GST oscillations, 29 Antarctica, 2, 13, 22, 167, 169, 171-172, 211, 230-231,260, 282 anthropogenic component, 6, 226 antipersistence, 299-301 aquifer, 149 Atlantic Subtropical High (ASH), 295 attenuation, 29, 127, 218, 272 autocorrelation function, 56, 78, 190 borehole climatology, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26-28, 30, 32, 34-38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86-88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118-120, 122, 124, 126, 128, 130, 132, 134-136, 138, 140, 142, 144, 146, 148, 150, 152, 154, 156, 158, 160, 162, 164, 166, 168, 170, 172, 176, 178, 180, 182, 184, 186, 188, 190, 192, 194, 196, 198, 200, 202, 204, 206, 208, 210, 212, 214, 216, 218, 220, 222, 224, 226, 228, 230, 232, 234, 236, 238, 240, 242, 244, 246,
248-250, 252, 254, 256, 258, 260, 262, 264, 266, 268-270, 272, 274, 276, 278, 280, 282, 284, 286, 288, 290, 292, 294, 296, 298, 300, 302, 304-306 borehole filling fluid, 37 geophysics, 37, 267 logging, 34, 93, 99, 206, 282 boundary conditions, 44, 50, 60, 75, 93, 139, 141,158-159, 169, 225, 289 Boussinesq approximation, 139 Brownian noise, 298-299 Canada, 22, 31, 33, 49, 76-77, 87, 92, 94, 107, 109, 118-119, 125, 127-128, 135, 137, 149-151,155, 161,164, 166, 176, 192, 194-195, 197-198, 200, 215, 221, 244-246, 256, 260, 288 characteristic distance, 58, 130 city heat-island effect, 7 climate, 1-32, 34-173, 175-270, 272, 274-290, 292, 294-298, 300, 302, 304-306 change, 3, 8-15, 17, 19-20, 22, 25, 29, 34, 37-39, 41-45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71-73, 75, 77-79, 81-85, 87, 89, 91-93, 95, 97, 99, 101, 103, 105, 107, 109, 111,113, 115, 117-119, 121,123, 125-129, 131-133, 135, 137, 139, 141,143, 145, 147, 149-157, 159, 161,163-165, 167-169, 171-173, 175-176, 179-181,183-184, 188-189, 196-199, 209, 211,213, 216, 218-219, 224-241,243, 250, 252, 256, 258-261, 264-266, 268, 270, 275,277-280, 282-283, 285-286, 295, 300, 304-306 change detection and attribution, 240 feedback, 8, 13, 229 reconstruction, 13-14, 19, 28, 34-35, 37, 40, 47-49, 52, 85-86, 92, 98, 126, 136, 138, 141,147, 165, 171,175-176, 192, 202, 206, 209, 211, 219-220, 222-223, 226, 232-233, 236, 262, 265, 267, 286, 305 331
332
Subject Index
reconstruction database, 286 variability, 2, 6, 15, 19, 36, 89, 171, 180, 199, 203-204, 208-209, 216, 226, 234-236, 240-241,249, 268-269, 279, 281,283, 285-288, 294-295, 297, 300, 304, 306 climate change long term, 19, 29, 42, 163, 265, 270 medium term, 19 short term, 10, 15 climatic time series, 57-58, 290, 295, 297-298, 300-301,303 climatology, 2-4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26-28, 30, 32, 34-38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86-88, 90, 92, 94, 96, 98-100, 102, 104, 106, 108-110, 112, 114, 116, 118-120, 122, 124, 126, 128, 130, 132, 134-136, 138, 140, 142, 144, 146, 148, 150, 152, 154, 156, 158, 160, 162, 164, 166, 168, 170, 172, 176, 178, 180, 182, 184, 186, 188, 190, 192, 194, 196, 198, 200, 202, 204, 206, 208, 210, 212, 214, 216, 218, 220, 222, 224, 226, 228, 230, 232, 234, 236, 238-240, 242, 244, 246, 248-250, 252, 254, 256, 258, 260, 262, 264, 266, 268-270, 272, 274, 276, 278, 280, 282, 284, 286, 288, 290, 292, 294, 296, 298, 300, 302, 304-306 CO 2 concentration, 7, 229, 230, 23 lf, 249 cooling, 3-4, 6, 9, 12, 29, 33, 43-44, 46, 77, 79, 90, 97, 106, 114, 123, 133, 137, 141, 161-162, 165, 170-173, 179, 182-183, 185-188, 191,195, 198, 204-206, 208-209, 216, 218, 222, 232, 240-241, 243, 253, 256, 258, 285 cosmic radiation, 278 covariance matrix, 56-58, 238 crustal radioactivity, 27, 259 cryosphere, 12, 268, 287 Cuba, 44, 176, 199, 201-203 cutoff approach, 55 Czech Republic, 29-30, 90, 99-100, 108, 130, 145, 176-182, 184-186, 196, 204, 216, 253, 255, 260, 270-271,273-276, 278 Darcy velocity, 139, 149 deep continental drilling, 250 deep boreholes, 250, 253, 257, 260, 261 deforestation, 6, 13, 94, 96, 117-122, 197, 199, 229, 242
differential heating, 19, 225 discharge, 134, 137-138, 140-141,144, 146, 148 discrete wavelet transform, 304 discretization procedure, 51 diurnal temperature range (DTR), 288 drilling, 35, 37, 39-41,119, 167-168, 171, 189, 250, 254-255,260-266, 283, 305 D-value, 56, 78-79 East Siberia, 152, 156-157 England, 7, 16, 18, 46, 112-113, 115 environmental change, 19, 87, 96, 123, 206 evaporation, 23, 90, 92, 96-97, 100, 106-109, 113-114, 117, 199, 244 evapotranspiration, 109, 116, 122-123, 126, 155,244, 274 external forcing, 10, 85, 128, 230-231, 238-241,244, 285, 291 extreme event, 9, 290 finite difference, 63, 159 finite element, 63, 159 Finland, 90, 187-188, 191,204, 222, 260, 265 five-century-long GSTH, 211 forcing function, 26, 46, 118, 127, 192, 194, 223, 243, 251,263 forward technique, 244 Fourier analysis, 291,304 fossil fuels combustion, 229 France, 18, 176, 204 frozen ground, 149, 160 functional space inversion, 50 Gaussian noise, 66, 70-71, 73-75 Gaussian process, 58-60, 303 general circulation, 19, 72, 128, 197, 225, 286, 289 General Circulation Model (GCM), 19, 24, 72, 82, 85, 105, 165, 197-199, 239, 244 Generalized Additive Model (GAM), 290 geothermal gradient, 38, 42-44, 46, 72, 94, 137, 140-141,150, 161-162 geothermal observatory (for climate), 1, 211, 212, 267 geothermics, 27, 37-38, 135, 177 glacial-interglacial cycle, 14 Global database of borehole and climate reconstructions, 211 Global database of borehole temperatures, 215
Subject Index global warming, 6-9, 15, 49, 92, 151, 164, 167, 171,186, 196, 198-199, 206, 222, 226-228, 230, 232, 241,245, 249, 269, 274, 278-279, 285 Granger causality, 92, 245-248, 250 greenhouse gases, 7-8, 13, 118, 196, 228-229, 288-289, 294 Greenland, 3-4, 6, 9, 22, 35, 151-152, 154, 156, 164, 167, 169-172, 233, 256, 259-260 ground freezing, 98, 103, 198 ground surface temperature (GST), 25, 39, 64, 175,267 groundwater circulation, 60, 62, 177 greenhouse effect enhanced, 229, 237 natural, 228 GST history, 29, 33, 35, 44, 48, 52, 54, 57, 60, 63-64, 66-80, 83, 85, 87-89, 116, 119, 128-130, 132, 135, 149, 159, 162, 169, 171-172, 177, 179-180, 183, 185, 190, 192, 195-197, 204, 206, 208, 211-212, 215-218, 220-221,249, 251-253, 255-256, 258, 265-267, 281,306 harmonic components, 290 heat capacity, 42, 44, 63, 77, 107, 126-127, 139-140, 158, 169, 263 conduction, 29-30, 43-44, 48, 50, 60-62, 65, 70, 75, 85-86, 92, 100, 129, 133, 150, 157-158, 249, 270, 304-305 flow, 27-28, 31, 34, 38-39, 42-43, 45, 47, 49-52, 63, 77, 88, 90, 93, 97-98, 102, 109, 129-132, 140, 149, 155, 161,169, 172, 178-179, 188, 216, 256-260, 263-265 propagation equation, 44 heat-valve effect, 90 hemispherical averages, 6 high-frequency climate variations, 222 high-resolution temperature monitoring, 282 historical documents, 15, 83, 92, 249 hockey stick, 25-26, 224, 233 Holocene climate, 6, 44, 250-251,263 human-forced climate change, 236 humidity, 12, 20, 109, 113 hydraulic conductivity, 99, 135, 144, 153 head, 139 hydrocarbon exploration, 151 hydrogeology, 27, 263 hydrothermal activity, 27
33 3
ice core, 2-3, 9, 18, 20, 22-24, 35, 48, 83, 92, 167-172, 21 l, 220, 223-224, 230-231, 249, 260 instrumental data, 83, 220 record, 14, 19, 92, 122, 128, 171,182, 186, 219, 236, 249, 305-306 insulation effect, 104 Intergovermental Panel of Climate Change (IPCC), 8, 25, 115,227, 229, 233, 237, 240, 286 International Geology Correlation Program IGCP, 270 International Heat Flow Commission (IHFC), 28, 97, 149, 176, 257, 259 inverse techniques, 49 inversion, 14, 19, 22, 33-35, 49-50, 52-58, 60, 62, 64-66, 68, 70, 72-74, 77-79, 82-83, 85-89, 93-94, 105, 124-125, 129, 132-133, 135, 141, 145, 149, 157, 159, 162, 164-165, 169, 171-172, 175, 177-178, 188, 190, 192, 198, 204-205,207, 211, 215-216, 225,240, 253-256, 258-259, 262, 265,270-271,278-279 Israel, 90-91 Kamchatka, 205-207, 254, 281 Kola superdeep project, 262 KTB German continental deep drilling, 260 kurtosis, 293, 301 Kyoto Protocol, 25, 227 -
last event analysis, 50, 52 Last Glacial Maximum, 3-4, 162, 170, 188, 253, 256, 265 Late Quaternary GST change, 250 latent heat, 97-98, 103, 105-107, 109, 114, 116-117, 126, 149, 155, 158-161 Laplace transformation, 51 least-squares inversion, 53, 54, 60, 135, 141 Little Climatic Optimum (LCO), 5, 78, 183 Little Ice Age (LIA), 1, 6, 11, 25, 65, 68, 78, 83, 89, 164, 169-172, 179, 181,183, 188, 191, 192, 194, 196, 206, 208, 234, 241,255, 258, 265, 285 mean global GST, 215 Medieval Warm Period, 5-6, 11, 25, 68, 78, 169, 179, 181,183, 188, 191-192, 206-208, 232, 241,255, 258, 285
334
Subject Index
melting, 8-9, 23, 102, 104, 150, 153-154, 158, 161,164, 167, 169, 233, 244, 256 meteorological data, 21, 48, 113, 204, 219, 223, 280-281 record, 15, 30, 32, 93, 110, 112, 128, 185, 204, 211, 216, 224, 267 meteorology, 17, 35, 106 micro-vegetation cover, 49 misfit function, 61, 64, 147 Monte Carlo method, 78, 169, 171 multiproxy data, 24, 83 near-surface temperature, 90, 121 noise free, 66, 68, 74, 88, 143 non-climate disturbances, 35, 93, 98 North America, 3, 6, 15, 20-21, 57, 75, 100, 102-103, 115-116, 121,124, 150, 171, 176, 197-200, 203,209, 211-212, 215-218, 226, 251,257, 259, 271,280, 287 North Atlantic Oscillation (NAO), 171,248 Ocean-atmosphere, 85 ozone hole, 13 paleoclimate, 10, 19, 23-24, 27, 49, 85, 92, 98, 126, 133, 138, 147, 156, 171,176, 192, 209, 219, 222-223,226-227, 231, 234, 236, 244, 262-265, 267, 305 parametrization, 127, 262 past climate reconstruction, 13, 19, 35, 52, 85, 136, 141,220, 232 periglacial, 161, 281 permafrost, 12, 98, 149-166, 169, 172, 188, 196-197, 205,217, 259-260, 269 persistence, 57, 78, 96, 102, 108, 125, 156, 189, 299 perturbation, 29, 34, 39, 43, 47, 49-50, 73, 129, 132, 149, 243, 261 phase shift, 29, 102, 122, 216, 270 phenology, 268 power spectrum, 302 precipitation, 12, 20, 42, 49, 90, 97-98, 100, 102, 106-111,113-116, 127-128, 142, 148-149, 153-155, 164, 167, 198, 274, 277, 285 pre-observational mean temperature (POM), 89, 128, 194 present-day warming, 36, 269, 278 probability distribution, 58-59, 285, 291,293, 297, 301-303 proxy methods, 13, 19, 48, 81-82
radiative forcing, 249 ramp model, 119, 201,202 rainfall, 98, 102, 106-109, 111-114, 123, 127, 295 recent climate change, 25, 92, 172, 196, 227, 236, 238, 240-241,243, 268, 275, 278, 305 Recent Global Warming, 15, 49, 92, 222, 230 recharge, 113-115, 137-138, 140-142, 148-149 recharge flux, 113 remote climate change, 209, 250, 259-261, 264, 266 scaling properties, 57, 297 spectrum, 298 seasonal change, 111, 114, 123, 126 shallow boreholes, 63, 88, 129, 196, 263, 269-270, 276, 278, 282, 306 short-term sensitivity, 48 signal-in-noise problem, 128, 236 singular value decomposition, 50, 53, 213 skewness, 293, 301 Slovenia, 204, 253-255,278 snow cover, 12, 35, 49, 90, 92, 97-98, 100, 102-106, 109, 111, 116-117, 121-124, 126-128, 152-156, 164, 249, 274, 279-280 snowfall, 22, 98, 102, 106, 108, 111, 113, 115 soil moisture, 90, 99-100, 103, 105-106, 114, 117, 155, 198, 267, 289 solar constant, 42 solar irradiance, 10, solar radiation, 7, 10, 236 soil-air temperature coupling, 49, 117, 123 spaghetti diagram, 75-76, 180-181, 183, 202, 205,209 spatial discretization, 63 spatial patterns of temperature variations, 223 steady-state temperature, 46-47, 50, 60, 62-63, 93, 129, 133, 141 step increase, 45 step model, 50, 52-53, 63, 119, 201-202 stochastic component, 295 Sub-Polar Low, 295 subsurface temperature, 10, 26-29, 33, 35, 37, 39, 41-45, 47, 49, 51-53, 55, 57, 59-61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81-83, 85-87, 89, 91, 93, 95, 97-101, 103-105, 107, 109, 111, 113, 115,
Subject Index 117-121, 123, 125, 127-135, 137, 139-141, 143, 145, 147, 149, 151,153, 155, 157, 159, 161, 163-165, 167, 169, 171, 173,222, 225, 244-245, 250-251, 260-261,267, 269, 271,273,275-277, 279, 281-283, 285, 287, 289, 291,293, 295,297, 299, 301,303-305 subsurface temperature monitoring, 100, 267, 269, 271,273, 275-277, 279, 281,283, 285,287, 289, 291,293, 295, 297, 299, 301,303-304 superdeep boreholes, 260 surface air temperature (SAT), 1, 92, 97, 176 surface vegetation effect, 113, 116, 154 surface warming, 29, 43, 46, 98, 104, 141, 161,192, 199, 223, 249, 271,273-274, 288 synthetic temperature profile, 30, 95, 159 temperature disturbance, 39-40, 46-47, 119, 140-141, 197, 264 gradient, 28, 39, 44, 49, 106, 121,129, 137, 139, 141,143, 145, 150, 159-162, 282 logger, 282 monitoring, 29-31, 90, 100, 102-103, 109, 118, 123-124, 126-127, 151-153, 155, 164, 267-273, 275-279, 281-283, 285-287, 289-291,293, 295,297, 299-301,303-304, 306 offset, 98 variability, 234, 287-289, 291,295 temperature-depth profile 14, 26-29, 33-37, 42-44, 47-50, 52, 63, 65-70, 77, 82, 86-89, 92, 93, 95, 115, 118, 123, 128, 132-134, 136-138, 140, 143, 149, 157, 159, 161-163, 165, 168, 171,175, 177, 189, 191, 192, 194, 196, 198, 199, 201, 203, 205, 209, 215, 221-223, 243-245, 251,252, 254-256, 258, 263, 265,267, 271,278, 281,282, 305 temporal discretization, 63
335
terrain effect, 60, 62, 86, 96, 121-122, 128, 130, 161-162, 192 thawing, 97-98, 103, 106, 109, 116, 118, 123, 126, 155, 157-165, 259, 282 thermal conductivity, 27, 38, 40-44, 63, 72-75, 77, 80, 88, 98, 107, 126, 130, 134, 139-140, 144, 158, 169, 178-179, 252-255, 260, 263,276 thermal diffusivity, 29-30, 40, 42, 46, 93, 104, 111,121,123-124, 126-127, 150, 160, 169, 251,270, 280 thermal equilibrium, 37, 150, 254, 278 memory, 47 recovery, 39 resistance, 54, 88 thermohaline circulation, 9, 12, 297 thermometer, 15-16, 37, 48 thermophysical parameters, 50-51, 53-54, 60, 62, 65, 68, 75, 129 transient signal, 146 transpiration, 90, 96, 100, 109, 113, 244 tree-ring data, 20, 219, 221,223 UN Environmental Program (UNEP), 227 United States, 99, 115, 197, 287, 295 urban heat island effect, 274, 289 urbanization, 13, 118, 199, 206, 228, 295 U-shape, 28-31, 44, 77, 94, 115, 132, 137, 140, 144, 162-163, 178, 189, 192, 196 variability measures, 293 volcanic aerosols, 85, 236 water-ice conversion, 155 weather, 1-2, 16, 19-20, 30, 32, 57, 90, 92, 99, 106, 117, 124-125, 127, 155, 187, 192, 197-198, 222, 277-280, 283, 285-286, 294-295,297-298, 300-301 winter severity index, 183, 185 World Climate Report, 25 zero-curtain effect, 103