Microclimate for Cultural Heritage Developments in Atmospheric Science

Foreword Several books have been written on microclimatology and boundary-layer physics, beginning with Rudolph Geiger's Climate near the Ground (first German Edition in 1927). Until now, however, nobody has produced a book on the effects of small-scale climate variability around and inside buildings, monuments and other cultural objects. So Professor Camuffo's well illustrated account, Microclimate for Cultural Heritage will be greatly welcomed by architects, engineers, preservers and restorers of cultural property, and the wider community of microclimatologists. What has "cultural heritage" to do with microclimatology? Forty years ago, the response from meteorologists would have been: "Very little". Let me cite a personal example. Back in the 1950s while studying engineering meteorology at the University of Michigan, I wrote a term paper on the weathering of exposed surfaces by atmospheric pollution, which was given an A grade, and which was subsequently published (Munn, R.E., 1959: Engineering Meteorology: the Weathering of Exposed Surfaces by Atmospheric Pollution. Bull. Am. Meteorol. Soc. 40, 172-178). But several scientists (including a famous professor of physics at McGill University in Montreal) were alarmed that such a topic should find its way into the meteorological literature, and made their views known. Thirty-five years later, the importance of microclimatological gradients is widely recognized in the preservation and restoration of cultural objects. Credit for this attitude change is largely due to the efforts of a few people like Dario Camuffo, who recognized early on, the importance of micrometeorology in studies of the preservation and restoration of cultural heritages. This monograph contains many practical examples of ways in which micrometeorological knowledge can help in assessments of the deterioration of surfaces that have been exposed to the environment over long periods of time. Not only does the book include interesting outdoor examples from the author's own experience but also indoor cases, like horizontal cross-sections of temperature in the Sistine Chapel and of mixing ratio in the Giotto Room in the Uffizi Gallery in Florence. I know that this book will be widely consulted by specialists in the cultural heritage field, and I am pleased to have been involved in a very small way by contributing this foreword. R.E. Munn

Institute for Environmental Studies

University of Toronto, Toronto, Canada

vii

Preface This book has been designed as a useful microphysics handbook for conservators and specialists in chemistry, architecture, engineering, geology and biology who work in the multidisciplinary field of the environment, and, in particular, in the conservation of works of art. It has been especially written following the continuous d e m a n d to fill a gap in the literature related to this i m p o r t a n t application of atmospheric sciences, i.e. to apply the thermodynamic processes of clouds, or the dynamics of the planetary boundary layer, to a m o n u m e n t surface or to a room of a m u s e u m . The aim is to furnish them with a b a c k g r o u n d familiarity with the u n d e r l y i n g physics behind mathematics, and to give a detailed description and interpretation of the main microphysical p h e n o m e n a which play a fundamental role in practical applications. Correct application of formulae is only possible when all the approximations made in their derivation and the limitations intrinsic to the basic hypotheses are known. In this complex field an effort is m a d e to substitute scientific d e m o n s t r a t i o n s for c o m m o n opinions or popular beliefs. The basis are given for non-destructive diagnostics to evaluate causes of damage and predict outdoor deterioration, determined by meteorological factors, as well as the negative effects in exhibition rooms, due t o u n s o u n d use of technology and mass tourism. To this aim, suggestions are given on the fundamental principles in designing heating, air conditioning, lighting and in reducing the deposition of pollutants on works of art. Theory and experience are coupled to describe the complex condensation mechanisms and the fundamental role played by water in the stone deterioration and the formation of crusts on monuments. Urban meteorology, air-surface interactions, atmospheric stability, dispersion and deposition of airborne pollutants are also key topics of this book, whose main aim has been to make comprehensible to a wider audience a matter that is only familiar to a few specialists. This book combines a theoretical background with m a n y years of accurate laboratory research, field surveys and practice. The first part, devoted to applied theory, is a concise treatise on micro physics, which makes a survey on the basic ideas especially on classical, kinetic and statistical t h e r m o d y n a m i c s which are necessary for e n v i r o n m e n t a l diagnostic and conservation. The second part,

Performing Microclimate Field Surveys, is devoted to the practical utilisation and shows in detail how measurements should be performed, with many suggestions and examples and the indication of some common errors that should be avoided.

viii

Acknowledgments

The book is based on direct experience on a large number of case studies, most of them funded by the European Commission (DG XII: Science Research and Development, Programmes STEP and Environment, Contracts ENV-757-I-SB, EV4V-0051-I-A, STEPCT90-0107-SSMA, ENV4-CT95-0088, ENV4-CT95-0092) and some of them supported by the National Research Council of Italy (CNR), e.g. Finalized Project 'Beni Culturali', ENEL, e.g. project Effects of Air Pollution on Human Health and Cultural Heritage, the Consorzio per la Torre di Pisa and the Consorzio Padova Ricerche. Studies also were made in the occasion of special commissions (e.g. European Union, UNESCO, NAPAP, Vatican, Italian Ministry of Scientific Research). This text utilises also lectures of Atmospheric Physics taken during the last ten years at the Physics Department, University of Padova, as well as those on microclimate and physical weathering of monuments at international schools (e.g. European University Centre for Cultural Heritage of the Council of Europe in Ravello; Community of Mediterranean Universities; UNESCO-ICCROM). A number of original contributions that were published in scientific journals, or presented at international symposia, are here summarised. Special thanks are due to whoever has contributed: all my co-workers, i.e. Dr. A. Bernardi, Mr. A. Ongaro, Dr. G. Sturaro, Dr. A. Valentino and Arch. P. Schenal for their cooperation especially in the field surveys and data analysis; the scientific officers of the European Commission, and particularly Dr. J. Acevedo for her interest, kind encouragement and friend assistance; the good friends and colleagues Prof. A. Arnold (Swiss Federal Institute of Technology, Ziirich), Prof. N.S. Baer (New York University), Dr. E. Bell (Trinity College, Dublin), Prof. P. Brimblecombe (University of East Anglia, Norwich), Dr. L. De Boek (Antwerp University), Prof. M. Del Monte (Bologna University), Prof. B. Fitzner (Technischen Hochschule, Aachen), Dr. P. Bacci (ENEL, Milan), Dr. C. Price (University College, London), Dr. C. Sabbioni (CNR FISBAT, Bologna), Prof. C. Saiz-Jimenes (CSIC, Seville), Prof. R. van Grieken (Antwerp University), Dr. S. Vincenzi (CNR-ISDGM, Venice), Dr. Th. Warscheid (Freie Hansestadt, Bremen) and Prof. F. Zezza (Bari Polytechnic) for having contributed in different ways. For figures, we must acknowledge the following: Fig.l.4, 2.6 and 4.4 are reprinted from European Cultural Heritage Newsletter on Research, and Bollettino Geofisico, joint edition 14, 3, 1-123, Camuffo D. and Bernardi, A.,: The microclimate of Leonardo's "Last Supper" (1991) with kind permission from the European Commission, DG XII, and the Bollettino Geofisico. Fig.l.6 is reprinted from Science of the Total Environment, 46, 243-260, Bernardi, A., Camuffo, D., Del Monte, M., and Sabbioni, C.:. Microclimate and Weathering of an Historical Building: the Ducal Palace in Urbino (1985) with kind permission from Elsevier Science - NL, Sara Burgherharstraat 25, 1055 KV Amsterdam, the Netherlands. Fig.l.13 and Fig.4.5b are reprinted from Bollettino Monumenti Musei Gallerie Pontificie, 6, 211257, Camuffo, D. and Bernardi, A.: Dinamica del microclima e scambi termoigrometrici tra pareti e atmosfera interna nella Cappella Sistina (1986) with kind permission of the Vatican Museums and Galleries. Fig.1.14 is reprinted from Bollettino d'Arte special issue "Giotto a Padova", Camuffo, D. and Schenal, P.: Microclima all'interno della Cappella degli Scrovegni: scambi termodinamici tra gli affreschi e l'ambiente, pp. 107-209 (1982) with kind permission of Ministero dei Beni Culturali ed Ambientali, via di S. Michele 22, Rome and Poligrafico dello Stato, Rome. \ Fig.5.7 has been kindly supplied by Prof. Marco Del Monte, Department of Geology, Bologna University. Fig.5.8a,b is reprinted from Water Soil and Air Pollution 21: 151-159, Camuffo, D.: Condensation-Evaporation Cycles in Pore and Capillary Systems According to the Kelvin Model Fig.2 and 3 pages 154 (1984) with kind permission from Kluwer

ix Academic Publishers, P.O. Box 17, 3300 AA Dordrecht, The Netherlands. Fig.6.1 is similar to Fig.3 page 44 in Camuffo, D.: Environment and Microclimate; pp. 37-50 in: N. Baer, C. Sabbioni and A. Sors (ed.s): Science Technology and European Cultural Heritage (1991) with kind permission from Butterworth Heinemann, Linacre House, Jordan Hill, Oxford OX2 8DP, UK. Fig.6.2a is reprinted from Atmospheric Environment 18 (19): 2273-2275, Camuffo, D.: The Influence of Run-Off in Weathering of Monuments. Fig.la, page 2274 (1984) with kind permission from Elsevier Science Ltd., The Boulevard, Langford Lane, Kidlington 0X5 1GB, UK. Fig.6.4 has been kindly supplied by Dr. Giancarlo Rossi, ENEL, Venezia-Mestre. Fig.6.6 is reprinted from the book Le deposizioni acide - I precursori. L'interazione con l'ambiente e i materiali, (L. Morselli ed.): Camuffo, D., Aspetti Microfisici delle precipitazioni acide in relazione al degrado dei monumenti, Fig. 2 page 348 (1991) by kind permission of Maggioli Editore, Guerrazzi 10, Bologna. Fig.6.10 is reprinted from American Journal of Science, 251, 884-898, Gordon, J. and MacDonald, F.: Anhydrite-Gypsum Equilibrium Relations, Fig. 3 page 892 (1953) with kind permission of American Journal of Science, 217 Kline Geology Laboratory, Yale University, New Haven, CT 06520-8109, USA. Fig.8.8 and Fig.8.9 are reprinted from Museum Management and Curatorship 10, 373-383, Camuffo, D.: Wall Temperature and Soiling of Murals Fig.1 and Fig.2 page 176 (1991) with kind permission from Elsevier Science Ltd., The Boulevard, Langford Lane, Kidlington 0X5 1GB, UK. Fig.8.20 is reprinted from Vercelli, F., L'Aria, UTET, Torino (1933). Photo taken on 1920. Fig.11.4 is reprinted from Environmental Monitoring and Assessment 6, 165-170. Camuffo, D. and Valcher, S.: A Dew Point Signaller for Conservation of Works of Art, Fig.1 page 167 (1986) with kind permission from Kluwer Academic Publishers, P.O. Box 17, 3300 AA Dordrecht, The Netherlands. The climatological analyses of meteorological data for the Venice and Rome were based on observations taken by the Meteorological Service of the Italian Air Force. A grateful thought to the memory of two good friends and leading scientists: Prof. O. Vittori, who was specialist of Atmospheric Physics and my Director, and Dr. G. Urbani, who was preserver and Director of the Istituto Centrale del Restauro, Rome, for their unforgettable scientific discussions and for their stimulating contributions to apply atmospheric microphysics theory and environmental survey practice to monument conservation. Finally, special acknowledgements are due to my family for all my missing time.

CHAPTER 1

Microclimate, Air and Temperature

1.1. THE MICROCLIMATE First of all, it m a y be useful to define the w o r d 'microclimate' to which we refer, as in the e v e r y d a y practice some terms such as 'global climate', 'macroclimate',

'mesoclimate', 'climate', 'microclimate', 'nanoclimate' and 'picoclimate' are used by people with different meaning, and the same is done also by specialists. It is clear that all these terms have been utilised to define the climate of a specific area, and the prefix is chosen to indicate the size of the area involved. Of course, we cannot proceed in the apparently most straightforward way, i.e. by stating a scale with the appropriate size unit, e.g. one kilometre in diameter, and then apply the well k n o w n definitions, i.e. milli = 10 -3, micro = 10 -6, nano = 10 -9, pico = 10-12, as in this case the 'micr0climate' w o u l d apply to a site sized only 10 -6 km =1 mm, and this is obviously ridiculous. S o m e b o d y uses the term 'microclimate' for an u r b a n area, 'nanoclimate'

for a

m o n u m e n t and 'picoclimate' for a very small portion of a m o n u m e n t , but this definition has not gained popularity. In principle, the prefix varies with the actual area size, as determined by geographic, topographic or other local factors, e.g. the requirement of reaching a basic homogeneity in some key parameters, but it m a y also vary with reference to the actual interest, in view of a peculiar application, and the list of the subjective elements which intervene in the choice of the appropriate w o r d may continue. In climate research, meteorology and physical geography, the distinction is rather clear and is determined by the field of interest, i.e. the 'global climate' refers to our planet, the 'regional climate' to a geographical homogeneous area, the 'local climate' to a small limited area like a mountain, a valley, a city. Similarly, for conservation, it is useful to use clear terms, derived from the above mentioned sciences, e.g. 'regional

climate' for the main characteristics of the geographic area where the m o n u m e n t is found, 'urban', 'rural', 'mountain', 'valley', 'coastal' and so on for the next dimensional Step, and 'microclimate' relating to the small location, e.g. a corner of street, a square, a

room, where the m o n u m e n t or the object is sited. This definition does not imply a precise size, but focuses the attention on a specific artefact (e.g. a historic building, a statue, a small exhibit) and its surrounding, so that the same term can also apply w h e n studying the interactions between a portion of a m o n u m e n t and the air nearby. In practice, it refers to the whole ambient which is necessary to study in order to know the factors which have a direct influence on the physical state of the monument and the interactions with the air and the surrounding objects. N o w that the prefix 'micro' has been explained, it might be useful to clarify also the w o r d 'climate'. The following definitions can be found: 'climate is the synthesis of the day-to-day weather conditions in a given area', 'climate is the statistical description of weather and atmospheric conditions as exhibited by the patterns of such conditions, in a given region, over a specified period of time long enough to be representative (usually a n u m b e r of decades)', 'climate is the fluctuating aggregate of atmospheric conditions characterised by the states and developments of weather in a given area' (Maunder, 1994). It is evident that in our case the w o r d 'weather' is inappropriate; only in exceptional cases observations exist over a n u m b e r of decades and in general new indicative measurements must be taken in the short term before undertaking restorations; the same definition should be applied either to indoor or outdoor environments. By adapting the previous definitions to our aims, the following interpretation can be given: 'microclimate is the synthesis of the ambient physical conditions (e.g. time and

space distributions, fluctuating values and trends, average and extreme values, space gradients and frequency of oscillations) due to either atmospheric variables (e.g. temperature, humidity, sunshine, airspeed) or exchanges with other bodies (e.g. infrared emission, heating, lighting, ventilating) over a period of time representative of all the conditions determined by the natural and manmade forcing factors'. When a survey cannot continue for a time interval which is statistically representative of all the conditions, it should at least d o c u m e n t one or a few examples of the main different conditions, just to understand the nature of the problem. Another key question is whether meteorological data, taken from a standard w e a t h e r station sited at a few km (or less) from a m o n u m e n t , can be used for the estimation or interpretation of microclimatic situations, or it is always necessary to carry out specific and expensive field tests. It is clear that the acquisition of existing data m a y be helpful for a more complete interpretation of the p h e n o m e n a , but we will see in the following (Chapter 9) that s t a n d a r d w e a t h e r stations operate m e a s u r i n g p a r a m e t e r s with different criteria and methodologies, so that some m e a s u r e m e n t s are useful to our aims, other of scarce relevance and other useless. In addition, several p a r a m e t e r s n e e d e d for the science of conservation are not

considered in w e a t h e r stations. For this reason special field s u r v e y s are indispensable, and only a few parameters, measured by weather stations in a compatible way, appear as a duplicate and could be omitted. However, it is more convenient to record in the same data acquisition system and with the same criteria the whole set of data which is useful for a specific study, and then add or compare further observations, if any.

In the field of conservation or for other particular

e n v i r o n m e n t a l purposes, observations are made to study certain individual problems, so that the instrumental apparatus as well as the operative methodologies are specifically tailored to fit the actual problem. On the other hand, it is evident that weather stations are planned and standardised for meteorological measurements as defined by international protocols, so that they are in principle interchangeable. Not only instruments and methods are generally inappropriate for conservation purposes, but also the free position where the standard weather station is located is not representative of the specific site of the monument, perturbed by nearby buildings, trees or other obstacles. For instance, it is sufficient to consider that, in the wake which forms downstream to a building, the wind direction is opposed to the unperturbed flow measured by the weather station. One of the aims of a field test for cultural heritage is just to describe the complex and 'perturbed' situation originated by the presence of all the obstacles near the monument, whereas the weather station is aimed to monitor the 'unperturbed' situation. It is absolutely restrictive to consider the individual parameters separately, omitting interactions and feed-backs. The microclimate is determined by the complex interaction of several factors and not always an accurate interpretation of what is h a p p e n i n g is possible, or also to forecast the future development of a certain situation. However, our knowledge progresses with small steps and the atmospheric thermodynamics offers a good start. Air and precious surfaces to study and preserve can be found everywhere, either indoors or outdoors. Although traditionally the indoor and the outdoor environments are considered very distinct, in practice they present similar problems: both undergo daily cycles of temperature and humidity, either forced by the solar cycle or by heating, ventilating and air-conditioning systems (HVAC); both are exposed to intense shortwave radiation which may be the direct solar irradiation on the open sky or through window, or artificial light; both are affected by advective air movements, i.e. wind, or air currents, or air infiltration through cracks and openings, or turbulence generated by sources of momentum, e.g. people movements, heat sources, surface roughness in the presence of advective movements. Rainfall and dew are considered typical of outdoor environments, but often rainfall penetrates inside through disconnections, or condensation forms on the

window panes, on the surface of cold objects or inside pores. External pollutants can penetrate through windows and doors and are transported from room to room, and deposit via the same mechanisms, either outside or inside. The same problems can be found outside or inside, although the scale may change as well as the level of complexity. The most important distinction is that the indoor microclimate can be controlled, at least in principle, and it is very important to know how to do it. Although the importance of the indoor microclimate has been stressed for a long time (Benoist, 1960; Camuffo, 1983; De Guichen, 1984; Tomson, 1986; Michalski, 1993; Padfield, 1994; Camuffo and Bernardi, 1995a) very often inappropriate standards of comfort are used, which are based on human well-being and not on the science of material conservation. Are museums oriented towards the well-being of humans or exhibits? Is the main aim of museums to show objects for cultural and educational purposes, or to preserve artefacts in the most appropriate conditions for conservation, to which visitors should adapt? Of course it is necessary to combine the two needs paying attention that the effects on works of art are cumulative and often irreversible. In Europe, the situation was better more than 35 years ago, when Benoist (1960) wrote: 'In winter, museums should be heated not only for visitors and

guardians, but also for works of art. In Europe, visitors are content with 15~ and in America with 21 ~ In Western Europe the above thermal level was appropriate for safely obtaining a correct relative humidity without the need of supplying continually too much moisture to mitigate the exceedingly dry environmental conditions. Unfortunately, Europe is today following the d a n g e r o u s USA temperature standard. In the past, local climate was carefully observed and exploited to the full to adapt buildings and activities to the external ambient and benefit of a natural

microclimate. For example, Hippocrates (De locis), Pliny (Epistulae, II, 17, 7-19), Vitruvious (De Architectura, VI, 4, 1-2) and Palladium (Quattro libri dell'architettura, Book II, Chap. XII), show how a building was constructed with respect to its exposure to the sun, wind and precipitation. Rooms were exploited according to the temperature and type of light that could enter through the windows. Nowadays, the modern technology often induces to think that the climate outside can be ignored, and that a new independent, artificial microclimate can be created inside a building, controlling humidity and temperature with advanced sensors and microprocessors. By maintaining intake air in excess of exhaust of air, commercial buildings and museums are maintained at an indoor pressure higher than the outdoor value, which reduces infiltrations of external air and pollutants, but creates an internal atmosphere, with its artificial microclimate, which is usually not in equilibrium with

walls, floors, ceilings, exhibits, and needs many frequent heat and moisture transfers, to balance the people influence, the air leakage, and the exchanges between air and surfaces. It has been calculated that about 30% of the moisture supplied to a room is absorbed by the room surface (Rosenhow et al., 1985) with the consequence that the benefit in mitigating the air dryness is negatively compensated in moistening surfaces. The excessive confidence on HVAC and their huge use caused in general more damage than advantages. The indoor temperature is regulated on man well-being without keeping into consideration the regional climate and in particular the natural value of the seasonal moisture content (except for calculating the power needed for the HVAC) in order to obtain a reasonable relative humidity. The desired level of temperature is assumed as a primary need, and the concentration of water vapour is increased or decreased accordingly, to create a new artificial microclimate. Several systems which control the humidity level in historical buildings or museums have been analysed with a number of field tests; however, although these systems are good in theory, and the machines operate correctly, the environmental impact has been often found to be disastrous. In fact, a cloud of moist, cool air is generated by these devices that are generally located near the walls where paintings or other precious works of art are positioned. This cloud moves with the internal air motions, and affects all the works with abrupt humidity and temperature changes. The technological limit of HVAC is not in designing new powerful or sophisticated machines, but rather in being able to distribute in a room the new air steadily and homogeneously. The homogeneous distribution of heat and vapour in a room would require too many diffusers, scattered everywhere at short distances. The inflows cause undesired air movements which increase inertial deposition of suspended particles. Unfortunately, present technological research is focused on making more and more sophisticated machines, not in studying and controlling their use. Atmospheric thermodynamics is a precious tool in environmental diagnostics and in the progress of our knowledge on the basic processes of m o n u m e n t deterioration, evidencing causes and effects.

1.2. AIR, WATER VAPOUR AND PERFECT GASES The dry air is composed of a mixture of several gases, mainly nitrogen (N2, 78.084% volume), and oxygen (02, 20.946%), with Argon (Ar, 0.934%), and some

other minor constituents, i.e. carbon dioxide (CO2, 360 ppm, variable), neon (Ne 18.182 ppm), helium (He, 5.24 ppm), methane (CH4, 1.77 ppm), krypton (Kr, 1.14 ppm); hydrogen (H2, 0.5 ppm), Xenon (Xe, 0.09 ppm). Many other trace gases and particles, considered pollutants, are dispersed in the atmosphere, some of them are non-reactive and most of the are reactive, e.g. SO2, NOx. Atmospheric chemistry studies the behaviour and effects of these substances which are reactive especially in association with atmospheric water. For sake of simplicity, the air is often treated as it were an ideal gas, composed of particles having the mass M = 28.96 which is the average weight of the molecules of this mixture. Water vapour is a variable constituent of the atmosphere, whose concentration depends on air temperature and weather vicissitudes, and generally ranges between 0.5 and 4%. This variability is a consequence of the fact that water vapour m a y change state, becoming liquid or solid, and may precipitate or be in different ways transferred from the atmosphere to the earth's surface, or vice-versa. The water molecule itself is far from being a "perfect gas" particle as it is composed of one oxygen and two hydrogen atoms which are 0.95 A far from the oxygen nucleus, and are disposed forming an angle H-O-H equal to 105 ~ This asymmetrical configuration generates an unbalance between positive and negative charges, so that the water molecule is an electric dipole which can orient in an electric field (exerting a strong dielectric action), or may interact with other molecules or bodies exerting van der Waals and electric forces. However, in a first approximation, when the water vapour does not undergo changes of state, for several purposes it can be treated as it were a perfect gas, although some departures may occur and must be considered, as we will see later. Main problems arise w h e n the water vapour approaches saturation, or w h e n a vapour molecule impacts on a surface whose temperature is below the dew point, or which is contaminated with hydrophilic salts. In these conditions, instead of exerting elastic impacts, the vapour molecule will stick on the cold surface, or on the salts (the same holds for condensation nuclei), and the effective number of "free" gaseous molecules decreases. In order to simplify things, the state of a gas is statistically represented by some key p a r a m e t e r s which characterise the average properties of the population of particles. A 'perfect gas' is an ideal reference gas, where the molecules do not exert any force on each other and all impacts are elastic; it is perfectly described by the so called state equation

p V = n .;,r

(1.1)

where p is the pressure, V the volume, n the n u m b e r of moles n = m/M (where m is the actual mass of the gas and M its molar mass),. ~/?~ the universal gas constant, i.e. .~/2~ = 8.3169x107 erg mo1-1 K - l = 1.986 cal mo1-1 K-l; T is the absolute temperature (degree Kelvin, K). For a particular gas X the gas constant is defined as .J2x = .~/2/Mx so that for dry air Ma = 28.965 g mo1-1 and .~/?~a = 0.2870x107 erg g-1 K-1 = 0.06857 cal g-1 K-l; for water v a p o u r Mv = 18 g mo1-1 and .t2v = 0.4615x107 erg g-1 K-1 = 0.1102 cal g-1 K-1. For the gas X the state equation becomes Px V = mx .~/2x T

(1.2)

where Px and mx are the partial pressure and the actual mass. Although a real gas may depart from the perfect gas model, this is, however, the basic equation which will be useful in the following treatment and can also be applied, within certain limits, to the water vapour.

1.3. TEMPERATURE

Temperature is the condition which determines the direction of the net flow of heat between two bodies, i.e. from the w a r m e r to the colder one. For this p r o p e r t y , a t h e r m o m e t e r can be p u t into equilibrium with a b o d y , in o r d e r to read the temperature of the b o d y on the thermometer, if the thermometer does not perturb the original temperature of the body and is not influenced by other factors. From the t h e r m o d y n a m i c point of view, the temperature T represents the average translation

kinetic energy Ec of the gas molecules, according to the principle of equipartition of the energy 3

Ec - -~k T

(1.3)

where k = 1.38x10 -16 erg K -1 is the Boltzmann constant, which represents the ratio .J2/.1J/fvhere ....l / - 0.6023x1024 is the Avogadro number, i.e. the n u m b e r of atoms or molecules which form a mole; the latter is obviously the a m o u n t of substance whose weight (expressed in g) equals the atomic or molecular weight of the substance. As the air is p r e d o m i n a n t l y composed of diatomic molecules characterised by 5 degrees

10 of freedom, the total kinetic energy Et is 5 Et = -2 k T.

(1.4)

For these relationships T is also called molecular temperature. In meteorology it is also called the dry bulb temperature as opposed to the wet bulb temperature which will be seen later. In the following the absolute thermodynamic temperature (K) will be indicated with the capital letter T and the temperature in degrees centigrade (~

with the

lower case t. As t = T-273.16, then AT = At. The value 273.16 is the thermodynamic temperature of the triple point of water, and is usually approximated 273. The concept of temperature can be easily extended from a gas to a liquid or a solid, and a theoretical thermodynamic definition is preferred to the empirical one:

the temperature is the variable measured by a thermometer. As it will be discussed in the following, in the absence of errors, the thermometer measures only the temperature of its bulb, which is not necessarily the same of the object under investigation. In fact, the thermodynamic equilibrium involves a balance between conductivity, convection and radiant heat exchange, which are different for each body. In particular, radiant heat is exchanged with other external bodies either nearby or far away, and this contribution is not included in the definition of temperature. The temperature is a consequence of the present and past energy balance which also includes advective contributions due to the transport of air masses, and only in rare cases is homogeneous in a body or in a room.

1.4. MECHANISMS OF TEMPERATURE DEGRADATION The temperature is a very important factor in conservation of works of art, as changes of this parameter induce differential expansions in the materials and tensile strengths between the surface and the subsurface structure. Temperature cycles induce a n u m b e r of mechanical weathering mechanisms and accelerate fatigue failure in susceptible materials; the faster the cycle, the greater the temperature gradient inside the material, the steeper the front of the thermal wave propagating inside the material, the greater the strength, the faster the ageing and the damage in the surface layer. In fact, the material acts as a low pass filter which attenuates the penetration of the rapid surface temperature changes: the shorter the duration of the

11 fluctuation, the thinner the layer affected by it (Camuffo et al., 1984). However, it must be remembered that the key part of the artistic value of monuments lies in the surface layer. For these reasons daily (or shorter) temperature cycles are much more important than the seasonal ones. Thermal cycles may cause mechanical disgregation of outer part of stones, beginning at the discontinuities included into the rock and the interfaces between the different minerals which form the stone. It is to be noted, however, that the pure thermal effect is an academic abstraction, as in the field the water activity is always superimposed to this variable with synergistic effects. A typical effect is the granular disgregation of magmatic and metamorphic rocks. The thermal anisotropy of the crystalline lattice, the size of the granules and their spatial association determine a system of internal tensions which result in surface disgregation of the granules. The greater the granules, the greater the tensions and the faster the deterioration rate. Sedimentary rocks are characterised by a more regular structure and composition, but the nature of the binding cement between granules acts as a discontinuity factor (Veniale, 1995).

Fig.l.1 The leaning Pisa Tower surrounded by loggias. In the daytime, the solar heating causes the expansion (and compression) of the columns and an additional temporary bending of the Tower which follows the apparent course of the sun.

12 The expansion mechanism may be also important for structural stability. For example, the Pisa Tower (Fig.l.1) is composed of a cylindrical body contoured by six orders of loggias, having thin columns. In the sunny days of the hot season, the stone temperature of the thick central body remains nearly unchanged, but the external parts, and in particular the columns, undergo daily cycles of some 20~

which cause

the expansion of the hot stone (Camuffo et al., 1996). Considering that the expansion coefficient for limestone is 8x10 -6 ~ and that the Tower extends for some 50 m in height, the above daily excursion causes 8 mm vertical expansion of the hot side and temporary bending of the tower. The daily movements of the top, which are forced by solar radiation (and/or wind) have been measured with a pendulum, and the maximum excursion is some 4 seconds of arc from East to West (Jamiolkowski, 1995), which corresponds to about 1 mm of horizontal displacement. The limestone expansion produces a compression of the thin columns and their capitals, most of them are severely damaged or have been substituted in the past. Another consequence of temperature variations are changes in the degree of saturation of the water vapour, and the amount of water adsorbed in the bodies. Several materials, e.g. wood, parchment, ivory, plaster, change their dimension with water content, expanding or contracting, shrinking, micro or macro fissuring and so on. The effects of an external temperature forcing are in general very complex. For instance, wood is characterised by a small heat conductivity, and the internal propagation of a temperature change is preceded by the propagation of a change of relative humidity due to the diffusion of vapour molecules dispersed in air, and this is followed by redistribution of the water absorbed into the grains. As a consequence, delayed differential stresses and shrinking are induced. Again, changes of temperature in porous stones cause changes of relative humidity, which in turn is related to the evaporation of the water in the pores, increasing the concentration of dissolved salts and arriving at the precipitation of them when the solution becomes supersaturated. In sunny days monuments are overheated by the solar radiation and dramatic temperature changes (thermal shocks) occur when the sun appears or disappears; in addition, marked short term (3-15 minutes) temperature fluctuations are a response to variations in wind speed and light cloud cover (Camuffo, 1981; Jenkins and Smith, 1990). Granular disgregation is frequently found on stones with granula r or crystalline texture, e.g. granite or marble, where stresses generated between grains or large crystals with crystallographic axes differently oriented, or having different expansion coefficients, produce fatigue failure along grain or crystal interfaces. For

13 example, calcite crystals expand along the principal axis and contract along the secondary one in the case of a temperature rise. In the long run, heating-cooling cycle will slightly displace crystals from their original position forming a less regular, weaker structure, which will lead to the disgregation and loosing of granules, called

sugaring. The damage is irreversible and cannot be restored (Fig.l.2). In addition to temperature forcing, also wetting-drying cycles cause expansion and contraction cycles in some kinds of stones. However, although disagreement persists over the effectiveness of insolation weathering as a direct cause of rock breakdown, the opinion is that most granular disgregation occurs as a result of a previous weakening of the rock, normally due to chemico-physical weathering mechanisms acting in combination or sequence and involving intrinsic rock properties (e.g. albedo, thermal conductivity and heat capacity, mechanical strength, porosity and specific surface), thermal variations, repeated stressing of the material and role of moisture and dissolved salts (Smith, 1978; Warke and Smith, 1994).

Fig.l.2 Granular disgregation of marble. The restoration had dramatic consequences. Aurelian Column, Rome. Finally, the air temperature is a key factor in determining the habitat for biological life and in controlling metabolisms. At temperatures below 20~ the metabolic processes are reduced and the biodegradation due to bacteria can be often prevented with an appropriate choice of this and other environmental variables (e.g. humidity, light, ventilation). However, although the temperature range from 20 ~ to 35~

generally favours the microbiological activity, the variable response and

adaptability of microorganisms to lower or higher temperatures, as well as to other extreme and stressing environmental conditions (e.g. water activity, pH-value,

14 ionic/osmotic strength), has to be strictly considered when preventive remedies against the microbial attack should be undertaken. Microbial biofilms covering the surface of stones or other materials have several negative consequences: they may enhance the deposition of particles, and the deposited material, as well as the biofilm form a composite layer which changes the albedo of the surface, the porosity and water vapour diffusion inside the material, the thermal conductivity and the water balance, especially in the outer, endangered uppermost layer (Warscheid and Krumbein, 1996). On the other hand, in some cases biofilms exert a protective function with their polymeric matrix, so that it is difficult to formulate an accurate balance between negative impacts and positive factors, especially in view of the variable response of the material contaminating mizroflora (Warscheid and Kuroczkin, 1997). A comparison can be made with the van't Hoff's rule for chemical reactions, which states that the conversion rate is doubled when the temperature is increased by AT = 10~

or is halved for the same drop of temperature. Although this

rule may describe in general the response of biology to temperature, it cannot be simply adapted to all biological reactions.

1.5. THE TEMPERATURE IN A BUILDING, A ROOM In a building, the external forcing (e.g. solar radiation, heat conduction across roof and walls, air exchanges through openings) depends upon the architectural features, and the materials choice. Thin or conductive walls are sensitive to the apparent daily course of the sun; windows may allows for penetration of solar beams and behave as a green-house; in addition they can regulate exchanges of external air. Different exposures in a building have a different heat balance, and not all the rooms have the same temperature. The inner rooms are more shielded and the external forcing is smoothed out; and this is particularly true for the ground floor, where the soil has an enormous heat capacity. The opposite holds for the last floor, being topped by a roof that receives solar radiation during the day and looses infrared (IR) radiation during the night. HVAC or people may completely change the natural equilibrium. Although rooms are often provided with one thermostat for the temperature control, the temperature in a room cannot be described with only one, although timedependent value, but is a four-dimensional function, i.e. of the specific point (x,y,z) and time. As the air is mobile and has a very small specific heat, the inside temperature will be determined by exchanges with floor, ceiling, walls, windows,

15 doors, and all the other sources or sinks of heat, e.g. heaters, air-conditioning systems, solar radiation, lamps, people. If there are open w i n d o w s or doors, or forced flows of air at different temperature, the advection of new air might be the dominant factor. In a closed room hot air rises, but its ascent is stopped by the ceiling: the air distributes according to its density, i.e. the hot and less dense in the top, and the cold and more dense in the bottom. For this reason a stable atmospheric stratification with temperature rising with height tends to form. However, if there are some sources of sinks of heat, or all the surfaces are not exactly in thermal equilibrium with the air at their height, the mass conservation requires that the ascent of warm air is always associated with an equal flow of descending air, and vice-versa. This may happen in several ways, determined by the boundary conditions and room architecture, as we will see with some different examples. (i) Everything is in equilibrium, except for a heat source inside the room. Over the heat source a rising column of hot air will form, it will be stopped and diverge at the ceiling level, will form a new less dense layer on the top, and all the previous ones will remain below, with a general subsidence of the whole volume. If the source is not too hot, the convective motion develops in height up to it finds air less dense, and will be stopped and diverge at this level, leaving unaffected the upper layers. Similarly, if the heat source is not located on the floor but at a middle height, the descending flow stops at the source height, as below it founds colder and denser air. As the mass should remain the same, the ascending and the descending fluxes are equal, so that the ratio between the ascending and the descending velocities equals the ratio between the cross section of the room deprived of the section of the ascending column, and the cross section of the ascending column. (ii) Everything is in equilibrium, except for the floor which is colder (e.g. ground floor in the summertime), o r the ceiling which is warmer than the adjacent air (e.g. metal roof or domes in a sunny day during the hot season). The air-surface exchanges increase the intensity of the atmospheric layering, and the air remains motionless. (iii) Everything is in equilibrium, except for the floor which is warmer (e.g. floor heating), or the ceiling which is colder than the adjacent air (e.g. metal or glass roof in the winter). The air becoming into contactwith a warm floor forms convective rising cells, associated with other descending air, like the convective movements inside a pot of boiling water. Similarly, the air coming into contact with the cold ceiling becomes denser and sinks, forming rivulets of descending cold air associated with convective rise which result in a continuous mixing of the whole atmosphere.

16 (iv) Everything is in equilibrium, except for the walls which are warmer. The heat exchanges form an internal boundary layer of ascending, warm air along the walls; the w a r m air substitutes the previous top layer below the ceiling and slowly displaces downwards the whole mass of stratified layers. If the walls are colder, the internal boundary layer flow is downwards, cold air accumulates above the floor and rises the whole mass of stratified layers. From the above examples it appears that, in general, a natural layering is expected in an inside atmosphere and some air motions may derive from the presence of bodies with different temperature. Thick walls of historical buildings have an enormous heat capacity, tend to maintain the same equilibrium and the typical condition is a steady condition of thermal layering except for the presence of perturbing factors, e.g. HVAC systems, lamps or people. The thick walls of historical buildings are very effective in damping the daily temperature cycles and also, to a minor extent, the seasonal wave, so that internal microclimate is homogeneous, weackly dependent upon the daily cycles and the external weather conditions and the seasonal variability is reduced. The best situation happens when the seasonal time-lag of walls, floor and roof are similar; when they are different the internal stability changes seasonally. For instance, in the case of churches, the ceiling follows the seasonal variations with a shorter time-lag, and the floor based on the ground with a much more longer one, so that in the summertime the relatively warm ceiling and the fresh floor generate an internal layering; in the wintertime the relatively warm floor and fresh roof tend to destroy the air stability with some internal mixing shown by an isothermal vertical profile. An example is given for the Basilica of $. Maria Maggiore, Rome. The external temperature cycle is some 10~

and the internal one order of magnitude less, being

governed by the limited exchanges with the exterior, the walls, the floor and the ceiling, and the heat accumulated (or lost) by these structures in the previous months. In the late summer (Fig.l.3a), the walls have reached equilibrium with the season climate, and the inside temperature is near the average of the external temperature cycle. The external weather conditions have a limited influence on the indoor microclimate, whose changes are mainly governed by the doors and windows openings, and by the nocturnal cooling of the metal domes. The effect of the opening of the two front doors is visible in the early morning, when cold air enters and a lowering of the air temperature is found by the sensor at 3 m level, but not by the sensors at 7 and 11 m. In the autumn (Fig.l.3b), the indoor temperature is greater than the average external values, being close to the daily maxima which equal the temperature of the walls which show a memory of the heat accumulated in

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T i m e (hr) Fig.l.3. External and internal temperature (measured at the heights 3, 7 and 11 m) in the Basilica of S. Maria Maggiore, Rome, in summer (top) and autumn (bottom). The thick walls are very effective in damping out the external daily cycle, and in autumn the heat accumulated during the hot season makes the internal temperature higher than the external average value. Cold air entering through the door is visible at the 3 m level at the opening in the morning (upward arrows in the summer example, 9 to 10 August 1996), and a rise of temperature is visible during the liturgical offices on Saturday evening and Sunday (downward arrows in the autumn example, 19 to 20 Ocober 1996).

18 the hotter months. Peaks of temperature were found in all the seasons during the liturgical offices celebrated Saturday evening and Sunday morning and evening, for the lighting made with incandescence lamps and the massive participation of faithful people. Also interactions between rooms are important. The most common situation is to find consecutive rooms with air flowing through the door and spreading from a room to another (Fig.l.4). The circulation may be forced by HVAC systems or existing pressure differences generated by external winds through w i n d o w s or doors.

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Fig.l.4 Air with a different temperature flowing through the door and spreading in the refectory of the Leonard's Last Supper, Milan (14 November 1982, after Camuffo and Bernardi, 1981a).

Fig.l.5 Interactions between different floors in the S. Rocco Oratory, Padova. In the winter, mild air rises from the cellar through the staircase, spreading in the Oratory. In the bottom of the room (i.e. the right of the map), the wall is milder, being contiguous with another, heated building (18 January 1996).

19 Other important interactions occur between different floors. For example, the San Rocco Oratory (Fig.l.5), Padova, has a staircase which connects the Oratory with an underground cellar. Both are without heating, but the cellar is less sensitive to the daily temperature changes and also attenuates the seasonal temperature wave. In the summertime, and especially during the daytime, the cellar is much colder than the Oratory, so that the cold air remains entrapped in the cellar without any exchange with the upper floor. In the wintertime, and especially during the night and morning hours, the cellar is milder, and this generated a continuous exchange through the staircase: cold air descends and mild air rises with some entrainment and mixing with ambient air up to the lighter air reaches the ceiling, and then spreads horizontally. In addition to the mild area near the staircase, another mild area is found near the opposite wall in the bottom of the room, as this wall is in common with another building which is heated. Another interesting example of interactions between an architectural structure and its surroundings was found at the Ducal Palace in Urbino, Italy (Fig.l.6). This

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Fig.l.6 The microclimate of the curtyard in the Ducal Palace, Urbino, is mainly determined by the daily course of the sun. On the right upper corner, the staircase drains out, as a gigantic chimney, the warm air, determining a cold airstream that invades the staircase (19 December 1982, after Camuffo and Bernardi, 1985, reprinted by permission of Elsevier Science).

20 beautiful Renaissance building has a courtyard which is surrounded by a loggia, and in a corner of the courtyard the staircase of honour connects the court with the upper floors. Particularly damaged are the decorations at the edge of the staircase, which has magnificent bas-reliefs in a local oolithic limestone which is not resistant to weather injuries, especially rainwater. Some field surveys were made to establish the cause of this degradation. In fine days the courtyard and the loggia h a d a t e m p e r a t u r e distribution that followed the apparent course of the sun and the middle of the courtyard was generally colder, for the better ventilation which is found increasing the distance from the architectonic structures, and colder was found also the staircase as the w a r m air was sucked in and drained a w a y as it h a p p e n s inside a gigantic chimney, but this situation was not linked with the damage. Also capillary rise was excluded as well a possible contamination from a back room that in the past was a deposit of sea salt. The cause was found during a rainy day, w h e n a stream of rainwater collected by the roof and gutters was seen to fall d o w n at each corner of the courtyard, being the building without drainpipes. The friction reached with the air after a few metres of free fall, caused the water stream to explode into a myriad of droplets, which were transported by the drainage flow through the staircase and splashed against the decorations. Of course the suggested solution was to apply a drainpipe, but the second hypothesis, i.e. a glass pane to protect the decorations and a glass door to stop the drainage was preferred. Modern buildings made of metal and glass have a conductivity which is higher than traditional brick walls and are more sensitive to the external w e a t h e r conditions. As the thermal capacity of walls and roof is relatively small, the building does not smooth out the seasonal wave. In the wintertime (and during the night) the outer structure cools and generally assumes a temperature which is intermediate between the heated interior and the cold exterior, so that the cold ceiling and walls generate a continuous internal mixing. For example, the Sainsbury Centre for Visual Arts, Norwich, which is built with metal and glass structures with some insulating panels, during a winter survey in a foggy week in December 1996 was found to have the internal air temperature Ti = 19.5~ were ranging between 14.2~

and 15.7~

the metal and glass ceiling panes and walls the outside temperature was To = 7.2~

The continuous mixing of the air masses generated by the contact with the cold structures is also artificially increased, and even in a much more enhanced extent, by the m a n y fans distributed all along the walls, to inject w a r m air in the room. In order to reach the interior of the wide room, and obtain a uniform temperature, the ventilation rate is very high. However, this violent mixing is not sufficient to produce a very uniform temperature (Fig.l.7) and exchanges of heat and moisture

21 are favoured, as well as the deposition of airborne particles. Possibly for this, for safety or other reasons, the main parts of objects is appropriately protected by an individual plexiglas case. On the other hand, in the sunny days of the w a r m season, the ceiling becomes hot forming internal layering, and the glass panes generate some green-house effect.

Fig.l.7 Horizontal cross section of the Sainsbury Centre for Visual Art, Norwich (U.K.), showing the temperature distribution. Modern buildings, made of metal and glass, do not benefit of the inertia of the thick wall, and the microclimate is conditioned by heat exchanges and forced mixing, but fans are not sufficient to obtain a very homogeneous temperature distribution. The 9 December 1996 at 16.30.

1.6. THE TEMPERATURE IN A SHOWCASE We have seen that inside buildings, the 'primary' external heat w a v e is smoothed out by the walls, but abrupt temperature changes are generated by local sources, and the perturbation spreads in different ways within the rooms. For this reason a further natural filter is often useful to smooth out these 'secondary' temperature changes, and show cases accomplish to this aim (Fig.l.8), in addition to protect delicate exhibits from dust deposition and accidental shocks. In this example taken from the Uffizi Gallery, the external daily wave reaches some 20~

and both

the room and the show case have waves with some 4~ amplitude, but the show case has a temperature which is smoothed out with a 2 hr time lag. The exhibits in the case are exposed to a slighly smaller temperature span as the unshielded objects in

22 the room, but are protected against rapid fluctuations or temperature (and humidity) changes. It might be useful to comment that the outside temperature was measured with a sheltered thermometer suspended 30 cm far from the wall, and the thermometer was immersed into the internal boundary layer of hot air which forms and rises along the wall when the latter is hit by solar radiation. This is actually the air which envelops the lighted side of the building, warms the window panes and penetrates through the windows fissures, but is different from the free air, as it would be measured with a standard weather station. 22 20

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Time (hr) Fig.l.8 Comparison between the outdoor temperature, the indoor value and the temperature inside a show-case. Pollaiolo Room, Uffizi Gallery, Florence, 11 to 13 March 1997. The lighting should be obtained with lamps placed outside the case; on the contrary, a lamp inside will act as powerful heater and most of the heat dissipated will remain entrapped inside the case. However, although the light source is external, when a show case is made of a material which is not fully transparent to the IR, it becomes a green-house which causes a dangerous overheating of both the air

and the exhibits preserved inside, as well as a drop of relative humidity. It is popularly known that glass is relatively opaque to the IR radiation, and that more appropriate are plexiglas (i.e. polymethylmethacrylate), polycarbonate, poly-ethylene, polypropylene. However, for all these materials the transmittance in the IR band is neither 1 nor homogeneous, but is generally good except for some narrow absorption bands (Touloukian and DeWitt, 1972; Saint-Gobain, 1977; Michalski et al., 1991) whose relevance changes with the intensity of the spectral band of the IR radiation having the same specific wavelength. For this reason, only

23 looking at the absorption spectra, it is difficult to decide which material is the best one and a laboratory test is much more useful to clarify ideas. Some identical show cases have been built, sized 20 x 10 x 10 cm and with panes 5 m m thick, made one of glass, one of plexiglas and one of polycarbonate, as well as others with panes having twice this thickness. In the bottom of these cases, a black sheet of paper has been placed in order to transform absorbed light into IR radiation, and a thermometer. All these cases have been lighted from outside, with a tungsten incandescence lamp, supplying 500 lux at the top of the boxes in order to obtain a clear effect. The panes, being partially transparent to the IR radiation, absorb part of IR the incoming from the incandescence lamp as well as part of the outgoing radiation, and the heat accumulated in the panes is re-distributed part inside and part outside. The result of this balance is shown in Fig.l.9.

glass 0.5 cm ~3 LJ o

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Time (min) Fig.l.9 Overheating, as a consequence of the green-house effect, of show cases made of: glass, plexiglas, polycarbonate. The cases are lighted with 500 lux from a tungsten incandescence lamp. It is clearly seen that plexiglas and polycarbonate practically behave in the same way, and that their overheating (i.e. 2.9~ 3.5~

is only slightly less than that of glass (i.e.

Making twice the pane thickness a delay is introduced because of the initial

advantage of a greater portion of the IR that is stopped (and accumulated) in the top pane and cannot penetrate inside; after some 2 hr this advantage is lost and the thicker thickness generates a more efficient green-house effect, as expected. After some 6 hr, the overheating is 3.1~

i.e. only 0.2~ more than the box having panes

with half thickness. This experiment clearly shows that, in the case of external

24 lighting with incandescence lamps, the plexiglas is slightly better than glass. A further advantage for short term lighting can be obtained increasing the thickness of the pane. This would reduce and make more gradual the internal overheating and, consequently, the drop in relative humidity. It is thus necessary to avoid the IR radiation, as far as possible, and fluorescent lamps might be a relatively good approach. The same experiment discussed above but with 500 lux generated with a fluorescent lamp led to no detectable overheating. However, these lamps should be controlled for the harmful ultraviolet (UV) emission, but the main drawback is that their irregular spectrum gives an unpleasant tune to colours. The best method consists of using fibre optic lighting, which are, or can be made, practically free of dangerous U V and IR radiation, as it will be discussed in Chapter 4. Showcases, wall display, display tables and so on are useful only if they are suitably built, with use of materials which are inert and no off-gassing, and are appropriately managed. Cases with forced ventilation do not meet the aim of smoothing out room temperature fluctuations. Airtight cases with a closed atmosphere to be dust free should be built with materials that do not release and accumulate noxious substances, or biological infection.

1.7. IS IT POSSIBLE TO COMBINE PEOPLE COMFORT, CONSERVATION NEEDS

AND LOW COST? When a building has a natural microclimate which is not comfortable for people (only rarely the problem is posed whether it is also suitable for conservation), HVAC systems are installed to obtain the desired conditions. Traditional systems are used, e.g. hot water radiators, fan coil convectors, radiant panels, humidifiers) following the everyday practice of keeping a temperature fluctuating around the desired level, or switching on/off the system according to the business times with sudden jumps or drops in temperature (and, consequently, in relative humidity). All these systems are characterised by intermittent use and are located in spot areas, so that they continually generate microclimate perturbations. The use of fans generally worsen the situation, forcing air currents in the rooms. The worst situation is reached in winter, in buildings used only at times, as in the case of churches attended weekly for the Saturday and Sunday liturgy. The first need for conservation is a constant climate, people need a mild climate, and a constant mild microclimate seems the most obvious conclusion, but it is expensive.

25 As it is not easy to combine man comfort, conservation needs and low costs, some different solutions have been attempted, but conservation is more often sacrificed. A compromise solution is to reduce at minimum the heating, warming only pews with electric wires at low temperature, when people is in. This method is aimed at giving a comfortable contact with pews where people seat and rest feet, and is acceptable for heavy dressed people and for a relatively short time. The air should remain unaffected or so. If the temperature is elevated and too much heat is transferred to the air, convective motions are generated, associated with downwards currents of cold air, having the ceiling and wall temperature. These cold flows are very unpleasant to people, and these internal air motions lead to increased deposition rate of candle smoke and other suspended particles. This method is not common in Italy, for the elevated cost of the electric power. Another popular compromise solution is to heat the floor in the pew area, just to mitigate the temperature where people stay. The underfloor heating system uses pipes which carry hot water, placed over an insulating layer and embedded in a conductive layer which constitutes the floor. Heat is transferred from the pipes to the floor and the room is heated by low temperature IR emission from the floor. An advantage of the floor heating is that a large mild temperature heating surface produces comfort at lower air temperature (about 2~

therefore reducing heating

requirement (Porges, 1995). However, when the warm surface is reduced to the pew area, the comfort is diminished, and in addition pews intercept the infrared radiation, leaving people in a relatively cold environment. In any case, floor heating is characterised by low risk for damage to frescoes, paintings, statues and other church decorations, but by high risk to historical pews which undergo enhanced temperature and humidity changes. When such a system is designed for daily use in business buildings, the highest efficiency is obtained with the combined effect of IR radiation and air heating via floor conductivity which generates important convective motions in the air. However, in the case of weekly use in churches, when walls and ceiling are much colder than the air temperature, the air which comes into contact with the cold surfaces sinks, forming down droughts of cold air which are harmful to both people and conservation. In order to avoid dangerous convective motions, the floor should radiate without transferring heat via conductivity to the air. For this reason materials with high IR emissivity and low surface conductivity should be used. Several materials are good emitters e.g. Dolomite which reaches 96% emissivity; granite 93%; brick, 93%; oak 90%, and have a different conductivity, e.g. the above materials have respectively 1.5, 2.9, 1.4, 0.16 W m -1 K -1, so that granite is much more conductive

26 than wood, which is quite an insulator. In most cases inappropriate materials are used for the floor, having a too low conductivity which reduces (or vanishes) the system efficiency or being too much conductive and generating enhanced convective motions, or being poor emitters. For example, the medieval church of Colle S. Lucia in the Italian Alps, 1400 m a.m.s.l., has an underfloor heating just below the pew, but with a w o o d floor. During a field survey in January, with the hot water in the pipe at 30~

the floor was at some 15~ and the air at 1 m was between 8 and 9~

the hot water temperature to 60~ the floor temperature rose to 23~

raising

but the gain in

air temperature was nearly insensitive, being only one degree or so (Fig.l.10). 25 23 ~-21 o

~ t~

19 17 T(floor) ~ 15 ...................................................

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Fig.l.10 Floor and air heating in the church of Colle S. Lucia (Italian Dolomites) from 16 January 1997 at 00.00 to the next day at 9.00. Floor temperature (thick line) and air temperature at 0.1; 0.5 and I m; the measurement at 2 m shown the same temperature found at 1 m. The sharp rise in floor temperature in the afternoon of the 17th is due to the rise of hot water in the underfloor pipe from 30~ to 60~ The air heating from 10.00 to 17.00 of the 16th is due to the external sunshine and warming. Systems based on floor heating need several hours before to w a r m the surface layer and reach the highest efficiency, so that they must be put into operation one or two days before the use, determining dangerous environmental cycles and reducing the spare of money. In practice, in order to abate costs and shorten heating times, these systems are often integrated with other faster systems, e.g. with inflows of hot air w h i c h have the negative consequence of increasing the a m p l i t u d e

of

environmental changes. If costs were neglected, and the floor heating system were continually kept into operation for the whole season, in theory the whole room, walls and ceiling w o u l d reach equilibrium and the problem would be easily solved, at least for the well-being

27 of people, but such a practice is not completely safe for conservation. An example of that was found in the refectory of the Leonard's Last Supper, Milan (Camuffo and Bernardi, 1991a), with a terracotta floor heating. The air, heated from below, was continually mixed by convective motions which led to a heavy deposition of suspended particles and blackening of the painting. The blackening occurred at a so high rate that the restorations works were interrupted for a certain time waiting for an improvement of the ambiental conditions. This obliged tO apply a number of mitigative measures, e.g. to insulate the ceiling to reduce the source of instability aloft, and to forbidden the local traffic which was an important source of soot. However, returning to the problems connected with the heating system, although the floor temperature was kept as low and homogeneous as possible, the temperature distribution inside the room was often characterised by a strong gradient determined by the penetration of w a r m air from the nearby room, where the heating was planned at a higher level for custodians and visitors (as already seen in Fig.l.4). In the general case, the floor heating, which generates air mixing and blackening, is not recommendable in the case of historical buildings with painted walls or ceilings, and exhibits should exposed appropriately protected into show cases. However, although it is not recommendable, in certain cases it might be accepted, with a very soft use, in order to avoid also worse heating systems. A very common system, which is preferred for its low cost, is the hot air heating. Violent airflows of hot air are injected before the people entrance, and are stopped when the people go out. The airflow partially mixes with the indoor atmosphere, generating a wide spectrum of air temperature: hot air forced by its buoyancy reaches the ceiling and forms there a hot layer; on the other hand the dense, cold air originally present" in the room accumulates near the floor; finally, air parcels having intermediate densities find their level of equilibrium, resulting in a strong atmospheric layering. For instance, in a small mediaeval church in the Alps at 1140 m above sea level, in order to reach a benefit of a few degrees rise at the pew level (i.e. 5 ~ at 1 m), a rise of more than 20~

is attained at 3 m and 25~

at 4 m

(Fig.1.11a). These impressive temperature changes in turn generate dramatic drops of relative humidity (Fig.1.11b) with the consequence of forcing internal stress to the canvas paintings and wood statues, which will undergo thermal expansion and moisture shrinking that will destroy the wood artwork in a short time. In addition, the forced inflow generates great atmospheric mixing in the environment with the result of an increased deposition rate of the candle smoke which sticks the cold walls with paintings and frescoes. This is one of the worst heating methods. A mitigative intervention would be to mix vertically air with fans in order to

28 30

rO

25

o

20 r~

15 10

0

10

20

30

40

50

60

40

50

60

T i m e (hr)

90 80 ,.~

,1-1

70

~ i,,,,,i

t~

6o

~

50

9,-, r~

40

~

30 20 0

10

20

30

Time

(hr)

Fig.1.11 (a) Sudden heating and cooling, and strong atmospheric layering, generated by a hot air heating system inside the Church of Rocca Pietore, Italian Alps. The indoor air temperature measurements were taken at the heights 1, 2, 3, 4 m. The measurement at I m is evidenced with a thick line, followed by the others with maximum temperature increasing with height. The values monitored at 3 and 4 m are very similar. The figure reports data from 24 to 26 December 1996, and the peaks correspond to the heating for the Eve and Christmas celebrations. (b) Relative humidity variations caused by the above temperature changes at I m (thick line) and 4 m (thin line).

29 destroy the thermal layering. This would reduce the dramatic temperature rise aloft with the associate humidity drop, but would increase the deposition rate of particles on the surfaces. In order to reduce the room turbulence, the fan can be inserted into a vertical tube, with the lower opening near the floor and the upper near the ceiling. This mounting will generate turbulence only near the two ends of the tube, i.e. in the zones of convergence and divergence of the forced flow. An also worse system, that was especially widespread years ago, was the use of mantle stoves, which burned liquid gas. The chemical reaction of the liquid gas with the atmospheric oxygen generated carbon dioxide and water vapour. In addition to the effects of the hot air discussed above, the most negative consequence originated by the combustion was the enormous production of moisture. Only a small fraction of it was visible when condensed on the cold windows forming rivulets of water, but the main part was absorbed by the porous surfaces of walls and decorations, condensing into the micropores, weakening the stuccoes, shrinking the wood, fading the tissues, favouring the microbial decay and so on. From the above examples it is evident that it is not easy to combine h u m a n comfort, conservation needs and low costs, and that a compromise is required, where the conservation needs should dominate in proportion with the importance of the cultural heritage and the building use. For instance, it could be said that the choice of the microclimate in a museum, which should be aimed at conservation, and where m a n y important items are concentrated, should be more rigorous than in a church which is more oriented to people use. It is also clear that every system presents a number of negative aspects, some of which may have a major impact in certain circumstances, or minor one in others. It this thus important to carry out a careful pros and cons analysis and choose, time by time, the system that provokes the minimum damage. Sometimes a combination of different systems might be considered in order to avoid the excessive impact of specific adverse factors; e.g. in a mountain church the combination of a radiant floor with an electrical pew heating might reach an acceptable comfort with a modest ambient perturbation, and might be better than the more common solution of a radiant floor heating associated with hot air inflows. A general comment, on the ground of the above negative examples, is that it might be preferable to reduce interventions to a m i n i m u m level, in order to also reduce negative effects to a minimum level. It can be argued that many objects have survived till today just because the modern heating was not yet invented and now it constitutes a new challenge. This is true in several cases; nevertheless, it is also possible to use this modern technology to improve natural negative situations, as e.g.

30 w h e n a room temperature is below the dew point and condensation forms everywhere. The conclusion is that heating systems should be installed by experienced engineers, but under the strict directives of experts in conservation science; afterwards, also the use of these thermo-technical devices should be managed under the strict control of experts in conservation. The real problem is that the conservation needs are too often disregarded.

1.8.

MONITORING

AIR

TEMPERATURE

TO

STUDY

AIR-SURFACE

INTERACTIONS AND FOR MICROCLIMATE DIAGNOSTICS The use of a thermohygrograph sited in a corner of a room is very common, but this instrument furnishes data representative only of the point where the sensor is located, not of the whole room, which is generally characterised by spatial gradients continually variable, with fast or slow rates. When the heating or cooling systems are turned on/off, they provoke an abrupt change of temperature, which in general reach few degrees C (Fig.1.12). These frequent and dangerous step changes, when are relatively modest, pass nearly unobserved in the thermograph strip chart records, whose resolution is generally +0.5 ~ or +1~

in that they are smoothed out by the

friction of the pen on the strip chart, or the loose mechanical coupling. Electronic records which are much more accurate and are not affected by mechanical friction, show m u c h better this situation which is c o m m o n to all the most important m u s e u m s and also worse in other situations. Mechanical strip chart recorders can only monitor important changes, as e.g. those induced by hot air heaters, which in the extreme case of churches heated once a week, generate impressive temperature rises,~e.g. 20~ in one or two hours. Measurements of the air temperature and humidity distribution, taken in many points in proximity of surfaces or in horizontal cross sections of rooms, can be used as a diagnostic tool to individuate the air-walls interactions, the causes of microclimate perturbation, the space gradients, the exchanges of heat, the path of the air masses, some deposition mechanisms. Comparing subsequent sections, it is also possible follow the temporal evolution. It is practically impracticable to disseminate a large number of sensors in a room, each having a wire connected with the data logger for two reasons: the wires will form and entangled spider's web in which people cannot move; not all the sensors will exactly have the same transfer function or calibration, and the instrumental response departures will be interpreted as microclimate anomalies.

31 22

20

r"

v

I..i

18

I.,4

~16

T(3)~

[.-, 14

T(O.05)

12

I

I

I

0

I

I

3

I

l

6

9

I

I

I

I

l

I

12

Time

I

I

I

15

l

I

I

18

I

I

21

24

(hr)

30

? t=1

29

I..i

28 [.-

27

9

0

9

I

3

.

9

I

6

.

,

I

9

|

9

I

9

12

,

I

15

|

|

I

18

9

|

I

21

,

.

24

Time (h) Fig.1.12 (a) Abrupt rise and drop of temperature in winter (18 February 1997), w h e n the heating system is turned on in the morning and off in the evening. Measurements respectively taken at 0.05, 1, 2, 3 m from the floor. During the daytime the air is well mixed above 2 m, and the temperture is the same. (b) In summer (11 August 1992), similar step changes are generated by the air conditioning system, but the air is well mixed and the curves at the different heights are practically indistinguishable. For this reason only one has been reported. The Pollaiolo and the Giotto rooms, Uffizi Gallery, Florence.

32 The monitoring is better made moving the same fast-response instrument along a chosen regular grid with points close to the walls as well as inside the room. Repetiting in time these runs, also the time evolution of the temperature distribution is obtained. The method is very effective and has been originally devised for the diagnostic of indoor environments (Camuffo, 1983), in order to find risk areas, causes and effects, and has been applied in many circumstances either indoors or outdoors (Camuffo and Schenal, 1982; Bernardi et al., 1985; 1995a,b; Camuffo, 1986; 1991; 1994; Camuffo and Bernardi, 1988; 1991a,b; 1993; 1995a,b; 1996; 1997). As it is essential to avoid intercalibration errors, the same fast-response instrument is used, i.e. a precision electronic psychrometer (Chapter 11). The spacing between measuring points and hence the number of observations is conditioned by the size of the room and the rate of ambient change. It is essential that in the time employed for the observations the ambient conditions do not change too much. An

uncertainty principle holds:

the greater the spatial resolution, the larger the number of

observation, the longer the time elapsed and the less representative the whole monitoring. In several cases some 40 observations have represented a reasonable compromise solution. The series of measurements can be repeated every 2 or 3 hours d u r i n g the daytime. During the night-time the whole ambient system relaxes without violent perturbing factors, and all the gradients tend to flatten or disappear. The intervals between consecutive measurements can be therefore increased. Ideally, the first observation should be made near sunrise, to monitor the less perturbed situation; then the next observation should be made during the cleaning time, when the windows are open; then two or three hours later and so on, in order to arrive at the end of the visiting time; after the museum closure a few observations are needed. In practice, security reasons limit the possibility of doing measurement outside the m u s e u m business time; fortunately the most important situations are found during the business time. All the cross sections must be monitored exactly following the same order, for two reasons: (i) first of all because if there is a time-lag effect in the monitoring, it repeats identically in all the distributions, and for each point the interval between two successive readings is exactly the same; (ii) then because it is less easy to do errors, and the data must be filed with the same order in the computer. It is also important to repeat for some days the measurements for two reasons: the former is to see whether the results are repetitive, and really representative of the seasonal situation; the latter is that small variations can be found, and their repetition helps to distinguish regular trends from casual fluctuations, i.e. small repetitive variations are not casual.

33 The grid of the measuring points in the horizontal plane is composed of two interconnected series of data: a first series of points at the same height, measured at regular intervals close to the walls, i.e. at 2 mm and at 20 cm from the walls, in order to detect the existing gradients and the exchanges of heat and vapour; the second series (always at the same height) is aimed to show the temperature and humidity distribution inside the room, and is composed of other points, distributed following a regular grid, the points being the vertex of rectangles with the same dimension. All the observations are made exactly at the same level, although the choice of the level is not so important. The height of 1 or 1.5 m from the floor is often preferred for being comfortable for the operator and being representative for the most part of the exhibits. After the observed values of temperature (or humidity) are reported in the cross section, it is possible to use computer graphics or manual interpolation to show the space distribution of the parameter, the anomalies, the intensity and the shape of gradients. Close isolines show gradients. Closed isolines spreading like water waves contain in their centre the source of heat if the temperature value is radially decreasing, or a sink of heat if is increasing. Alternatively, they can show the zone of divergence (or convergence) of air when there is a three dimensional convective motion. In a room, isolines shaped like a tongue which begins from a door or a window show the penetration of external air masses and their path inside. Isolines parallel to the wall surface show that the wall is adsorbing heat if the temperature decreases approaching the wall, or vice-versa. In the same way a gradient of temperature is an index of transport of heat, a gradient of moisture content is an index of transport of vapour and condensation (if the minimum is at the air-surface interface) or evaporation from the surface (the maximum at the interface). Gradients of air temperature are also gradients of air density, and the lighter air gains buoyancy. A thermal minimum along a wall means that the air in contact with it is denser and sinks, a m a x i m u m means that is lighter and is rising up. Therefore, horizontal gradients of temperature may also help to interpret the dynamic state of the air inside a room, the transport and (partially) the deposition of pollutants. An example is shown in Fig.1.13 which reports two horizontal temperature distributions in the Sistine Chapel, first in the early morning when it is open for cleaning, and then a few hours after the entrance of visitors (Camuffo and Bernardi, 1986; 1995a). In the first map, the inside atmosphere was originally in equilibrium with the thick walls, but the opening of three doors (two on the top and one on the right) causes the entrance of cold air: chiefly from the door on the right. The air in the middle of the room, far from the doors, is warmer, but even more warmer is the air

34 close to the walls, which benefits of the heat released from the walls. This air gains buoyancy and forms an uprising current along the walls. This air current tends to increase the deposition rate of airborne pollutants via inertial impaction

(see

Chapter 8), although the positive gradient of temperature tends to partially to counteract it. In the second map, the external atmospheric warming, the presence of visitors and the energy released by the lamps have changed the situation: the air is now w a r m e r than the walls, and a heat island is formed in the central part of the room, where the visitors stay longer. The gradients near the walls are now negative and the heat flows from the air to the walls. The air in proximity of the walls becomes denser and sinks forming a downwards current. The deposition rate is now increased as the negative temperature gradient generates a thermophoretic transport whose effect is added to the contribution of the inertial impaction.

Fig.1.13 Air temperature (~ in a horizontal cross section of the Sistine Chapel when it is opened for cleaning (a) and after the entrance of visitors (b). (7 May 1983, after Camuffo and Bernardi, 1986, reprinted by permission of the Boltettino dei Musei e Gallerie Pontificie).

35 The same method can be applied to investigate the vertical distribution of the air temperature. An example with three different situations found in summer in the Giotto Chapel, Padova, is shown in Fig.1.14 (Camuffo and Schenal, 1982; Camuffo, 1983). In the early morning, when the door is open for cleaning, cold external air enters through the door and fills the lower part of the room up to the height of the door. Above this cold layer, the warm (and less dense) air which was before inside the building remains entrapped there, opposing that new air enters and fills the volume above the height of the door. The isolines are not horizontal, being tilted by the dynamic effect of the external air mass which is entering the room transporting momentum and inducing oscillations in the cold layer. At mid morning, the external air which enters through the door and goes out through some windows in the apse, has a temperature (and a density) which is intermediate between the tongue of cold air which extends from the northern apse as far as the middle nave and the warm air layer which is entrapped below the ceiling. After noon, the solar radiation through the three mullioned window on the facade hits the floor in the front part of the nave, and also heat is released from the hot door. The front part of the nave has the same temperature along the vertical, showing a continuous mixing of the air in the homogeneous region. However, the part of the Chapel near the apse remains unaffected by this perturbation and there the air is thermally stratified (horizontal isotherms), showing a transition zone (curved i s o t h e r m s ) i n the middle of the Chapel. The more vertical the isolines, the more intense the mixing. Sometimes the architectonic features of the rooms are more complicated or the situation is apparently more complex. An interesting example (Fig.1.15) is found in the Cour Marly, Louvre Museum, Paris, which was obtained by closing with a glass roof a courtyard, and the floor is divided into three levels connected with stairs. The top level (on the left) is C shaped and embraces part of the middle level floor; this is Y shaped and surrounds the rectangular bottom level (on the right). Summer air conditioning is accomplished with violent flows of air ejected out of long linear slits sited at the edges of the floor and suction is made with other horizontal slits on walls. The high speed of the airflow facilitates the mixing with the ambient air up to a distance of a few metres from the slits. In addition to the cold air injected by the floor slits, cold air conditioned from some exhibition rooms which face the top level, enters the Cour through open windows and doors. The cold air tends to descend to the lower levels of the Cour flowing along the staircases and jumping over the parapets of the upper floors, and is sucked out by the intake slits. At the bottom level of the Cour, four doors allow free air exchanges between the Cour and the corridor which is connected with the entrance hall. When the corridor is colder, cold air enters

36

24.1

23.7

25.1

26.2

/

/

26.0

Fig.1.14 Vertical cross sections of the Giotto Chapel, in the summertime. (a) In the early morning (8 a.m., the 9 July 1977) cold air penetrates through the door and above the cold layer the warm air remains entrapped. (b) At mid-morning (11.30 a.m., the 8 July 1977) external air penetrates through the door, and has a density intermediate between the cold tongue near the floor on the apse, and the warm air entrapped aloft. (c) In the early afternoon (14.25, the 9 July 1977), the hot floor generates mixing and isothermy in the front part of the nave; after a transition zone in the middle of the Chapel the air in the apse remains unaffected and thermally stratified. (After Camuffo and Schenal, 1982, reprinted by permission of the Bollettino d'Arte).

37 the Cour Marly and forms a cold lake of stable air in the lowest part of the Cour, which is in front of the four doors. When the corridor is warmer (as in this example), the hot air enters, gains buoyancy and rises immediately, forming an uprising flow. This w a r m current rises up to it is stopped at a certain height by w a r m e r air layer stratified below the hot glass roof, or by the roof itself. Whatever is the level aloft where the vertical motion stops, at that level the air flow changes direction and diverges without loosing momentum: it becomes horizontal, crosses the Cour and other colder air sinks, closing the cellar motion. The warmer air found at the bottom layer and the colder one on the top is an index of a very unbalanced situation, and shows that the air is continually moving to reach an equilibrium which is impossible to attain until the forcing factors remain active. In addition, in summer, when the sun is higher on the horizon and solar beams can reach the edge of the floors, hot spots are found which generate a secondary local uprising flow.

21.5

21.9

4-, 21.5

4--

:o' ~ oOoq.

22,3

Fig.1.15 Air temperature (~ measured above each of the three levels of the Cour Marly, Louvre Museum, the 11 August 1993. Hot air enters at the bottom level through the four doors (airflow indicated with arrows) which lead to the entrance hall of the Museum. The hot air rises immediately forming a convective, rotating motion with descent of colder air on the opposite side. Cold air penetrates also through the windows and doors of the exhibition rooms faced to the top floor level, in the opposite side (on the left). The uprising 'bubble' of hot air entering from the four doors (evidenced with arrows) at the bottom level is evidenced with shading.

38 1.9. DRAWING AIR TEMPERATURE AND OTHER ISOLINES Three-dimensional computer graphics give a very elegant visual presentation, but less useful for diagnostic purposes, as several details are masked by the perspective view (Fig.1.16). Two-dimensional maps are much more convenient, as they show with great detail and without distortion the actual distribution and the existing gradients. Computer graphics have been developed to interpolate linearly, quadratically, or with more complex functions, the values between pairs of points.

Fig.1.16 Three-dimensional representation of the temperature distribution at the Sainsbury Centre for Visual Art, Norwich, U.K. (the 9 December 1996 at 16.30, shown in Fig.l.7), and projection of the contour levels in a horizontal plane, which furnishes the two-dimensional diagram. Several details of the 3-D representation are masked by the perspective view. However, this software can be satisfactorily used for a single room with a simple geometry, e.g. a rectangle, but is still unable to well represent the temperature distribution in a complex array of rooms which constitute the floor of a building. In fact, all the data are interpolated in the same way either in the free air or across walls, so that the interpolation is exactly the same for areas in the same room or including walls and different rooms, without considering that the heat flow by advection through an open door is different from the conductive flow across a wall. Computer graphics have not yet reached the level of sophistication which is necessary to equalise the quality of hand drawn isolines in complex architectonic systems. The reason is that this is not only a problem of mathematical interpolation, but of a

39 correct physical interpretation of the data. In the case of building temperature or humidity maps, the distribution is complicated by the presence of sources or sinks of heat or moisture, horizontal advective transports, vertical convective movements, irregular geometry of architectural structures and other perturbation factors. Careful reasoning and experience constitute the best guideline, but some basic directives can be here summarised. A beginner can proceed with successive elementary steps. The first step is to write, on the side of each grid point Ox,y the observed values V(Ox,y). After, one starts by choosing an arbitrary point Ox,y (it is convenient, however, to choose a maximum or a minimum) and drawing the segments which join this point with all the neighbouring points, e.g. the 8 points Ox-l,y-1, Ox-l,y, Ox-l,y+l, Ox,y-1, Ox,y+l, Ox+l,y-1, Ox+l,y, Ox+l,y+l in the case of a regular squared or rectangular grid. Once chosen the map resolution, i.e. the unit step from isoline to isoline (e.g. 0.1~ for air temperature T or dew point spread DPS, 1% for relative humidity RH, 0.1 g kg -1 for specific humidity SH or mixing ratio MR, 0.1 g m -3 for absolute humidity AH) all these segments are divided in equal parts which are determined by the number of times the unit step is included in the difference between the numeric values of the correspondent grid points V(Ox,y) - V(Ox-l,y-1), V(Ox,y) - V(Ox-l,y+l), and so on. For example, if V(Ox,y) = 18.3 and V(Ox-l,y-1) -- 18.7, AV=0.4 and the segment Ox,y Ox-l,y1 is divided into 4 sub-segments which are divided by the equally spaced points 18.4, 18.5 and 18.6. In this way it is possible to note at the extremes of each sub-segment all the values which have been obtained by interpolation. Continuing with this method, it is possible to interpolate the space between all the pairs of points in the grid. Joining by a line all the points having the same value, observed or interpolated, a map is obtained which corresponds to a linear interpolation. All the isolines are closed or end on the walls. This is done in a very short time by several computer programs. However, hand drawn isolines may take into account several other factors. It is possible to distribute more gradually the gradients from flat zones to more perturbed ones instead of using a rude linear interpolation. It is also possible to take into account the presence and location of heat or moisture sources or sinks (e.g. diffusion intakes or suction outlets for hot, cold, humid or dry air) and improve the detail. Even more important is to consider the dynamics of the room, with advective transport from doors or windows, and vertical convection. The dynamics is well represented with analogy to the weather maps and the representation of fronts. In the weather maps a continuity is assumed not only on the values of the parameter, but also in its first and second space derivative. This means that all the isolines and

40 their curvatures (i.e. concavity and convexity) present a progressive and coherent increase or decrease, and that all the points of greatest curvatures are distributed along a line, that in a weather map may represent a front and that has a physical meaning also in a thermal or hygrometric map. In the actual case, when external air masses with different characteristics from the inside air, can penetrate through a door and flow horizontally for a certain path, several successive isolines start from the door, and protrude inside having the m a x i m u m curvature lying on an imaginary line which is the core of the air stream. Two methods are possible: the line oriented point of view, i.e. connecting with an isoline all points having the same value, which is common in topography, and the area oriented criterion, i.e. including between two isolines the belt which has the same

values V(Ox,y) or values which fall within the upper and the lower limit represented by the two contiguous isolines. The field variability obliges to prefer the first or second criterion: line oriented is necessary with a wide range of parameter variability, e.g. climatological maps; the area oriented in the case of a little variability. For instance, if in a room the observed values range in a span of a few tenths of degree, or one degree, the area oriented method is appropriate with resolution 0.1~

if the

span is several degrees, it is practically impossible to keep the same resolution and draw so m a n y lines, and is convenient to choose a larger resolution, e.g. 0.5 ~ or 1~ In this case m a n y data fall within each class and it is preferable to use the line oriented method. The area oriented method is necessary when there are several scattered points having the same value and determining homogeneous areas: e.g. in the case of two contiguous zones characterised by the values 18.3 and 18.4, the band 18.3 includes all the points from 18.30 to 18.39 but not distinguishable because of the truncation at the first decimal, and the separation line ideally joins all the points between 18.39 and 18.40, e.g. 18.399 which of course do not appear in the graph. If we use an accurate psychrometer, whose resolution is 0.1~

but only because the display is truncated

after the first decimal digit, the precision of the transducer being of the order of 0.01~

then the number 18.3 represents any figure from 18.30 and 18.39. This shows

that all the data having the same figures on the display are only apparently identical, being truncated and being directly classified within a class of values. In any case, when a map is drawn, all the space is subdivided with vertical steps and horizontal belts. The line oriented method joins with the vertical steps the few identical values which can determine a line and leaves on the belt the m a n y values between an isoline and the next; the area oriented method groups on the same belt all the m a n y identical values which are scattered over a wider area, where the values are apparently identical, being the result of a truncation, or only slightly

41 different, but fall within the values of two contiguous isolines. The two methods are conceptually the same, if one considers that in the area criterion an isoline instead of separating two areas, ideally connects all the non existing points having a value between the two contiguous classes, as in the example of the truncation. A very practical method for beginners is to facilitate drawing with colours that evidence the maxima and the minima in the map. For example, all the maxima can be evidenced with red, and the minima with blue. All around the maxima the red colour is attenuated (i.e. the saturation of the colour is reduced) as the observed values V(Ox,y) decrease, forming concentric coloured areas with the same pencil but less and less marked. The same can be made with blue, starting from the minima, and leaving untouched the intermediate values. Drawing isolines in a coloured map becomes m u c h easier. After having sketched the first coloured draft, a better and more detailed map can be drawn with a pencil on a new paper sheet. In particular, when all the isolines have been drawn, a very good practice is to colour again the belts, using two different colours for each parameter, one for the upper part of the span of values and one for the lower, and with colour saturation decreasing from the extreme to intermediate levels. The intermediate values can remain white. The visual effect is more immediate making better understandable the microclimate, the forcing factors and the dynamics of the air masses. Finally, it might be useful to compare the practice of the rounding off of a number with that of truncating it, i.e. 16.6 becomes 17 in the first case and 16 in the second one. It is merely illusory to think that the former is more precise, as the figure 17 is in reality 17+0.5, and may indicate any number from 16.5 to 17.4, so that the span of uncertainty is 1. This is exactly the same in the case of truncation, as 16 represents any value from 16.0 to 16.9. The main consequence is that the average of a large population of r a n d o m numbers is different if the numbers are truncated or rounded off, being 0.5 lower for truncated numbers; i.e. truncation makes level to the lowest value of the last digit and rounding off makes level to the middle value of it. In the case of a map of isolines drawn following the former or the latter criterion, the distribution is absolutely the same, but the values (and the isolines) being displaced by 0.5 of the last digit.

42

CHAPTER 2

Humidity

2.1. PARTIAL PRESSURE OF THE WATER VAPOUR The popular term humidity is often used when speaking of the moisture present in the atmosphere; however it is an ambiguous, generic word. Several specific terms exist, each of them represents a different parameter useful to describe a peculiar property. The first hygrometric parameter is the partial pressure of water vapour, conventionally indicated with the letter e. Evaporating new water molecules this pressure increases to a certain limit; when reached, the n u m b e r of molecules escaping from the liquid water is equal to those returning to it from the atmosphere, establishing a dynamic equilibrium between evaporation and condensation. This limit condition is determined by the temperature T, but is irrespective of the dry air pressure according to the Dalton law of the independence of the partial pressures, i.e. the behaviour of any gas in a mechanical mixture is independent of the presence of other gasses and the total pressure is equal to the sum of the partial pressures. The state of being saturated is a characteristic of the vapour, not of the air. The saturation

pressure, also called vapour tension, esat(t), is computed by means of the empirical formula attributed to Magnus or Tetens esat(t) = esat(O) xlOat/(b+t )

(2.1)

where esat(O) = 6.11 hPa (note that in meteorology the mbar unit is more common, and 1 mbar = 1 hPa), a = 7.5, b = 237.3~

The graphical representation of this

equation is shown in Fig.2.1. In the presence of ice, the tension must be calculated with reference to the solid phase with a = 9.5, b = 265.5~

As the tension for ice is

lower than for liquid water, if the two phases coexist, the water molecules will progressively evaporate from the liquid and sublimate on the ice. This equation gives very accurate values at the usual atmospheric temperatures, but is less accurate near the boiling point, where esat(lO0) = 1013 hPa.

43 100 908070c~ v

6050403020100_~, -20

-10

0

10

20

30

40

30

40

Temperature (~ 100

10 c~

0,1 -20

-10

0

10

20

Temperature (~ Fig.2.1 Saturation pressure (esat) of the water vapour (thick line) and partial pressure (e) of the water vapour at different values of relative humidity (RH), i.e. at R H = 90, 80, 70 .... 10%. Of course the thick line is for RH = 100%. The first graph is with linear scales in order to be more immediate to non specialists and present a better resolution of the ordinary vapour partial pressures. The second graph can be better appreciated by specialists: it has the ordinate with logarithmic scale and represents more clearly the physical relationship between vapour partial pressure and air temperature. The lines are not exactly straight, and the departure shows how much the Magnus equation departs from a purely exponential function, giving a clear idea of the approximation made using a such simplified formula.

44 It can be noted that eq.(2.1) is independent of V, so every isothermal compression causes a faster condensation rate until the dynamic equilibrium is established; in the case of an isothermal expansion the evaporation continues until equilibrium; only when all the liquid is evaporated does the water partial pressure decrease, according to eq.(1.2).

2.2. DERIVATION OF THE LATENT HEATS The first law of the thermodynamics states that the increase of the specific energy U of a system that undergoes a change is equal to the mechanical equivalent of the heat absorbed Q plus the work W expended in producing the change.

(Uv-UI ) = Q + W

(2.2)

Gas

P Liq

D A

C B

i i i | |

i

i i t |

gli q

gva p

W

Fig.2.2 Thermodynamic cycle to derive the Clausius Clapeyron equation. Let us consider a liquid in equilibrium with its vapour; Vv is the specific volume V/M of the saturated vapour and Vl the specific volume of the liquid; Pv - Pl

45 are the pressures of the vapour and the liquid (please note that Pv

has been

previously indicated as esat(t), but in this context the new symbol has been introduced for uniformity with the liquid phase, and to make possible the following mathematical treatement); Uv and UI are the two specific energies U/M of the two phases. All these quantities are only functions of the temperature T of the system. In a p versus V diagram, a reversible evaporation-condensation cycle (Fig.2.2) close to the Carnot one can be applied to a sample of water. The cycle is as follows: first the system undergoes an isothermal and isobaric evaporation with increase of V, from A to B; then a little adiabatic heating by compression from T to T + dT from B to C; then an isothermal and isobaric condensation with decrease of V from C to D; finally a cooling by adiabatic expansion to the original state. During the vaporization, the variation of the specific energy of the system is (Uv - UI ) and the external work, negative, is W = Pv (Vv-VI ); the heat Q absorbed in this phase is the latent heat of vaporisation Lv of the liquid, i.e. Q = Lv = (Uv- UI ) + Pv (Vv-V! ).

(2.3)

For the entire cycle, the work is given by the area ABCD between the two isobaric and the two adiabatic transformations, and in the first approximation by the rectangle d W = (Vv -VI) d p . However, the Carnot efficiency is 7/= dT/T = dQ/Q = dW/Q, so that dW = Q dT/T and, combining this with the above equations dT d W - (Vv-Vl ) dp - Q T

(2.4)

i.e.

dp Q = T (Vv-VI) dT

(2.5)

By equating the two values of Q we get dpv (Uv- Ul ) + pv (Vv-VI ) = T (Vv-VI ) dT"

(2.6)

Remembering that Q = Lv the following equation is obtained: dpv Lv = T (Vv-Vl ) dT

(2.7)

46 which was deduced by Clapeyron from Carnot's theory (for this reason it is also called the Clapeyron equation) and proved by Clausius. This equation allows the computation of the value of Lv for every T when the specific volumes are k n o w n as well as the relationship between the increase of saturation pressure and T. For example, for pure water at boiling point T = 373 K and standard pressure Pv = 1013 hPa, Vv = 1674 cm 3, V1 = 1 cm 3, dpv/dT = 36.15 hPa K -1 = 3.62x104 dyne cm -2 K -1 , one obtains Lv = 2260x107 erg gq. The Clapeyron equation shows that the latent heat of vaporisation is due partly to the increase of specific energy and partly to the external work. In order to find a relationship between these two quantities it is necessary to find the ratio between W and Lv

W Pv (Vv- V1)_ P___cvdT Lv Lv - T dpv

(2.8)

and in the above conditions W / L v = 0.075. This means that the external work forms only a small part of the latent heat of vaporisation. A simple approximation of the Clapeyron formula (Fermi, 1958) is obtained by neglecting VI in comparison with Vv (the ratio of the volumes of a molar mass of water in the liquid to the gaseous state is 18:24,000 = 0.75x10 -3) and assuming t h a t the state equation (1.1) for perfect gases is still valid. Under these reasonable assumptions, the formula becomes

Lv = .Jd~vT2 dpv Pv dT

(2.9)

and in the critical case of boiling water the computed value of Lv is Lv = 547.5 cal g-l, slightly greater than the observed value Lv = 538.7 cal g-1. This difference is due to the fact that the specific volume of the saturated vapour at 100~

is less than the

value computed by means of the equation for perfect gases. For usual atmospheric temperatures this approximation is good. The above equation can be rewritten dlnpv Lv dT - . ~ v T2

(2.10)

and, if we assume Lv is constant over a wide temperature interval, this equation can

47 be solved:

Cv

(2.11)

Pv = A e x p ( - . ~ v T)

and this gives the exponential relationship between the saturation pressure and the temperature, theoretically derived. Another approximated formula (Plank, 1926) can be obtained by substituting in eq. (2.6) the formula for the specific energy, Uv = Cv T + constv where Cv is the specific heat at constant volume, which holds for perfect gases in the isothermal processes, when Q +W = 0 and is Cv = 3.~/~v = 0.331 cal g-1 K-1. If for the liquid the specific heat at constant pressure, c! = 1 cal g-1 K-l, is assumed to be constant and the external work is neglected, one gets U! = cl T +constl similar to before, and (Uv - U! ) = (Cv- c! )T. In addition, if the the specific volume of the liquid V! is neglected in comparison with that of the vapour, V v , with the help of the equation for perfect gases (1.1), the following approximations Pv ( V v - V ! ) = ,~/gv T and ( V v - V ! ) = , ~ v T/pv. can be found. By substituting these finding into eq.(2.6), it follows that

(Cv- cl )T + , ~ v

9~ v T2 dpv T +ocnst = - Pv dT

(2.12)

Multiplying both sides by dT/T 2, this equation can be integrated and one obtains Pv = A ' T (Cp-ci ) / . ~ v

A" ) exp(--T-

(2.13)

where A' and A" are positive constants, and Cp = 0.441 cal g-1 K-1 is the specific heat of the vapour at constant pressure. The exponent of T has been obtained considering that . ~ v

Cv - Cl

=

(Cp- Cv ) and, consequently, 1 + .~v

-

Cp - Cv + Cv - Cl

.JZ~v

Cp - Cl

= .~v " This is

another theoretically derived expression. Equation (2.11) can be rewritten in other forms, of wide use, as follows. 9 Lv

esat(T) = e s a t ( ( 2 7 3 K ) e x p ( ~

1

1

( 273 - T- ))

Lv

esat(T) = esat((273K) e x p ( ~ v 2732 (T- 273))

(2.14)

(2,15)

48 0.0318t

esat(T) -~ 6.11x10

(hPa)

(2.16)

where 0.0318 = (Lv/.J?~v 2732) loge (e is the Neper number 2.71828182845904...). From the above formulae the latent heats of vaporisation (or condensation) L v, fusion (or

melting) Lf, and sublimation Ls, can be derived, as follows Lv = 597.3 - 0.57 t,

Lf = 79.7 + 0.52 t,

Ls = 677- 0.05 t

(2.17)

with all the units in cal g-1. Naturally Lv + Lf = Ls.

2.3. MIXING RATIO OF DRY AIR AND WATER VAPOUR The mixing ratio w of moist air (i.e. dry air and water vapour) is the (dimensionless)

ratio of the mass of water vapour mv to the mass of dry air ma, and this ratio represents the ponderal mixture of these two gaseous substances, i.e. mv

w -ma

(g/g)

(2.18)

If e is the partial pressure of water vapour and p the atmospheric pressure, then the partial pressure of dry air is Pa = P - e, and substituting this in the equation of state for perfect gases in the form (1.2), the previous equation can be written in terms of pressure:

w

"

-

-

e .~a p-e.~v

m

e e 0.622 P - e ~0"622p

(2.19)

where 0.622 equals the ratio between the molar masses of the water and the air and, consequently, also .~/~a/.~v. It is e v i d e n t that w is i n d e p e n d e n t of the t e m p e r a t u r e T, v o l u m e V and a t m o s p h e r i c p r e s s u r e of the air parcel and r e m a i n s constant except w h e n condensation, evaporation or mixing with other air masses occur. As a consequence, w can be considered as a characteristic value, which is useful to recognise an air mass and its h y g r o m e t r i c exchanges with the environment, being invariable to either adiabatic (i.e. w i t h o u t exchange of heat) or diabatic (i.e. with exchange of heat), isobaric or non isobaric heating or cooling. For example, in the elevated air masses a

49 decrease of w gives an indication of the amount of water which has been precipitated as rainfall. This parameter, is adimensional as the natural unit is g g-l, representing the fraction of gram of vapour mixed with one gram of dry air, and might also be expressed in percent; however, as the numeric value of w is very small, it is common to multiply this number by 1000 and use the practical unit M R = 1000 w, expressed in g kg -1, which represents the number of grams of vapour mixed with one kilogram of dry air. A plot of this parameter is shown in Fig.2.3. As the atmospheric pressure p is fairly constant (i.e. +4%), a common approximation is to write 1000 hPa instead of p, which simplifies the calculations. At every environmental temperature T the M R increases proportionally to the mass of vapour that is emitted into the atmosphere, until the saturation limit is reached, i.e. when the vapour pressure e equals the upper value esat(t), given by the Magnus eq.(2.1), and the relative humidity RH = 100%. Under saturation conditions, the M R is indicated by MRsat and is computed by means of eq.(2.14), using esat(t) instead of e (for a quantitative evaluation of the error, see the psychrometric chart). Again, as for every T, e is proportional to RH, measuring RH it is possible to calculate MR., i.e. w h e n esat(t) is computed, the saturation value M Rsat is obtained using

eq.(2.14), and the actual M R is: M R = RH x MRsat. By dividing the graph of MRsat versus temperature into fractional parts, one obtains graphically the values of M R at different values of RH. The parameter MRsat is an increasing function of T, with a trend similar to that of esat(t). At usual meteorological conditions, M R 0. When a wall is hit by direct solar radiation it warms (AT > 0), evaporates (zkMR > 0) and the opposite situation occurs. These obvious facts appear as a paradox w h e n i m p r o p e r l y described: the air is dryer in proximity of a surface where condensation is occurring and more moist near an evaporating surface. This paradox derives from the fact that 'more dry' or 'more moist' are not specified in terms of MR, and people generally associate the concept of dry and moist with that of relative humidity RH which will be analysed later. From the definition, the air is dry or humid in terms of MR as a consequence of its water vapour content only, independently of the temperature T of the system; in terms of R H it means how close the vapour is to saturation, and this depends upon two factors: T and MR. A 'dry' air parcel in terms of MR becomes 'humid' in terms of RH when it is sufficiently cooled; one 'moist' in terms of MR becomes 'dry' in terms of RH when sufficiently warmed.

2.5. SPECIFIC HUMIDITY The specific humidity s of moist air is the (dimensionless) ratio of the mass of water vapour mv to the mass of moist air ma+mv, and this ratio represents the ponderal dilution of the vapour in the atmosphere, i.e. my

s - ma+m--------~

(g/g)

(2.21)

It is also called mass concentration or moisture content of moist air. Substituting eq. (2.21) into (2.18),

55 W S

1+w

t"."z)

and, operating similarly to (2.19)" e

S

0.622 p - 0.378 e

e

0.622 p

w-.~oj

Like the mixing ratio, this parameter is adimensional, the natural unit being g g-1. It might also be expressed in percent; however, in order to avoid the use of small decimal numbers, the practical unit S H = 1000 s, expressed in g kg -1, has been introduced. This represents the n u m b e r of grams of v a p o u r dispersed in one kilogram of moist air. In practice, it can be observed that in the d e n o m i n a t o r of eq.(2.22) w < < l and is therefore negligible; similarly in eq.(2.23) 0.378e can be neglected in comparison with p. As a consequence, the values of w and M R are very similar to s and SH respectively, with differences of the order of 1%. The same properties of the M R can be extended to the SH and the saturation specific humidity

SHsat; also the same graphical representation can be used in a first approximation. Both M R and SH are conservative for adiabatic or diabatic changes of temperature, pressure or volume but are not conservative for evaporation or condensation, as changes of mv are involved.

2.6. ABSOLUTE HUMIDITY The equation of state (1.1) for the water vapour can be written in the form mv~

e = V .... v T = a . J 2 ~ v T

(2.24)

by defining absolute h u m i d i t y a the density of the water vapour, i.e. the mass of vapour contained in the unit volume of moist air mv

a = -~-

(2.25)

From this definition it follows that a is variable with m v, i.e. condensation, evaporation, mixing with other air masses, as well as V, i.e. compression or

56 expansion, d u e to e.g. changing atmospheric pressure or height; from eq. (2.24) it is also e v i d e n t that a is directly p r o p o r t i o n a l to e and inversely p r o p o r t i o n a l to air temperature. Of course, a is e x p r e s s e d in g cm -3, but in o r d e r to avoid the use of small d e c i m a l n u m b e r s , the practical unit A H = 106 a, e x p r e s s e d in g m -3, has b e e n introduced. A H represents the mass of v a p o u r contained in 1 m 3 of moist air. As at s t a n d a r d p r e s s u r e and t e m p e r a t u r e , 1 m 3 of a t m o s p h e r e contains the mass of 1.255 kg of air, the values of A H are numerically similar, but always greater than those of M R or SH. In fact, M R and S H represent the mass of v a p o u r contained in I kg of dry

or moist air, which occupies some 80% of I m 3. The absolute h u m i d i t y can be c o m p u t e d by means of the equation of state (2.24) by considering that the v a p o u r density is the inverse of the specific v o l u m e Vv, i.e. 1

1

e

1

e

a - V v - .~/~v T -.~/?~v 273 (1+ at )

w h e r e the last term comes from the transformation from K to ~

(2.26) i.e. T = 273 (l+c~t)

w h e r e c~ = 1/273 - 0.00366. D e p e n d i n g u p o n the units in which e is expressed, the formula to c o m p u t e A H a s s u m e s one of the following forms. If e is in hPa or mbar (more usual), e

e

1

1+o~t

A H = 220 ; = 0.806 ~ =

0.806e

(2.27)

If e is in d y n e cm-2: e

e

1

l+ott

A H '-- 0.22 ; = 0.806x10 - 3 ~

= 0.806x10 -3 e

(2.28)

or, if e is in m m Hg: e

e

1

1 +o~t

A H = 290 ~ = 1.062 - - =

e

(2.29)

The latter s h o w s that at t = 16.4~ the A H is numerically equal to e m e a s u r e d in m m Hg; at usual meteorological values of t, these two parameters (in the above units) are numerically similar. Using the saturation value esat(t) instead of e, the saturation absolute h u m i d i t y

5? 100

80

~E~

60

,
65%, but in already contaminated materials it should be considered that, due to the humidity conserving biofilm, the microorganisms will survive or even act at humidity levels > 50%. High levels of RH, especially when associated with T > 20~ favour biological rotting especially in the case of organic materials whose composition is appreciated by parasites or may offer a good substratum for the development of microbiological life. Besides RH and T, the intensity of microbial attack is basically controlled by the structure and chemistry of the respective substrate (e.g. porosity, inner surface, biosusceptibility of the material) and is secondly determined by air pollution levels (e.g. salts and organic materials) as well as further environmental conditions (e.g. ventilation, light, pH and redoxpotential) (Warscheid and Kuroczkin, 1997). It is should be considered that microflora lives at the interface between a solid substrate and the air: these two media may have a different temperature and moisture content, e.g. with water being adsorbed or trapped into pores. In certain cases, the dynamic situation generated by daily cycles which are transmitted with a phase delay in the two media, may lead to the fortunate circumstance that microorganisms may benefit alternatively from one or the other medium, so that considering only the physical characteristics of the air is analysing only a part of the problem. As far as the atmospheric part is concerned, the appropriate environmental conditions should be carefully chosen as a whole, including not only RH and T, but also ventilation and turbulence (which regulate the deposition and removal of spores), light, pH, air pollution levels, and the relevance of each of these factors may change in the case of indoor or outdoor environments. For instance, in the past when the air pollution was modest, lichens colonised many monuments especially in the Mediterranean belt, where solar radiation and rainfall were most appropriate and many lichens can still found in rather unpolluted zones of Portugal, Spain, Italy, Greece and so on. Later, when the SO2 and sulphates reached elevated levels, the atmosphere became toxic for them, and they disappeared from most cities, leaving on stone monuments typical signs of their past presence, e.g. pitting, oxalates. However, the microflora of stones represents a complex and highly adaptable ecosystem, metabolising inorganic and organic substrates from natural or anthropogenic sources. Because of their metabolic flexibility and remarkable tolerance against osmotic stress (e.g. salts) or toxic compounds, air pollution might cause considerable shifts in the composition of the stone colonising microflora, but will hardly control or stop biodeterioration processes.

68 2.10. WHAT IS THE BEST TYPE OF MICROCLIMATE FOR CONSERVATION? It has been clearly seen that some humidity levels are often associated with specific deterioration mechanisms, or may accelerate them. The water molecules which are absorbed into the material may determine internal stress a n d some deformation to the structure; the amount of absorbed water (and therefore internal stress and deformation) is in equilibrium with the RH and also, to a lesser extent, with T. These deformations tend to be reversible in plastic, new materials, but irreversible and extremely dangerous in aged materials. This is a good reason for suggesting some allowed or non-allowed microclimate conditions. For the materials most frequently used in creating works of art, some recommended values (or spans) of T and RH can be found in the literature, with the aim of determining the conditions of physical well-being, suitable for an appropriate conservation. These values are recommended with the aim of taking advantage from experience, or avoiding the repetition of errors already made by other colleagues, or keeping off from dangerous situations discovered with laboratory tests. However, a fundamental question arises: are microclimate norms and guidelines always useful and should they be always followed? It is useful to underline that recommended values of T and RH which are in principle suitable for materials are not always appropriate for individual artefacts. In fact, specific artefacts which have been kept for centuries under determined T and

RH, have been subjected to internal stresses and eventually have reached a new equilibrium of internal tensions with possible (permanent) deformation of their structure. Now, an old artefact, which has adapted to its environment according to the past internal system of tensions, and has lost its initial elasticity, is unable to adapt again to a new microclimate, and any change is very dangerous. This is a well known problem for wood conservation and when archaeological terracotta or glass is dug up to light. For this reason, an accurate knowledge of the past conditions is needed, and the previous microclimate should be kept untouched, or modified towards a new equilibrium very slowly and with extreme care, only in the case of real need. In addition, once these objects have adapted to some specific values of RH and T, they need very steady conditions as every fluctuation of these parameters works against the durability of the object. For this reason, all the abrupt changes are dangerous (it is common that archaeological pottery breaks when removed from u n d e r g r o u n d due to environmental shock) as well as the daily cycles of these microclimatic parameters. The daily cycles are repetitive and the effect of the stress is

69 of cumulative nature, and soon or later causes mechanical damage (fatigue failure). Seasonal changes, although they have a wider span, are less dangerous, as they occur more slowly, in a time much longer than the relaxation time of the object and with a rate slower than the penetration of heat and moisture in the material, so that there is no significant stress between the external layer and the interior. However, also these changes may be dangerous in the case of non homogeneous materials. It is evident that a furniture, or also a panel built with wood slabs constrained between them and having grains differently oriented, will undergo important internal stress when an element shrinks in a different way. It is obvious that for 'rigid' hygroscopic materials, e.g. aged wood or ivory, need a very constant microclimate, and the risk associated with a rapid change of the physical environment is greater than for more elastic or deformable materials, e.g. paper, parchment, tissues. However, the difference between materials and objects is often substantial: e.g. an old book with paper sheets and parchment cover, bound together with wire, is composed of parts that cannot expand or contract freely, so that microclimate cycles that are harmless to the individual components, may lead rapidly to severe damage of the object. When an object is not irreversibly conditioned by its past microclimate, and it is possible to choose the most appropriate conditions for preservation, these can be found by means of its adsorption isotherm (see Chapter 5). The goal is to avoid the intervals of RH where a small change of RH causes a great change of adsorbed water and to keep the object in one of the intervals where changes of RH do not affect (too much) the amount of adsorbed water and do not provoke new internal tensions. However, it is not always true that the best choice is the one indicated by the physical analysis of the material. In fact, if the experimentally determined 'best' interval is far from the natural local conditions, it might be better to choose a naturally stable microclimate than an artificial one, which is conditioned by the good functioning of complex devices. On this ground, Thomson (1986) suggested 60% RH for m u s e u m in Great Britain, and this value was deduced from the mean natural climatic values of that country. Similarly, in order to avoid shocks to the objects, the National Gallery, London, for reasons of continuity kept the standard 55%, which was the RH value in equilibrium with the moisture content in wood preserved in the Gallery prior the installation of an air conditioning (Padfield, 1994). These values have been acritically transferred to other natural climatic contexts. It is not common to find papers w h o criticise (as Padfield correctly did) the acritical use of microclimate normative or standards, some of them are widely used in everyday practice although without having been scientifically demonstrated.

?0 2.11.

KEEPING

CONSTANT

RELATIVE

HUMIDITY

IN

ROOMS

AND

SHOWCASES Relative humidity is of primary importance in the problem of conservation of works of art, and in exhibition rooms should be kept both homogeneous in space and constant in time. However, in practice several variations exist and dramatic changes occur, especially in the morning when windows and doors are opened d u r i n g cleaning, or when the heating system is switched on. In several cases humidifiers are introduced to mitigate or compensate the effect of the temperature change, but this system is never well balanced and hardly successful (Fig.2.12). Air conditioning systems and humidifiers cause repetitive 'ocal variations which are very dangerous. Active devices which create artificial microclimates are unable to ensure a very homogeneous distribution of the moisture and are very dangerous especially when bad functioning or power supply interruptions cause failure of the system. It is evident that the clouds of moisture generated by humidifiers displaced in rooms produce local perturbations also in terms of RH, with the effects that have been previously discussed.

80

-

t

RH(1)

"~" 7 0 RH(3)

.

~

60

~

50

40 0

3

6

9

12 Time

15

18

21

24

(hr)

Fig.2.12 Change in relative humidity at 1 and 3 m above the floor, i.e. RH(1) and RH(3), when the heating system and the compensating humidifiers are operating during the visiting time (for the temperature change see Fig. 1.13a). The humidifiers are too much powerful and, instead of mitigating the dry air, the net result is a moistening. The Pollaiolo room, Uffizi Gallery, Florence, 18 Febuary 1997.

71 Different systems to control the relative humidity are popularly used. For instance, in the Uffizi Gallery, Florence, a number of different systems can be found and they give the opportunity of very interesting comparisons, as follows. The Giotto room has a system which is based on controlled air introduced from grille diffusers sited in the ceiling above the Madonna d'Ognissanti by Giotto; as an equal flow is removed by intake slits on the wall near the floor level, this system generates a preferential path for the controlled air masses which cross the room and partially mix with the room air. For this reason this system is integrated with some traditional box humidifiers close to the walls. The result is a non homogeneous distribution of the humidity inside the room, and in particular in the summertime the cold flow of air conditioned falls just on the Giotto's painting (Fig.2.13). The Leonard room has a more sophisticated system which is based on the emission aloft of treated air released from line sources, i.e. four pipes hung to the ceiling, which lie parallel to the walls, but at a certain distance, so that the cold air falls far from paintings. In principle, this system is preferable, as the emission is not from a few points but is distributed from lines, and far from the exhibits. However, the treated air is transported by the depression generated by intake slits on the wall near the floor level, and by air currents exixting between a room and another. Although the system is good in principle for a single room, the overall result in the context of a buildings, where rooms are interconnected and air masses are transported from a room to another by internal temperature or pressure differences, the result (Fig.2.14) is not very satisfactory and practically not better than the simpler system in the Giotto room (Bernardi and Camuffo, 1995a). A number of rooms has box humidifiers sited close to walls and paintings, following an incorrect, dangerous practice very frequently found in museums and galleries. More appropriately, the Botticelli room has some humidifiers located in the centre of the room, far from paintings. Also very sophisticated automatic systems which control the ambient relative humidity keeping it in a span between two determined, relatively close, levels, cause continuous fluctuations between the lower and the upper levels (Fig.2.15). Although the range of variability lies within a few percent and the period is relatively short, so that the wave of the hygric perturbation cannot reach deep layers on artefacts, all of these repeated cycles have a very negative impact, especially on objects with small thickness, e.g. canvas paintings. It is easy to imagine the tremendous consequences that hot air heating systems have in churches heated once a week. In the example shown before for the church at Rocca Pietore, Italian Alps (Fig.1.11), the rise of temperature found at I m height, i.e. AT = 7~

causes a humidity drop ARH = 10%; the temperature rise found at 3 and 4

72

~///////////~'////////////////A

~

~'/////////~

5 8______ . 57

Fig.2.13 Relative humidity in the Giotto Room, Uffizi Gallery, Florence. In the hot season, the cold air conditioned released through diffusers in the ceiling, falls generating a perturbed zone. 12 August 1992 at 12.00. 'G' shows where the Giotto's panel is located.

~ ~ / /// / / / / / / / / / / / / / / ~ 62

I, 63

8

~////////////////////~

Fig.2.14 Relative humidity in the.Leonard Room, Uffizi Gallery, Florence. In the hot season, the sophisticated air conditioning system releases treated air from an extended source below the ceiling, but also this system is unable to guarantee ideal conditions. 13 August 1992 at 18.20. 'L' shows where the Leonard's panel is located.

73 m, i.e. AT = 20~

causes a dramatic humidity drop A R H = 50%, so that canvas

paintings, tablets and wood artefacts will contract and shrink, as we have already discussed.

In the long run, the repetition of these cycles has t r e m e n d o u s

consequences. 50 48 46

44 42 40

!

0

I

2

!

I

4

!

I

6

!

I

8

!

I

10

!

I

!

12

I

14

!

I

16

!

I

18

!

I

20

!

I

22

i

24

Time (h)

Fig.2.15. Fluctuations in relative humidity (RH) generated by a sophisticated controlling system, which controls this variable within two stated limits, i.e. the span 45 < RH < 50%. (Private Gallery of Modern Paintings, Parma, February 1996).

Some porous or fibrous materials characterised by large heat capacity maintain constant both T and RH: e.g. a thick wall tends to keep a constant microclimate in its proximity, and paintings hung to it or statues in niches benefit from these conditions; wooden boxes protect small objects against sudden changes of RH. One of the most effective materials, widely used in showcases, is the silica gel, characterised by many fine pores and therefore extremely adsorbent. This material smoothes out abrupt changes of RH, but does not ensure steady, pre-determined conditions. Silica gel is often pre-conditioned at some desired R H levels by keeping it for a sufficient long time at a determined humidity level until equilibrium is reached. At this point the silica gel behaves as a buffering agent, i.e. if the R H drops it will desorb moisture, and if R H rises it will absorb moisture in order to offset changes. However, the silica gel slowly adapts to the new average environmental conditions and the buffering level changes in a rather incontrolled way, so that it is necessary to change often the silica gel in the case with other silica gel, just conditioned at the desired level. This makes complex the management of the case. In addition, the amount of silica gel necessary for good conservation of exhibits in show cases has been calculated to be

74

25 kg per m 3 of air to control (Thomson, 1986). This figure shows clearly that it is e x t r e m e l y difficult to preserve objects at constant R H avoiding fluctuations, disturbances or slow changes. Whenever possible, it is advisable to improve the natural microclimate with the help of all the passive systems which ensure the best stability and reliability. A good method to maintain constant the RH at a desired level inside an airtight case, is to place in the bottom of the case a vessel containing a super-saturated solution of pure water with an excess of a certain solid substance which is in equilibrium with a specific value of RH, a number of these substances being listed in Chapter 11. These super-saturated solutions are characterised by a constant, typical vapour pressure and, consequently, by a constant value of RH. If the R H inside the case lowers, some water evaporates from the vessel to re-establish the equilibrium and, vice-versa, some vapour condenses in the solution if the inside R H increases. The choice can be extended to a large number of buffered RH levels, of course by choosing chemical substances that are not noxious to the exhibits. Sometimes showcases have a humidity level which is controlled by a micro climate generator which adjusts the RH by adding or removing moisture as required. The treated air is continually circulated between the case and the m o i s t u r e controlling unit. The RH sensor which is in the case drives in the control unit a feedback of moisture exchanges and the treatment stops when the desired RH level is reached. If the whole system, i.e. the case and the control unit have exactly the same temperature, there is a good probability that the desired RH is reached in average, i.e. w i t h several dangerous fluctuations around the mean level. H o w e v e r , if temperature differences are found in the system, although the mixing ratio is exactly the same, the relative h u m i d i t y will present d e p a r t u r e s and the r e q u i r e d homogeneity is lost. This happens normally for several reasons, e.g. the case and the control unit m a y have a different temperature, or the exhibit is heated by the lighting system, or the case has not exactly the same temperature everywhere because the most lighted panes w a r m the air near to them or the hot air accumulates in the top part of the box leading to an internal temperature stratification. These active systems are not fully reliable, need continuous control, are rather expensive and expose the works to the risk of dangerous departures in the case of bad control or work.

2.12. DEW POINT: THE TEMPERATURE OF CONDENSATION The dew point temperature, commonly termed dew point, DP is the temperature

75 to which a parcel of moist air must be cooled at constant pressure and constant water vapour content in order for saturation to occur. It can be alternatively defined as the temperature at which the actual pressure of the vapour contained in an air parcel equals the saturation pressure, under constant pressure and mixing ratio. Although it is popularly called dew point of the 'air', it is a property of the vapour that might be extended to the 'air parcel', i.e. the little mass of mixture of dry air and vapour taken into consideration.

From the definition it is a conservative property of the air parcel with respect to isobaric heating or cooling without addition or subtraction of vapour. It is non conservative with respect to adiabatic expansion or compression. Of course, in a completely dry atmosphere there is no any temperature at which water can condense and this parameter does not make sense. This parameter can be easily computed from the relative humidity and air temperature, starting from the consideration that the dew point is reached with an isobaric process, so that the vapour pressure at the original dry bulb temperature equals the saturation pressure at dew point, i.e. e(T) = esat(DP). By substituting this finding in the formula (2.20), one obtains with the help of the Magnus formula: aDP/(b+DP) e(t) esat(DP) esat(O)xl0 [aDP/(b+DP)] - [at/(b+t)] u - esat(t) - esat(t) = at/(b+t ) = 10 esat(O) xl0

(2.37)

hence aDP at logu = b + DP" b + t

(2.38)

and

DP-

b + DP

a

b + DP at b +t logu + ----a--- b +------t--~ logu + t

(2.39)

where the last approximate finding has been obtained substituting t to DP in the right hand side of the first identity. Of course, the first term is negative as u < 1 and logu < 0. Another formula can be deduced considering an air mass over an evaporating surface. The air temperature lowers, while the increase of mixing ratio raises the DP. The air temperature t continues to drop to the temperature of the evaporating surface, called wet bulb temperature, tw, is reached. When the vapour evaporated causes saturation, t = tw. Starting from the Clapeyron equation and the definition of

76 w, and always considering the difference D P - t w , after some laborious steps and approximations the following formula is obtained:

b logu+t logu+at D P = b -al~ - -b l o g u - t ~ gu

(2.40)

where a and b are the Magnus coefficients for vapour in equilibrium with the liquid phase. The eq.(2.39) is a better approximation. The above formulae can be used once the R H is known, and obviously logu = log(RH/lO0) = logRH- 2. The D P < T and D P = T only when R H = 100%. The D P is determined once the air temperature T and the R H are both known, or also when only the M R (or S H or A H ) is known. In particular, maxima of M R correspond to minima of D P and vice-

versa, so that the D P can be used for diagnostic purposes instead of the MR. The d e w p o i n t s p r e a d (also called spread), i.e. the difference A D P = T - D P basically depends upon both the actual air temperature T and the M R . Following the approximation (2.39) it can be expressed as a function of air temperature and relative humidity b+t A D P -- - ----a- logu.

(2.41)

It physically shows how much the air temperature is close to, or far from, the DP. The zones having the smaller A D P are more prone to form condensation and to allow micro biological life and weathering to occur. Useful maps of this parameter can be easily done for diagnostic purposes. However, although the R H is a very different, but related parameter, the areas with maximum R H are the same as those in which the A D P is minimum, and if the critical cooling is not requested, maps of R H are sufficient to give a qualitative description of these micro climatic problems. The d e w has the typical form of droplets and especially forms on leaves during the nocturnal cooling due to the IR emission. The formation of dew on leaves is favoured by the local excess of moisture due to the stomatal transpiration. The surface tension of water tends to displace the larger droplets on the edges of the leaves and in particular on the points of leaves, especially the lance-shaped ones. The u p w a r d IR loss during clear nights is a very effective cooling mechanism. The surfaces on which dew forms are free from any upper shield, and in practice are the same as those which are wet by rainfall. This is the reason that people often believe that dew falls similarly to the drizzle. If a non porous surface cools until it reaches the DP, the environmental vapour

77 begins to condense onto it, forming films of liquid water or droplets. A well known example is the condensation on the window panes during winter, especially in rooms with an elevated M R due to the presence of people, w h e n the glass conductivity cools below the DP the pane surface. Another important example of the same principle, is the condensation which typically occurs in spring in the Mediterranean region, when the air becomes mild and rich of moisture (i.e. with an elevated DP), and especially when the w a r m and humid Sirocco wind blows. Historic buildings have thick walls with high heat capacity and a large thermal inertia, whose temperature keeps a memory of the past cold season. The contrast between the elevated DP of the air, and the low temperature of the thick walls which remain below the DP, causes heavy condensation on the surface (Fig.2.16). If the surface is porous, the effects of the surface tension can favour condensation in the micropores also at temperatures above the DP, as we will see in Chapter 5. For this reason, in spring, thick walls of non heated buildings are very frequently damp. As the dew forms on all the surfaces whose temperature drops below the DP, irrespective of the environmental value of the RH, it is completely useless to insufflate the surface of cold walls or monuments with heated air, which has a lower RH but the same MR and, therefore, the same DP. Due to the large thermal inertia of these structures, the ventilation brings in contact with the cold surface a greater amount of air and vapour, thus increasing the condensation rate. This method was originally proposed by Massari (1959; 1971; 1977) as the windscreen effect, considering the analogy with the method used by cars to remove the misting of the windscreen. However, the vapour mists over the windscreen when the pane temperature T is T < DP of the air, irrespective of the RH of the airflow, but eventually the internal surface of the pane, which is poorly conductive and needs a relatively little amount of heat to warm, rises its temperature above the DP. At this point condensation stops and the misting evaporates. A nice example that the surface condensation is independent of the air temperature is given by a stainless steel pot, half filled with cold water, when this is put over the methane fire. Although the flames lick the pot, the cold pot is immediately covered with dew. A few seconds later, the droplets disappear from the upper half of the pot (i.e. the part which is empty and has a lower thermal capacity) when it is warmed above the DP. The droplets in the lower half of the pot, which is filled of water and has a greater heat capacity, disappear simultaneously several seconds later, when also the water inside the pot is warmed over the DP. For this reason, in some specific cases, condensation on limited surfaces can be eliminated either increasing the surface temperature, e.g. with IR radiation or direct warming, or diminishing the environmental MR. Some results can be also reached by

"/8

Fig.2.16 In spring, the contrast between the air rich of moisture (i.e. with an elevated DP), and the low temperature (below the DP) of the thick walls, causes heavy condensation on the surface, which is damp and fully covered with droplets. In this picture, taken in a room of Castel del Monte (Southern Italy), the 27 March 1996, when the surface is perpendicular to the flash light, the light crosses the droplets which are transparent and invisible, but when the surface is nearly parallel, the light undergoes a multiple reflection inside droplets which appear brilliant, with a silver like appearance. The red colour on the white part of the marble columns is a biopatina.

79 impregnating the surface with hydrorepellent substances which increase the contact angle 0 of the water droplets, as we will see in Chapter 5.

2.13. FROST POINT: THE TEMPERATURE OF FREEZING The frost point FP is defined in the same way as the dew point, but reference is made to ice and in the eq.s (2.39) and (2.40) the Magnus coefficients are a = 9.5 and b = 265.5~

From these equations it follows that FP < T and FP = T only when RH =

100%. In addition, FP - 0~ only in the case that at this temperature RH = 100%. In general, the frost forms at a temperature below 0~

which depends u p o n the

moisture content of the air. The frost (also called hoar, hoar frost, crystalline frost, white frost) is generated by the direct sublimation of the vapour, which forms needle-shaped crystals of ice. It is different from the frozen dew (also called white dew, silver frost) which has the appearance of ice spherules. Similarly to dew, the frost also prevalently covers the horizontal surfaces that loose heat by IR radiation toward the clear sky. Different is soft rime, which is due to the rapid freezing of very small supercooled water droplets in fog or cloud when they impact on (prevalently) vertical surfaces with temperature below 0~

In this way windborne droplets stick

forming a dendritic accretion, and all the trees are white on the side facing the wind, and iceless on the opposite side. The ice is white, porous, and is constituted of very small granules separated by few or many air inclusions. Similar to soft rime, but formed with drizzle droplets of micronic size, is hard rime. In the case that the concretion of ice has been generated by ice needles already formed in the atmosphere, this phenomenon is known as advection hoar frost (or also ice fog, frozen fog, frost fog, air hoar, rime fog). If the drops splashing on the cold surface are even larger, i.e. rain drops, the coating is more homogeneous and translucent, known as glaze (or also glazed frost, clear ice or ground ice for the soil). The windborne droplets and the splashing from them may cover surfaces differently oriented and the branches of trees may break due to excessive weight of the ice.

2.14. WET BULB TEMPERATURE: THE TEMPERATURE OF EVAPORATION The w e t bulb temperature Tw (or tw) or isobaric wet bulb temperature, is the

80

temperature an air parcel would have if cooled adiabatically to saturation at constant pressure by evaporation of water into it, all latent heat being supplied by the parcel. This temperature is directly measured by the wet bulb of a psychrometer, or can be obtained indirectly by means of a psychrometric diagram or formulae, after the dry bulb temperature and one hygrometric value (i.e. e, MR, SH, AH, RH, DP) are known. From the thermodynamic point of view, Tw is the temperature that an air parcel would have when some liquid water is supplied gradually, in very small quantities and at the same temperature as the environmental air, and then this water is evaporated into the air adiabatically (i.e. the latent heat being supplied by the air) at constant pressure, until the saturation is reached. The saturation is reached for the combined action of two factors due to the evaporation: the increase in MR and the drop in T. Consequently, Tw is the lowest temperature that an air parcel would have by evaporating water, the latent heat being subtracted to the air and utilised for the change of state of water from liquid to vapour, until saturation is reached. Tw is also the equilibrium temperature of an evaporating surface of water. Applying the first law of the thermodynamics to an air parcel formed by 1 g of dry air with a mass of vapour mv, i.e. with mixing ratio w = mv, and experiencing the above process, Tz0

mw

f Cpm (l+ mv) d T : T

f Lvdmv

(2.42)

my

where

Cpm

is the isobaric specific heat of the moist air that can be expressed in terms

of isobaric specific heat of dry air Cpd (Cpd = 0.240 cal g-l K-1 = 1.003 Joule g-l K-l), i.e. Cpm = (1+0.8 mv)Cpd and Lv is the latent heat. After integration, by dividing both sides by (Cpd + <w> Cpv), the wet bulb depression ATw = T- Tw is obtained

ATw

(msat,w - m v) Lv =

(2.43)

Cpd + < w > Cpv

where <w> is the average mixing ratio during this process, msat,w is the saturation mixing ratio at the temperature Tw a n d Cpv is the isobaric specific heat for the water vapour (Cpv = 1.81 Joule g-1 K-l). A further approximation of the wet bulb depression is obtained by using the formula (2.19) for w and considering that Cpd + <w> Cpv = Cpd (i.e. <w> 0

(2.45)

where the identity holds only for RH = 100% when DP = Tw = T. It might be noted that in the atmosphere the saturation is usually found on foggy days, especially during night-time. In general, during fog, the RH is 95 < RH , "

~. "'
e(o

Fig.5.2 Ideal e x p e r i m e n t s u g g e s t e d b y Kelvin, b a s e d on the b a r o m e t r i c formula.

, ....,.,...,-~

e(r)

,.

< e(oo) .

.

.

.

.

.

.

.

' .

.

.

":::" "'::::.?i:i:i::: :::::::::::::::::::::::: .

.

.

.

.

iil i

.

.

.

.

.

.

iii:;iii!iiiii:iiiill :

:

:.:.:-.. :.:-'.-:-:.'-" =========================== .

.

.

,,,..-.,

9 .,...-.-.-.-.,.-.,

9:i:::i?i?i?i:ili?i:i:i:i? .:....'.:.

".:.;....:...

.:.:.:.:.:....:::.

"'"" ": "':':':":" ., .

9 .:.:

.

.

.

...:.:.:.:."

::i::::.i':':"'"'"':i::"

-.

"'::i.i":'::i:':"'-::i: . . . . . . . . . . . . .

".:.:...

I e(oo)=

e(zl)

Fig.5.3 P a r a d o x that w o u l d arise if the external p r e s s u r e w e r e not d i s t r i b u t e d a c c o r d i n g to the b a r o m e t r i c formula, b u t w e r e constant w i t h height.

137 If the external pressure were not distributed in accordance with the barometric formula, but were constant with height, the following paradox would arise (Fig.5.3). Let us consider a closed vessel containing water in the bottom in equilibrium with its vapour; then a vertical capillary tube is partially immersed in the liquid, all at the same temperature. In the capillary a column of water goes up and stops at the height determined by equalising the Stevin's and Laplace's pressures. The pressure of the saturated vapour in contact with the liquid is not the same over the flat surface of the water in the bottom and over the meniscus, being lower over the meniscus where the surface is concave. In the vessel, if the vapour pressure were constant with height, the equilibrium pressure would be e(oo) and the vapour would gradually migrate towards the meniscus in the capillary, where the pressure is e(r ) < e(oo), establishing a gradient of concentration, and possibly of pressure, into the vessel. In the top of the capillary, the vapour would become supersaturated with respect to the meniscus curvature and would condense, adding new liquid into the water column. The molecules which condense into the meniscus would be replaced by other molecules which w o u l d evaporate from the free water surface at the bottom where the equilibrium tension is e(~). Thus, partiallly or totally neglecting the natural decrease of the vapour pressure with height, the above process would indefinitely continue with evaporation from the bottom, migration of v a p o u r into the capillary, condensation onto the capillary meniscus, displacement of the column to re-establish the original level and so on, in a perpetuum mobile mechanism similar to a reversed fountain. With the approximate Kelvin formula a p e r p e t u u m mobile is get; an equilibrium without perpetuum mobile is found with the rigorous formula (5.12).

5.2.2. Derivation of the Kelvin equation from the Gibbs potential Gibbs derived independently the Kelvin equation, on the basis of chemical potentials. Here the main guideline will be followed; details can be found elsewhere (Byers, 1959; 1965; Mason, 1971; Pruppacher and Klett, 1980, Young, 1993). Gibbs considered the conditions in an isothermal and isobaric system of more than one component, such as a solution, where there can be a change in the number of moles of a component. To this aim three main parameters should be defined: the Gibbs surface free energy G = U + Ps Vs-T . ~

(5.15)

the free enthalpy of the system

..~= U + Ps Vs

(5.16)

138 the Helmholtz free energy. . 7 = U - T .5r

(5.17)

where U is the free energy of the system at temperature T, Ps its pressure, Vs its volume, .~r

entropy.

W h e n the v a p o u r molar fraction Nn/M is transported from the plane surface of the liquid (or from the atmosphere) to the droplet, the increase in free energy is

~n AG = ~ - . ~

(e(r )

(5.~8)

T I n ~,e(oo)J"

After this v a p o u r has condensed, the increase AG is due to the increase of surface energy which is linked to the free surface S of the liquid under the action of surface tension c~, i.e. AG = cy ~ S. For a spherical droplet, the surface is S = 4~r 2 and the increase is dS = 8~r dr ; the volume V is V =(4/3)~r 3 and dV = 47r r 2 dr ; the mass which condenses is dm = p dV = 4re p r 2 dr ; hence dS = 2 d m / p r and AG = 2 cy @n p r. Substituting this finding in eq.(5.18) and considering that M / p = Vm, the Kelvin equation is obtained. This derivation is very general, and the Kelvin formula can be rewritten for any shape of meniscus, by using the ratio of the incremental values d S / d V of the meniscus surface and related volume (RH(r ) o Vm dS lnx 100 ) - . ~ / g T dV

(5.19)

e.g. d S / d V = 2 / r for a sphere; d S / d V = [(1/rl ) + (1/r2)] for ellipsoids with principal radii rl and r2; d S / d V

= [(1/rl ) - (1/r2)] for saddles with principal radii rl and r2;

d S / d V = 1 / r for a right circular cylinder (Fig.5.4) or a circular torus (where r is the radius of the cylinder or the generating circle, respectively; note that the formula is independent of the cylinder height or torous radius); and finally, for a cone of height h. one obtains d S / d V = 3(2r 2+h 2)/(r 2h ~ r 2+h

2).

5.3. THE FORMATION OF DROPLETS IN THE ATMOSPHERE: H O M O G E N E O U S A N D HETEROGENEOUS NUCLEATION The first problem in the formation of droplets is that r > 0 a n d this requires a supersaturation, i.e. RH>> 100%, or the intervention of other p h e n o m e n a which m a y counteract this physical effect. The Kelvin equation in the form (5.19) considers the

139 100

"

90 80

~9

70 6o

".~. ~

50 40 30

.......

0,001

0,01

0,1

1

Radius (~m) Fig.5.4 Relative Humidity (RH, %) in equilibrium with a concave meniscus of water with radius r (~tm), according to the Kelvin law. C: cylindrical meniscus; S: spherical meniscus.

;urface ..~ o

3

,-~ x

2

Energy

(U

0 rt-4 -1

Total

Energy

-2

Volume

Energy

-3 -4 -5 i 0,001

'

,

,

,

,

,

,I)

r*

, I

'

Radius

.

.

.

.

.

.

.

. 0,1

0,01

(~tm)

Fig.5.5 Free energy of a pure water droplet versus droplet radius and critical radius r*. Lines refer to the surface free energy, the volume free energy and the total energy (thick line).

140

energy balance derived from two counteracting factors: the positive work against the surface tension in the formation of the free surface of the meniscus (proportional to r 2) and the negative work deriving from the energy released by the vapour-liquid change of phase of some water molecules (proportional to r 3) which comes from the tendency of water molecules to aggregate in the liquid state. In the formation of a droplet by condensation, the surface area is 4Jrr 2 and the free surface energy is 47rr2c~; and considering in a similar way the contribution due to the increase of the volume, the elevation of the free energy due to the curvature of the surface is 4 (e(r)~. AG = 47r r 2 r~--~ ~ r3/9 .~/2~TIn ~,e(oo)J

(5.20)

The algebraic sum of these two contributions, characterised by different powers of r, determines a graph whose maximum AG* is a maximum of instability for the physical process, and the corresponding critical radius is r* (Fig.5.5). The critical radius can be determined under the condition d ( A G ) / d r = 0, and is 2

r* = /9 . ~

Gm

(e~r, ) ~ T ln~,e(oo)j

~

(5.21)

All the droplets with r < r*, called embryos, are unstable and tend to dissipate; after the critical radius is surpassed, the embryo droplet grows in microseconds to a 'mature' cloud or fog droplet. The growth may occur by accidental aggregation of other molecules, collision with other droplets, or coalescence. The formation of a pure water droplet, without the intervention of heterogeneous condensation nuclei, is called homogeneous nucleation. In this case, the system is composed of micro spheres of water floating in the air, and the radius of the droplets is positive and great supersaturation is required for equilibrium with the curved water surface, i.e. RH>>100%, T T w where Tw is the wet bulb temperature of the air. Observation of the value of Ts allows us to distinguish between the two processes and d e t e r m i n i n g for example w h e t h e r a surface is wet because it is cold (condensation) or it is evaporating as a consequence of capillary rise. However, contamination with soluble salts lowers the equilibrium R H (and raises the DP), or the presence of micropores causes departures from this simple scheme and condensed water may be found in micropores at usual conditions, and also in relatively dry environments. In the droplets, all the water is in liquid state. In porous bodies, or in general over a hydrophilic surface, the water molecules in contact with the material are absorbed and strongly bound with the internal surface due to the presence of dipoles or image forces; the bound is so strong that this water is considered to be in the solid state. Beyond this solid layer, others water molecules are in the liquid phase and free. In pores with radius rp < 0.1 ~tm the physical effect dominates; in pores with rp > 1 ~tm and c o n t a m i n a t e d by soluble salts, the physico-chemical effect which determines the equilibrium pressure for solutions may also cause condensation at lower RH, and this typically occurs in a marine environment due to contamination with sea salts. Water supplied by condensation causes dissolution of the material matrix, condensation-evaporation

cycles cause m i g r a t i o n

of d i s s o l v e d

salts and

recrystallisation in other parts, e.g. efflorescences and subflorescences, thus weakening the material a n d causing loss of the aesthetic value. This mechanism is clearly shown in thin sections of stones, where reprecipitated crystals are found in the pores (Fig.5.7). Wet materials, e.g. rocks or mortars, may have their mechanical resistance diminished. In other cases, the presence of a film of water may decrease the free surface energy of the material, weakening it (Winkler, 1986). In certain cases, as for e.g. argillaceous (containing clay minerals) limestone, water may alter the structure of the material, causing expansion, stress and fractures. In fact, the crystal structure is composed of a series of wafers and positive ions are frequently trapped between the wafers. Water is able to penetrate the crystal as it is attracted by the hydroxy groups causing the clay to swell. Of course, this happens only for clay minerals with expanding lattice, e.g. montmorillonite, vermiculite, but not for non-expanding ones, e.g. caolinite, illite, chlorite. When the RH decreases, the adsorbed water evaporates, but the structure between the wafers may have changed due to the formation of new crystals. The contraction leads to hysteresis, and in the

148 long run, adsorption-evaporation cycles cause irreversible damage (Torraca, 1981; 1994). The hygric dilatation may be of the order of 1 m m / m , and water repellent treatments cannot prevent hygric swells and shrinking, although they may be delayed (Wendler, 1997).

Fig.5.7 Thin section of oolitic limestone, where reprecipitated crystals are found in the pores. Authigenic dog toothed calcite crystals cover the oolites; gypsum is more frequent inside the pores. A large authigenic hexagonal calcite crystal is growing in the cavity. Material dampness and air humidity favour biological life and weathering; this negative phenomenon becomes greater and greater when the duration, or the frequency, of the time of wetness (TOW) increases. The TOW is an important descriptor for the growth conditions of microorganisms on materials. It reflects the correlation between material structure (e.g. porosity, inner surface, cation exchange capacity) and the biosusceptibility of the material, meaning the tendency to allow micrqbial contamination (Warsheid et al., 1993). Inside, the biological contamination is frequently restricted to certain physiological groups of microorganisms (e.g. fungi), whereas outside the microbial infections are mostly characterised by a complex network of algae, bacteria, fungi and lichens. During the time in which a metal or a stone is wet, chemical reactions occur between the pollutants deposited and the material (Laurenzi Tabasso and Marabelli, 1992); the damage is linked to the

TOW, although no general formula has been yet found to link the damage to the TOW. Condensation is also responsible for increasing the deposition rate of airborne pollutants. This fact is due to two different factors: (i) the particles and the hydrophilic gases that impact on a wet surface stick to it without bouncing, so that the capture efficiency of the surface is increased; (ii) when condensation occurs, near

149 the wet surface several microphysical processes occur, the ultimate result of which is the increased transport of gases and particles towards the surface as we will see in Chapter 8. The problem of surface moisture and condensation is very complex, and depends on the chemico-physical characteristics of both the atmosphere and the surface. The RH within a pore is a function of temperature, mixing ratio, pore geometry, presence and nature of soluble salts, and can be considerably different from pore to pore as well as from atmospheric RH. Total porosity, total pore surface, spatial association of pores (that may form pockets and necks), pore size, pore form, and pore radii distribution are important variables in monument weathering. Stones are characterised by a wide variety of pores and necks, with different shapes and sizes, which range from angstroms to millimetres and can be classified in several classes, depending upon their properties based on laboratory analysis (Fitzner, 1994) and mineralogical characteristics (Jeannette, 1997). The porosity may change with time, especially in the subsurface layer where migration of salts, leaching, dissolution, erosion, and other physical, chemical and biological attacks occur (Biscontin et al., 1993). However, although the situation is more complex, it is useful to introduce two basic types of pores: open and internal pores (Camuffo 1984; 1988). 'Open pores', with very large outlets compared to the pore volume are found especially on the surface of bodies. The typical shape is that of a hemisphere, or a portion of a hemisphere (Fig.5.8a). Open pores behave symmetrically with reference

Fig.5.8 (a): Condensation in an open pore. (b): Condensation in an internal pore. (After Camuffo, 1984, reprinted by permission of Kluwer Academic Publisher). to droplets suspended in the atmosphere: the smaller the pore, the lower the RH required for equilibrium with the water meniscus. For each open pore, condensation begins at a low critical RH(rp) determined by the effective radius of curvature of the

150 pore rp. This is the geometric radius of the curvature of the pore minus the thickness of the mono or bi-molecular layer of water molecules adsorbed and b o u n d in the solid state. When the RH increases, condensation occurs and the radius of curvature of the meniscus (rm) increases, i.e. the concavity of the meniscus flattens, following the equilibrium with the variations in RH according to the equation

/'m

2 r~Vm RH = ./r In (1--0-0)

(5.29)

An increase in RH corresponds to an increase in both condensed water and rm and vice versa. The hemisphere is completely filled at RH = 100%. All the steps occur in equilibrium with RH and the process is reversible.

'Internal pores', with ,~mall outlets, are typically found inside bodies (and connected to the atmosphere by a small hole facing the surface or entering other pores or capillaries, see Fig.5.8b) and these behave in a different manner. The condensation into the pore begins at the low critical R H = R H(rp), which is in equilibrium with the radius of curvature of the pore rp just wetted with a film of water. After a short time, when some condensation has occurred, the free space into the pore has been reduced and so the free surface area of the meniscus and the radius of curvature of the new meniscusrm. The smaller the new radius rm, the lower the equilibrium RH(m,). However, the actual RH inside the cavity, which initially was in equilibrium with the greater radius of curvature of the pore rp, now corresponds to supersaturation for the smaller rm,, i.e. RH(rp) >RH(m,) and the process is accelerated. Therefore, the initial level RH(rp), is no longer a neutral equilibrium value, but a critical value of unstable equilibrium which triggers off the complete filling of the pore. As a consequence, the process is now irreversible. Condensation in capillaries occurs similarly to internal pores, as condensed water makes smaller and smaller the radius of curvature of a cylindrical meniscus, ..

determining a condition of unstable equilibrium and accelerating the condensation. When a capillary is full of water, a spherical meniscus forms at the beginning of the capillary and the evaporation starts in a reversible way, as in open pores. Interesting is the case of the so-called 'ink-bottle' pores, i.e. cavities connected to other major cavities through smaller ducts, forming aggregates that can be compared to bottles having their neck in communication with the major cavity. According to the Kelvin law, in a porous material condensation occurs first in necks, which are the cavities with the smallest radius of curvature. When the necks are filled with water, air-pockets remain entrapped in the pores and further condensation is impossible in steady state conditions. Internal condensation may only continue when variations or

151 fluctuations in temperature or atmospheric pressure cause the displacement of the water inside the pore necks. Nocturnal cooling of the body may reduce the pressure inside the pores and cause the water condensed in the neck to be sucked into the pore. According to the Cantor's law, the required excess pressure is inversely proportional to the neck radius. When the excess pressure is sufficient, plugs of condensed water can be pushed out and trapped inside the pores, or can be forced to migrate into the material. Condensation may continue by means of these steps, so that the amount of adsorbed water is also a function of the pumping efficiency of these variations. Similarly, evaporation from an open pore starts at its outlet, removing water from the pore and increasing the radius of the free meniscus. Evaporation is triggered off when the ambient RH drops below a critical value which is calculated according to the Kelvin formula, using the radius of curvature of the pore outlet (ro), i.e. RH(ro). This critical value is lower than all the equilibrium values RH(rm) which can be calculated for all the increasing values rm, from ro to rp, which assumes the radius of the meniscus when the latter enlarges following the loss of liquid water. Inside the pore, after some evaporation, the relative humidity in equilibrium with the meniscus RH (rm) becomes relatively higher and higher in comparison with the external relative humidity which is R H < RH(ro) so that the external condition favours further evaporation. Consequently, the process is accelerated and is irreversible. Evaporation continues until all the liquid water (i.e. all the water inside the pore, except the first and second molecular layer in contact with the surface which is attached with a stronger ice-type bond) has evaporated. The condensation-evaporation cycles being thermodynamically irreversible present noticeable hysteresis as condensation occurs when triggered off by RH(rp) and evaporation by RH(ro). In practice RH(rp) and RH(ro) are not just two precise levels of RH, but two ranges, determined by the actual distribution of rp and ro in the porous material.

5.6. ADSORPTION ISOTHERMS The condensation-evaporation cycles can be represented by the so called BET (Brunauer, Emmett and Teller) adsorption isotherms (Brunauer, 1945; Gregg and Sing, 1967; Mikhail and Robens, 1983), in which the amount of adsorbed water (WA) is plotted against RH. In practice, this graph shows the change of weight due to the adsorption of water by an initially dry sample of material when the RH increases from 0 to 100% and then decreases again to 0%. The most common type (Fig.5.9) is

152 composed of branches forming a hysteresis loop. The first branch AB, characteristic of the very low RH, occurs w h e n all the material surface, both the external and internal (i.e. the visible surface and the surface in contact with the air, but inside the pores), is progressively covered with a layer of water in the solid state, with a final thickness of two or three molecular diameters. In this branch the graph of the adsorption is coincident with the desorption one. The condensation-evaporation process is characterised by a one-toone correspondence and is reversible depending linearly upon changes in RH.

E .~ o

D C rar~

~t

..q,.a

B

0

20

40

60

80

1O0

Relative Humidity (%) Fig.5.9 Adsorption isotherm for a condensation-evaporation cycle: water absorbed (WA) versus relative humidity (RH). In the intermediate RH range, after the total surface has been covered with this solid layer, a further increase in the RH leads to the formation of bulk, liquid water in the internal pores. This second branch (i.e. lower BC) becomes steeper and steeper as the pores are filled with water. In every pore with a radius rp the condensation occurs w h e n triggered by RH(rp) or by the chemical effect. If all the pores have the same size the condensation branch is very steep. In this branch the process is no longer reversible: if the RH decreases some minor hysteresis loops start. The third branch CD is characterised by very high RH, when all the internal pores are filled with water. In theory, this branch should be horizontal, as no further increase of W A is possible, also because w h e n RH = 100% the surface is in t h e r m o d y n a m i c equilibrium with the same number of molecules condensing and evaporating. In practice, this branch is tilted because the spectrum of the pores is wide and before reaching RH = 100% there are always some large pores which are

153 empty and which become progressively filled. In addition, the presence of contaminants or soluble salts causes the condensation to occur earlier, so that the vapour surrounding the sample is in a situation of supersaturation and condensation will occur, forming liquid films or droplets on the external surface (i.e. final rise DE). A similar condition of supersaturation occurs when the surface temperature drops below the DP, so that at the interface between the sample surface and the air the RH >100%. In any case, the amount of liquid water that can adhere to the external surface is modest, and the final branch is slightly tilted, with a sharper rise near the upper extreme due to the solution effect: If condensation stops before the droplets fall from the damp material, this branch is again characterised by a one-to-one correspondence and is reversible. On lowering the RH, the process first develops along the last condensationdesorption branch ED and then DC, until the external water has evaporated. Continuing to lower the equilibrium RH after all the pores have been filled with water, evaporation may proceed, emptying the pores and this may occur only when triggered by RH(ro). As RH(ro)
= 0, and r =0. As the dimension of ~: can also be interpreted as energy density, by analogy with the dissipation of the kinetic energy of the wind which is dispersed by the e d d y turbulence per unit of volume of air, it is possible to introduce a fictitious speed u, that is homogeneous along the vertical, and is called

friction velocity as

it is linked with the friction, defined as

Given that u , has the dimension of a speed, it derives from t u r n i n g a complex p h e n o m e n o n into a useful p a r a m e t e r which does not i m m e d i a t e l y correspond to any definite physical entity. In the turbulent layer, on the basis of the

Reynolds

stress, the friction velocity is defined by m e a n s of the eddies

contribution as

u , = ~

(7.8)

and in the viscous layer by the continuous, laminar increase of the wind speed as

u, =

~/ I~ 3u

(7.9)

~ Oz"

From these expressions it can be seen that u, is physically linked with the transport of m o m e n t u m from one level to a different one. In a general way, u, can be expressed as a fraction of the average wind speed , i.e.

213

u,--

N

(7.10)

where the index of roughness N varies from 3 for perfectly smooth surfaces such as snow or a calm lake surface, to 13 for grassy land.

7.7. THE VERTICAL FLUXES OF HEAT, MOISTURE AND MOMENTUM In the atmosphere, a vertical profile of air t e m p e r a t u r e also implies a vertical transport of heat, as well as a wind shear implies a vertical transport of m o m e n t u m . The vertical fluxes of heat H, moisture L~E and m o m e n t u m r are defined respectively:

H = p Cp = p Cp f o ' ( t ) x w'(t) dt = - p Cp KH

LyE - p Lv <m vW'> = p Lv

r = -p

=

3 3z

/ m, v(t) x w'(t) dt - - p L~KE

-pfu'(t)

xw'(t)dt

= p KM

3

3 3z

(7.11)

(7.12)

(7.13)

where p is the density of the air, Cp the specific heat at constant pressure, w is the vertical

wind

component,

the latent heat of vaporisation and E the

Lv

evaporation (or condensation) rate. As the vertical displacements involved are generally modest, the air temperature T can be used instead of the potential temperature O. As usual, the brackets indicate the average value and the label ' indicates the fluctuating value, e.g. u (t) = + u ' ( t ) . The integrals of the correlation p r o d u c t s b e t w e e n the fluctuating values of the vertical w i n d component w' and the corresponding fluctuations of the (potential) temperature p

O', moisture m v ( t ) o r

speed u

p

represent the net transport of the related

properties along the vertical. The sign minus has been introduced because in the surface boundary layer the fluxes are counted positive upwards. The coefficients K H , Ka, and KM, represent diffusivities, and several rough assumptions are often made in the surface PBL to make easier the mathematical

214 treatment of this complex mechanism. The first assumption is that the vertical fluxes are constant with height (i.e. no accumulation or horizontal divergence); the second, often used quite successfully in engineering applications, is that all the coefficients are equal, although this has been verified only in near adiabatic conditions. This assumption allows to predict the distribution of a particular flow from measurements of another one. However, during strong inversions the radiative heat exchange and the pressure fluctuations may cause important departures for the heat and m o m e n t u m transfer. For a discussion on this implication on diffusion models see Lumley and Panofsky (1964). The coefficient of heat exchange, KH, also known as the eddy diffusivity of

heat, refers to the heat flow due to the vertical transport of heat, either because of the convective motion o r / a n d the vertical component of the wind fluctuations. It is defined as the coefficient of proportionality between the turbulent heat transfer and the vertical gradient of the air temperature,

KH = - ~

3O 3z

(7.14)

This formulation represents the physical process that typically occurs near the soil surface in superadiabatic conditions. When the soil is hot, the air in the viscous sublayer near the surface which is in contact with the soil is heated by conduction, gains in buoyancy and eventually escapes out of the viscous sublayer. This hot air mixes with the environmental air above, i.e. in the superadiabatic layer, and forms bubbles of warm air that tend to rise for their buoyancy (thermals). At this point the lower atmosphere is characterised by a positive temperature gradient and a convective motion develops. This motion is formed by many individual cell motions, with the hot cores formed by uprising thermals, associated with lateral descent of colder air which closes the cells. A net upward transport of heat is originated when the vertical uprising movements of the air w' are associated with the transport of warmer air (O') as well as d o w n w a r d movements with colder air, i.e. >0, for both the upward and the downward transport, as both 6)' and w' change sign. The same result can be found also in another particular case, although in the absence of convective cell motion. This happens in the central part of windy days when the atmosphere is neutral, but the soil is hot. In this case the wind eddies coming from below are warmer than those

215 coming downwards, leading to the same result. When the soil is colder than the air, in the presence of fresh wind, the eddy turbulence transports heat d o w n w a r d and 3<mv> 3z

(7.15)

The coefficient of mechanical exchange, KM, also called eddy diffusivity of

momentum or kinematic coefficient of eddy viscosity, represents the capacity of the atmosphere to exchange vertically the momentum as a consequence of the eddies induced by wind, and is defined as the coefficient of proportionality between the vertical momentum transfer and the gradient of the wind speed:

KM = 3

(7.16)

3z If the wind speed increases with height, the turbulence which exists between two levels brings up some parcels of air with slower velocity, and brings down some faster ones, exchanging m o m e n t u m . The greater the turbulence (and the coefficient KM ), the greater the tendency for the distribution of the wind speed to become uniform.

7.8. HEAT BALANCE AT THE SOIL OR THE MONUMENT SURFACE The atmospheric stability, the dynamics of the PBL and many interactions between the soil (or a monument) and the atmosphere are governed by the heat balance at the soil. This balance considers how the net flux of radiant energy q~ is partitioned. The net flux q~ is the global solar income I$ minus the shortwave

216 radiation Sq" reflected from the soil and the longwave component LI" reflected and emitted as black body infrared thermal emission, i.e. cI) = 1,1,-(S'r+L'~).

(7.17)

Therefore, q~ is the radiant energy adsorbed or emitted by the soil. During the day the solar income dominates and q~ > 0; during the night the radiative loss dominates and q~ 0, and vice-versa q~l" < 0. Every day, the integral value jq~ (t) dt = 0; from winter to summer these 24 hr integrals are generally small and positive showing the seasonal daily gain of heat, from summer to winter negative. At the soil (or m o n u m e n t ) surface, the radiant flux of energy q~ is transformed into three heat fluxes: i.e. heat conduction G into the ground (or the material), sensible heat H into the atmosphere and latent heat L~E into the atmosphere. This can be expressed by means of the equation of partitioning of the energy per unit surface and unit time, called also heat balance equation: = G + H + LyE.

(7.18)

Given the convention adopted for the sign of q~, the other fluxes are positive when the heat flow proceed in the direction shown by the arrows: i.e. G$ from the soil surface to the deeper layers, HI" and LvE'~ from the soil surface to the atmosphere; the opposite sign indicates respectively: -G, the conduction of heat from the deeper layers to the soil surface, -H, the soil is cooling the air, -LYE, the surface condensation. The rate at which heat flows through a building wall or a soil level at a depth z below the surface is directly proportional to the temperature gradient that is found at that depth, i.e.

G -

- ct

3T 3Z

(7.19)

where ct, called thermal conductivity, is a coefficient of proportionality which is constant only for a homogeneous medium. In the ground this is not strictly valid, as the moisture content in the soil, affected by rainfall, dew, evaportation and fringe diffusivity, changes with time and depth. For an infinitely thin layer,

217 the heat transfer is regulated by the equations 3G 3z--C

3T 3t

(7.20)

3T 32T 3t - K 3z 2

(7.21)

w h e r e C is the heat capacity of the m e d i u m and K = c t / C is called t h e r m a l diffusivity. The latter coefficient physically expresses the speed of propagation of a

t h e r m a l w a v e into a m e d i u m , w h i c h is p r o p o r t i o n a l to the capability of t r a n s m i t t i n g heat in the presence of the unit t e m p e r a t u r e g r a d i e n t (thermal conductivity) and inversely proportional to the capability of storing heat (heat capacity). W h e n all the fluxes are positive, the heat balance equation shows how the radiant energy adsorbed by the soil surface is partitioned among the heating of the deeper layers of the ground, the heating of the atmosphere and the evaporation; w h e n one or more of these fluxes change their direction and become negative, the equation shows the w a y in which each flux is transformed, supplies to or receives energy from the other fluxes (Fig.7.4). One or more components of this balance m a y be also zero, e.g. 9

= 0 w h e n the sky is completely overcast or

slightly after the sunrise or before sunset; G = 0 twice a day w h e n the heat flux into the ground inverts direction, or in the case of non conductive surfaces; H = 0 w h e n air and soil surface have the same temperature and there is no evaporation or condensation; LvE = 0 w h e n the soil is dry and there is neither condensation nor evaporation. Marble and bronze m o n u m e n t s have a very little porosity in comparison with the soil, so that the a m o u n t of water adsorbed in the pores is extremely modest. For them LvE -- 0 and the energy balance is practically reduced to 9 = G + H. The white Carrara marble of the Trajan Column, Rome, becomes some 10~ hotter than the air and dark surfaces become m u c h more hotter (Camuffo, 1993; Camuffo and Bernardi, 1993). Dark stones become some 20~

hotter. Bronze

m o n u m e n t s are hollow, and the thickness of the bronze layer is of few m m , so that the term G might appear negligible at first sight. However, this is not true: the very great thermal capacity of the m o n u m e n t absorbs a huge a m o u n t of heat, which reflects in a rise of temperature. Dangerous fluctuations of m o n u m e n t temperature occur with the oscillations of the wind speed or w h e n passing clouds

218 temporarily s h a d o w the monument. For example, in clear s u m m e r days the temperature of the St. Mark horses, Venice, fluctuate within a 6 min period due to the turbulence induced by the city on the sea breeze, and every day the t e m p e r a t u r e d r o p p e d some 15~

in 15 min when the horses entered in the

shadow of the bell tower; afterwards they experienced a nearly symmetric rise of temperature which accelerated fatigue failure, especially on the tree legs which are b o u n d on the Istrian stone basement, less sensible to expansions (Camuffo, 1981a; Camuffo and Vincenzi, 1985). -~

50-

4030 rO 2o

~

=" ~

lO o

-lo 6

8

10

12 Time

14

16

18

20

(h)

Fig.7.4 Energy balance 9 = G + H + LyE during the daytime, at Padova, Italy (46~ lat N), in August. Legend: q~, thick line; G, thin line; H, dotted line; LyE, dashed line.

The daily cycles of q~ change slowly with the season, are affected by the cloudiness or abrupt changes of soil albedo, e.g. after showers, and vary with the seasonal change of the solar radiation and the vegetation. The moisture content of the soil, and the vertical gradient of it affect the amplitude of G, H, LyE and cause some asymmetry or delay. In fact, after a drizzle or an abundant dew, the u p p e r layers are moister, so that the evaporation rate is greater in the morning than in the evening, when the soil is dryer. The curve of LvE is skew with the m a x i m u m i n the morning, and H has a similar skewed trend, but with the m a x i m u m in the afternoon, when the evaporation is reduced and more energy is employed to w a r m the air. After some clear days, the upper layer of the soil will dry, so that the evaporation rate will increase in the afternoon, w h e n the heat wave reaches the deeper, moister layers. In this case the curve of LvE is skew

219 showing a greater evaporation rate in the afternoon and, consequently, the maximum of H occurs in the morning. By plotting in a Cartesian reference frame the instantaneous values at the time t of the fluxes G(t), H(t), or LvE(t) versus ~(t) for a whole day, an ellipse is obtained, which is clockwise or counterclockwise, with the major axis more or less tilted, and the minor axis more or less wide, the entire ellipse being slightly displaced upwards or downwards (Fig.7.5). Therefore, the daily cycles of G, H, LvE can be calculated by means of the equations:

3q~(t)

G(t) - al q-~(t) + a2 3t

3q~(t)

H(t) = bl qXt) + b2 3t

+ a3

(7.22)

+ b3

(7.23)

3q~(t) LvE (t) = cl q~(t) + C2 3t

+ C3

(7.24)

where the coefficients al, bl, c1 indicate the first order proportionality between each flux and the radiative income, i.e. the inclination of the major axis of the ellipse; a2, b2, c2 indicate the influence of the gradient of moisture into the ground which causes positive or negative departures from linearity, i.e. the width of the ellipse, and the sign shows whether the ellipse is described clockwise or counterclockwise; a3, b3, c3 indicate the background flux, independent of qL and the experimental problem of the divergence of the fluxes a n d / o r the storage of energy, as the four fluxes that appear in the balance equation cannot be measured exactly at the same level as three fluxes are in the atmosphere and one is underground.

7.9. MAIN PARAMETERS USED IN MEASURING ATMOSPHERIC STABILITY AND TURBULENCE 'A precise definition of turbulence is difficult, if not impossible,

to give'

(Plate, 1982). For this reason several parameters have been introduced, each of them may be, time by time, very useful or inappropriate. However, turbulence, and the opposite physical regime, characterised by still air, are fundamental in governing the mechanisms

of pollutants

deposition

and heat and mass

220 30

.J J J

25 ,_r r

20 r,,J b,O

u.a

15

=

10 .

-

j

J

Y

-5

|

i

0

,

i

20

,

i

40

|

60

80

( m w / c m 2)

@

50

J J J J J J

40 c4 r,J

30 bO

20 ~4

10

J J 9

J

J J |

0

I

10

.

i

20

,

i

,

30

i

40

.

i

50

.

60

(mw / cm 2 )

Fig.7.5 Plot of the evaporation rate LvE (mg cm -2 h -I) versus the net radiative flux q~ (mw cm -2) at Padova: (a) at the end of August, a few days after a shower, (b) in September, several days after a late August shower .

221 exchanges. Monitoring atmospheric turbulence or stability in field surveys is very important and often extremely difficult. For this reason it is fundamental: first, to become familiar with the most important definitions and their physical meaning, and then to balance theory with the specific problem under consideration, as well as w i t h the i n s t r u m e n t a l facilities and the experimental limits. W i t h o u t this effort,

the

environmental

monitoring

risks

to be

a mere

collection

of

meaningless data. A t m o s p h e r i c stability can be defined as the t e n d e n c y to mitigate (or accentuate) vertical m o v e m e n t s or existing turbulence. M a n y p a r a m e t e r s have been i n t r o d u c e d to w h o l l y and quantitatively describe certain a t m o s p h e r i c conditions, each of which illustrates a particular characteristic. These are not just limited to providing mathematical models, but have also resulted in furnishing new criteria for classification which have been particularly useful. It w o u l d be here advisable to r e m e m b e r some of the better known ones, those that have led to successive d e v e l o p m e n t s in the interpretation of this p h e n o m e n o n . These parameters are all somewhat abstract in nature, in that they have been introduced to give greater flexibility in forming the mathematical formulation of turbulence, and their importance lies within this context. However, it is always possible to give a physical explanation - even though this m a y not always be i m m e d i a t e l y clear- and shall be underlined wherever possible.

Kinematic

viscosity ( v )

The kinematic viscosity is an atmospheric variable which is useful to define the next parameter of stability. It is the ratio between the dynamic viscosity ~ and the density p. of the fluid, i.e.

v =P

(7.25)

and depends upon both air temperature and pressure. For air at sea level pressure and 20~

p = 1.205x10 -3 g cm -3 and v = 0.15 cm 2 s -1. It is the factor of

proportionality in the equation relating the accelerating (retarding) effects on the air motion, i.e. 3u ~ a t , generated by fluid friction in a given wind speed profile:

3U

32U

3t - v 3z----~ 9

(7.26)

222 Equating eq.(7.7) to eq.(7.9), and operating with the help of eq.(7.6) and eq.(7.13), the kinematic viscosity v results equal to the kinematic coefficient of e d d y viscosity KM. This is only a logical similarity as the e d d y visciosity was i n t r o d u c e d in 1877 by Bussinesq in analogy with the laminar flow relation existing between the stress and the velocity shear. Physically, for reasons of continuity, this equalisation applies only to the transition zone between the viscous layer and the external turbulent regime to which the above equations respectively refer. In fact, although KM is analogous to v, it is expected to be much larger than I~/p to account for the greatly increased flux capabilities of the turbulent flow in comparison with the molecular transport (Brown, 1991).

Reynolds number (Re) Re is the non-dimensional ratio between inertial and viscous forces of a moving fluid: Lu

Re = ~

(7.27)

where L and u are, respectively, the characteristic length and speed of the system, while v is the kinematic viscosity of the fluid. The physical significance of Re can be deduced from the fact that the inertial forces tend to separate parcels of fluid that had, initially, distinct speeds. On the other hand, the viscous forces tend to lead to a certain uniformity in the speeds at points close together and attenuate the dissimilarities. At low Re values, when the viscous forces predominate over the inertial ones, the flow is laminar. A critical Rec value is reached w h e n the inertial forces become so great with respect to the viscous ones, that turbulence is set up. The Re number is often used in the field of hydrodynamic stability and in the onset of turbulence. For example, in the case of a fluid that flows at a certain speed u over a surface, a internal boundary layer near the surface develops, that is initially laminar and becomes turbulent after the fluid has covered a distance L so that Re reaches the critical value Reo which generally lies between 105 and 3x106. In the atmosphere, Re is generally greater than Rec, so that the air is most frequently in a turbulent regime. Outdoor Rec is greater than in other closed systems; in pipes for example, it is 2500 < Rec < 5000.

223

Richardson (gradient) number (Ri) Ri is expressed in the form of a gradient (Richardson, 1920) and is the nondimensional ratio between the buoyancy forces (Archimedes) and the inertial ones due to the wind: g 3p g 30 ~2 p 3z 0 3z Ri - [3u~2 -- ~U 2 -- ~,~U ,~2 ,

(7.28)

,

where co represents the Brunt-V~iis~il~i frequency. The temperature gradient (and the related heat flow) which appears at the numerator, is normally negative during the day; during the clear, windless nights is positive, but may be negative during the windy or rainy nights. The sign of this number is determined by the temperature gradient, while the denominator is always positive, the negative values being an index of instability and the positive of stability. The numerator of Ri measures the density stratification or static atmospheric stability due to the temperature gradient. The denominator is of dynamic nature and measures the destabilising effect, linked with the wind profile. In practice, the Ri represents the ratio of the work done against the gravitational stability and the energy transferred from the ensemble motion to the eddy turbulence. When this, and the following parameters, are measured in the air close to the ground, there is no difference between the actual temperature T and the potential temperature @. In practice, considering equal the two parameters at the soil level, at the height 10 m the difference @- T equals 0.1~ which falls within the limits of experimental accuracy. For this reason, in microclimate studies, these two parameters are used without distinction and often T is preferred.

McVehil ratio (KM/KH) This parameter is the ratio of two coefficients which define the vertical transport of m o m e n t u m (KM) and heat (KH) between two adjacent layers of the atmosphere (McVehil, 1964). When (KM/KH) > 1, the mechanical turbulence generated by the wind dominates over the thermal convection. When, however, (KM/KH)< 1, the convective mixing dominates over the eddy turbulence. Often, for reasons of simplicity and in the lack of observations, modelists assume (KM/KH)= 1;

224 however, this a s s u m p t i o n is valid in near-neutral and unstable conditions (Lumley and Panofsky, 1964).

Richardson flux number (Rf) Rf is linked with Ri and to the previous ratio:

KH

Rf - Ri KM

(7.29)

which quantifies the role of the turbulence in the vertical transport of heat and m o m e n t u m , by means of the vertical flows of these properties. Rf can be written as a non-dimensional ratio of two fluxes: the nominator is linked with the production (or destruction) of turbulent kinetic energy by means of the vertical heat flux H of the thermal convective motions, the denominator with the shear p r o d u c t i o n (or destruction) due to the dynamic action of the wind, which involves the vertical transport of m o m e n t u m and the gradient of the wind speed, i.e. the wind shear. The Rf number can be rewritten in the following way:

g 0

Rf--

~u

(7.30)

3z This p a r a m e t e r has the sign minus as it was introduced to obtain positive n u m b e r s in the original studies on the onset of turbulence in a thermally stratified atmosphere. At Rf ~ 0.2 a balance is reached between the generation and destruction of turbulence, and for this reason this value is called the critical

Richardson

number.

Monin-Obukov length (L) L is a dimensional ratio (it has the unit of a length) which characterises a diabatic wind speed profile (i.e. with an exchange of heat) that involves both the sensible heat flow H, and the friction velocity u, (Monin and Obukov, 1953). The Monin-Obukov is defined as:

225

3 L=-u,

cpp 3 cpp 6) H =-u* k g H kg 0

(7.31)

3

where k ~ 0.4 is the von Karman's constant. The term u, p at the n u m e r a t o r represents a dynamic factor; the denominator involves the heat flow in entropic terms i.e. H/O. As u, represents the shearing stress, L is determined from the boundary conditions of drag and gain of entropy at the surface. When the heat flux vanishes, this length is infinite. It is negative during superadiabatic conditions and positive during inversions. In clear night conditions, a transition height is found, where the eddies generated by the wind shear begins to be counteracted by buoyancy and Rf-- 1. This transition height can be individuated as the Monin-Obukov length.

H6gstr6m ratio (S) S compares the thermal stability given by the vertical gradient d O/dz, with 1

the wind destabilization pressure ~p 2

due to the wind kinetic energy

(H6gstr6m, 1964) as follows

30 3z S - 2.

(7.32)

All of the above parameters require measurements that are either very difficult to realise or not particularly reliable. For this reason, the H6gstr6m parameter has been introduced, as it involves the static and dynamic coefficients in a simpler form.

Sutton turbulence index (n) and the logarithmic wind profile This and the following parameters do only consider the wind profile. It is much simpler to measure the wind profile alone (or only the temperature profile), rather than complex measurements of the above parameters. However, when only a single profile, representing approximately either the thermal or dynamic aspects, is taken into account, the degree of approximation should be considered case by case, depending on the aims and the degree of accuracy

226 required. The Sutton turbulence index has been defined for the theoretical study of wind turbulence (Sutton, 1947) and is based on the analysis of the vertical profile of the wind speed measured at two levels, z I and z 2: U(Zl) U(Z2 ) --

(~22)n/(2-n)

(7.33)

The Sutton turbulence index n generally lies between 0 and 1 in cases of maximum and minimum turbulence, respectively, and is generally in accordance with other results, but not always unequivocally. This index only considers the bulk effects of eddy turbulence and convective mixing on the wind profile and gives the degree of erosion on the basis of the logarithmic profiles, as suggested by the theory of similarity. This theory requires that, expressing the atmospheric variables in an appropriate dimensionless form, the profiles of these new variables must have a unique form when stated in terms of the basic independent parameters, also expressed in dimensionless form. Under this circumstance,

the mathematical

formulation is the same, w h a t e v e r

the

atmospheric parameter involved. The similarity theory is very practical, not always rigorous. The logarithmic wind profile was derived from the observation (in wind tunnel experiments) that in the turbulent regime the mean wind speed varies with the distance from the surface following the law O

3z

U.

--

-kz

(7.34)

where k is the von Karman's constant, and the shearing stress has been found constant throughout an air layer close to the ground, called surface layer or constant stress layer. By integrating the above equation, the logarithmic wind profile is obtained, i.e.

1 z - k lnz--~o

(7.35)

U,

where the constant of integration Zo is called roughness length and physically represents the height at which the average wind speed vanishes, i.e. = O.

227

Deacon number (~) Defined as ~U

3 In 3z (7.36)

/~= 3 1 n z

is only related to the vertical profile of the wind speed, as the Sutton's index, without discriminating the effects due to the transfer of heat and m o m e n t u m (Deacon, 1949).

R parameter The R parameter only takes into account the wind profile or, more precisely, the wind attenuation at the ground due to friction and the exchange of momentum and is represented by: Us

R - Ug

(7.37)

where Us represents the wind at ground level and Ug the gradient wind (i.e. the wind determined by the pressure pattern, undisturbed by the soil roughness).

Wind standard deviation (ry) The standard deviation ry of the wind, is the wind turbulence statistically defined in terms of amplitude and frequency of the departures from the average value. Both the fluctuations in the wind direction 0, i.e. c0, and speed u , i.e. ryu are considered; the normalised value ryu/ is used directly in the equation to determine the concentration distribution in the Gaussian diffusion models, as we will see later this Chapter, as well as in Chapter 12.

7.10. PLUME DISPERSION Several models

have been developed

to predict

the concentrations

downwind of a single source. The Gaussian model has been widely used for its simple mathematical representation and the agreement with the observed data

228 for long term averages. This model assumes that the dispersion is due to the random effect of the eddies in the atmosphere which broaden out the plume when it progresses in the d o w n w i n d direction. In the case of a neutral atmosphere and steady wind direction, the maximum concentration is found along the plume centreline and lateral diffusion is due to atmospheric turbulence; in the case of a wind direction continually variable around a prevalent direction, the plume meanders and the maximum concentration is again statistically found along the mean wind direction, d o w n w i n d from the source. The crosswind distribution of concentrations is represented by a bell shaped curve very narrow near the source and gradually broadening with increasing distance from it, i.e. as time elapses after the smoke release. If a Cartesian reference is assumed, with the x axis along the wind direction, the y perpendicular to it, but in the horizontal plane, showing the lateral displacement, and the z on the vertical, the atmospheric stability will differentiate the standard deviations of the wind fluctuations in these three directions, respectively ~x, ryy, ~z (also called diffusion coefficients) and the plume dispersion will be affected accordingly. When the atmosphere is unstable, vertical motions are favoured by convection, and ~z dominates; when the atmosphere is neutral the diffusion coefficients are similar; when the atmosphere is stable, vertical turbulence is suppressed, i.e. ryz---~0, and O'y describes the fanning or the meandering of the plume in the horizontal plane. For an effective height h of an elevated point source, e.g. a stack, the solution for the plume concentration at ground level ~,(x,y,z=O,h) takes the Gaussian form Q e x p - (2Gryy + ~,(x,y,O,h) ~ ryx ryy

(7.38)

where Q is the source strength and the average wind speed at the height of the plume. Of course, the ground level concentration directly d o w n w i n d of the source is found by putting y = 0 in the previous equation, which reduces to

K(x,0,0,h)-

~ryxryyQexp-( h~2z2).

(7.39)

The maximum ground level concentration Xmax is obtained by equalling to

229 zero the time derivative of the previous equation, i.e. 2 Q ryz Xmax = e rr < u> h 20"y

(7.40)

(where e is the Neper number) and occurs at the distance x where ryz- h~ ~/7.2. The effective

height of the source h is the height at which the plume

stabilises after an initial rise. h is therefore given by the geometrical stack height

hst plus the plume rise Ah which is due to the momentum effect (determined by the vertical speed of the smoke into the chimney and the interaction between the vertical stack jet and the horizontal wind flow) and the b u o y a n c y effect (determined by the emission temperature, i.e. the low density of the smoke, which is w a r m e r than the surrounding air). Several formulae exist, which depend

upon

the jet speed

and

emission

temperature

as well

as the

environmental air speed, temperature and stability.

7.11. STABILITY CATEGORIES TO EVALUATE THE ATMOSPHERIC STABILITY From a practical point of view, the routinely use of complex parameters which describe the atmospheric stability, is limited, substantially, to very few cases where detailed m e a s u r e m e n t s can be carried out. Even u n d e r ideal conditions without any discontinuity at ground level and in stationary regimes, where it could be assumed that Gaussian diffusion prevails, forecasting the wind turbulence or simply deducing it from other meteorological parameters without calculating it from wind fluctuations and the vertical temperature gradient is still a problem. Many scientists have dedicated much of their time in search of a reliable method which supplies reasonable values of wind variance and plume dispersion from other simple observations. Practically, the method consists in determining classes of stability and linking them to typical values of ry. The stability classes are determined on the basis of observations and very simple considerations that are, however, valid only in a general sense. These criteria tend to focus on the link between the dynamic evolution of the PBL and bulk classes of turbulence which summarise the situation. This practical point of view leads to the definition of classes of stability, as follows.

230 7.11.1.

Brookhaven

The first f u n d a m e n t a l contribution is due to the Brookhaven National L a b o r a t o r y (Singer and Smith, 1953), which defined five classes of w i n d turbulence and tried to correlate each with temperature gradients, wind intensity, seasonal and d i u r n a l cycles, solar radiation, cloud cover and the Sutton t u r b u l e n c e index. The Brookhaven turbulence categories, referring to w i n d records taken over a period of one hour, are defined as follows: TABLE 7.1 Brookhaven turbulence categories A B2 B1

C D

fluctuations in the wind direction of more than 90~ fluctuations of between 90~ and 45~ fluctuations of between 45~ and 15~ the anemographic trace, because of the continuous and regular fluctuations, seems to be a wide, uniform band the trace can be compared to a continuous line and any eventual fluctuations do not exceed 15~

The categories are closely linked with the temperature gradient and more precisely, in order of decreasing instability: A, B2, B1, C and D. The D class is characterised by dispersion in a stratified atmosphere, and the stability is m u c h greater with respect to the other classes and is often associated with m a r k e d inversions, but sometimes with unstable conditions too. The correlation with the wind intensity is less strict. The A and B2 classes are generally associated with weak winds while the C one with strong winds. The B1 and D classes a p p e a r u n d e r considerably variable conditions. The w i n d s associated with D under stable conditions, in particular, are weaker at ground level and more intense higher up. By combining these results, the class, depending upon the type of turbulence is obtained: convective or mechanical. The A and B2 types, characterised by weak w i n d s u n d e r unstable conditions, are, essentially, of a convective nature. The C type is mainly of a mechanical nature, being associated with strong winds and neutral gradients. The B1 is of a mixed nature, while the D type is characterised by very modest turbulence. The seasonal character is visible but not very m a r k e d .

The h o u r l y

distribution is, on the other hand, evident. The A and B2 types make very little contribution and only occur in the m i d d l e of the day. Similarly B1 varies seasonally from 10 - 20% to 85%, while D is almost complementary to B1, the sum

231 of these two represents approximately 85% of the total cases. The C type, in qualitative terms, has the same trend as B1 but is much less marked. The correlation with direct solar radiation confirms what has already been said about A and B2 but the C class is mostly associated with weak sunlight or cloud cover, while D is linked with clear night-time sky or weak daylight sunshine, or extensive cloud cover and isothermy or transitory phenomena late in the afternoon. Singer and Smith also underlined that their results, when supported by a clear correlation, could be extended to other sites in open countryside at any latitude and climate similar to Brookhaven, as long as an anemometer with similar characteristics was used at an altitude of about 100 m. Their study, in practice, shows which parameters are most closely connected with certain classes of turbulence at a given site, confirming some precise dynamic relationships. At the same time, the study showed that any correspondence is of a statistic nature, the

values

often

varying

greatly

and

are

not,

therefore,

one-to-one

correspondences, and should thus only be used for broad considerations.

7.11.2. Pasquill A further contribution to this problem was made by Pasquill (1961, 1962, 1974) who tried to combine, in a more flexible way, the theoretical and experimental results obtained by the various research groups. The basic hypotheses were: stationary wind conditions with both vertical and horizontal Gaussian distribution of the concentration; wind constant with height and airsoil interactions which allow the representation of the dispersion coming from an actual source, or from a virtual source. Pasquill stated that even under these conditions the effective height reached by a plume and the lateral spread must be calculated by measuring the variance of the wind fluctuations. However, in the absence of any direct measurement, in the case of brief emissions (lasting a few minutes) and fairly close to the ground in open, flat countryside, Pasquill proposed using approximate evaluations of the plume spread and height for the six stability categories that can be characterised in terms of wind intensity, sunshine (in England) and cloud cover. The advantage is that the categories can be attributed on the ground of the knowledge of prevalent local climatological characteristic. Under conditions of great stability, he suggested that no values be proposed, because the results could be somewhat erroneous. It should be quite clear that such values can not be used in urban or industrialised

232 areas because of the additional dynamic turbulence generated by buildings. The six categories determined by Pasquill mirror the results obtained by the Brookhaven climatic correlations, and are defined in Tables 7.2 and 7.3, where the sunshine intensities defined "strong" or "weak" relate to the values m e a s u r e d at m i d - d a y in the s u m m e r or winter, respectively, in England. Night is defined as the period that runs from one hour before sunset to one hour after sunrise, w h e n the balance of the radiant exchange between the earth and the sky is annulled (in England) passing from a positive flux during the day to a negative one at night. It was suggested that the D category be used for the first and last hour of the day, as defined above, and for the periods, night or day, characterised by completely overcast sky. The conditions of great stability were introduced successively.

TABLE 7.2 Pasquill Stability Categories A: extremely unstable conditions B: moderate instability C: slight instability

D: neutrality

E: slight stability F: moderate stability G: great stability

TABLE 7.3 Key to Pasquill Stability Categories Surface wind speed (at 10m) (m/s)

daytime: strong insolation

daytime: moderate insolation

daytime: slight insolation

nighttime: thiny overcast >_4/8 low cloud

6

A A-B B C C

A-B B B-C C- D D

B C C D D

E D D D

nighttime: clear sky or cover > 1, i.e. D is much smaller than ~, and molecular impacts occur individually and punctually, each with their own singularity after random time intervals. In the continuum regime Kn dt 2

dx\2 = 0;

_~

<m (-d--/) > =

"

(8.9)

The principle of the equipartition of energy <m (dx/dt)2> = k T, where k is the Boltzmann constant, i.e. k = 1.38

1 0 -16

erg ~

allows the calculation of the

value ot = 6 k T / f , and the mean square displacement can be expressed:

2 6kTt 9 = f

(8.10)

240 This equation, first derived by Einstein (1905), constitutes a probabilistic representation of the displacement expected. The mean square displacement of the diffusing particles increases linearly with elapsed time and fluid temperature T; it decreases inversely to the (dynamic) fluid viscosity/1. The dispersion of particles which were originally close, is the most probable result due to the natural re-organisation of the internal distribution of a system as a consequence of individual and casual molecular impacts. This happens without the intervention of collective organised motions which characterise the hydrodynamics, which holds in the continuum regime and is governed by fields of force or pressure gradients. The diffusion coefficient can be derived in terms of random walk (Seinfeld, 1986) by integrating the equation which governs the concentration C of Brownian particles 3C 3t - ~ V 2 C which gives 3<x 2 >/3t = 2 ~ a n d

(8.11) <x 2 > = 2 ~ t . Equating the value of <x2> =

(1/3) given by eq.(8.10) with the result obtained integrating eq.(8.11), the Brownian diffusivity ~ i s obtained (Fig.8.1): kTCc = 3 n ~t D

(8.12)

This is the fundamental Stokes-Einstein relation which has been improved with the addition of the empirical Cunningham slip correction factor Cc (Fig.8.2). In the continuum regime, C c--~ 1, and ~ varies as D - l ; however, in the discontinuum regime, when the aerodynamic mobility of the particle increases, Cc is given by the equation 2~ Cc ~ 1+ 1.657D

(8.13)

and ~ varies as D -2. In practice, Cc increases the efficacy of the Brownian process for the smaller particles, when the number of simultaneous molecular impacts becomes smaller and smaller, and the net resultant is less and less attenuated. The Stokes-Einstein formula shows that the diffusivity is proportional to the air temperature which determines the molecular excitation, but is inversely proportional to the fluid viscosity and particle diameter; in the case of large

241 particles a very great number of random impacts is averaged and the net resultant tends to zero, as well as the diffusivity. The diffusivity is i n d e p e n d e n t of the particle density, unlike the velocity arising from the thermal excitation. 0,11

]

0,01 0,001 0,0001 (/]

0,00001 0,000001 0,0000001 0,00000001 0,000000001 0,001

0,01

0,1

I

D

I0

I O0

(l.tm)

Fig.8.1 Brownian diffusivity ~ (cm2/s) of particles in the size range from 0.001 >1 and the Cunningham Cc varies as D -1. The particle density usually ranges between pp = 1 g cm -3, e.g. water droplets and pp = 2.65 g cm -3, e.g. quartz granules. In the case of non-spherical particles the aerodynamic effect due to the shape, expressed in terms of equivalent aerodynamic diameter, can'be calculated. Note that dust and desert sand granules acquire a spherical shape because of constant rolling. Sedimentation deposits the larger particles on horizontal surfaces and is particularly efficient in calm air, especially for particles having a diameter greater than 2 gm. The settling velocity Vg is shown in Fig.8.5. When convective motions occur, the descending and uprising airflows apparently compensate and the average effect of d o w n w a r d s and u p w a r d s motions leaves unaffected the average values. However, the presence of convection generates mixing and turbulence, so that the Stokes law cannot be applied. The turbulent drag is much greater and particles remain much longer in suspension following the microscale air movements. Therefore, during the daytime, when HVAC systems and people movements generate turbulence and resuspension, the concentration of coarse particles is higher than during the night, when they sediment more quickly in still air (Fig.8.6).

256 100

10

0,1 0,01 0,001 0,0001 0,00001

0,000001 [ 0,001

i

i

i

iiiii

i

0,01

i

i

i

i iiii

|

i

i

i

i iiiii

i

0,1

1

D

(~tm)

i

i

i iiiii

10

i

i

i

i iii

100

Fig.8.5 Gravitational settling velocity Vg of the suspended particles vs. particle diameter D (~tm). 100000 10000

,9,

1000

r,J

100 ,.~

10

12

0,1

24

0,01 0

1

10

Particle Diameter (~tm) Fig.8.6 Changes in spectral distribution of the concentration of suspended particles during the day. During the visiting time, the sources, resuspension and turbulence determine a given concentration distribution (thick line) which in the following hours, when the air is still, is impoverished of coarse particles, which sediment more quickly. Museum Correr, Venice, measurements at 12.00, 24.00, and 6.00 of the next day, the 12 and 13 February 1996

257 8.8. ELECTROPHORESIS Deposition due to electrostatic forces does not differ very much from gravitational sedimentation, in that both cases involve movement generated by a force field. There are, however, some differences that should be pointed out. The first- and the most obvious - is that electrostatic Coulomb forces are positive or negative, are inversely proportional to the square of the distance and integer multiples of the elementary charge e of an electron, corresponding to the degree of ionisation of the particle or the surface on which the particles is attracted. This may be caused, for example, by ultraviolet radiation or violent impacts of gas molecules or particles (colliding with each other or foreign bodies). Atmospheric dusts are highly charged. The principal mechanism of charging is the so called

diffusion charging i.e. airborne

ions

and

the development of charge through random collisions of particles.

Particles

formed

by condensation

at room

temperatures are initially uncharged, but they rapidly become charged by gaseous ions which diffuse to them. Splashing raindrops form a myriad of charged fine droplets which are attracted by and stick on nearby surfaces. Smokes resulting from combustion are highly charged when first formed, e.g. 74% of particles in smoke tobacco where found charged (Cadle, 1965). Smoking cigarettes in closed environments is extremely dangerous as the electrostatic charges lead particles to stick on surfaces in a short time. The electrostatic forces, however, do not only arise when both the particle and the surface are charged, but also a charged particle can generate an equal and opposite charge (image charge) on the approaching an uncharged surface, or a charged surface may generate a dipole on a conducting particle, such as for example, on water droplets. Furthermore, electrical charges may be generated even when neither of the two bodies was initially charged

(contact charging).

Electrical forces may arise because of the difference of potential that is generated when two different bodies meet because of the local interaction of the permanent charges on the surface of the two bodies. Contact charging occurs during the separation of non-metallic (semi-conductor) particles from solid surfaces. Dust and paint, for example, are both semi-conductors and the electrical interaction depends upon the relative donor-acceptor properties of the surfaces that come into contact with each other. Electrostatic deposition becomes important only in the presence of low relative humidity, while in damp environments the conductivity of the air increases and the surface is covered with a film of water molecules so that the

258 p h e n o m e n o n is greatly reduced; on the other hand, h u m i d i t y increases the adhesion of particles on moist surfaces, enhancing the capture efficiency of the surface (Phenix and Burnstock, 1990; Buffle and van Leeuwen, 1992). It should be noted that the 'particle' is not only an agglomerate of inorganic a n d / o r organic molecules, or a fragment of a mineral, but also implies biological structures such as fungal and bacterial spores, 'dwarf cells' or even vegetative cells. Due to their specific surface charge, depending on their nutritional status and related growth pattern, as well as on the composition of the s u r r o u n d i n g a t m o s p h e r e and surface solution, they are even attracted or repelled by the material surface (Marshall, 1984).

8.9. PHOTOPHORESIS When a suspension of particles is subjected to an intense beam of light, a motion is generated, called

photophoresis. This

phenomenon is measurable only

with black particles containing elemental carbon, e.g. candle smoke, soot or fly ash g e n e r a t e d by the combustion of wood, charcoal, oil. There is not an universally accepted theory to explain this mechanism. The first idea is to think that photons possess a m o m e n t u m q hv h q = --~ = ~

(8.46)

(where h is the Planks constant, v the frequency and )~ the wavelength associated with the photon and c is the light speed) and therefore a light beam may exert a force on the particles which absorb or reflect photons. The pressure p exerted by a light beam is E P = c (I+R)

(8.47)

w h e r e E is the energy incident on the unit surface per unit time and R is the reflection coefficient, i.e. R = 0 for a totally absorbing black body, and R = 1 for a totally reflecting mirror. A mirror undergoes a pressure which is twice the pressure exerted on a black surface. However, this simple explanation based on the so called radiation pressure is not realistic, as suspended particles do not straightforwardly advance as they were p u s h e d by a pressure, but they proceed either linearly, or in the form of

259 spirals, loops and so on. This behaviour is more commonly interpreted in terms of radiometer effect, i.e. the absorbed photons generate temperature unbalances on the particles and the surrounding gas, so that the resulting effect is similar to that for particles in a temperature gradient. Spiralling motion is therefore generated by the particle rotation which changes the orientation of the temperature gradient and the associated thermophoretic effect. In fact, laboratory experiences ,on the radiometer effect in a gas (Landsberg, 1979) have shown that the effect of light pressure is largely overwhelmed by the effect of the convective motions in the gas, generated by the temperature unbalances due to the light absorption. The radiometer theory (Cadle, 1965) predicts that the m a x i m u m pressure pmax is exerted when the gas mean free path equals the effective dimensions of the particle, i.e. Kn = 1, and is given by the equation

848,

Pmax - 2 D

(where/~ is the dynamic viscosity and M the molecular weight of the gas) so that the photophoretic force Fph is described by equations which change with the gas pressure p, i.e. it varies as the cube of the particle diameter at low pressure, as the square at intermediate pressure, and linearly at high pressure, as follows:

Fph =

a p D3

24 T

Gp

for Kn >> 1

(8.49)

which is the formula derived by Rubinowitz in 1920 for the low pressure, where a is an accommodation coefficient and G p is the thermal gradient within the particle; in the transition region where the particle size is about equal to the gas mean free path, Hettner derived in 1926 this formula

Fph = 0.25 ~ /a D 2 Gp

~

a .~

- P - + Pmax

MT Pmax P

for Kn = 1

(8.50)

and the following one for the high pressure region

FPh=

3 ~ ].12D .~Gp 2pM

for Kn of a set of N values of the variable x: 1

<X> = ~ - ~X i

Median: the middle value in a set of values. Mode: the value which occurs most frequently. Percentile: a value in the range of set of data which separates the range into two groups, so that a given percentage of data lies below this value.

Precision: the closeness of the output to the true measurand value. Range: the interval of values that are intended to measure, or that are potentially measurable, or that have been measured, specified by their upper and lower limits.

Reliability: the probability that a t r a n s d u c e r will satisfactorily p e r f o r m its function. It can be measured by the variance of repeated measurements of the same value of the m e a s u r a n d p a r a m e t e r , taken u n d e r the same conditions.

Repeatability: the ability to reproduce the same output when measuring the same value of the measurand variable, taken under the same conditions. It can be expressed as the m a x i m u m difference of the output readings or in + percent of the range.

Representativity Also w h e n the measure is not affected by instrumental errors, not always the o u t p u t characterises the actual value of the m e a s u r a n d parameter in the site and the time instant under investigation. This happens typically w h e n the value of the parameter is not homogeneously distributed or the measurement is taken in a point where the measurand has a singular value. Measurements are done to define the parametric values of a surface or a site, and observations are limited to one or few points which should characterise a wider space. A measurement that characterises the value of the variable in its context, as expected, is called representative.

Resolution: the ratio of the output step change to the full scale output, generally expressed in percent. It represent the smallest detectable change of the measurand parameter. If the output varies with continuity, the resolution is infinite.

Response time: the length of time required for the output to rise to a percentage of its final value, w h e n the m e a s u r a n d parameter has u n d e r g o n e a step

314 change. When the percentage is 63.2 %, it is called time constant. About 95% of the step change is reached after 3 time constants. Of course, the response time (and the time constant) are i n d e p e n d e n t of the span of the o u t p u t change.

Sensor: the functional part of the instrument, which couples it to the m e a s u r a n d variable (i.e. the input) generating a mechanical or electrical signal which is the output of the sensor.

Sensitivity: the ratio of the change in the transducer output to a change in the value of the measurand parameter.

Specificity to the response: the capability of an instrument to respond only to the changes of the variable that it is designed to measure and be insensitive to all the other ones.

Threshold: the m i n i m u m value of the m e a s u r a n d variable that can be detected by the transducer. If the variable does not start from zero, the threshold is the smallest change of the variable which results in a measurable change of the output, but in this case it is better to speak in terms of resolution.

Time constant: the time required to detect and indicate 1/e = 63.2 % of a step change. See also response time.

315

C H A P T E R 10

Measuring Temperature

10.1. MEASURING AIR TEMPERATURE

10.1.1 Choice of the sensor Several kinds of good sensors are commercially available, not all equally suitable

for microclimate

study. The principal

types are: liquid-in-glass

thermometers (i.e. mercury or spirit thermometers); bimetallic thermometers; electrical resistance thermometers (metal resistance sensors and thermistors); thermocouples. The choice is determined by several factors, i.e. compatibility with the ambient conditions, measuring range, resolution, accuracy, response time, drift, compatibility with the recording instrument and cost. The outdoor measurements generally require a much greater temperature range than the indoor ones. If the sensor has a sufficiently elevated resolution, by limiting the range and expressing data as a percentage of the range, more accurate measurements can be obtained. In this sense, indoor measurements can be more precise than outdoor ones.

10.1.2. Response to the air temperature and infrared radiation It is i m p o r t a n t to avoid the s i m u l t a n e o u s use of different kinds of thermometric transducers. Any thermometer furnishes the temperature of the sensor, which is not exactly the same of the air, as each sensor responds in a different way to the infrared radiometric forcing as well as to conductivity and convection. When different kinds of well calibrated sensors are immersed in a water or oil bath, they give the same o u t p u t because their t e m p e r a t u r e is conditioned only by the bath temperature. In fact, the external IR radiation is shielded by the bath vessel or is completely adsorbed after the radiation is penetrated a few micrometers into the liquid. The specific heat of water is 3 order of magnitude greater than that of air. Sensors which respond in the same way to the air temperature but not to the radiometric forcing may give different readings

316 and generate confusion. Screens may attenuate this problem, but not solve it. The rise of temperature of a thermometer exposed to environmental I R radiation is the principle on which globe thermometers are based. These consist in a temperature sensor placed at the centre of a hollow 'black' sphere which absorbs IR from surrounding surfaces. Frequently, these globes are made of metal (e.g. copper, aluminium) and the sphere is painted with black colour. There is no doubt that the sphere absorbs the visible radiation and appears black to the eye, but the metal below the coating may reflect the IR, as it often occurs. For this reason the coating should be very thick and made of pigments absorbing in the IR region, which do not necessarily appear black to the eye. After the sphere has reached equilibrium, the temperature measured at the centre of the sphere gives an approximate measure of the effective temperature experienced by people or objects in that room. The overheating, i.e. the globe thermometer temperature minus the air temperature, gives the contribution of the radiant heat. This method is used in health physics to study the heat stress in workshops. This principle which furnishes the above useful application, is also a drawback in that IR radiation affects any thermometric measurement, and is negligible only for very thin metallic sensors which are reflecting the I R radiation, e.g. thermocouples, platinum resistance transducers. An abundant literature exists on this subject, and special reference has been made to UK Meteorological Office (1981); WMO (1983; 1986); Benedict (1984); Schooley (1986); Michalski et al. (1991); Nicholas and White (1994). 10.1.3. Thermometers A short description is here reported of the most c o m m o n l y used instruments, discussing their advantages and limits, especially in view of their

application in the field of microclimate analysis and diagnostics. Mercury-in-glass

thermometers The mercury-in-glass thermometers is, or at least was, commonly used for

routine measurements and as a secondary laboratory standard to which compare other kinds of sensors which undergo rapid ageing or drift. Meteorological station mercury thermometers are some 40 cm long and cover the range -30 to 60~

with scale division 0.2~

The advantages of the mercury as thermometric

liquid are: small thermal capacity, high thermal conductivity, small deviation from linearity, high boiling point and freezing point at-38~ This is a problem only for mountain sites or polar regions, b u t with the addition of thallium the

317 freezing point is lowered to -58~ The change of output, expressed as change of the mercury column length `4h due to the change of temperature AT, is given by the equation:

,4h = AT

Wo (~1- ~2) A

(10.1)

where Vo is the volume of mercury inside the bulb at standard temperature, ~1 and ~2 are the cubic coefficients of thermal expansion of m e r c u r y and thermometric glass, i.e. ~1 = 1.8 lx10-4 ~

]32 = 2.53x10-5 ~

respectively, and A

the cross-sectional area of the capillary. The sensitivity of the m e r c u r y thermometer is given by the ratio ,4h/,4T and the larger the reservoir Vo and the smaller the section A of the capillary, the higher the sensitivity. This can be represented by the equation ,4 h ,4 W Wo (]~1- f12) AT Wo (~1- f12) AT -re r2 AT = re r 2 AT = /1; r2

(10.2)

where r is the capillary radius. This equation shows that the sensitivity increases proportionally to the bulb volume and with the inverse of the square of the capillary radius. However, the larger the volume Vo the greater the heat capacity and the longer the time constant of the thermometer, so that sensitivity a n d time of response have opposite requirements. The main errors of this kind of thermometer are: (i) Thermometer heating, when the observer goes too close to the thermometer for reading the scale, and remains for a too long time, influencing its temperature, or when the thermometer is not adequately shielded against infrared radiation. (ii) Parallax, when the reading is made with the eye placed not at the same height of the top of the mercury column. (iii) Emergent stem, when the temperature of the bulb is not the same of the surrounding

medium,

i.e. w h e n

the t h e r m o m e t e r

is not completely

surrounded by only one medium having the same temperature. This error may be important for measurements of solid bodies. (iv) Drift, when the characteristics of the thermometer change slowly with time, e.g. the bulb of the thermometer tends to contract slowly over a period of years, rising the temperatures. (v) Departure from linearity and inequality in the expansion of the liquid and

318 glass. (vi) Capillarity, which may influence the height of the mercury in the capillary tube. (vii) Elastic errors, due to exposure to a large range of temperature in a short time, or to large changes in external pressure. (viii) Scale division and calibration. Also spirit or other thermometric liquids are used, for their greater sensibility (thanks to a much larger expansion coefficient) but they have some problems: adhesion to the glass, stronger deviation from linearity, drift due to polymerisation and slow changes of the liquid properties, breaking of the liquid column. Their use is not recommended. Liquid-in-metal

thermometers

Liquid-in-metal or pressure thermometers consist of a sensitive bulb, an interconnected capillary tube and a pressure measuring device such as a Bourdon tube. They follow an equation similar to the eq.(10.1) which has been discussed for liquid in glass thermometers, i.e. (10.3)

A V = Vo (~1 - 3a) AT

but with the appropriate coefficients, and ,62 has been substituted with 3a, where a is the coefficient of linear thermal expansion of the bulb material. In meteorology, this sensor is used to drive the arm of the recording pen of thermographs, and in the US this is accomplished according to the Weather Bureau specification No. 450.1201. The time constant is some minutes, so that all the short period temperature fluctuations are smoothed out. This kind of transducer is used in industry and sometimes in meteorology, but is not relevant in microclimate studies. Bimetallic

thermographs The bimetallic t h e r m o g r a p h

is c o m m o n l y

used

both

in

standard

meteorological stations and museums. It is mainly associated with a hair hygrometer and the resulting instrument is the well known thermo-hygrograph. The bimetallic sensor is composed of two thin metal strips having different coefficients of thermal expansion, roll-welded together along one of its flat sides. It provides a mechanical output, i.e. the displacement of the free end of the strip. This end is usually connected with a pen, whose movement is amplified and

319 used to trace the temperature records in clock thermographs. It is useful to remark the two main characteristics of this instrument. (i) The thermograph is a linear transducer, as the displacement of the free end of the strip is a linear function of the temperature change. (ii) The sensitivity of the sensor is directly proportional to the square of the length of the strip and p r o p o r t i o n a l to the difference in the thermal coefficients of expansion of the two metals, but is inversely proportional to the thickness of the strip. (iii) The time constant is few minutes, so that this instrument smooths out all the short period temperature fluctuations. (iv) The resolution in the strip chart recorder is generally from 1 to 1.5 m m per ~ and the time scale division is 15 min for daily clocks and 2 hours for weekly clocks. The resolution in reading the strip chart is some 1~ (v) The accuracy is no better than +1% of the range which generally varies between 45 ~ and 90~ (vi) The friction between pen and chart is excessive compared with the force supplied by the bimetallic strip, so that the graph is smoothed out, with underestimate of the maxima and overestimate of the minima. These instruments are not accurate, but are very popularly used in museums. The most common sources of error are: (i)

Lack of maintenance and periodic calibration.

(ii) Exposure in a position non representative of the parts of the room where works of art are placed, e.g. near the room corners where the air is stagnant and on the floor, at a height different from that of the exhibits. (iii) Dirt, dust and pollution which increase the friction of the instrument. (iv) Excessive friction between pen and strip chart. (v) Corrosion or mechanical damage to the bimetallic strip. All the above causes of error show that this instrument needs a frequent cleaning, and particularly of the bimetallic strip and the pen. The latter should be carefully cleaned with alcohol. After cleaning, the instrument calibration should be controlled as well as the fine regulation of the three adjusting screws (i.e. bimetallic

element,

magnification,

pen

pressure).

Monthly

control

and

maintenance is recommended, but in practice this necessary operation is usually neglected. Platinum resistance sensors A l t h o u g h iron, copper, nickel and other metals have a t e m p e r a t u r e

320 coefficient of electrical resistance greater than platinum, p l a t i n u m resistance sensors are preferred for their stability in time and non corrodibility, which are i m p o r t a n t characteristics especially in h u m i d or polluted environments. The platinum resistance sensor is an electrical resistance, made of very pure platinum wire, 0.1 m m in diameter or less, used sometimes as a wire and more usually w o u n d on a glass or ceramic rod. However, thin deposited p l a t i n u m films are also common, as well as several type of probes with special windings for different purposes. For a metal, the electrical resistance R ( T )

is described by a MacLaurin

expansion of the successive powers of the increase of temperature, R ( T ) = R(To) (1 + a A T + b A T 2 + ..... )

(10.4)

where R ( T o ) is the resistance of the sensor at the reference temperature To = 0~ AT is the temperature change and a, b .... are constants, characteristics of the metal used. The p l a t i n u m resistance is characterised by the following values a = 3.968x10 -3 ~

b = -5.847x10 -7 ~

c = -4.22x10 -12 ~

but within the interval of

meteorological observations is in a very good approximation described by the first two linear terms of the series and is linear within +0.3% of the whole range. As it presents an excellent stability, the measurements are reproducible within 0.01~ A n o t h e r a d v a n t a g e of these sensors is that they are cheap. Metal resistance thermometers should be compared with. a standard every year. Thermistors

Thermistors are essentially semiconductors which behave as resistors with a high t e m p e r a t u r e coefficient of resistance. The electrical resistivity varies with the t e m p e r a t u r e

and

is u s u a l l y negative,

i.e. decreases

with

increasing

t e m p e r a t u r e unlike metals. The response function is an exponential one of the type:

R(T)-Ro

exp(A)

(10.5)

w h e r e all the coefficients are constant and depend on the material used. By differentiating the above equation, the temperature coefficient B is obtained

B =

dlnR A dT - - T 2

(10.6)

321 which has a negative, parabolic dependence upon temperature. The sensitivity of thermistors varies with temperature, but at ordinary values it is one order of m a g n i t u d e higher than that of platinum resistance sensors. It is important to note that thermistors are heated by the current load, and that the supply should be very well calibrated in view of the limited natural heat dissipation. Thermistor t h e r m o m e t e r s should be c o m p a r e d with a s t a n d a r d thermometer every year, if they are of good quality, or every month if they are of low quality, and re-calibrated because the characteristics of the sensors are not very stable and suffer ageing. The main disadvantage of thermistors is the functional dependence which is characterised by a non-linear resistance versus temperature. Linearisation is mainly obtained using analogue circuit techniques, but also sensor linearisation is possible and has been accomplished p r o d u c i n g linear o u t p u t t h e r m i s t o r assemblies. These consist of two or three thermistors assembled as a single thermistor and of an additional resistor. With an a p p r o p r i a t e choice of the elements, these packages are interchangeable within a stated tolerance. Although standard

thermistors

are

generally

inexpensive,

the

cost

of

linear,

interchangeable, low drift thermistors is elevated. Linear response transducers have the advantage of a simpler electronic circuit or data processing, and have a h o m o g e n e o u s accuracy on the whole range. Linear thermistors in a selected range of t e m p e r a t u r e s are obtained with a suitable combination of two subcomponents:

a thermistor

composite

and

a resistor

set c o m p o s e d

of a

c o m p e n s a t i n g n e t w o r k of two or three precision metal film resistors. Further details on these and other temperature transducers can be found in Schooley (1986), Doebelin (1990), Michalski et al. (1991), Nicholas and White (1994). A c o m m o n method to obtain linearisation of standard thermistors is to use a Wheatstone bridge circuit (Fig.10.1) with the resistance sensor RT(T) which constitutes one arm of the bridge, and measuring in the deflection m o d e (i.e. with the bridge out of balance) the output voltage. This is, in general, a linear function of the b r i d g e excitation E (i.e. the bridge b a t t e r y voltage after stabilisation), but a non linear function of the resistance of the elements R1, R2, R3 and R T(T) of the four arms. W h e n the sensor calibration curve R T(T) is known and expressed with a polynomial regression, the appropriate resistance of

R1, R2 and R3 of the other three arms can be properly calculated and adjusted, so that the exponential curvature of the sensor is compensated by means of the non linearity of the bridge circuit which has been appropriately unbalanced.

322

R1

IMI Fig.10.1 The basic Wheatstone bridge in deflection mode for the case of a thermistor T. The two resistors R2 and R3 are adjustable to set up the bridge to linearise the response ofT, as seen by the meter M. E is the stablised excitation voltage. The m e t e r M,

which measures

the o u t p u t

voltage across the t e r m i n a l s ,

instantaneously follows the variations of the sensor, and with an appropriate choice of R1, R2 and R3, the o u t p u t voltage directly equals the value of the thermistor temperature. O u t p u t accuracy and departure from linearity can be better than 0.1~

Main sources of errors are: instability of the bridge excitation;

c o n d e n s a t i o n or rainfall which forms a shunt of liquid w a t e r b e t w e e n the thermistor leads if these are not well insulated; drift of the thermistor or other resistors of the bridge. For psychrometric measurements, the assembly of two basic Wheatstone bridges for two thermometric sensors T1 and T2, are necessary. It is possible to change from the reading of T1 to T2 or vice versa operating on a commutator. Two adjustable resistors are used to set up the bridge for the thermistor, during the calibration of the device. If the meter has an elevated impedance (as the main part of the electronic meters have), the current across it vanishes and the meter measures the output voltage R1

R(T1)

e(T) = ( R1 + R2- R(T1) + R3

) E.

(10.7)

Both p l a t i n u m resistance sensors and linear thermistor transducers are very small (Fig.10.2), accurate (better than 0.1~

repeatable and reliable, linear or

323 linearisable, interchangeable within 0.1~

and with fast response, e.g. time

constants < 1 s can be found. However, it is advisable to buy one or some tens of sensors and calibrate all together in a calorimetric bath. It is so possible to individuate whose of them give a closer response, so that it is then possible to operate substitutions or match two or more of them with a very similar response. In practice, the precision of 0.1~ is satisfactory in most cases, and matching of the order of +0.01~

can be done without difficulty. Linearised thermistors are much

more sensitive than p l a t i n u m resistance transducers, but also m u c h more expensive.

Fig.10.2 Small thermistors used for fast response in psychrometers: one is free and one is inserted into a hypodermic needle, forming a fast response probe.

Thermocouples Thermocouples are based on the Seebeck effect, i.e. a small thermoelectric current is generated w h e n two different metal wires are put into contact at both ends with their junctions having a different temperature. If one junction is open, a contact electromotive force is generated. The current, or the electromotive force, is in a first approximation proportional to the temperature difference AT between the two junctions. A better approximation is obtained with a MacLaurin expansion with the second power of AT. The electromotive force of some of the most c o m m o n junctions is: iron-constantan: 52 pV/~ pV/~

copper-manganin: 41 pV/~

alumel: 41 p V / ~ pV/~

copper-constantan: 43

manganin-constantan: 41 pV/~

p l a t i n u m - c o n s t a n t a n : 34 p V / ~

chromel-

p l a t i n u m - r h o d i u m : 6.4

The strongest electromotive forces are obtained with the less expensive

324 junctions, and not with the rare metals which are generally used to resist to high temperatures. The materials used for thermocouples should be carefully aged by electrical annealing because the electromotive force is influenced by mechanical deformations. A problem is that the wire it conductive and can transport heat, changing the temperature at the point under investigation. The main advantages they offer is that they have a very low sensitivity to IR radiation and a small time constant, of the order of 1 s. If more than one set of thermocouple junctions is used in series, the electromotive force is increased proportionally to the number of junctions. Another important advantage is that they are very cheap. As thermocouples respond directly to differences of temperature, they are convenient to measure temperature gradients. For this reason they are in principle suitable for measuring the wet bulb depression in psychrometers, as this instrument requires an accuracy better in detecting the temperature difference between two sensors than in knowing the exact value of the dry bulb thermometer. However, the electromotive force generated by the wet bulb depression is very weak. The sensistivity of a thermocouple to temperature changes is much lower than that of a platinum resistance sensor and especially of a thermistor. Thermocouples need a cold reference junction that is usually immersed in melting ice. This fact limits the practical use of these sensors. Another alternative is to compensate the cold junction temperature by using a resistance bridge compensation circuit (WMO No.622, 1986). The change of resistance of the thermocouple with changing ambient temperature creates an out-of-balance bridge potential, compensating for the missing cold junction. A further possibility is to measure with an independent thermometer the reference temperature at one juction of the thermocuple, and then measure with the other juncion the differences in temperature.

Quartz thermometer The sensor is a quartz piezoelectric resonator which is connected to an electronic solid state oscillator. The latter supplies a small amount of power to the resonator which acts as a highly selective filter that holds the oscillation frequency very close to the natural frequency of the resonator. The resonant frequency of the quartz crystal sensor undergoes a change in frequency which depends upon the change in temperature, following a third-order polynomial equation of T. By a proper choice of the cutting planes of the crystal, the

325 coefficients of the second and third order powers of T can be made zero, and in this case the resonant frequency becomes a linear function of the temperature (Michalski et al., 1991). Once the probe has reached the equilibrium with the surrounding fluid, the quartz t h e r m o m e t e r readings are very accurate and may constitute a good reference s t a n d a r d for calibrating other t h e r m o m e t e r s or m a y be used in precision calorimetry. The probe response time is a few seconds in stirred water, and is quite long in still air. However, by counting all the oscillation pulses, it is possible to integrate with a great precision over a time interval: the longer the sampling time, the higher the resolution. For this reason commercially available instruments have options for different sampling intervals and c o r r e s p o n d i n g resolutions, e.g. increasing by 10 the sampling period, the last digit represents a resolution 10 times greater, so that incredibly high resolutions, as far as 10-5~ or 10-6~ can be attained. It should be remembered however, that these readings are accurate only in the case the probe has really reached equilibrium with the fluid, and the temperature is stationary, otherwise the precision is merely illusory and misleading, being only a precise average of the sensor temperature during the sampling time interval. 10.1.4. Screen

The result of a temperature m e a s u r e m e n t is a signal p r o v i d e d by the transducer as a function of the sensor temperature. However, the temperature of the sensor does not necessarily coincide with that of the air or the surface. The thermal equilibrium of the sensor includes not only the conductive heat exchange with the air which comes into contact with the sensor, but also the energy arrived with visible or infrared radiation from remote bodies. In fact, the air is transparent to the visible and to the main part of the infrared spectrum. The incoming radiation is an important source of error, and may cause departures from some tenths to several degrees. Under extreme conditions the difference may reach 25~

A screen is necessary to reflect this income. However, it is never

possible to reflect completely the energy income, or avoid the nocturnal radiative loss. The double louvered screen of standard weather stations may introduce an error of +2.5~

during strong sunshine and calm of wind, and -0.5 on clear, calm

nights (WMO, 1983). Another source of error is rainfall, when the wet screen evaporates and approaches the wet bulb temperature. For outdoor measurements of temperature and humidity, the instruments should be installed inside a shelter to minimise the effects of sunshine, rainfall,

326 and other adverse w e a t h e r situations. In the case of standard meteorological observations, the Stevenson screen is popularly used, i.e. a box m a d e of a low c o n d u c t i v i t y material (generally wood or plastic), painted white inside and outside to reflect radiation, having double louvered walls which enable good ventilation while minimising the effects of radiant heat. The roof is m a d e of two layers of w o o d with an air layer between them and the floor is slatted to permit free air circulation. The door is on the northern side and enables the personnel to observe or do the maintenance of the instruments. These are placed between 1.25 and 2 m above the ground. Meteorological shelters need to be cleaned frequently and repainted every year but this recommendation is often neglected. Several kinds of screen have been designed to house electrical type t e m p e r a t u r e sensors. They are characterised by a single or double, highly reflective shield (mirror or white paint) with natural or forced ventilation. The shield m a y consist of one or two concentric tubes, a single or double d o m e or multiple plates, made of metal, plastic or mirrored glass. The multiple plate non v e n t i l a t e d version is an extension of a m o d e l with acrylic plastic dishes developed by Hadlock et al (1972). In windy, rainy regions, the radiation error is negligible, ventilation is not necessary and the shield m u s t protect the sensor against rainfall arriving from any angle. In sunny, low wind regions, a motor blower which induces a forced ventilation (e.g. 3 m s -s) in the area of the sensor is applied to reduce stagnant air and overheating. For non ventilated shields the overheating error varies with the wind speed, e.g. in a sunny day the overheating of a white thermoplastic multiplate radiation shield is +1.5~

at 1.5 m s -1 wind

speed, +0.7~ at 2 m s -I and +0.4 at 3 m s -l. The best results are obtained with a double wall glass tube, silvered on all interior surfaces, then evacuated and sealed, like a heavy d u t y v a c u u m bottle with open bottom. The cylinder is kept vertical, with the open bottom facing d o w n w a r d s and with a blower located at the upper top which continually forces the ventilation inside. In this case the error is limited within +0.05~ Also indoor measurements need a screen, but in the case that the sensor is n e v e r hit by direct solar b e a m s or spot lamps light, the screen m a y be less sophisticated. Good results are obtained with two methods c o m m o n l y used for radiosondes: (i) a tube is made of white polystyrene foam which is reflective, bad conductor and has a very low thermal capacity; (ii) a tube is built with a very thin foil of a l u m i n i u m , perfectly reflecting on the outer side and blackened on the internal one. In the case of metal shield a lower disturbance is obtained with a double concentric shield and this caution c a n b e used in the absence of forced

327 ventilation. A c o m m o n size is a cylinder with some 10 cm diameter and 20 cm height. The sensor is placed in the middle of the tube and radiosonde ascent provides ventilation; for use in a fixed location a fan can be included on the bottom. When the sensor is located in sites where all the surfaces have a nearly h o m o g e n e o u s t e m p e r a t u r e and there are no important sources of radiative perturbation, there is no need for shields. 10.1.5. Instrument location

The site of a s t a n d a r d

weather

station should be m e t e o r o l o g i c a l l y

representative of the area in which it is located and free from local perturbations generated by trees, buildings, water bodies, air pollution. A plot of level ground, sized 6 by 9 m and covered with short grass is generally used for the installation of meteorological instruments. Meteorological phenomena take place on time and space scales completely different

from

those

of m o n u m e n t s ,

which

are g o v e r n e d

by the

local

microclimate. Differently from standard meteorological or airport observations, it is not possible to state a similar guideline for conservation. In the case of microclimate m e a s u r e m e n t s for the cultural heritage, observations m u s t be made when and where necessary, according to the aim of the survey. However, it might be useful to remember that the air temperature is not the same at all the heights, and that the choice of the height is very important. O u t d o o r the air temperature is essentially governed by the soil temperature: during the night time the soil is coldest and the temperature increases with height; during day the soil is hottest and the temperature decreases with the height. In summertime, in the central part of the day the bare sand may reach 70~

and the air temperature rapidly decreases by 30-40~

in the first 2 meters of

atmosphere. This show h o w the 'air temperature' m a y a p p a r e n t l y change locating the sensor a bit up or down. The essential point is that there does not exist a generic 'air temperature' T, but T is a punctual and instantaneous value of a function which is variable in the space and time coordinates. Also in closed rooms the temperature is not the same at all the heights, but tends to stratify in horizontal layers, the hotter air being trapped below the ceiling and the colder and denser air being closer to the floor, with a difference of the order of 1 or 2~ in usual conditions, but that may reach 20~

or more. Measurements made to

test the horizontal homogeneity of the temperature in one room or in one floor must be all exactly made at the same horizontal level; in the case of alpine churches with hot air heating, where a vertical gradient of some 7 ~

was

328 found (Chapter 1, Fig.1.11), a vertical displacement of 10 cm of the sensor will introduce an apparent change of temperature of 0.7~ When an ambient monitoring can be performed using only one instrument (e.g. a thermohygrograph), it is extremely important to know the representativity of the instrument location, with reference to the whole room or the site. In fact, temperature and humidity vary either temporally and with space, e.g. responding to the solar radiation through glass panes, the opening of doors and windows, the switching on/off of light, or other HVAC systems. Measurements made in points particularly shielded or too much exposed to air currents, or in the proximity of HVAC, or perturbed for the presence of h o t / c o l d water pipes are non representative of the real situation and their interpretation may induce to a wrong management of the ambient conditions. A micro-mapping survey should be made to know the temperature distribution inside a room in order to choose the most representative point for the location of the instrument and especially of the sensors for the control of the room temperature and humidity.

10.1.6. Measuring vertical profiles of air temperature and room atmospheric stability Vertical profiles of air temperature are very important as they constitute a measurement of the atmospheric stability responsible for the dispersion of airborne pollutants and their deposition via inertial impaction. Outside, profiles are measured with tall towers, or mini radio-sondes raised by small spherical balloons (in urban areas a small cluster of balloons is preferred for safety reasons, Fig.10.3) or heavier radio-sondes raised by large tethered balloons, e.g. kytoons (Fig.10.4), shaped as a dirigible with small wings at the back which are inflated by the,wind and stabilise the kytoon by damping the oscillations forced by wind gusts. The gas used in meteorology to blow up balloons is hydrogen, but this gas should be managed by well trained personnel only, because it is very dangerous and risks to explode especially in the presence of electrically charged bodies. helium is safe, but much more expensive and determines a slightly less buoyancy (the mass of helium is twice the mass of a hydrogen molecule). The suggested practice is to fill balloons with a hydrogen and helium mixture popularly used for toys balloons which is cheap, light and non explosive. In urban areas, for the onset of wind, the balloon may reach ground far from the operator and it constitutes a strong attractive for children.

329

Fig.10.3 In urban areas, mini radio-sondes raised by a cluster of small lattice balloons are preferred for safety reasons.

Fig.10.4 Heavier radio-sondes raised by large tethered kytoons, shaped as a dirigible with small wings at the back which are enflated by the wind and stabilize the kytoon.

330

Balloon Wind

Radiosonde Fwt Motor Whinch

/

\

Fig. 10.5 Forces acting on a tethered balloon: Fwd horizontal, very strong, due to the wind drag; Fwt along the wire due to the tension which becomes dominant during the recovering operation and is now tilted, forming an obtuse angle with Fwd; finally, the weak vertical force due to the buoyancy Fb. Meteorological radiosondes and low troposphere radiosondes (resolution 0.1~

1% R H and 0.5 hPa atmospheric pressure) with lattice or neoprene balloons

are made to be launched only once and be lost. However, if the study is limited to the lower part of the planetary boundary layer (PBL), e.g. the nocturnal inversion layer and first kilometre of the diurnal mixed layer, it is also possible to use several times the same radiosonde. The method consists in tethering the balloon, which can be launched and recovered with a nylon fishing wire, 0.7 m m diameter (Camuffo, 1980; 1982). During the ascent the buoyancy force of the balloon turns freely the wire roll; the descent is made winding the fishing wire on the roll by means of an electric motor. This operation is possible only in case of calm or low wind speed. In the case of no wind the forces are only two, opposed along the vertical: Fb, the upward buoyancy and Fwt, the d o w n w a r d traction of the wire. The operation is easily made controlling the d o w n w a r d force. In the presence of wind the balloon is subjected to three forces (Fig.10.5): Fwd horizontal, moderate to strong, due to the wind drag; Fwt along the wire due to the tension which becomes dominant during the recovering operation, and forms an obtuse angle with Fwd; finally, the weak vertical force due to the buoyancy Fb. The resultant of these three forces obliges the balloon to descend

331

slantwise and the wire curvature risks to approach too much, or touch the ground. In u r b a n e n v i r o n m e n t s miniaturised systems are often preferred, but small balloons risk to break for the lattice tension when they are recovered. If two or t h r e e b a l l o o n s are used to diminish the risk of catastrophic b r e a k d o w n and fall, the turbulence generated by the balloons cluster forces violent vibrations and increases the risk of bursting. An effective remedy has found by enveloping the cluster, or the only one balloon, with a light hunting or fishing net, and attach the wire to the net. The surface stress of the lattice is therefore better distributed and the b r e a k d o w n risk reduced. The minisonde attached to a balloon (size: 1 m 3) or a balloon cluster makes possible vertical runs also in city centres, operating in very small gardens and small roof terraces, as we did e.g. in Venice, and the cost is m u c h cheaper than the use of 80 m 3 tethered balloons which need a m u c h larger operating space so that they can be used only in rural environments. Using the same radiosonde several times, the data of each run are taken with the same instrument,

and

are a b s o l u t e l y c o m p a r a b l e , w i t h o u t

the p r o b l e m

of the

intercalibration errors. By reporting the results of each run in a d i a g r a m and drawing

the isolines, vertical time cross sections of the t h e r m o d y n a m i c

properties of the PBL are easily obtained. Fixed towers or portable masts can be used for profiles on a smaller vertical extent. Some 10 m folding masts with a tripod b a s e m e n t are commercially available, but even more easy to use are extensible masts, with the antenna composed of an assemblage of 5 concentric sections with clamp collars to which instrument can be hung. This mast can be extended by p u m p i n g air with a hand pump. Opening the valve and loosening the clamp collars, the mast retracts. Inside buildings, u n d e r non perturbed conditions, the air is near always stratified in horizontal layers, whose density decreases with height. The layers are not horizontal, or the stratification m a y even disappear, w h e n there are sources of m o m e n t u m (air currents) or heat (formation of convective cells). In addition, in m u s e u m s vertical profiles show the difference of t e m p e r a t u r e of the air masses which come into contact with the lower part and the top of a painting or a statue. In m u s e u m s , small portable masts with sensors placed at floor level, 1, 2 and 3 m are in general sufficient, as this height is representative of the air layer where exhibits are exposed. W h e n rooms or churches with i m p o r t a n t d o m e s are too tall for being controlled with a portable mast, and an opening exist on the ceiling, it is possible to let d o w n a rope with sensors and record the temperature and h u m i d i t y profile on that vertical. This method was used several times, e.g. for the Giotto's Chapel,

332 P a d o v a (Camuffo and Schenal, 1982), with thermistors or high resolution radiosondes for the lower troposphere. An easier system, not conditioned by the presence of openings, is to fill with the hydrogen and helium mixture a black tethered meteorological balloon and slowly rise it into the room. As it reaches quickly equilibrium with the surrounding air, by training it with a radiometer, it is possible to know the temperature of the air at various heights, which are determined by means of the tethering wire length. The balloon should be inflated not too much in order to preserve elasticity and reduce vulnerability if a rough surface is touched, and the black colour is preferable to avoid reflected radiation. In order to furnish a well visible target also in tall rooms the size of the balloon might be 2 m in diameter, and for this size 300 g balloons are needed. For non exceptionally tall rooms 100 g balloons are sufficient. This m e t h o d is more attractive than easy. A common sampling time for indoor temperature and humidity is one data acquisition every 10 minutes or less, in order to monitor transient p h e n o m e n a such as room cleaning, w i n d o w s and doors opening for ventilating and so on. Longer intervals (e.g. one acquisition every hour) might not monitor important perturbations, e.g. room cleaning with open windows. In Chapter 7 several criteria have been presented for the measurement of the atmospheric stability. The majority of them take into account that the atmospheric turbulence is determined by two main factors: (i) a vertical temperature gradient generated by the contrast of temperature between air and soil, which in the case of hot soil originates convective mixing and instability; in the opposite case of colder soil, thermal layering (ii)

and stability; the eddies generated by the wind and expressed in terms of wind gustiness,

shear, speed. It is evident that outside the wind plays an important role, but inside it is practically absent, or is substituted by a very modest ventilation or local convective motions. For this reason, inside the thermal factor becomes largely dominant and in general it is sufficient to measure the vertical profile of the air t e m p e r a t u r e with a chain of sensors, or to measure the floor and ceiling temperatures with two fixed radiometers, as it has been previously discussed. However, dealing with a closed environment, several causes of stability and instability must be considered in addition to the floor and ceiling temperatures. Stable conditions are generated when HVAC systems introduce in the room new air with density very different from the ambient air. In the case of hot air, it rises

333

for its buoyancy up to is trapped by the ceiling and diverges, and part of it mixes with the ambient air. The hot air cushion aloft, the cold ambient air in the bottom, and the mixed air at the intermediate levels, determine a thermal layering and atmospheric stability. Similarly, when cold air is introduced, it sinks generating again a thermal layering. In the absence of HVAC, thermal stability is generated only when the floor is colder and the ceiling is warmer and the walls have intermediate temperatures. A cold ceiling generates instability like a warm floor for the symmetric reason; hot walls induce uprising air currents and cold walls descending ones; in general this perturbation is appreciable only close to the walls, but these are often painted, or there are paintings or tapestries. As floor, ceiling and wall temperature anomalies cannot be excluded, the indoor stability is better monitored by an integrated system composed of a vertical chain of air temperature sensors and some fixed radiometers pointing at the floor, the ceiling and the walls. If some ventilation (either natural or forced) exist, a measurement of the air speed should be included. If only one air speed sensor is used, e.g. a hot wire anemometer, the stability can be expressed in terms of the H6gstr6m ratio which considers the ratio between the vertical gradient of t e m p e r a t u r e and the destabilisation effect of the wind kinetic energy, measured in only one point, intermediate between the two points in which the temperature sensors are placed. Vertical temperature gradients might be measured with thermocouples. This kind of sensor simplifies the problem of the perfect intercalibration of sensors, and is theoretically convenient when differential measurements are needed, because the electromotive force which is generated is a function of the t e m p e r a t u r e difference between the two junctions. However, in order to overcome the problem of a weak signal generated by a small t e m p e r a t u r e difference, well calibrated and matched thermistors are generally preferred.

platinum

resistance

sensors

or

10.2. MEASURING SURFACE TEMPERATURE Surface thermometers and radiometers are commonly used to monitor surface temperatures. Thermometers should reach thermodynamic equilibrium with the surface without perturbing it or suffering for other external influences; radiometers do not need time to reach thermal equilibrium, but are sensitive to

334 reflected IR radiation. Both present advantages and problems, as follows. 10.2.1. Contact sensors

Contact sensors have a flat surface which is put into contact with the object to investigate. The equilibrium is reached when, at the interface b e t w e e n the sensor and the m e a s u r a n d surface, the exchange of heat stops; however, also a bad contact m a y led to the same result, leaving sensor and surface at different temperatures. This particularly happens when the surface is rough so that only a few points of the artifact are in contact with the sensor, and the small air pocket w h i c h remains b e t w e e n the artifact surface and the sensor acts as a good insulator. In order to improve the thermal contact, a grease or a gelatine can be smeared on the flat side of the sensor. A commonly used material in industry is silicone grease with included metal p o w d e r to improve the heat transmission. This m e d i u m , however, can not be applied in conservation, as it stains the work of art, and other clean substances should be preferred. Another problem is that the outer side of a contact sensor is exposed to the a t m o s p h e r i c agents, e.g. different air t e m p e r a t u r e and solar radiation. To minimise these perturbing factors this side is isolated but, if it is exposed to direct solar radiation, it needs an extra shield. A further problem is that the presence of the sensor perturbs the surface temperature, especially in the case of a surface which is w a r m e d by the solar radiation. In fact, the skin of the surface that is hit by solar beams becomes hot, but the small area to which the sensor is attached remains shielded and colder. The sensor exchanges heat with the deeper layers below it, in the colder area, and mainly becomes in equilibrium with them, although it receives some heat which converges laterally from the hot lighted surface. Consequently, the surface sensor instead of measuring the skin temperature measures the temperature of a colder, sub-surface layer. This is a problem of representativity of the measurement, not an instrumental error. The opposite occurs during the night time, w h e n the m o n u m e n t looses heat by infrared radiation, except the small area which is in contact with the sensor. Similarly~ ~w h e n the m o n u m e n t is wet and its surface temperature drops to the wet bulb temperature, the area in contact with the sensor is not affected by forced evaporation and a different temperature is found. As always, the variable that is monitored is the sensor temperature and the actual surface t e m p e r a t u r e remains unknown, except for the contact sensor approximation. In steady-state conditions it is assumed that a body is in equilibrium with its

335

s u r r o u n d i n g atmosphere. When a sensor is put into contact with the surface, it alters the radiative balance and the conductive and convective exchanges, so that the t h e r m a l distribution of the b o d y surface is locally altered. The sensor generates a new heat flow from (or to) the surface, and where the thermal contact is not ideal, a thermal contact resistance is introduced. Therefore, it can be concluded that a sensor will always interact with the surface under investigation, so that measurements will be in any case perturbed. W h e n p a s s i n g from the s t e a d y - s t a t e to the d y n a m i c conditions,

the

departure between the actual temperature and the measured value will increase. This is apparently expected w h e n the thermal response of the sensor is slower than the response of the body surface, but in practice this always happens because the presence of the sensor perturbs the heat exchange between the surface and the environment. Only w h e n the radiative balance does not affect too m u c h the surface temperature and the ambient conditions remain stationary for a sufficiently long time, the m e a s u r e m e n t becomes representative of the surface t e m p e r a t u r e . When the radiative gain or loss makes the skin temperature of the body different from the subsurface layer, a possible w a y to monitor the real t e m p e r a t u r e is to leave free the surface and then touch it with the sensor for a very short time. H o w e v e r , the heat capacity of the sensor affects the t e m p e r a t u r e of the few protruding points of the surface in contact w i t h the sensor. For this reason it is necessary to proceed with further steps. The m e t h o d consists in touching the monument

surface w i t h

the sensor in points

different

from that u n d e r

observation in order to bring the sensor to a closer and closer temperature so that the observed point will not be affected by the sensor influence, as follows. When the sensor touches a surface, in a short time it reaches a new equilibrium and its temperature goes closer to the u n k n o w n value under examination. Repeating a n u m b e r of times this operation, a better and better approximation is obtained, with the sensor approaching more and more the undisturbed skin temperature. After some of these m a n u a l operations, w h e n the o u t p u t readings r e m a i n u n c h a n g e d , the asymptotic value is reached, and it is possible to read the t e m p e r a t u r e of the point u n d e r observation m i n i m i s i n g the influence of the sensor. This m e t h o d has been successfully applied several times, e.g. the Aurelian and Trajan columns, Rome (Camuffo and Bernardi, 1993) or Pisa Tower; the drawback is that it needs an operator.

336

10.2.2. Radiometers and remote sensing

Radiometers provide indirect measurements of area temperatures, based on the principle of measuring the IR emission of bodies. In order to reduce the effects of atmospheric absorption of some IR bands due to the presence of water vapour, CO2, 03 and other green-house gases, the 8-14 ~tm window is generally adopted. Radiometers are essentially of two types: those which reproduce the thermal image of the objects and the non-imaging transducers which measure the total power of the IR radiation which reaches the sensor. These measurements have the advantage that they do not physically perturb the surface under investigation and do not cause damage to the works of art to which contact sensor cannot be stuck. They constitute a non-destructive method which is particularly appreciated in the field of works of art. Another important aspect is that they are remote sensing devices, and make possible measurements on ceiling or other surfaces reachable with difficulty, or on moving surfaces. Finally, their output is representative of a more or less large area, being less conditioned by local departures or fluctuations. On the other hand, the measure is affected by: (i) the presence of extraneous reflected IR radiation which constitutes a serious problem for outside measurements during the daytime, (ii) the emissivity of the surface and its Lambertian nature, (iii) suspended aerosol or moisture which adsorb the IR signal. For further details see Wolfe and Zissis (1989), Kondratyev et al. (1992). Imaging instruments (e.g. thermovision based on television sensing systems using electron-beam scanning) are expensive but a thermal image is of immediate understanding for specific problems, showing hot spots, energy loss, cold zones that might possibly be generated by water percolation or other u n k n o w n reasons. They are useful in the building diagnostics, especially when rapid temperature changes and uneven heat transmission put into evidence surface temperature anomalies due to subsurface inhomogeneity. The analysis of the IR image is made with the help of false colours and advanced computer techniques. Non-imaging

instruments

(infrared

thermometers)

are

commonly

employed in field surveys for measuring the temperature of non accessible surfaces. They measure the heating of a sensor placed in the point of convergence of the cone of the flux of IR radiation, whose optical angle is controlled by a diaphragm. The diaphragm is fixed or adjustable; adjustable diaphragms allow the use of the instrument for close or remote monitoring, or for averaging the temperature over a small or wide area. Close position a n d / o r small angles give

337 high resolution and point measurements; long range a n d / o r wide angles give the temperature averaged over a wide area. A cause of error is the diffraction of the collecting radiation at the limiting aperture, which d e p e n d s u p o n I R wavelength and therefore object temperature. A real surface both emits and reflects radiation with a relative intensity which varies from one material to another; the m e a s u r e m e n t is based on the emitted component, but the radiometer (as well as the operator) is unable to distinguish it from the reflected one. The mechanism is also complicated because the reflected radiation from liquid or solid bodies consists of two components: the well k n o w n surface

reflection and the bulk reflection, i.e. the portion of the

radiation which was transmitted into the material, and was reflected by internal backscatter; the latter is independent of the surface condition. The problem in taking reliable m e a s u r e m e n t s especially arises w h e n there are other i m p o r t a n t sources of IR radiation, or the surface under investigation has a low emissivity and a high reflectivity. In this case the measurement is not representative of the body temperature. When a metal or another reflecting surface is investigated, particular care should be placed in order to avoid the IR radiation emitted by the operator, or other bodies, in particular the sun and clouds. If the surface is Lambertian (this approximation is particularly good for a rough surface), the operator influence can be avoided by observing the surface with slant angles. However, for most surfaces the emissivity is dependent upon the angle o~f view and drops near grazing incidence. In this case a nearly n o r m a l incidence is preferred. Radiometric m e a s u r e m e n t s are based on the k n o w l e d g e of the surface emissivity r and the spectral radiance in the band used by the instrument. The simplest case (blackbody) is r = 1 and a known, continuous spectrum; in general, however, the uncertainty about these two characteristics is a source of error. Bodies with the same t e m p e r a t u r e but different emissivity generate different radiometer outputs. An adjustable emissivity control in the instrument permits to correct the output, adapting the transducer to the characteristics of each surface, in order to obtain accurate temperature measurements. However, the emissivity of the object is u n k n o w n . A used method is to cover the surface target with a coating (e.g. soot) or a film with known emissivity in the IR band used for the radiometric

measurement.

H o w e v e r , this m a y alter the b o d y - a t m o s p h e r e

interactions and the surface temperature. The actual value of r can be found empirically,

adjusting

r on the r a d i o m e t e r setting until the true surface

temperature (known by means of a surface thermometer) is indicated.

338 It is necessary to pay attention that the emissivity of a surface may change with time from a value typical of the dry material to a value close to 1 (i.e. surface wet by rainfall or covered w i t h a film of water when the surface temperature is below the dew point), and this happens frequently with outdoor monuments. The emissivity changes during the day with the water content of the surface layer, in the presence of drying-wetting cycles, and with the surface temperature or w i n d s p e e d .

H o w e v e r , surface soiling, particle deposits, efflorescences,

hygroscopicity of surface salts, biopatinas and other factors may substantially alter the b o d y emissivity. The same occurs for the surface reflectivity, and this also changes with the angle of incidence. For instance, the reflectance R from a water surface varies from 2.5% at normal incidence, and becomes R = 8% at 60 ~ 35% at 80 ~ and 97.5% at 90 ~ incidence. As the emissivity is r = 1-R , this factor is very important, as a wet surface observed at small incidence (grazing) angles becomes a pure reflector and the emissivity of the water film which envelops the b o d y vanishes. In such a condition, the only IR radiation which reaches the observer is originated by other extraneous bodies. Another important factor is that the emissivity is a function of the spectral wavelength ~, i.e. r = ~(~), and materials have a more or less deep valley in the spectral emissivity which can fall in the instrument bandwidth, thus changing the a p p a r e n t radiometric temperature. Most organic materials, e.g. w o o d , parchment, have a low emissivity in the visible part of the spectrum, and high in the IR. On the other hand, metals covered with a thin layer of oxide seems very dark, but the oxide becomes transparent at longer wavelength, so that in the IR range the surface becomes reflecting and with low emissivity, typical of a pure metal (Nicholas and White, 1994). Of course, it is convenient to compare radiometric observations with other horhogeneous (i.e. radiometric) measurements, and for this reason a complete set of measurements (e.g. ceiling, floor, walls and murals) should be made with the same type of transducer. The instrument calibration should be verified before and after the use, by pointing the radiometer at a reference surface, which behaves as a perfect black body. A used reference is the free surface of a bucket of water, as in the normal direction r = 0,96 i.e. close to 1. However, care must be taken that the water tends to stratify in layers with different density, and the surface layer is affected by evaporation so that its temperature tends to drop to the wet bulb temperature. As the IR radiation is absorbed in a few micrometers of water, the radiation emitted is originated in the very surface layer which has a temperature

different from the bulk water, where the bulb of the truth

339 thermometer is immersed. The best reference is a blackbody cavity, which has an emissivity which approaches the unity. This can be obtained with a can blackened inside, with the internal size very large and the aperture very small, so that the internal reflections are so many that there is equilibrium inside and an external radiation that penetrates is practically extinguished. If the internal surface of the cavity has gradients in temperature, the blackbody emission is a combination of spectra, and introduces an error in the calibration. In order to be isothermal, the can should be immersed in a mixed liquid with known temperature. Mixing should be made generating turbulence with up and d o w n movements, not with rotation that does not destroy density layering. When the reflectivity of an external radiation is zero, also the emissivity equals the unity. A practical formula which determines the effective value of the emissivity IBeffo f a cylindrical cavity with a small opening is 2

ra s

=

1- (1-ec)

(10.8)

2 ~'c

where ec is the emissivity of the internal surface of the cavity, r a and r c the radius of the aperture and the cavity, respectively (Nicholas and White, 1994). It is useful to know the emissivity of some materials, some of which are reported in Table 10.1, which suggests that e.g. stones or heavily oxidised metals can be measured with a radiometer, but this practice is not r e c o m m e n d e d for polished or slightly oxidised metals or other IR reflecting surfaces. As an example of the characteristics of commercially available instruments, the main technical specification of the IR transducers most widely used for microclimate measurements are: spectral band-pass 8 to 14 pm, field of view from 4 ~ to 20 ~ scale r a n g e - 3 0 ~ to 100~ resolution +0.1~

accuracy +0.5~

repeatability +0.1~

noise effective temperature less than 0.05~

than 1 s, operating e n v i r o n m e n t - 1 0 to 50~

response time less

and R H < 90%. More sophisticated

i n s t r u m e n t s are also available, with accuracy, repeatability and resolution improved by an order of magnitude. They are particularly useful in detecting anomalous

areas

during

transient

conditions.

However,

the

better

the

i n s t r u m e n t characteristics, the more elevated the cost, and the thinner the surface layer that takes advantage of the finer investigation as very small, and short period, temperature changes (i.e. AT ~ +0.01~

are smoothed out in a very

short depth so that only skin, or just sub-skin disturbances can be detected.

340 TABLE 10.1 Emissivity of some materials Material

Emissivity

Material

Emissivity

Water Grass Snow (old-fresh) Clay (dry-wet) Sand (dry-wet) Soil (dry-wet) Lacquer (white-dark) Oil paint Paper (white) Wood (oak) Glass Porcelain, glazed Brick (glazed -red)

0.96 0.90-0.98 0.82-0.99 0.95-0.97 0.84-0.96 0.90-0.98 0.92-0.97 0.87-0.98 0.93 0.90 0.91-0.94 0.92 0.75-0.93

Concrete Plaster (rough coat) Soot on a solid surface

0.92 0.91 0.91-0.94

Asphalt Basalt Dolomite Dunite Feldspar Gypsum Granite Quartz (agate) Silicon sandstone Brass (polished-oxidised) Bronze (polished) Copper (polished-oxidised) Iron (polished-oxidised) Iron rust Lead (polished-oxidised) Steel (polished-oxidised)

0.96 0.90-0.92 0.96 0.89 0.87 0.93 0.81-0.93 0.71 0.91 0.03-0.61 0.1 0.05-0.78 0.21-0.78 0.75 0.05-0.63 0.07-0.79

(Source: Platridge and Platt, 1976; Oke, 1978; Green and Maloney, 1984; Wolfe and Zissis, 1989; Lide, 1990) Comparing

a

radiometer

having

accuracy

+0.5~

with

a

contact

t h e r m o m e t e r h a v i n g the same class, observations with the m a x i m u m d e p a r t u r e of +1~

are expected. However, this is not always true, also excluding errors due

to IR reflection. The reason is that a r a d i o m e t e r and a t h e r m o m e t e r m e a s u r e t e m p e r a t u r e s at different depths below the surface. The radiometer observes the

effective radiation temperature w h i c h is representative of a t e m p e r a t u r e b e l o w the surface at a depth 1/A()~), where A(X) is the spectral absorption coefficient of the material. In absorbing materials, this layer is the skin. On the other hand, to reach e q u i l i b r i u m , a contact t h e r m o m e t e r exchanges heat for a d e e p e r layer, w h o s e extent d e p e n d s on the heat capacity of the sensor and the initial difference of t e m p e r a t u r e , so that the m e a s u r e m e n t is more p r o p e r l y r e p r e s e n t a t i v e of a deeper subsurface layer. This problem arises w h e n there are subsurface gradients, as it always occurs in dynamic conditions, or w h e n the body is irradiated by direct or diffuse solar radiation, or is cooling via IR emission, or is utilising latent heats of e v a p o r a t i o n or condensation. Historic buildings or stone m o n u m e n t s m a y sustain very large t e m p e r a t u r e gradients, as their heat transfer to the a t m o s p h e r e is v e r y low. This m a k e s difficult a c o m p a r i s o n b e t w e e n r a d i o m e t r i c t h e r m o m e t r i c observations.

and

341

C H A P T E R 11

Measuring Humidity

11.1. MEASURING AIR HUMIDITY

11.1.1. Measuring principles Several kinds of instruments, based on different principles, have been devised to measure the a m o u n t of v a p o u r in air. The h y g r o m e t e r s can be grouped in several categories, some of them more, and some less known. (i) H y g r o m e t e r s d e p e n d i n g on the addition or removal of water vapour, e.g. p s y c h r o m e t e r , diffusion h y g r o m e t e r , gravimetric, volumetric and p r e s s u r e methods. The p s y c h r o m e t e r may be considered as a s t a n d a r d for accurate observations; the other methods are of minor interest. (ii) Hygrometers based on sorption methods, e.g. mechanical hygrometers with h u m a n hair or p a r c h m e n t sensors; electric h y g r o m e t e r s with thin film capacitance sensor, or with resistance polymer sensor, or with aluminium oxide, polyelectrolyte, carbon, piezoelectric sensors. The measuring principle may be a mechanical displacement, a change of the electric resistance, capacity or inductance, or a change of vibration frequency. These sensors, and in particular thin film capacitors or resistors are largely used in commercial instruments because of their low cost, high resolution and fast response. The negative aspect is drift, especially after contamination. (iii) H y g r o m e t e r s b a s e d on condensation, e.g. dew point or frost point h y g r o m e t e r s , water equilibrium h y g r o m e t e r s for particular s a t u r a t e d salt solutions. None of them is reliable at low or very low RH and only a few at very e l e v a t e d R H values. All p r e s e n t i m p o r t a n t drift or d e p a r t u r e s after contamination or ageing, or both. For this. reason careful maintenance and frequent calibration are essential. An analysis of all these transducers would be too long, and of limited interest as only few types are recommendable in this field. In the following only

342 the most important types will be commented. For information about other kinds of hygrometric sensors please see Wexler (1965), Meteorological Office (1981), WMO (1983; 1986), Doebelin (1990), Harriman (1990).

11.1.2. Hygrometers Hair hygrometer There is no doubt that the most widespread instrument is the well known hair hygrometer which, since a long time, has served a huge variety of users and is especiallyappreciated for its easy use. It is desirable that the user of this kind of transducer be aware of its errors (typically between 3 and 30%), advantages and limitations (see Davey, 1965, and the above reference books). The response of the sensor is only very little affected by temperature; the hair responds to relative humidity but is also dependent upon mechanical load and surface contamination. The length of the human hair, when the grease has been thoroughly removed, increases by a value ranging from 1.7 to 2.5% when the RH rises from 0 to 100%, and the elongation AL/Lo, where Lo is the dry air length, is approximately proportional to the logarithm of RH, at least for not too dry environments, i.e. for RH>20%, and is usually calculated by means of the equation

AL L--ff= k ln(RH )

(11.1)

where k is a coefficient of proportionality. However, better approximations on the whole range 0 < RH < 100 % for increasing values of RH and hydrated hair are given by the functions:

AL Lo

kl ~/ RH

(11.2)

AL Lo = k2 ln2(1 +RH)

(11.3)

AL Go

=

k 3 ln2(1 +~[RH )

(11.4)

=

k4 ln(1 +RH) ln(1 +qRH )

(11.5)

AL no

343 AL Lo = k5 R H 2 + k6 R H + k7

(11.6)

which give similar results, and the constants depend u p o n the final elongation at saturation; in general 17x10 -4 < kl < 25x10-4; 8x10 -4 --- k2 --- 12x10-4; 30x10 -4 _

~ = cos

exp(- 2_?o)

(12.7)

and finally the variance of the wind fluctuations is obtained: 2

~ 0 - -2 In

<sin 8> sin


(12.8)

so that the coefficient of dispersion can be simply obtained from average values m e a s u r e d with a sine cosine transducer, or c o m p u t i n g these trigonometric functions. 12.2. MEASURING INSIDE AIR MOTIONS In conservation studies the point of view is far from that of the w e a t h e r analysis: the interest is not focused on the unperturbed wind far from obstacles but on its interaction with the m o n u m e n t . On a free site the w i n d speed is a function of time only, v(t), but around a m o n u m e n t it is v(x, y, z, 0;t), as this variable changes point by point on the m o n u m e n t surface for the aerodynamic interactions and depends also upon the attack angle 8. This means that a standard

373 normative on the best m e t h o d of taking m e a s u r e m e n t s cannot be applied and field observations should be m a d e only after a p r e l i m i n a r y analysis of the problem, the site t o p o g r a p h y and m o n u m e n t geometry, in order to determine

why, what, where, when and how to measure. 12.2.1. Hot wire anemometry Observations of: low air speed, turbulence, thin airstream on a developing surface b o u n d a r y layer or thin airstream passing below a closed door, cannot be taken with ordinary mechanical anemometers (e.g. cup or propeller types), due to their elevated inertia and threshold, or for the unbalanced effect on the opposed cups or the i n h o m o g e n e o u s pressure distribution on the blades. Miniature hot wire (or film) a n e m o m e t r y responds (although not completely) to this d e m a n d and is extensively used for its simple use and low cost. The size of the sensor is of the order of one or few m m in length, and the diameter is of the order of 5 ~tm. The hot wire measures airspeeds above 10 cm s -1 and the time constant is of the order of 0.001 s. A lower threshold, i.e. 5 cm s -i, is obtained with a nickel thin film deposited by sputtering on a spherical glass sensor, with a diameter of 3 m m (Dantec, 1996). The relatively larger mass increases the time constant to 0.08 s and the overheating generates a convective motion which interferes with the air m o v e m e n t at low air speeds. This interference determines the lower limit of reliable measurements which is around 3 cm s -1 As a single wire responds to the velocity component perpendicular to it, a variety of probe exists, m o u n t e d either single, or coupled orthogonally in a plane or three-dimensionally, s u s p e n d e d between the tips of a fork-like support, for detecting one, two or three c o m p o n e n t s of the airstream. Some probes are inserted into a cylindrical shield (a tube) in order to m e a s u r e the s t r e a m component along the cylinder axis. However, the edges of the tube disturb the flow field and generate turbulence. It is convenient to remove this shield and insert the bare probe into the airstream, with the wire n o r m a l to the flow direction. The physical principle (DISA, 1976; Doebelin, 1990) is the thermal loss of a heated resistance sensor which is an overheated wire. The heat loss is not only dependent upon the air speed but also upon a number of parameters such as air temperature and pressure. If only the air speed changes, or the influence of the other parameters is compensated through the use of other sensors and suitable electronic units, the o u t p u t gives the air speed. The characteristic transfer function is in first approximation composed of an exponential and a square root function, but the signal can be linearised, so that the processed output is simply

374 proportional to the airspeed. Two different circuits are available for this kind of sensors: the constanttemperature and the constant-current anemometer. The c o n s t a n t - t e m p e r a t u r e type consists of a Wheatstone bridge and a servo amplifier and the sensor acts as active arm of the bridge. The current through the wire is adjusted to keep the wire temperature constant and is a measure of the flow velocity. The constantcurrent type has the sensor powered by a constant current supplied by a generator having high internal resistance in order to be independent of any resistance changes in the bridge. The wire attains a temperature which is in equilibrium with the convective heat loss due to the airstream. The heat generated is the product of the electrical resistance by the square of the current intensity, the wire temperature, and hence the airspeed is measured in terms of the electrical resistance. In practice, the constant-temperature anemometers are preferable and are effectively popular for their easy use, fast response and low cost. 12.2.2. Sonic anemometry The velocity of a sonic wave in a medium is known and depends upon the elastic properties of the medium. When a sonic wave is superimposed upon an air stream, its transmission speed is equal to the sum of the velocity of the sound with respect to the medium, plus the velocity of the medium. Sonic pulses are transmitted

in opposite directions over the same path on each axis of

measurement. The pulses are exchanged between two miniature piezoelectric transducers which are used to alternatively transmit and receive, and the sonic anemometer measures the average value of the speed of propagation of these pulses. The measurement is representative of the average airflow which crosses a cylinder, i.e. the sonic beam having the cross section determined by the transducer size and the path length L equal to the transducers spacing. The space resolution is determined by the transducer size (typically of the order of 1 cm diameter) and the value of L which varies with the model, e.g. 15 cm, 40 cm. However, the higher the space resolution, the greater the perturbation caused by the transducers to the fluid motion. The operating principle (Beaubien and Bisberg, 1968) is that the sound wave transmitted in still, or moving air, introduces a time lag which depends upon the air speed and direction. The first equation which governs the operating principle is the definition of the velocity C of sound which propagates in still air, i.e.

1

C = "~[

T M

(12.9)

375 where 7 is the ratio between the specific heats at constant pressure and volume, and M the molecular mass of the gas. At T - 273K, the speed in the air is 33,145 cm s -1. Therefore, a sonic a n e m o m e t e r is always associated with a precise t h e r m o m e t e r w h o s e m e a s u r e m e n t s are necessary to enter the formulae and compute the sonic velocity. However, also the elevate presence of moisture may cause d e p a r t u r e s to the m e a s u r e m e n t s increasing the sonic speed. As water v a p o u r has a mass noticeably different from the other gases constituting the atmosphere, the following empirical equation holds for humid air

C = 2006.7

e

T (1 + 0.3192~ )

(cm s -1)

(12.10)

w h e r e e is the water v a p o u r pressure and p the atmospheric pressure. The variable vapour pressure is a source of error and the m a x i m u m error is found in s u m m e r ; e.g. at T = 303 K and RH = 70%, e = 30 hPa and this variation is equivalent to 0.3~

shift in air temperature. The error is smaller in the cold

season. When the airstream is moving at the speed u and with an angle 0 with reference to the transducer alignment, the sonic anemometer measures the speed component u cos0 by means of the sonic transit time At which is given by

At =

2L u cos0 u2

(12.11)

ca(I-v)

which is the basic equation for sonic anemometry. The main interest for the sonic anemometer is that it has no threshold and is a totally passive instrument, which does not interfere with the fluid motion, except for the presence of the transducers which can generate turbulence. The experimental array can be composed of only one, two or three axes, each having a pair of aligned transducers, depending upon the n u m b e r of dimensions that should be taken into account. For the above reasons the measurements are not so punctual as with a hot wire, and cannot go close to a surface as a hot wire, but these goals are much better attained with a laser-Doppler anemometer.

12.2.3. Laser-Doppler anemometry The laser Doppler anemometry is based on the well k n o w n principle that a

376 moving source emitting or reflecting a wave generates a frequency shift. A number of different configurations exist, but the mostly used is the differential Doppler, also called fringe mode. The air is transparent to laser light, but a number of reflecting particles introduced in the airflow may diffuse light, introducing a Doppler shift generated by their movement. By crossing two coherent light beams having plane wave fronts (i.e. two laser beams generated by the same source), an interference fringe is generated in the crossing area. The fringe spacing is proportional to the wavelength of the light )v and inversely proportional to the angle 20 between the two beams. A particle moving in the intersection of the two beams will scatter light whose intensity will vary according to the intensity pattern of the light as determined by the brightness of the interference fringe. The frequency of the light scattered by the particles transported by the airflow is characterised by a Doppler shift generated by the velocity of the particles. A photomultiplier detects these variations and the frequency of the resulting signal is determined from the Doppler analysis (Durst et al., 1981). The frequency f of the electric signal generated by a particle moving across the fringe volume with a velocity component u normal to the fringes is u

f=2

sin0 )v

(12.12)

so that for a typical wavelength and 0 = 30 ~ f is of the order of 105 Hz (Doebelin, 1990). The method is more sensitive when the fringe pattern is perpendicular to the airflow, and for this reason the fringe can be rotated to obtain the highest sensitivity (and find the flow direction), or to obtain the two components of the velocity vector in the plane parallel to the surface. This method is very accurate as the interference fringe area can be very small (i.e. with size of the order of a tenth of millimetre) and can be sited very close to the surface, or in contact with the surface, i.e. within the internal boundary layer which forms on the surface. This is the only instrument able to measure air motions very close to a surface and is potentially very useful for s t u d y i n g air-surface interactions and aerodynamic deposition. Another important advantage is that the measure is direct, the flow remaining undisturbed by measurement, without needing the introduction of solid probes or mobile items into the flow. The response is immediate. The negative aspects are substantially three. The first is that the air must be seeded with tracers, i.e. particles that may deposit on the surface, soiling and damaging it. The second is that the introduction of these tracers near the surface

377 perturbs the natural dynamic equilibrium under investigation. Last but not least, these devices are very expensive. 12.2.4. A simple analysis of atmospheric turbulence

Several approaches exist to study the atmospheric turbulence, and several books have been written on this subject, e.g. Sutton (1960), Pasquill (1962, 1974), Lumley and Panofsky (1964), Tennekes and Lumley (1973), C s a n a d y (1980), Vinnichenko et al. (1980), N e w s t a d t et van Dop (1984), Landahl and MolloChristensen (1986), Clifford et al. (1993) and many others exist on the statistical analysis of time series. However, it may be useful to report some notes on a statistical m e t h o d that was originally introduced by Rice (1944; 1945) for the telephone r a n d o m noise and then adapted by some oceanographers (Cartwright and Longuett-Higgins, 1956; Longuett-Higgins 1957; 1962; Kinsman, 1965) to the analysis of the sea waves. The results can be applied to the a t m o s p h e r i c turbulence, as the instrumental records of the instantaneous sea level and the wind speed are very similar: the average sea level is substituted by the mean wind speed and the fluctuating waves by the eddies. Although the theory is quite complex, the application is very simple, and needs only counting the n u m b e r of times the signal crosses the mean level, and the total number of fluctuations. It gives the mean airspeed, average period of eddies, the modes of the gusts and the lulls, the spectral width parameter, the first three even spectral moments. The zero-crossing period is defined as the average period ~:(0) for which a sensor placed at the average sea level (which is a s s u m e d as zero level) is alternatively submersed by waves and then emerged, and is expressed as r(O) = Ti/N(O) where Ti is the observing time interval and N(O) represents the n u m b e r of times that the waves have exceeded the calm sea level. In the same way the

crossing period ~:(r/) is defined as well as the number of crossings N(rl) for any arbitrary level 7/, i.e.:

r(rl) -

Ti

N(O) - "c(O)- N(ll) N(ll)

(12.13)

and the m e a n zero-crossing frequency F(O), or the 7/ level frequency F(rl), are obviously defined as the inverse of ~:(0) and ~:(,/), respectively. To apply this statistical method to our case, some obvious substitutions are required: the eddy turbulence for the waves; the airspeed or wind direction for the sea level; the mode of the instantaneous air velocity or direction for the average sea level. If mo is the zero-order moment, i.e. the standard deviation of the wave

378

height, the second order moment of the spectrum is m2 = mo (2rr f(O)) 2. The plot of the distribution N(rl) versus r/(Fig.12.1) is bell shaped with the m a x i m u m at N(O), and the standard deviation can be graphically obtained by measuring the half of the segment which intercepts the plot of N(r/) at the frequency level "~N(O) = 0.607 N(O). Please note that the maximum at N(O), i.e. the mode, is determined as a first approximation, being conditioned by the choice of the crossing levels, the resolution being the step between two levels. The distribution

N(rl) lies between two limit distributions, i.e. the symmetric Gaussian one 7"/2 N(71) = N(O) exp(-2-~o)

(12.14)

for a wide-band spectrum, i.e. random components, and the asymmetric Rayleigh distribution

N(n) = N(O)

mo

7-/2 exp(-~-G--)

(12.15)

for a narrow-band spectrum, i.e. when the spectrum is sharply peaked around a definite frequency. Cartwright and Longuett-Higgins (1956) found a general analytical expression for the distribution of any shape of spectrum, given by the probability distribution Pr(~) of the maxima between the levels r/and rl + 6r/ 1

~2

co

~2

PF(~) = ~ [ e x p ( - 2 - ~ 2) + ~ql-l;2exp(--~ -) fexp(-~)dx]

(12.16)

-oo

where m = (~/~)~ 1-~2. The transition from the two limit distributions (Gaussian and Rayleigh) is determined by the value of the spectral width parameter ~ which ranges from 0 and 1 and is defined by the 0th, 2nd and 4th order moments, 2 mo m4 - m2 mo m4

(12.17/

The Gaussian distribution is obtained with ~ = 1 and the Rayleigh one with a = 0. The above authors demonstrated that the value of e can be simply determined by counting the number of the zero crossings and the number of maxima Nm which have occurred in the same interval, i.e.

379

0,8

0,6

olml

0,4

r~

0

0,2

0

imP"9

v

9

l

0

,

!

10

'

'

u

30

20

1-

40

Velocity (cm/s) Fig.12.1 Normalised crossing frequency of the velocity levels 0, 2, 4, 6.... c m / s in an internal boundary layer along a wall. The distribution is skew, being slowed down by entertainment of calm air.

0,4 I 0,2

rO

~ t~

-0,2

0

-0,4

-0,6

I 0

.

. . 10

.

. 20

.

. 30

40

Velocity .(cm/s)

Fig.12.2 Plot of the incremental values N(Th) - N(11i-1), i.e. the number of times the speed has exceeded the velocity level rM but not the level rli, plotted versus the airspeed.

380 ~/

N(O)2

~=

1-

(12.18)

2

Nm and in addition the mean frequency of the zero crossings F(O) and the mean frequency of the maxima F(max), are linked with the even moments as follows

lq

F (O) - ~ j ~

mo

lqm4

F (m ax ) = T i - X [ ~

m---2

(12.19)

The graphs of the incremental values N ( r l i ) - N(rli-1), i.e. the number of times the fluctuations (originally: the waves) have exceeded the level r/i-1 but not the level r/i, plotted versus 77 are more or less symmetrical with reference to the origin and are characterised by two peaks, one positive and one negative (Fig.12.2). The intercept between

the line 0 crossings increment

(which

corresponds to the maximum of the crossing frequency) with the plot gives a better approximation of the mode. The peaks provide a useful information about the distribution of the fluctuations which recur most frequently, i.e. the mode of the gusts and the lulls. The method simply requires to count the number of times some arbitrarily chosen

levels of speed

(or some directions) have been crossed by the

instantaneous wind speed (or direction) and the number of maxima of this i n d e p e n d e n t variable during the same observing interval. There are two operational procedures: (i) to measure continually or to sample with a high frequency the variable, and the arbitrary crossing levels can be chosen after the measurement, by subdividing in equal intervals the range of variability of the measured variable; (ii) to select the crossing levels before the measurement, and simply record the number of crossings and the number of maxima. The former method requires to store a huge amount of data and the memory of the recording instrument should have an elevated capacity. The latter requires a special device, or a data acquisition system programmed to this aim; the advantage is that a much more smaller memory capacity is sufficient, and the data processing is much simpler. By the way, this is a further method to measure the time distribution of the wind direction, based on the principle of dividing the compass in a number of equally spaced directions, and counting the number of times these directions have been crossed, which avoids the problem of averaging a r o u n d discontinuity 0-360 ~.

the

381

C H A P T E R 13

Measuring Rainfall and Windborne Droplets

Precipitation is defined as a hydrometeor made up of an aggregate of aqueous particles, liquid or solid, crystallised or amorphous, which fall from a cloud or a group of clouds and reach the ground (WMO, 1966). This definition, which is the most accredited one, includes drizzle, rain, shower, snow, sleet and hail, but does not include dew, rime, hoar frost and mist because: they form for direct condensation or sublimation, they are not associated with a cloud and, finally, they do not fall. However, these latter h y d r o m e t e o r s are s o m e t i m e s found included, as e.g. (WMO, 1983) or are called occult precipitation. The first obvious, but never sufficiently remembered consideration, is that precipitation is not h o m o g e n e o u s l y distributed in time and space, but is a variable amount of water or ice which falls as a consequence of the type of cloud, its past and present history (which determines the droplets or ice crystals size), the cloud vertical development, transit speed and path. C u m u l u s clouds develop vertically, with strong convective currents in the interior, which make faster the growth of droplets or hail, and in this case the precipitation occurs abruptly and violently, forming patches which displace with the cloud passage and w i n d transport. On the other hand, stratus clouds spread horizontally, are rather u n i f o r m and s u p p l y droplets more regularly, with a m o r e h o m o g e n e o u s distribution in time and space. A rain gauge sited below the centre of a cumulus cloud w h e n it is passing, or one collecting rainfall w h e n the w i n d aloft drops, will m e a s u r e a precipitation a m o u n t m u c h greater than other gauges sited in different places nearby, so that rainfall can vary significantly over distances of a few kilometres or less. The same occurs for the passage of fronts. With stratus clouds the departures are much smaller and measurements are representative of a more general phenomenon.

382 13.1. METEOROLOGICAL PRECIPITATION MEASUREMENTS Although weather data are not directly useful to evaluate the total a m o u n t of water fallen on monuments, they are in any case representative of the climate in which m o n u m e n t live, and constitute an environmental information that is useful in u n d e r s t a n d i n g the causes of the m o n u m e n t decay in their natural context. In meteorology, precipitation gauges (UK Meteorological Office, 1981; WMO, 1983; 1984; 1986; 1994) are used to monitor the precipitation that has fallen in a given time interval or to monitor the instantaneous rate of fall. The gauges are m a d e of a collecting receiver in the form of a funnel, with a horizontal circular aperture of known size, and the collected water is then measured in one of the following ways. (i) The tipping bucket rain recorder is based on a bucket divided into two equal compartments,

mounted

on a spindle in the m i d d l e

(Fig.13.1). The two

water inlet pipe

tipping bucket

l!iii

i

iil

i iii iiiiii

@ @

................I iiii iii iii i i~ii ii iiiii

Fig.13.1 Mechanism of the tilting bucket rain gauge transducer

c o m p a r t m e n t s are symmetrically disposed so that the bucket is balanced in unstable equilibrium about a horizontal axis. In its normal position it rests against one of the two stops, which prevent it tipping over completely. Rain

383

flowing out of the funnel falls into the uppermost compartment and w h e n has filled it, the centre of gravity is displaced and the bucket overbalances, tips and empties

the precipitation.

This p i v o t i n g m o v e m e n t

displaces the second

compartment in the uppermost position in which it receives the rainwater until is filled and tips discharging the water in it. Counting with a magnetic reedswitch the n u m b e r of tips, it is possible to know the amount of water that has been collected and discharged. Of course, this method does n o t s u p p l y a continuous record, but only proceeds by counting increments of precipitation with resolution 0.2 mm. An error is due for the rainfall lost during the time employed in the tipping motion, which m a y be appreciable during heavy precipitation. The time of the very beginning and ending of drizzle or very light rain cannot be accurately measured. N o t w i t h s t a n d i n g these limits, this kind of gauge is the most convenient and popularly used as it is the most suitable for recording rainfall automatically with an electronic datalogger. (ii) The

float type, w i t h a u t o m a t i c s i p h o n i n g a r r a n g e m e n t s , r e c o r d s the

movement of a light float in a float chamber which receives the rain collected by the funnel. The float is connected with a pen which registers on a d r u m or a strip chart the level, i.e. the rainfall amount. When the chamber is full of water a natural, or a tilting siphon system, makes water to flow out of the float chamber until the level falls to the zero level; the siphoning action ceases, and the cycle starts again. Some rainfall is lost during the siphoning action. This type is used in the British Isles. (iii) The

weighing type operates by recording the total Weight of the water

collected in a can. The weight of the collecting can is recorded continuously, either by means of a spring mechanism (e.g. the can descends against the compression of a spring) or the displacement of a weight. This system is accurate and continuous, but normally it has no provisions for emptying itself. This is used in cold climates where it is desired to record either snow, hail or rainfall, and the solid precipitation does not have to be melted in order to be measured. In mild or w a r m climates evaporation losses are reduced by adding oil to form a film 1 m m thick over the free water surface in the container. In regions where snow or sleet are common, automatic measurements are possible only with gauges provided of a heater to melt ice and measure it as liquid water. If the funnel is not heated, surface condensation such as dew, hoar frost, rime and also fog can provide some water, which is neither rainfall, nor

384 strictly precipitation, but the gauge interprets and measures it in the same way. In the case of hail, the bouncing of hailstones on the funnel causes an important loss of ice precipitated. A number of other causes of error can be found in measuring precipitation, and the minor ones are: evaporation, which may contribute for-1% of the total and may be also more important in hot regions; droplets adhesion, i.e. -0.5%; colour, -0.5%; funnel inclination, -0.5%; large droplets splashing, +1%, with a total error -1.5%. However, the main error is due to exposure, and this error cannot be exactly evaluated. The World Meteorological Organisation suggests that the amount of precipitation collected by a rain gauge may be 3 to 30% less than the actual precipitation reaching the ground (WMO, 1981) and the UK Meteorological Office suggests a much wider range, i.e. 5 to 80% less (UK Meteorological Office, 1981). Such a large error is especially made when the wind is strong, and the droplets tend to be transported parallel to the horizontal plane of the funnel mouth and the turbulence generated near the funnel may disperse the droplets loosing them and decreasing the collection efficiency. This effect becomes especially important with snow-flakes that are more sensitive to wind transport and departures in the wind field. In order to minimise the effect on the wind field disturbance, the site should be chosen accurately, which should be actually representative of the area u n d e r consideration. To this aim the gauge should be free of o v e r h a n g i n g obstructions. If the area has vegetation, this should be uniformly distributed, and the funnel should be at the average height of the vegetation. Some appropriate fence structures could be installed to homogenise the area characteristics. Wind shields are suggested around the gauge orifice to shelter it from high wind speed parallel to the mouth, generating an appropriate turbulence. These shields are built with metal strips forming a truncated cone with the vertex pointing at the base of the gauge, but leaving some free space between strip and strip. The gauge should be at a sufficient distance from obstacles to avoid local eddies. In order to avoid interferences with the wind field, the m i n i m u m distance allowable for obstructions should be twice their height. Sometimes a greater distance is suggested, e.g. the WMO report No 266 (1984) suggests four times their height. Observation of precipitation using radar or satellite remote sensing are used for general weather purposes, but are not of interest for m o n u m e n t preservation, except in the case of forecast and alert for large and important storm systems. However, also in this case the attention is focused in the civil protection, and not in undertaking safety measures for monuments.

385 13.2. PRECIPITATION ON MONUMENTS Standard weather m e a s u r e m e n t s are taken in the u n d i s t u r b e d ,

open

country, and the precipitation is not the same than in towns. Towns are generally warmer and the higher temperature generates convective motions which favour the formation of clouds; the turbulence induced by buildings exchanges momentum and mixing with the effect of slowing down the wind field, making colder the lower layers and transporting heat aloft; traffic and domestic heating are a source of pollutants which act as condensation nuclei. All these factors contribute to increase the frequency of precipitation, and in particular with showers and thunderstorms over the large towns. It has been demonstrated that the precipitation over towns is greater than over the surrounding country, and that the average frequency of precipitation in working days is higher than during Saturday and Sunday (Landsberg, 1981). Weather measurements are not much representative of the rainfall which has fallen on monuments located in the centre of a town, where the situation is complicated by the shielding of buildings, the street channelling of the wind field, or m a n y other aerodynamic disturbances. In addition, metal domes or also wetted buildings may generate strong anomalies in the electric field in the presence of charged clouds. As the water molecule is a dipole, droplets may be charged by induction and attracted. In addition, all the droplets and aerosols formed by raindrop splashing are charged and their behaviour depends upon the wind drag, gravity force and electric field. Weather measurements are representative of the undisturbed rainfall. On monuments, the rainfall intensity is relevant because intense rainfall is more effective in washing the surface and in causing erosion. This situation totally changes in windward and leeward surfaces. The airflow and the electric field may reduce the precipitation in one place and increase it in another. Weather observations

are representative

of the water fallen into a

horizontal circular aperture, whereas monuments mainly have a vertical extent, and the number of raindrops intercepted by the monument varies with the wind speed, direction and local aerodynamic disturbance. For this reason vertical collectors are sometimes used in proximity of a monument surface, and they are representative only of the rainfall that hits a vertical surface having their particular orientation in the specific point where they are located. No normative exists for these methods or other similar experiments. Another possibility is to collect the water flowing down the monument and

386 measure it, if the m o n u m e n t is not constituted of a porous material which absorbs water. In any case the run-off is sometimes collected in order to perform chemical analyses on leached ions and dissolved stone. A third method, based on standard instruments, is to collect precipitation on the horizontal plane with a recording rain gauge and associate the measurement with the wind speed and direction. As the trajectory of a falling raindrop is determined by the combined action of the falling velocity (Fig.13.2) and wind drag, the impact on a vertical surface can be calculated once the droplet diameter and the wind speed are known. Unfortunately, there are not easy methods to measure the droplet diameter, and only approximate evaluations can be made with a crude estimate of the drop diameter and the other variables.

10 or3

8

-~ 6 @

4 2 ,

0

!

1

,

i

2

,

!

3

'

!

'

4

i

5

|

!

,

6

7

Drop Diameter (mm)

Fig.13.2 Terminal velocity of free falling droplets. (Source: Houghton, 1985)

However, even in the case of a successful tentative of knowing the rainfall which crosses a vertical plane, this result can be hardly applied to the actual case of a true surface, although with a very simple geometry, e.g. the facade of a building. In fact, in the case of a calculation of raindrops crossing a vertical plane, there is no interference between the chosen area and the wind; in the actual case of a building surface, the wind field is perturbed by the architectural shape and, consequently, the horizontal drag changes as well as the resulting path of raindrops. For instance, the top part of the building is hit by raindrops that have been dragged till the last few seconds by a wind stream that is passed nearly

387 undisturbed above the obstacle; the lower part is hit by droplets that in the last part of their path have been dragged by an air stream travelling not against the surface, but parallel to it, so that the droplets are deviated laterally and dispersed, and those which reach the surface for their inertia are only a very small fraction. This is the reason w h y the upper side of buildings is generally washed out better than the lower one (Fig.13.3). In the case of a m o n u m e n t the situation is also worse, as the more complex shape and all the local changes in the surface relief, orientation and so on make extremely difficult to evaluate the interactions with raindrops and run-off.

Fig.13.3 The efficiency of windborne droplets in washing the top of monuments is evident at the Colosseum, Rome. The upper part is washed out by rainfall, whereas in the intermediate and lower part, dust and soot accumulate.

The run-off on historical buildings was measured in several occasions and in a number of ways, either collecting directly running water into a funnel placed under an edge, or building simple devices to this aim. For instance, Leysen et al. (1989) placed longitudinally against the wall of the Mechelen Cathedral a plastic cylinder with a longitudinal slit 3 cm wide, with the lower edge firmly fixed against the wall. The running water was collected into the cylinder and flowed through a hole in the bottom and a tube, arriving into a plastic bottle to be taken

388 away and analysed in the laboratory. The same authors used also gutters pressed against the wall to collect water running off the cathedral walls, i.e. 'runoff water' and 'washout water' with different content of eroded material, arriving at a r o u g h estimate of the annual material loss and surface recession rate.

13.3. WET AND DRY DEPOSITION SAMPLERS It is evident that m o n u m e n t s react with the chemical substances which deposit on them and not with the gases and particles which are simply suspended in the atmosphere. Most gases and aerosols may remain in the a t m o s p h e r e because they have a very low deposition rate, so that a measurement in the air is useful for studies on health (in fact lungs p u m p and filter air with s u s p e n d e d pollution), but not for m o n u m e n t decay. For this reason, the ! so called wet-anddry deposition sampler has been invented to measure, separately, the acid rain and the airborne particles which deposit on a horizontal surface d u r i n g dry periods. Some slightly different devices have been invented (e.g. Georgii and Pankrath, 1982; Munn and Rodhe, 1985), but the most widespread type consist in two equal buckets, made of glass, plastic (e.g. PVC, polyethylene), stainless steel or other non reactive materials, one to collect dry deposition and one for the wet one, with only one lid, which is alternatively displaced over the dry or the wet bucket, driven by a rainfall sensor. The rainfall sensor is constituted of a resistance sensor with several parallel unshielded metal resistors which are t r a n s f o r m e d in a short circuit by rainwater; another c o m m o n sensor is a capacitive one, where absorbed water changes the dielectric capacity in a condenser; another system is to interrupt an IR beam emitted by a diode, but several other possibilities exist. After a week, or another chosen time interval, it is possible to pick up the two buckets and analyse separately the content of the dry bucket, i.e. dust and particles, and the acid rain collected in the wet one. This device is obviously located in an open area, far from obstacles or pollution sources. The collection vessels are equipped with an external metal ring with needles, or crossed wires, in order to avoid that birds can land and stay on the funnel edge and contaminate the sample with their droppings. This crude device has been largely used in the last two decades, but presents several problems, as follows. Although the lid is over the wet bucket during the sunshine, the bucket becomes hot and some water evaporates, changing the p H of the wet sample. In addition, condensation nuclei, dust (especially Saharan dust

389

in Europe) or other solid particles fallen with the rainfall may eventually dissolve and buffer the solution changing the pH and the ionic composition. Real-time measurements automatically carried out during the precipitation event are preferable (Camuffo et al., 1984; 1988; Camuffo, 1990). Also biological life, especially algae, may develop in the rainwater perturbing the chemical equilibrium. The w e t / d r y sensor which displaces the lid is not very fast and is provided of a selected lag to confirm the signal and avoid false alarms; therefore the dry bucket receives the very first rain droplets, which often are the most polluted ones. A problem is that the d r y / w e t sensor may respond also to dew, frost and fog, inappropriately opening the cover of the wet bucket and collecting there, for many hours, especially during the night-time, the dry deposition. It is not clear what the dry bucket collects. Substantially, it gather in the bottom all the coarse particles which deposit via gravitational settling, and in the outer and inner surface it attracts the charged particles that are driven by the electric field generated by the bucket when it is hit by solar radiation or is rubbed by the wind friction. In sunny days the bucket is always heated by solar radiation; it becomes hot and thermophoresis tends to w e a k l y counteract the other deposition mechanisms. For this reason the bucket interacts with the suspended particles with a variable selective action on the deposition mechanisms. In any case, the dry deposit which is collected with this method is in some way representative of the coarse and giant particles, i.e. the so called dustfall, which accumulates on the upward horizontal surface of monument and is mainly composed of soot, dust, pollens, fibres). This is very different from the measurement of the suspended particulate matter performed with high-volume samplers which are composed of filter, motor blower and flow meter. The latter measurement practically samples all the suspended particles which are larger than the average aerodynamic size of the filter pores, independently these particles will later deposit or not. A simpler, earlier version of the wet-and-dry deposition sampler is the so called bulk precipitation sampler constituted of only one funnel and precipitation collector which remains uncovered for the whole sampling period, collecting whatever is depositing, either in the dry or the wet phase. This instrument is intended to monitor the deposit which forms on a monument, or a plant, irrespective of approximation being without hot climates or

the distinction between the dry or the wet phase. However, the is very crude and the representativity uncertain. In addition, automatic cover, the evaporation loss may be very important in dry periods. Likethe dry collector of the wet-and-dry sampler, the

390 bulk sampler m a y be contaminated by local dust, which m a y significantly alter the

pH.

Although this method had some success in the past, the data are vague

and difficult to interpret. This kind of information is very difficult to obtain, and f u r t h e r research is n e e d e d monitoring.

to devise a reliable i n s t r u m e n t for a u t o m a t i c

391

References CHAPTER 1

1.1. Theory and general applications Maunder, W.J., 1994: Dictionary of Global Climate Change. UCL Press, London, 257 pp. Michalski, L., Eckersdorf, K. and McGee, J., 1991: Temperature Measurement. Wiley, New York, 514 pp. Porges, F., 1995: HVAC Engineer's Handbook. Butterworth Heinemann, Oxford, 278 pp. Rosenhow, W.M., Hartnett, J.P., and Ganic', E.N., 1985: Handbook of Heat Transfer Applications, Mc Graw-Hill, New York. Saint-Gobain, 1977: Manuale Tecnico del Vetro. Fabbrica Pisana, Milano, 331 pp. Touloukian Y.S. and DeWitt D.P., 1972: Thermal Radiative Properties of Nonmetallic Solids. Thermophysical Properties of Matter, Vol.8. IFI/Plenum, New York.

1.2. Applications to conservation Benoist, L., 1960: Musdes et Musdologie. Presses Universitaires de France, Paris, 128 pp. Bernardi, A., Camuffo, D., Del Monte, M., and Sabbioni, C., 1985: Microclimate and Weathering of an Historical Building: the Ducal Palace in Urbino. Science Total Environment, 46, 243-260. Bernardi, A. and Camuffo, D., 1995a: Uffizi Gallery in Florence: a Comparison between two Different Air Conditioning Systems. Science and Technology for Cultural Heritage 4,2, 1122. Bernardi, A. and Camuffo, D., 1995b: Microclimate in the Chiericati Palace Municipal Museum, Vicenza. Museum Management and Curatorship, 14, 5-18. Camuffo, D., 1981: Hot-Horse Anemometry. Atmospheric Environment, 15, 1767. Camuffo, D., 1983: Indoor Dynamic Climatology: Investigations on the Interactions between Walls and Indoor Environment. Atmospheric Environment, 17, 1803-1809. Camuffo, D., 1986: Deterioration Processes of Historical Buildings, pp. 189-221 in: T. Schneider (ed.): Acidification and its Policy Implications, Elsevier, Amsterdam. Camuffo, D., 1991: Environment and Microclimate; pp. 37-50 in: N. Baer, C. Sabbioni and A. Sors (ed.s): Science Technology and European Cultural Heritage Butterworth, Oxford. Camuffo, D., 1994: Effects of Air Pollution on Historic Buildings and Monuments. Scientific Basis for Conservation: Case Studies in the Deterioration of Stone Monuments in Italy. European Cultural Heritage Newsletter on Research, 8,1, 7-15. Camuffo, D. and Bernardi, A., 1986: Dinamica del microclima e scambi termoigrometrici tra pareti e atmosfera interna nella Cappella Sistina. Bollettino dei Monumenti, Musei e Gallerie Pontificie, 6, 211-257. Camuffo, D. and Bernardi, A., 1988: Microclimate and Interactions between Atmosphere and the Orvieto Cathedral. Science Total Environment, 68, 1-10. Camuffo, D. and Bernardi, A., 1991a: The microclimate of Leonardo's "Last Supper"; joint edition European Cultural Heritage Newsletter on Research, and Bollettino Geofisico, special issue, 14, 3, 1-123. Camuffo, D. and Bernardi, A., 1991b: Indoor and Outdoor Microclimate: the Trajan Column and Sistine Chapel; pp. 295-305 in: N. Baer, C. Sabbioni and A. Sors (editors): Science Technology and European Cultural Heritage Butterworth, Oxford. Camuffo, D. and Bernardi, A., 1993: Microclimatic Factors affecting the Trajan Column. Science Total Environment, 128, 227-255. Camuffo, D. and Bernardi, A., 1995a: The Microclimate of the Sistine Chapel, Joint edition European Cultural Heritage Newsletter on Research, 9, 7-32 and Bollettino Geofisico, 18 (2) 7-32.

392 Camuffo, D. and Bernardi, A., 1995b: Study of the Microclimate of the Giant Hall of the Da Carrara's Royal Palace, Padova. Studies in Conservation, 40, 237-249. Camuffo, D. and Bernardi, A., 1996: Deposition of Urban Pollution on the Ara Pacis, Rome. Science Total Environment, 189/190, 235-245. Camuffo, D. and Bernardi, A., 1997: Controlling the Microclimate and the Particulate Matter inside the Historic Anatomic Theatre, Padova. Museum Management and Curatorship, 15, 285-298. Camuffo, D. and Schenal, P., 1982: Microclima all'interno della Cappella degli Scrovegni: scambi termodinamici tra gli affreschi e l'ambiente, pp. 107-209 in: Ministero dei Beni Culturali ed Ambientali: Giotto a Padova, special issue of Bollettino d'Arte, Poligrafico dello Stato, Rome. Camuffo, D., Sturaro, G. Valentino, A., Gattolin, M., Enzi, S., and Bernardi, A., 1996: Analisi del Microclima e delle interazioni ambiente-manufatto per la conservazione della Torre di Pisa. Report to Consorzio della Torre di Pisa, Pisa. Camuffo, D., Vincenzi, S. and Pilan, L., 1984: A First-Order Analysis of the Heat Wave in the Soil. Water, Air and Soil Pollution, 23, 441-454. De Guichen, G., 1984: Climate in Museums. ICCROM, Rome. Jamiolkowski, M., 1995: Leaning Tower of Pisa - Description of the Behaviour, pp. 203-226 in: F. Zezza (ed.): The Conservation Project: Knowledge of the Functional Elements for the Planning of the Interventions and Geotechnical Aspects of the Protection. Community of Mediterranean Universities, Adda, Bari. Jenkins, K.A. and Smith, B.J., 1990: Daytime Rock Surface Temperature Variability and Its Implications for Mechanical Rock Weathering: Tenerife, Canary Islands. Catena, 17, 449-459. Michalski, S., 1993: Relative Humidity: a Discussion of Correct/Incorrect Values. ICOM Committeee for Conservation,, 336.C. Padfield, T., 1994: Role of Standards and Guidelines, pp. 191-199 in W.E. Krumbein, P. Brimblecombe, D.E. Cosgrove and S. Stainforth (ed.s): Durability and Change, Wiley, New York, 307 pp. Smith, B.J., 1978: The Origin and Geomorphic Implications of Cliff Foot Recesses and Tafoni on Limestone Hamadas in the Northwest Sahara. Z. Geomorph. N.F. 22 (1), 21-43. Veniale, F., 1995: Minerali costituenti le rocce: processi e sequenze di alterazione, pp. 11- 32 in: R.A. Lef6vre (ed.): La pietra dei monumenti nel suo ambiente fisico. Istituto Poligrafico e Zecca dello Stato, Rome. Warscheid, T. and Krumbein, W.E., 1996: Biodeterioration of Inorganic Nonmetallic Materials - General Aspects and Selected Cases, pp. 273-295 in: E. Heitz, W. Sand and H.C. Flemming (ed.s): Microbiatly Induced Corrosion of Materials. Springer Verlag, New York. Warke, P.A. and Smith, B.J., 1994: Short Term Rock Temperature Fluctuations under Simulated Hot Desert Conditions: Some Preliminary Data, pp. 57-70 in: D.A. Robinson and R.B.G. Williams (ed.s): Rock Weathering and Landform Evolution, Wiley, New York. CHAPTER 2

2.1. Theory and general applications Fermi, E., 1958: Termodinamica. Boringhieri, Torino, 179 pp. Giordano, G., 1993: Tecnica delle costruzioni in legno. Hoepli, Milano, 826 pp. Jones, D.A., 1996: Principles and prevention of Corrosion. Prentice Hall, Upper Saddle River, N.J., 572 pp. Plank, M., 1926: Treatise on Thermodynamics, Dover, New York, 297 pp. Summit, R. and Slicker, A., 1980: Handbook of Material Science, Vol. IV: Wood. CRC Press, Boca Raton, Florida, 459 pp.

393

2.2. Applications to conservation Bernardi, A. and Camuffo, D., 1995: Uffizi Gallery in Florence: a Comparison between two Different Air Conditioning Systems. Science and Technology for Cultural Heritage 4,2, 1122. Coped6, M., 1991: La carta e il suo degrado. Nardini, Florence, 165 pp. Laurenzi Tabasso, M. and Marabelli, M., 1992: II degrado dei monumenti in Roma in rapporto all'inquinamento atmosferico. Betagamma, Viterbo, 169 pp. Massari, G., 1959: Risanamento igienico dei locali umidi. Hoepli, Milan, 437 pp. Massari, G., 1971: Batiments humides et insalubres - Pratique de leur assainissement. Eyrolles, Paris, 526 pp. Massari, G., 1977: Humidity in monuments. ICCROM, Rome, 47 pp. Newton, R. and Davison, S., 1989: Conservation of Glass. Butterworths, London, 322 pp. Padfield, T., 1994: Role of Standards and Guidelines, pp. 191-199 in W.E. Krumbein, P. Brimblecombe, D.E. Cosgrove and S. Stainforth (ed.s): Durability and Change, Wiley, New York, 307 pp. Richardson, B.A., 1993: Wood Preservation. E & FN Spon (Chapman & Hall), London, 226 PP. Thomson, G., 1986: The Museum Environment. Butterworths, London, 293 pp. Warscheid, T. and Kuroczkin, J., 1997: Biodeterioration of Stones, in Studies in Museology, Biodeterioration of Cultural Properties, ed. R.J. Koestler and A.E. Charola. ButterworthHeinemann, London, in press.

2.3. Books consulted for the definitions of the meteorological variables in this and the next chapter Harrison, L.P., 1965: Fundamental Concepts and Definitions Relating to Humidity, pp. 3-69 in: A. Wexler (editor): Humidity and Moisture, Measurement and Control in Science and Industry, Vol 3: Fundamentals and Standards. Rehinold, New York. Huschke, R.E., 1959: Glossary of Meteorology. American Meteorological Society, Boston, 638 PP. List, R.J., 1971: Smithsonian Meteorological Tables. Smithsonian Institution, Washington DC, 527 pp. Parker, S.P., 1988: Meteorology Source Book. McGraw-Hill, New York, 304 pp. Saucier, W.J., 1989: Principles of Meteorological Analysis, Dover, New York, 438 pp. UK Meteorological Office, 1991: Meteorological Glossary. HMSO, London, 335 pp. World Meteorological Organization, 1966: International Meteorological Vocabulary. WMO N.182, Geneva, 276 pp. World Meteorological Organization, 1987: International Cloud Atlas, Vol.II. WMO, Geneva, 212 pp. CHAPTER 3

3.1. Theory and general applications Goody, R., 1995: Principles of Atmospheric Physics and Chemistry. Oxford University, New York, 324 pp. Kasahara, A., 1974: Various Vertical Coordinate Systems Used for Numerical Weather Prediction. Monthly Weather Review, 102, 509-522.

3.2 Further reading Belinski, V.A., 1948: Dynamic Meteorology. Ogiz, Moscow, 591 pp. Brutsaert, W.H., 1982: Evaporation in the Atmosphere. Reidel, Dordrecht, 299 pp. Byers, H.R., 1974-General Meteorology, McGraw-Hill, New York, 461 pp.

394 Haltiner, G.J. and Martin, F.L., 1957: Dynamical and Physical Meteorology. McGraw-Hill, New York, 454 pp. Houghton, D.D., 1985: Handbook of Applied Meteorology. Wiley, New York, 1461 pp. Iribarne, J.V. and Godson, W.L., 1981: Atmospheric Thermodynamics. Reidel, Dordrecht, 259 PP. Matveev, L.T., 1967: Physics of the Atmosphere. Israel Program for Scientific Translations, Jerusalem, 699 pp. Petterssen, S., 1956: Weather Analysis and Forecasting, Vol.II. McGraw-Hill, New York, 265 PP. CHAPTER 4

4.1. Theory and general applications Andrews, J.E., Brimblecombe, P., Jickells, T.D. and Liss, P.S., 1996: An Introduction to Environmental Chemistry. Blackwell, Oxford, 209 pp. Born, M., 1952: Atomic Physics. Blackie & Son, London, 437 pp. Einstein, A., 1905: Ueber einen die Erzegung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt, Annalen der Physik, 17, 132-148. Kondratyev, Ya, 1969: Radiation in the Atmosphere. Academic Press, New York, 912 pp. Robinson, N., 1966: Solar Radiation, Elsevier, Amsterdam, 347 pp. Varshneya, A.K., 1994: Fundamentals of Inorganic Glasses. Academic Press, Boston, 570 pp.

4.2. Applications to conservation Bernardi, A. and Vincenzi, S., 1994: Diurnal Variation of Solar Radiation on Differently Orientated Surfaces of Monuments. Nuovo Cimento 17C (4), 431-442. Camuffo, D. and Bernardi, A., 1991: The microclimate of Leonardo's "Last Supper"; joint edition European Cultural Heritage Newsletter on Research, and Bollettino Geofisico, special issue, 14 (3), 1-123. Camuffo, D. and Bernardi, A., 1986: Dinamica del microclima e scambi termoigrometrici tra pareti e atmosfera interna nella Cappella Sistina. Bollettino dei Monumenti, Musei e Gallerie Pontificie, 6, 211-257. Ortega-Calvo, J.J., Hernandez-Marine, M. and Saiz-Jimenez, C., 1991: Biodeterioration of Building Materials by Cyanobacteria and Algae. International Biodeterioration 28, 165186. Vittori, O. and Mestitz, A., 1975: Artistic Purposes of some Features of Corrosion on the Golden Horses of Venice. Burlington Magazine, 864 (98), 132-139. Warscheid, T. and Kuroczkin, J., 1997: Biodeterioration of Stones, in: R.J. Koestler and A.E. Charola (ed.s): Studies in Museology, Biodeterioration of Cultural Properties. ButtherworthHeinemann, Oxford (in print). Wypych, G., 1995: Handbook of Material Weathering. Chem Tec, Toronto, 564 pp.

4.3. Further reading Liou, K.N., 1980: An Introduction to Atmospheric Radiation. Academic Press, San Diego, 392 PP. Liou, K.N., 1992: Radiation and Cloud Processes in the Atmosphere. Oxford University Press, New York, 487 pp. List, R.J., 1971: Smithsonian Meteorological Tables. Smithsonian Institution, Washington DC, 527 pp. Platridge, G.W. and Platt, C.M.R., 1976: Radiative Processes in Meteorology and Climatology. Elsevier, Amsterdam, 318 pp.

395 CHAPTER 5

5.1. Theory and general applications Adamson, A. W., 1986: A Textbook of Physical Chemistry, Academic Press, San Diego 972 pp. Brunauer, S., 1945: The Adsorption of Gases and Vapors. Princeton University Press, Princeton, 511 pp. Byers, H.R., 1959: General Meteorology. McGraw-Hill, New York, 461 pp. Byers, H.R., 1965: Elements of Cloud Physics. University of Chicago Press, Chicago, 191 pp. Camuffo, D., 1984: Condensation-Evaporation Cycles in Pore and Capillary Systems According to the Kelvin Model. Water, Air and Soil Pollution, 21, 151-159. Clifford, J., 1981: Properties of Water in Capillary and Thin Films, in F. Franks (ed.): Water, a Comprehensive Treatise, Vol.5, Water in Disperse Systems. Plenum, New York, 366 pp. Everett, D.H., 1961: The Thermodynamics of Frost Damage to Porous Solids. Trans. Faraday Soc., 57, 1541-1551. Fagerlund, G., 1973: Determinations of Pore-Size Distribution from Freezing Point Depression, Materiaux et Constructions, 6, 215-225. Gregg, S.J. and Sing, K.S.W., 1967: Adsorption, Surface Area and Porosity, Academic Press, London, 371 pp. Iribarne, J.V. and Godson, W.L., 1986: Atmospheric Thermodynamics. Reidel, Dordrecht, 259 PP. Kikoin, A. and Kikoin, I., 1978: Molecular Physics, Mir, Moscow, 480 pp. Madonna, L.A., Sciulli, C.M., Canjar, L.N. and Pound, G.M., 1961: Low Temperature Cloud Chamner Studies on Water Vapour, Proc. Phys. Soc. 78, 1218-1222. Mason, B.J., 1951: Spontaneous Condensation of Water vapour in Expansion Chamber Experiments, Proc. Phys. Soc. B64, 773-779. Mason, B.J., 1971: The Physics of Clouds, Clarendon Press, Oxford, 671 pp. Matveev, L.T., 1984: Cloud Dynamics, Reidel, Dordrecht, 340 pp. Matveev, A.N., 1985: Molecular Physics, Mir, Moscow, 448 pp. Mikhail, R.S. and Robens, E., 1983: Microstructure and Thermal Analysis of Solid Surfaces, Wiley, New York, 496 pp. Pruppacher, H.R. and Klett, J.D., 1980: Microphysics of Clouds and Precipitation. Reidel, Dordrecht, 714 pp. Sedunov, Yu.S., 1974: Physics of Drop Formation in the Atmosphere, Wiley, New York, 234 pp. Sivuchin, D.V., 1986: Corso di Fisica Generale, Vol.2, Mir, Moscow, 583 pp. Thomson, W. (Lord Kelvin), 1870: On the Equilibrium of Vapour at a Curved Surface of Liquid. Proc. Roy. Soc. Edinburgh, 7, 63-69. Weast, R.C., 1985 CRC Handbook of Chemistry and Physics 1985-86, 66th ed., CRC Press, Boca Raton, Florida, pp.D213-D214. Wright, H.L., 1936: The Size of Atmospheric Nuclei: Some Deductions from Measurements of the Number of Charged and Uncharged Nuclei at Kew Observatory. Proc. Phys. Soc. 48, 675-699. Young, K.C., 1993: MicrophysicaI Processes in Clouds. Oxford University Press, New York, 427 PP.

5.2. Applications to conservation Biscontin, G., Driussi, G., Maravelaki, P. and Zendri, E., 1993: Physico-Chemical Investigations of Stone Architectonic Surfaces in Venice: the Scuola Grande dei Carmini; pp. 125-136 in G. Biscontin and L. Graziano (ed.s): Conservation of Architectural Surfaces: Stones and Wall Covering. I1 Cardo, Venice. Camuffo, D., 1988: Surface Moisture and Conservation. European Cultural Heritage Newsletter on Research, 2,5, 6-10.

396 De Quervain, F., 1967: Technische Gesteinskunde. 2 Aufl. Min. Geotechn. Reihe, Bd 1, Birkh~iuser Verlag, Basel. DIN 66131, 1973: Bestimmung der spezifischen Oberfl~iche von Festoffen durch Gasadsorption nach Brunauer, Emmett und Teller (BET), Grundlagen. Fitzner, B., 1994: Porosity Properties and Weathering Behaviour of Natural Stones, pp. 43-54 in F. Zezza (ed.): Stone Material in Monuments: Diagnosis and Conservation, 2nd International Corurse on Monument Conservation, Adda, Bari, 222 pp. Ginell, W.S., 1994: The Nature of Changes Caused by Physical Factors, pp. 81-94 in W.E. Krumbein, P. Brimblecombe, D.E. Cosgrove and S. Stainforth (ed.s): Durability and Change, Wiley, New York, 307 pp. Graedel, T.E., 1994: Mechanisms of Chemical Change in Metals Exposed to the Atmosphere, pp. 95-105 in W.E. Krumbein, P. Brimblecombe, D.E. Cosgrove and S. Stainforth (ed.s): Durability and Change, Wiley, New York, 307 pp. Klopfer, H., 1985: Feuchte, in Lutz et al., Lehrbuch der Bauphysik; 265-434 and 628-635 (Lit.). Teubner, Stuttgart. Jeannette, D., 1997: Structures de porosit6, m6canismes de transfert des solution et principales alt6rations des monuments, pp. 49-77 in: R.A. Lef6vre (ed.): La pietra dei monumenti in ambiente fisico e culturale, European University Centre for Cultural Heritage, Ravello. Laurenzi Tabasso, M. and Marabelli, M., 1992: II degrado dei monumenti a Roma in rapporto all'inquinamento atmosferico. Betagamma, Viterbo, 169 pp. Torraca, G., 1981: Porous Building Materials. ICCROM, Rome. 141 pp. Torraca, G., 1994: Physical Condition. A Primary Factor in the Durability of Stone, pp. 52-57 in F. Zezza (ed.): Stone Material in Monuments: Diagnosis and Conservation, 2nd International Corurse on Monument Conservation, Adda, Bari, 222 pp. Waller, R., 1992: Temperature- and Humidity-Sensitive Mineralogical and Petrological Specimens, pp. 25-50 in F.M. Howie (ed.): The Care and Conservation of Geological Material: Minerals, Rocks, Meteorites and Lunar Finds. Butterworth Heinemann, Oxford. Warscheid, T., Becker, T.W., Braams, J., Gehrmann, C., Krumbein, W.E. and Petersen, K., 1993: Studies on the Temporal Development of Microbial Infection of Different Types of Sedimentary Rocks and Its Effects on the Alteration of the Physico-Chemical Properties in Building Materials, pp. 303-310 in M.J. Thiel (ed.): Proceedings of the International RILEM/UNESCO Congress "Conservation of Stone and Other Materials" Vol.l: Causes of Disorders and Diagnosis, E&FN Spon, London. Wendler, E., 1997: New Materials and Approaches for Conservation, pp. 181-196 in N.S. Baer and R. Snethlage (ed.s):Saving Our Architectural Heritage: The Conservation of Historic Stoine Structures. Wiley, Chichester. Winkler, E.M., 1986: A Durability Index for Stone. Bull. Assoc. Engin. Geol. 23, 344-347. CHAPTER 6

6.1. Theory and general applications Adamson, A. W., 1986: A Textbook of Physical Chemistry, Academic Press, San Diego 972 pp. Blanchard, D.C. and Woodcock, A.H., 1980: The Production, Concentration, and Vertical Distribution of the Sea-Salt Aerosol, pp. 330-347 in T.J. Kneip and P.J. Lioy (Eds.): Aerosols: Anthropogenic and Natural, Sources and Transport, Annals of the New York Academy of Sciences, Vol. 338, New York, 618 pp. Brimblecombe, P., 1987: The Big Smoke. Methuen, London, 185 pp. Brimblecombe, P., 1992: History. of Atmospheric Acidity, pp. 267-304 in M. Radojevic and R.M. Harrison (Eds.): Atmospheric Acidity, Elsevier, London. Brimblecombe, P., 1995: History of Air Pollution, pp. 1-18 in H.B. Singh (Ed.): Composition, Chemistry and Climate of the Atmosphere. Van Nostrand Rehinold, New York.

397 Camuffo, D., 1984: Condensation-Evaporation Cycles in Pore and Capillary Systems According to the Kelvin Model. Water, Air and Soil Pollution, 21, 151-159. Camuffo, D., 1990: Acidic Precipitation Research in Italy, pp 229-265 in: A.H.M. Bresser and W. Salomons (eds): Acidic Precipitation Vol.5, Springer Verlag, New York. Camuffo, D. and Enzi, S., 1995: Impact of Clouds of Volcanic Aerosols in Italy in the past Centuries. Natural Hazards, 11, 135-161. Dullen, F.A.L., 1979: Porous Media. Fluid Transport and Structure. Academic Press, New York. 396 pp. Gordon, J. and MacDonald, F., 1953: Anhydrite-Gypsum Equilibrium Relations. American Journal of Science, 251, 884-898. Kireev, V., 1977: Physical Chemistry. Mir, Moscow, 572 pp. Price, C. and Brimblecombe, P., 1994: Preventing Salt Damage in Porous Materials, pp.90-93 in Proc. Preventive Conservation, Ottawa. Prodi, F. and Fea, G., 1979: A Case of Transport and Deposition of Saharan Dust over the Italian Peninsula and Southern Europe. J. Geoph. Res. 84, 6951-6960. 6.2. Applications to conservation Arnold, A., 1983: Determination of Mineral salts from Monuments. Studies in Conservation, 29, 129-138. Arnold, A. and Zehnder, K., 1990: Salt Weathering on Monuments. pp. 31-58 in F. Zezza (ed.): The Conservation of Monuments in the Mediterranean Basin. Grafo, Bari. Arnold, A. and Zehnder, K., 1991: Monitoring Wall Paintings Affected by Soluble Salts, pp. 103-135 in S. Cather (ed.): The Conservation od Wall Paintings, Paul Getty TrUst, Thien Wah Press, Singapore. Beadecker, P.A. and Reddy, M.M., 1993: The Erosion of Carbonate Stone by Acid Rain. Journal Chemical Education, 70 (3), 104-108. Becker, T.W., Krumbein, W.E., Warscheid, T. and Resende, M.A., 1994: Investigations into Microbiology, pp. 147-190, in H.K. Bianchi (ed.): IDEAS - Investigations into Devices against Environmental Attack on Stones. GKSS-Forschungszentrum, Geesthacht (F.R.G.). Bernardi, A., Camuffo, D., Del Monte, M. and Sabbioni, C., 1985: Microclimate and Weathering of a Historical Building: the Ducal Palace in Urbino, Science Total Environment, 46, 243-260. Camuffo, D., 1984: The Influence of Run-Off in Weathering of Monuments. Atmospheric Environment, 18, 2273-2275. Camuffo, D., 1986: Deterioration Processes of Historical Monuments, pp. 189-221 in: T. Schneider (ed.): Acidification and its Policy Implication, Elsevier, Amsterdam. Camuffo, D., 1991a: Aspetti microfisici delle precipitazioni acide in relazione al degrado dei monumenti, pp 339-350 in L. Morselli (ed.): Deposizioni acide, i precursori, l'interazione con l'ambiente e i materiati, Maggioli Editore, Rimini. Camuffo, D., 1991b: Environment and Microclimate; pp. 37-50 in: N.S. Baer, C. Sabbioni and A.I. Sors (ed.): Science, Technology and European Cultural Heritage, ButterworthHeinemann, London. Camuffo, D., 1992: Acid Rain and Deterioration of Monuments: How Old Is the Phenomenon? Atmospheric Environment, 26B, 241-247. Camuffo, D., 1994: Aspetti meteorologici e microclimatici nel degrado dei materiali lapidei. Accademia Nazionale dei Lincei, Contributi del Centro Linceo Interdisciplinare ~Beniamino Segre~, 88, 9-27. Camuffo, D., 1995: Physical Weathering of Stones. Science Total Environment, 167, 1-14. Camuffo, D., Del Monte, M. and Ongaro, A., 1984: The pH of Atmospheric Precipitation in Venice, Related to both the Dynamics of Precipitation Events and the Weathering of Monuments. Science Total Environment, 40, 125-139. Camuffo, D., Del Monte, M. and Sabbioni, C., 1987: Influenza delle precipitazioni e della condensazione sul degrado superficiale dei monumenti in marmo e calcare, pp 15-36 in:

398 Ministero dei Beni Culturali ed Ambientali: "Materiali Lapidei", special issue of Bollettino

d'Arte, Poligrafico dello Stato, Rome. Camuffo, D., Del Monte, M., Sabbioni, C. and Vittori, O., 1982: Wetting, Deterioration and Visual Features of Stone Surfaces in an Urban Area. Atmospheric Environment, 16, 2253-2259. Camuffo, D. and Valcher, S., 1986: A Dew Point Signaller for Conservation of Works of Art. Environmental Monitoring and Assessment, 6, 165-170. Del Monte, M. and Sabbioni, C., 1980: Authigenic Dolomite on Marble Surface. Nature, 228, 350-351. Del Monte, M. and Sabbioni, C., 1984a: Morphology and Mineralogy of Fly Ash from a CoalFlueded Power Plant. Arch. Met. Geoph. Bioclim., 35, 93-104. Del Monte, M., Marcazzan, G.M., Sabbioni, C. and Ventura, A., 1984b: Morphological, Physical and Chemical Characterisation of Particles Emitted by a Coal-Fired Power Plant. J. Aerosol Sci. 15, 325-327. Gummerson, R.J., Hall, C. and Hoff, W.D., 1980: Water Movement in Porous Building Materials - II Hydraulic Suction and Sorptivity of Brick and Other Masonry Materials. Building and Environment, 15, 101-108. Hall, C., 1981: Water Movement in Porous Building Materials - IV The Initial Surface Absorption and the Sorptivity. Building and Environment, 16, 201-207. Padfield, T., 1995-97: An Introduction to the Physics of the Museum Environment. Natural Museum, Danmark, published in the website http://www.natmus.min.dk/cons/tp. Sabbioni, C., Zappia, G., Gobbi, G. and Pauri, M.G., 1993: Deterioration of Ancient and Modern Buildings Materials Due to Environmental Factors, pp. 235-242 in: C.A. Brebbia and R.J.B Frewer (ed.s): Structural Repair and Maintenance of Historical Buildings. Computational Mechanics Publications, Southampton. Saiz-Jimenez, C., 1995: Microbial Melanins in Stone Monuments. Science Total Environment 167, 273-286. Warscheid, T. and Kuroczkin, J., 1997: Biodeterioration of Stones, in: R.J. Koestler and A.E. Charola (ed.s): Studies in Museology, Biodeterioration of Cultural Properties. ButtherworthHeinemann, London. (in print). Warscheid, T., Oelting., M. and Krumbein, W.E., 1991: Physico-Chemical Aspects of Biodeterioration Processes on Rocks with Special Regard to Organic Pollution. International Biodeterioration 28, 37-48. Winkler, E.M., 1994: Stone in Architecture. Springer Verlag, Berlin, 313 pp. Wittenburg, C., 1994: Trokene Schadgas- und Partkeldeposition auf vershiedenen Sandsteinvariet~iten unter besonderer Ber~icksichtigung atmosph~irischer Einftut~gr6t~en. PhD Thesis, Hamburg. CHAPTER 7

7.1. Theory and general applications Anfossi, D., Bacci, P., Giraud, C., Longhetto, A. and Piano, A., 1976: Meteorological Surveys at La Spezia Site. In A. Longhetto (ed.): Atmospheric Pollution, Elsevier, Amsterdam, 531-54. Berlyland, M.E., 1991: Prediction and Regulation of Air Pollution. Kluwer, Dordrecht, 312 PP. Brimblecombe, P., 1987: The Big Smoke, Methuen, London, 185 pp. Brown, R.A., 1991: Fluid Mechanics of the Atmosphere, Academic Press, San Diego, 486 PP. Camuffo, D., 1980: Fog and Related Diffusion Potential at Venice: Two Case Studies. Boundary Layer Meteorology, 18, 453-471. Camuffo, D., 1981b: Fluctuations in Wind Direction at Venice, Related to the Origin of the Air Masses. Atmospheric Environment, 15, 1543-1551.

399 Camuffo, D., 1984: Anlysis of the series of precipitation at Padova, Italy, Climatic Change, 6, pp.57-77. Camuffo, D., 1990: Clima e uomo. Garzanti, Milano, 207 pp. Camuffo, D. and Bernardi, A., 1982: The Diurnal Trend in Surface Mixing Ratio at Padova, Italy. Boundary Layer Meteorology, 22, 273-282. Camuffo, D. and Bernardi, A., 1982: An Observational Study of Heat Fluxes and their Relationships with Net Radiation. Boundary Layer Meteorology, 23, 359-368. Camuffo, D., Bernardi, A. and Bacci, P., 1982: Computing the Flux of Moisture from Net Radiation and Soil Wetness. Boundary Layer Meteorology, 22, 503-510. Camuffo, D. and Zardini, F., 1996: Controlling the Homogeneity of a Long Meteorological Series: the Series of Padova (1725-today), 12 pp. in: Subba Rao (editor): Applications of Time Seriesfor Meteorology and Astronomy, Chapman & Hall, London (in print). Cayan, D.R. and Douglas, A.V., 1984: Urban Influences on Surface Temperatures in Southwestern United States during Recent Decades. J. Clim. Appl. Meteorol., 23, 1520-1530. Deacon, E.L., 1949: Vertical Diffusion in the Lowest Layers of the Atmosphere. Quart J. Roy. Meteor. Soc., 75, 89-103. Dobbins, R.A., 1979: Atmospheric Motion and Air Pollution. Wiley, New York, 323 pp. Echols, W.T. and Wagner, N.K., 1972: Sourface Roughness and Internal Boundary Layer near a Coastline. J. Appl. Meteor., 11, 658-662. Elliot, W.P., 1958: The Growth of the Atmospheric Internal Boundary Layer. Trans. Amer. Geophys. Union, 39, 1948-1954. Gifford, F.A., 1961: Uses of Routine Meteorological Observations for Estimations of Atmospheric Dispersion. Nuclear Safety, 2, 47-51. Gifford, F.A., 1976: Turbulent Diffusion Typing Schemes: a Review. Nuclear Safety, 17, 68-86. H6gstr6m, U., 1964: An Experimental Study on Atmospheric Diffusion. Tellus, 16 (2), 205-251. Jones, P.D., Raper, S.C.B., Bradley, R.S., Diaz, H.F., Kelly, P.M. and Wigley, T.M.L., 1986: Northern Hemisphere Surface Air Temperature Variations: 1851-1984. J. Climate Appl. Meteorol., 25, 161-179. Landsberg, H.E., 1981: The Urban Climate. Academic Press, New York, 275 pp. Lee, D.O., 1992: Urban Warming? - An Analysis of Recent Trends in London's Heat Island. Weather, 47 (2), 50-56. Lumley, J.L. and Panofsky, H.A., 1964: The Structure of Atmospheric Turbulence. Interscience, New York, 239 pp. Mc Elroy, J.L., 1969: A Comparative Study of Urban and Rural Diffusion. J. Appl. Meteor., 8, 19-31. Mc Vehil, G.E., 1964: Wind and Temperature Profiles near the Ground in Stable Stratification. Quart. J.Roy. Meteor. Soc., 90, 136-146. Monin, A.S. and Obukov, A.M., 1953: Dimensionless Characteristics of Turbulence in the Layer of Atmosphere near the Ground. Doklady Akademii Nauk SSSR, 93, 257-267. Munn, R.E., 1966: Descriptive Micrometeorology, Academic Press, New York, 245 pp. Munn, R.E. and Rodhe, H., 1985: Compendium of Meteorology Vol.II, Part 6 - Air Chemistry and Air Pollution Meteorology. World Meteorological Organisation, WMO No.364, Geneva, 209 pp. Panofsky, H.A. and Townsend, A.A., 1964: Change of Terrain Roughness and the Wind Profile. Quart. J. Roy. Meteor. Soc., 90, 147-155. Pasquill, F., 1961: The Estimation of the Dispersion of Windborne Material. Meteorological Magazine, 90, 33-49. Pasquill, F., 1962: Atmospheric Diffusion, first ed., Van Nostrand, London, 297 pp. Pasquill, F., 1974: Atmospheric Diffusion, second ed., Wiley, New York, 429 pp. Plate, E.J., 1982: Engineering Meteorology. Elsevier, Amsterdam, 740 pp.

400

Richardson, L.F., 1920: Some Measurements of Atmospheric Turbulence. Phil. Trans. Roy. Soc., London, Ser A, 221, 1-28. Schlicting, H., 1955: Boundary Layer Theory, NewYork, Mc Graw-Hill, 535 pp. Simiu, E. and Scanlan, R.H., 1986: Wind Effects on Structures. Wiley, New York, 589 pp. Singer, I.A. and Smith, M.E., 1953: Relation of Gustiness to Other Meteorological Parameters. Journal of Meteorol., 10, 121-126. Smith, F.B., 1972: A Schema for Estimating the Vertical Dispersion of a Plume from a Source near Ground Level. In NATO/CCMS Proceedings of the 3rd Meeting of the Expert Panel on air pollution modeling, Tech. Report N. 14, XVII, 1-14. Smith, M., 1970: Recommended Guidefor the Prediction of the Dispersion of Airborne Effluents. American Soc. Mechanical Engineers, New York. 85 pp. Sutton, O.G., 1947: The Theoretical Distribution of Airborne Pollution from Factory Chimneys. Quart. J. Roy. Meteor. Soc., 73, 426-436. Turner, D.B., 1964: A Diffusion Model for an Urban Area. J. Appl. Meteor., 3 (1), 83-91 Van Der Hoven, I., 1967: Atmospheric Transport and Diffusion at Coastal Sites. Nuclear Safety, 490-499.

7.2. Applications to conservation Camuffo, D., 1981a: Hot-Horse Anemometry. Atmospheric Environment, 15, 1767. Camuffo, D., 1993: Reconstructing the Climate and the Air Pollution of Ancient Rome During the Life of the Trajan Column. Science Total Environ. 128, 205-226. Camuffo, D. and Bernardi, A., 1993: Microclimatic Factors affecting the Trajan Column. Science Total Environ., 128, 227-255. Camuffo, D., Vincenzi, S. and Pilan, L., 1984: A First-Order Analysis of the Heat Wave in the Soil. Water, Air Soil Pollution, 23, 441-454. Camuffo, D. and Vincenzi, S., 1985: Computing the Energy Balance of a Statue of Bronze: the San Marco's Horses as a Case Study. Science Total Environ., 44, 147158. CHAPTER 8

8.1. Theory and general applications Bagnold, R.A., 1941: The Physics of Blown Sand and Desert Dunes, Chapman and Hall, London (3rd ed.1984). Barndorff-Nielsen, O.E. and Willetts, B.B., 1991: Aeolian Grain Transport, 1: Mechanics, 2: The Erosional Environment. Acta Mechanica Supplementums 1 and 2, SpringerVerlag, Wien. Bouma, P.J., 1947: Physical Aspects of Colour. Philips Gloeilampenfabrieken, Eindhoven, 312 pp. Buffle, J. and Van Leeuwen, H.P., 1992: Environmental Particles. Lewis, Boca Ration, Vol.I: 554 p., Vol.II: 426 pp. Cadle, R., 1965: Particle Size, Theory and Industrial Applications. Reinhold, New York, 158 PP. Caporaloni, M., Tampieri, F., Trombetti, F. and Vittori, O., 1975: Transfer of Particles in Nonisotropic Air Turbulence, J. Atmos. Sciences, 32, 565-568. Chandrasekhar, S., 1943: Stochastics Problems in Physics and Astronomy. Rev. Modern Phys., 15 (1), 2-89. Einstein, A., 1905: Uber die von der molekularischen Theorie der W~irme gefordete Bewegung, von in ruhenden Fltissigkeiten suspendierten Teilchen. Ann. d. Physik 17, 549-560. This and other related papers have been translated and reprinted in A. Einstein, 1956: Investigations on the Theory of the Brownian Movement, edited with notes by R. Ftirth, Dover, New York, 119 pp.

401 Epstein, P.S., 1924: On the Resistance Experienced by Spheres in their Motion through Gases. Phys. Rev. 23, 710-733. Fletcher, B., 1976: The Incipient Motion of Granular Materials. J. Phys. D: Appl. Phys., 9, 2471-2478. Friedlander, S.K., 1977: Smoke, Dust and Haze. Wiley, New York, 317 pp. Gillette, D., 1980: Major Contributions of Natural Primary Continental Aerosols: Source Mechanisms, pp. 348-358 in T.J. Kneip and J. Lioy (ed.s): Aerosols: Anthropogenic and Natural, Sources and Transport. New York Academy of Sciences, New York, 618 PP. Goldsmith, P., Delafield, H.J. and Cox, L.C., 1963: The Role of Diffusiophoresis in the Scavenging of Radioactive Particles from the Atmosphere. Q. J. R. Met. Soc. 89, 43. Hidy, G.M., 1984: Aerosols, an Industrial and Environmental Science. Academic Press, San Diego, 774 pp. Hidy, G.M. and Brock, J.R., 1970: The Dynamics of Aerocolloidal Systems. Pergamon, Oxford Hidy, G.M. and Brock, J.R., 1972: Topics in Current Aerosol Research. Pergamon, Oxford, 384 pp. Hicks, S.B.B., 1982: Wet and Dry Surface Deposition of Air Pollutants and their Modeling, pp. 183-196 in: N.S. Baer (ed.): Conservation of Historic Stone Buildings and Monuments, National Academy Press, Washington D.C., 365 pp. Hinds, W.C., 1982: Aerosol Technology: Properties, Behavior, and Measurement of Airborne Particles. Wiley, New York, 424 pp. Isachenko, V.P., Osipova, V.A. and Sukomel, A.S., 1977: Heat Transfer. Mir, Moscow. Landsberg, G.S., 1979: Ottica, Vol.2 MIR, Moscow, 478 pp. Ming Chen Wang and Uhlenbeck, G.E., 1945: On the Theory of the Brownian Motion II. Rev. Modern Phys., 17 (2/3), 323-341. Nazaroff, W.W. and Cass, G.R., 1987: Particle Deposition from a Natural Convection Flow onto a Vertical Isothermal Plate, J. Aerosol Science, 18, 445-455. Phenix, A. and Burnstaock, A., 1990: The Deposition of Dirt: a Review of Literature, pp. 11-18 in S. Hckney et al. (eds.): Dirt and Pictures Separated, the U.K. Institute for Conservation, Belton, England, 56 pp. Prodi, F. and Tampieri, F., 1982: The Removal of Particulate Matter from the Atmosphere: the Physical Mechanisms. Pageoph, 120, 286-325. Pruppacher, H.R. and Klett, J.D., 1980: Microphysics of Clouds and Precipitation, Reidel, Dordrecht, 714 pp. Pye, K., 1987: Aeolian Dust and Dust Deposits. Academic Press, London, 334 pp. Schlichting, H., 1979: Boundary-Layer Theory. McGraw-Hill, New York, 817 pp. Sehmel, G., 1980: Particle and Gas Deposition: a Review. Atmospheric Environment, 14, 983-1011. Seinfeld, J.H., 1986: Atmospheric Chemistry and Physics of Air Pollution. Wiley, New York, 738 pp. Slinn, W.G.N. and Hales, J.M., 1970: Phoretic Processes in Scavenging, Atomic Energy Commission Symp. Ser. 22, U.S. Atomic Energy Committee, pp. 411-422. Smith, B.J. and McAlister, J.J., 1986: Observations on the Occurrence and Origins of Salt Weathering Phenomena near Lake Magadi, Southern Kenia. Z. Geomorph. N.F., 30 (4), 445-460. Talbot, L., Cheng, R.K., Schefer, R.W. and Willis, D.R., 1980: Thermophoresis of Particles in a Heated Boundary Layer. J. Fluid Mechanics 1014, 737-758. Tritton, D.J., 1988: Physical Fluid Dynamics. Clarendon, Oxford, 519 pp. Vercelli, F., 1933: L'Aria. UTET, Torino, 711 pp. Vittori, O., 1973: Scavenging of Atmospheric Particles by Growing Ice Crystals: a Contribution to a Proposed Mechanism. J. Atmos. Sci., 30 (2), 321-324. Vittori, O., 1984: Transient Stefan Flow and Thermophoresis around an Evaporating Droplet. Nuovo Cimento, 7C (2), 254-269

402

W a l d m a n n , L. and Schmitt, K.H., 1966: Thermophoresis and Diffusophoresis of Aerosols in C.N. Davies (ed.): Aerosol Science, Academic, New York. Wax, N., 1954: Noise and Stochastic Processes, Dover, New York, 345 pp. Zimon, A., 1982: Adhesion of Dust and Powder, Consultants Bureau - Plenum, New York.

8.2. Applications to conservation Ashurst, J. and Ashurst, N., 1989: Practical Building Conservation. Volume 1 Stone Masonry. Gower, Aldershot (U.K.), 100 pp. Camuffo, D., 1987: L'illuminazione negli ambienti di conservazione; First part Rassegna Beni Culturati, 3 (4), 40-44 and second part, item 3 (6), 38-40. Camuffo, D., 1990: Ambiente e monumenti: microclimatologia di ambienti chiusi e c o n s e r v a z i o n e di opere pittoriche. Accademia Nazionale Lincei, Giornata dell'Ambiente, 82, 157-166. Camuffo, D., 1991: Wall Temperature and Soiling of Murals. Museum Management and Curatorship 10, 373-383. Camuffo, D. and Bernardi, A. 1986: Dinamica del microclima e scambi termoigrometrici tra pareti e atmosfera interna nella Cappella Sistina. Bollettino Monumenti Musei Gallerie Pontificie, 6, 211-257. Camuffo, D., 1993: Controlling the Aeolian Erosion of the Great Sphinx. Studies in Conservation, 38, 198-205. Camuffo, D. and Bernardi, A., 1991: The Microclimate of Leonardo's "Last Supper"; joint edition European Cultural Heritage Newsletter on Research, and Bollettino Geofisico, special issue, 14 (3), 1-123. Camuffo, D. and Bernardi, A., 1995: The Microclimate of the Sistine Chapel, Joint edition European Cultural Heritage Newsletter on Research, 9, 7-32 and Bollettino Geofisico, 18 (2), 7-32. Camuffo, D., Del Monte, M. and Sabbioni, C., 1987: Influenza delle precipitazioni e della condensazione sul degrado superficiale dei monumenti in marmo e calcare, pp. 1536 in Ministero Beni Culturali ed Ambientali "Materiali lapidei", special issue of Bollettino d'Arte, Poligrafico dello Stato, Rome. Camuffo, D. and Schenal, P., 1982: Microclima all'interno della Cappella degli Scrovegni scambi termodinamici tra gli affreschi e l'ambiente, pp. 107-209 in Ministero dei Beni Culturali ed Ambientali "Giotto a Padova", special issue of Bollettino d'Arte, Poligrafico dello Stato, Rome. Eastaugh, N., 1990: The Visual Effects of Dirt on Paintings pp. 19-23 in S. Hackney et al. (eds.): Dirt and Pictures Separated, the U.K. Institute for Conservation, Belton, England, 56 pp. Getty Conservation Institute, 1990: Conservation Research Proposal for the Great Sphinx Presented in Cairo. Getty Conservation Institute Newsletter, 5 (8.2), 1-2. Koestler, R.J., Warsheid, T. and Nieto, F., 1996: Biodeterioration: Risk Factors and Their Management, pp. 25-36 in: N.S. Baer and R. Snethlage (editors): Saving Our Architectural Heritage: the Conservation of Historic Stone Structures. Wiley, Chichester. Lazzarini, L. and Laurenzi-Tabasso, M., 1986: II restauro della pietra. Cedam, Padova, 320 pp. Marshall, K.C., 1984: Microbial Adhesion and Aggregation. Springer Verlag, Berlin, 424 pp. Thomson, G., 1986: The Museum Environment. Buttherwords, London, 293 pp. Zezza, F., 1976: Caratteristiche litogenetiche e forme della degradazione delle pietre da costruzione calcaree di origine biochimica e detritica. Rassegna Tecnica Pugliese Continuit?z, 10 (2), 3-28. Zezza, F., 1994: Evaluation Criteria of the Effectiveness of Treatments by Non Destructive Analysis, pp. 198-212 in: F. Zezza (ed.): Stone Material in Monuments: Diagnosis and Conservation, 2nd Course of the Community of Mediterranean Universities. Adda, Bari.

403 CHAPTER 9

9.1. General theory on sampling and turbulence Lumley, J.L. and Panofsky, H.A. 1964: The Structure of Atmospheric Turbulence. Wiley, New York, 239 pp. Munn, R.E., 1970: Biometeorological Methods. Academic Press, New York, 336 pp. Pasquill, F., 1962: Atmospheric Diffusion, 1st ed., Van Nostrand, London, 297 pp. Pasquill, F., 1974: Atmospheric Diffusion, 2nd ed., Wiley, New York, 429 pp. Plate, E.J., 1982: Engineering Meteorology, Elsevier, Amsterdam, 740 pp. Tennekes, H. and Lumley, J.L., 1973: A First Course in Turbulence. MIT Press, Cambridge, Mass., 298 pp. Vinnichenko, N.K., Pinus, N.Z., Shmeter, S.M. and Shur, G.N., 1980: Turbulence in the Free Atmosphere. Consultants Bureau, New York, 310 pp. Wei, W.W., 1990: Time Series Analysis. Addison Wesley, Redwood City, Ca., 478 pp.

9.2. Instruments and measuring techniques Doebelin, E.O., 1990: Measurement Systems - Application and Design. McGraw Hill, New York, 960 pp. Linacre, E., 1992: Climate Data and Resources. Routledge, London, 366 pp. Moses, H., 1968: Meteorological Instruments for Use in Atomic Energy Industry, pp. 257-300 in D.H. Slade (Ed.): Meteorology and Atomic Energy 1968. U.S. Atomic Energy Commission, Div. Tech. Info. World Meteorological Organisation, 1983: The Guide to Instrument and Methods of Observation, WMO Technical Publication No 8, Geneva. World Meteorological Organisation, 1986: Compendium of Lecture Notes on Meteorological Instruments for Training Class III and Class IV Meteorological Personnel, WMO Technical Publication No 622, Geneva. CHAPTER 10 Benedict, R., 1984: Fundamentals of Temperature, Pressure, and Flow Measurements. Wiley, New York, 532 pp. Camuffo, D., 1980: Fog and Related Diffusion Potential at Venice: two Case Studies. Boundary Layer Meteorology 18, 453-471. Camuffo, D., 1982: The Nocturnal IBL over an Hilly Island with Reference to the Diffusion of Radioactive Nuclei. Boundary Layer Meteorology, 22, 233-240. Camuffo, D. and Bernardi, A., 1993: Microclimatic Factors affecting the Trajan Column. Science Total Environment 128, 227-255. Camuffo, D. and Schenal, P., 1982: Microclima all'interno della Cappella degli Scrovegni: scambi termodinamici tra gli affreschi e l'ambiente, pp. 107-209 in: Ministero dei Beni Culturali ed Ambientali: Giotto a Padova, special issue of Botlettino d'Arte, Poligrafico dello Stato, Rome. Green, W. and Maloney, G.O. (ed.s), 1984: Perry's Chemical, Engineers Handbook, Sisth Ed., McGraw-Hill, Singapore. Hadlock, R., Seguin, W.R. and Garstang, M., 1972: A Radiation Shield for Thermistor Development in the Atmospheric Boundary Layer. J. Appl. Meteorol.,11, 393-399. Lide, D.R. (ed.), 1990: CRC Handbook of Chemistry and Physics, 71 Ed. CRC Press, Boca Raton, Fla. Kondratyev, K.Y., Kozoderov, V.V., Smokty, O.I., 1992: Remote Sensing of the Earth from Space: Atmospheric Correction. Springer-Verlag, Berlin, 478 pp. Michalski, L., Eckersdorf, K. and J. McGee, 1991: Temperature Measurement. Wiley, New York, 514 pp.

404 Nicholas, J.V. and White, D.R., 1994: Traceable Temperatures - An Introduction to Temperature Measurement and Calibration. Wiley, New York, 358 pp. Oke, T.R., 1978: Boundary Layer Climates, Methuen, London, 372 pp. Platridge, G.W. and Platt, C.M.R., 1976: Radiative Processes in Meteorology and Climatology. Elsevier, Amsterdam, 318 pp. Schooley, J.F., 1986: Thermometry. CRC Press, Boca Raton, Fla., 245 pp. UK Meteorological Office, 1981: Handbook of Meteorologicat Instruments- VoI.2 Measurement of Temperature. Her Majesty's Stationary Office, London. Wolfe, W.L. and Zissis, G.J., 1989: The Infrared Handbook. Environmental Research Institute of Michigan. World Meteorological Organisation, 1983: The Guide to Instrument and Methods of Observation, WMO Technical Publication No 8, Geneva. World Meteorological Organisation, 1986: Compendium of Lecture Notes on Meteorological Instruments for Training Class III and Class IV Meteorological Personnel, WMO Technical Publication No 622, Geneva. CHAPTER 11 Camuffo, D. and Bernardi, A., 1986: Dinamica del microclima e scambi termoigrometrici tra pareti e atmosfera interna nella Cappella Sistina. Bollettino dei Monumenti, Musei e Gallerie Pontificie, 6, 211-257. Camuffo, D. and Valcher, S., 1986: A Dew Point Signaller for Conservation of Works of Art. Environmental Monitoring and Assessment 6, 165-170. Davey, F.K., 1965: Hair Humidity Elements, pp. 571-573 in A. Wexler (ed.): Humidity and Moisture Vol. 1: Principles and Methods of Measuring Humidity in Gases. Rehinold, New York, 687 pp. Fisher, P.D., Lillevik, S.L. and Jones, A.L., 1981: Microprocessors Simplify Humidity Measurements. Transactions on Instrumentation and Measurements IM 30 (1), 57-63. Harriman, L.G., 1990: The Deumidification Handbook, Munters, Cargocaire, 186 pp. List, R.J., 1971: Smithsonian Meteorological Tables, Smithsonian Institution, Washington D.C., 527 pp. Mamillan, M, 1992: Mdthodes d'dvaluation des ddgradations des monuments en pierre, pp. 175-181 in F. Zezza (ed.): Weathering and Air Pollution. Adda, Bari. Murphy, W., Smith, J.D. and Inkpen, R.J., 1996: Errors Associated with Determining P and S Acoustic Wave Velocities for Stone Weathering Studies, pp. 228-244 in: B.J. Smith and P.A. Warke (ed.s): Processes of Urban Stone Decay, Donhead, London. Nappi, A. and C6te P., 1997: Non-Destructive Methods Applicable to Historic Stone Structures, pp. 151-166 in N.S. Baer and R. Snethlage (ed.s): Saving Our Architectural Heritage: The Conservation of Historic Stone Structures, Wiley, Chichester. UK Meteorological Office, 1981: Handbook of Meteorological Instruments, Vol.3: Measurement of Humidity. Her Majesty's Stationary Office, London, 43 pp. Weast, R.C., 1977/78: CRC Handbook of Chemistry and Physics, CRC Press, West Palm Beach, Fla. Wexler, A., 1965: Humidity and Moisture Vol. 1: Principles and Methods of Measuring Humidity in Gases. Rehinold, New York, 687 pp. Wiederhold, P.R., 1975: Humidity Measurements part I: Psychrometers and Percent RH Sensors. Instrum. Technol. 22, 31-37.

405 CHAPTER 12

12.1. Anemometry Beaubien, D.J. and Bisberg, A., 1968: The sonic Anemometer. Cambridge System, Newton, Mass., 5 pp. Camp, D.W., Turner, R.E. and Glichrist, L.P., 1970: Response Tests of Cup, Vane and Propeller Wind Sensors. J. Geophysical Research 75, 5265-5270. Camuffo, D., 1976: How to Obtain Mean Value and Variance of Wind Direction by Using a Sine-Cosine Transducer. Atmospheric Environment 10, 167-168. Camuffo, D. and Denegri, A., 1976: A Method for Measurement of Mean Wind Direction with the use of Standard Potentiometric Transducers. Atmospheric Environment 10, 415. Camuffo, D., 1979: Graphic Recording and Averaging the Wind Direction. II Nuovo Cimento 2C, 607-618. Dantec, I996:54N50 Low Velocity Flow Analyzer Mark II, Dantec Electronics, Skovlunde, Denmark, 8 pp. DISA, 1976: Description of the DISA Constant Temperature Anemometry System, DISA Electronics, Skovlunde, Denmark, 56 pp. Doebelin, E.O., 1990: Measurement Systems - Application and Design. McGraw Hill, New York, 960 pp. Durst, F., Melling, A. and Whitelaw, J.H., 1981: Principles and Practice of Laser-Doppler Anemometry. Academic Press, London, 437 pp. Horst, T.W., 1973: Corrections for Response Errors in a Three-Component Propeller Anemometer. J. Appl. Meteorol. 12, 716-725. Hyson, P., 1972: Cup Anemometer Response to Fluctuating Wind.Speeds. J. Appl. Meteorol., 11, 843-848. Moses, H., 1968: Meteorological Instruments for Use in Atomic Energy Industry, pp. 257-300 in D.H. Slade (Ed.): Meteorology and Atomic Energy 1968. U.S. Atomic Energy Commission, Div. Tech. Info. Newstadt, F.T.M. and Van Dop, N., 1984: Atmospheric Turbulence and Air Pollution Modelling. Reidel, Dordrecht, 358 pp. Ramachandran, S., 1970: A Theoretical Study of Cup and Vane Anemometers. Quart. J. R. Met. Soc. 96, 115-123 Smith, S., 1970: Thrust-Anemometer Measurements of Wind Turbulence, Reynold Stress, and Drag Coefficient over the Sea. J. Geophys. Research, 75, 6758-6770. UK Meteorological Office, 1981: Handbook of Meteorologicat Instruments, Vol.4: Measurement of Surface Wind. Her Majesty's Stationary Office, London, 43 pp.

12.2. General theory on turbulence Cartwright, D.E. and Longuett-Higgins, M.S., 1956: The Statistical Distribution of the Maxima of a Random Function.Phil. Trans. Roy. Met. Soc., Ser. A 237, 212-232. Clifford, N.J., French, J.R. and Hardisty, J., 1993: Turbulence. Wiley, Chichester, 360 pp. Csanady, G.T., 1980: Turbulent Diffusion in the Environment. Reidel, Dordrecht, 248 pp. Goody, R., 1995: Principles of Atmospheric Physics and Chemistry. Oxford University Press, New York, 324 pp. Kinsman, B., 1965: Wind Waves, Prentice Hall, Englewood Cliffs, N.J., Landahl, M.T. and Mollo-Christensen, E., 1986: Turbulence and Random Processes in Fluid Mechanics Cambridge, Cambridge, 154 pp. Longuett-Higgins, M.S., 1957: The Statistical Analysis of a Random, Moving Surface.Phil. Trans. Roy. Met. Soc., Ser. A 249, 321-387. Longuett-Higgins, M.S., 1962: The Distribution of Intervals between Zeros of a Stationary Random Function. Phil. Trans. Roy. Met. Soc., Ser. A 254, 557-599. Rice, S.O., 1944: Mathematical Analysis of Random Noise. Bell System Tech. J., 23, 282-332. Rice, S.O., 1945: Mathematical Analysis of Random Noise. Bell System Tech. J., 24, 46-156.

406 Sutton, O.G., 1960: Atmospheric Turbulence. Methuen, London, 111 pp. CHAPTER 13

13.1. Weather precipitation measurements Houghton, D.D., 1985: Handbook of Applied Meteorology. Wiley, New York, 1461 pp. Landsberg, H.E., 1981: The Urban Climate. Academic Press, New York, 275 pp. UK Meteorological Office, 1981: Handbook of Meteorological Instruments - Vol.5 Measurement of Precipitation and Evaporation Her Majesty's Stationary Office, London. World Meteorological Organisation, 1966: International Meteorological Vocabulary, WMO Technical Publication No 182 TP.91, Geneva. World Meteorological Organisation, 1983: The Guide to Instrument and Methods of Observation, WMO Technical Publication No 8, Geneva. World Meteorological Organisation, 1984: Compendium of Lecture Notes for Training Class IV Meteorological Personnel, Vol.2 Meteorology. WMO Technical Publication N o 266, Geneva, 455 pp. World Meteorological Organisation, 1986: Compendium of Lecture Notes on Meteorological Instruments for Training Class III and Class IV Meteorological Personnel, Vol.1 WMO Technical Publication No 622, Geneva. World Meteorological Organisation, 1994: Guide to Hydrological Practices. WMO Technical Publication No 168, Geneva.

13.2. Precipitation on monuments and wet and dry deposition samplers Georgii, H.W. and Pankrath, J., 1982: Deposition of Atmospheric Pollutants. Reidel, Dordrecht, 217 pp. Camuffo, D., 1990: Acidic Precipitation Research in Italy, pp. 229-265 in: A.H.M. Bresser and W. Salomons (editors): "Acidic Precipitation", Vol.5, Advances in Environmental Science, Springer Verlag, New York. Camuffo, D., Del Monte, M. and Ongaro, A., 1984: The pH of Atmospheric Precipitation at Venice, Related to both the Dynamics of Precipitation Events and Weathering of Monuments. Science Total Environment, 40, 125-140. Camuffo, D., Bernardi, A. and Zannetti, M., 1988: Analysis of the Real-Time Measurement of the pH of Rainfall at Padova, Italy: Seasonal Variation and Meteorological Aspects. Science Total Environment, 71, 187-200. Leysen, L., Roekens, E. and Van Grieken, R., 1989: Air-Pollution-Induced Chemical Decay of a Sandy Limestone Cathedral in Belgium. Science Total Environment, 78, 263-287. Munn, R.E. and Rodhe, H., 1985: Compendium of Meteorology Vol.II, Part 6 - Air Chemistry and Air Pollution Meteorology. World Meteorological Organisation, WMO No.364, Geneva, 209.

407

References index Adamson, A. W., 159, 180 Andrews, J.E., 126 Anfossi, D., 206 Arnold, A., 179, 181, 182 Ashurst, J., 290 Ashurst, N., 290 Bagnold, R.A., 284, 287 Barndorff-Nielsen, O.E., 287 Beadecker, P.A., 163 Beaubien, D.J., 374 Becker, T.W., 169 Benedict, R., 316 Benoist, L., 6 Berlyland, M.E., 234 Bernardi, A., 6, 18, 19, 27, 32, 33, 34, 53, 71, 111, 118120, 164, 192, 217, 273, 335, 355 Bisberg, A., 374 Biscontin, G., 149 Blanchard, D.C., 183 Born, M., 105 Bouma, P.J., 270 Brimblecombe, P., 162, 183, 207 Brock, J.R., 247 Brown, R.A., 222 Brunauer, S., 151 Buffle, J., 237, 258 Burnstaock, A., 258, 266, 270 Byers, H.R., 132, 137 Cadle, R., 257, 259 Camp, D.W., 364 Camuffo, D., 6, 11, 12, 18, 19, 27, 32, 33, 34, 35, 36, 53, 71, 118, 120, 149, 161, 162, 163, 165, 166, 172, 178, 187, 210, 217, 218, 234, 263, 273, 275, 281, 287, 330, 332, 335, 355, 360, 361, 368, 369, 370, 371, 389 Caporaloni, M., 261 Cartwright, D.E., 377, 378 Cass, G.R., 274 Cayan, D.R., 209 Chandrasekhar, S., 238 Clifford, J., 157 Clifford, N.J., 377 Coped6, M., 66 C6te P., 357 Csanady, G.T., 377 Dantec, 373

Davey, F.K., 342 Davison, S., 65 Deacon, E.L., 227 De Guichen, G., 6 Del Monte, M., 163, 164 Denegri, A., 370 De Quervain, F., 131 DeWitt, D.P., 22 DIN 66131, 131 DISA, 373 Dobbins, R.A., 234 Doebelin, E.O., 295, 321, 342, 373, 376 Douglas, A.V., 209 Dullen, F.A.L., 172 Durst, F., 376 Eastaugh, N., 270 Echols, W.T., 206 Einstein, A., 103, 238, 240, 241, 245 Elliot, W.P., 206 Enzi, S., 162 Epstein, P.S., 245, 246 Everett, D.H., 156, 158 Fagerlund, G., 157 Fea, G., 162 Fermi, E., 46 Fisher, P.D., 347 Fitzner, B., 131, 149 Fletcher, B., 284 Friedlander, S.K., 237, 247 Georgii, H.W., 388 Getty Conservation Institute, 287 Gifford, F.A., 232 Gillette, D., 284 Ginell, W.S., 159 Giordano, G., 61 Godson, W.L., 157 Goldsmith, P., 250, 253 Goody, R., 98, 354 Gordon, J., 184, 185 Graedel, T.E., 155 Green, W., 340, 352 Gregg, S.J., 151 Gummerson, R.J., 178 Hadlock, R., 325 Hales, J.M., 247, 250 Hall, C., 178 Harriman, L.G., 342

408 Hicks, S.B.B., 261 Hidy, G.M., 237, 247 Hinds, W.C., 237 HOgstrOm, U., 225 Horst, T.W., 364 Houghton, D.D., 386 Hyson, P., 364 Iribarne, J.V., 157 Isachenko, V.P., 263 Jamiolkowski, M., 12 Jeannette, D., 149 Jenkins, K.A., 12 Jones, D.A., 65, 209 Jones, P.D., 209 Kasahara, A., 97 Kikoin, A., 132 Kikoin, I., 132 Kinsman, B., 377 Kireev, V., 180 Klett, J.D., 137, 237, 247, 250 Klopfer, H., 131 Koestler, R.J., 267 Kondratyev, K.Y., 336 Kondratyev, Ya., 111 Krumbein, W.E., 14 Kuroczkin, J., 14, 67, 127, 169 Landahl, M.T., 377 Landsberg, G.S., 259 Landsberg, H.E., 207, 385 Laurenzi Tabasso, M., 65, 148, 290 Lazzarini, L., 290 Lee, D.O., 209 Leysen, L., 387 Lide, D.R., 340 Linacre, E., 295 List, R.J., 352 Longuett-Higgins, M.S., 377, 378 Lumley, J.L., 211, 214, 224, 377 MacDonald, F., 184, 185 Madonna, L.A., 141 Maloney, G.O., 340, 352 Mamillan, M., 358 Marabelli, M., 65, 148 Marshall, K.C., 258 Mason, B.J., 132, 137, 141, 142 Massari, G., 77 Matveev, A.N., 146 Matveev, L.T., 132 Maunder, W.J., 4 McAlister, J.J., 284

McElroy, J.L., 234 McVehil, G.E., 223 Mestitz, A., 108 Michalski, S., 6 Michalski, L., 22, 316, 321, 325 Mikhail, R.S., 151 Ming Chen Wang, 238 Mollo-Christensen, E., 377 Monin, A.S., 224 Moses, H., 298, 364 Munn, R.E., 209, 295, 388 Murphy, W., 358 Nappi, A., 357 Nazaroff, W.W., 274 Newstadt, F.T.M., 377 Newton, R., 65 Nicholas, J.V., 321, 338, 339 Obukov, A.M., 224 Oke, T.R., 340 Ortega-Calvo, JJ., 127 Padfield, T., 6, 69, 189 Pankrath, J., 388 Panofsky, H.A., 206, 211, 214, 224, 377 Pasquill, F., 231, 377 Phenix, A., 258, 266, 270 Plank, M., 47 Plate, E.J., 208, 219, 353 Platridge, G.W., 340 Platt, C.M.R., 340 Porges, F., 25 Price, C., 183 Prodi, F., 162, 247, 250 Pruppacher, H.R., 137, 237, 247, 250 Pye, K., 287 Ramachandran, S., 364 Reddy, M.M., 163 Rice, S.O., 377 Richardson, B.A., 66 Richardson, L.F., 223 Robens, E., 151 Robinson, N., 111 Rodhe, H., 209, 388 Rosenhow, W.M., 7 Sabbioni, C., 164, 167 Saint-Gobain, 22 Saiz-Jimenez, C., 167 Scanlan, R.H., 208 Schenal, P., 32, 35, 36, 281, 332 Schlichting, H., 206, 262 Schmitt, K.H., 246

409 Schooley, J.F., 316, 321 Sedunov, Yu.S., 132 Sehmel, G., 237, 261 Seinfeld, J.H., 237, 240 Simiu, E., 208 Sing, K.S.W., 151 Singer, I.A., 230 Sivuchin, D.V., 132 Slicker, A., 63 Slinn, W.G.N., 247, 250 Smith, B.J., 12, 13, 284 Smith, F.B., 234 Smith, M.E, 230 Smith, S., 365 Summit, R., 63 Sutton, O.G., 226, 377 Talbot, L., 246, 247 Tampieri, F., 247, 250 Tennekes, H., 377 Thomson, G., 6, 64, 74, 270 Thomson, W. (Lord Kelvin), 135 Torraca, G., 148, 156 Touloukian Y.S., 22 Townsend, A.A., 206 Tritton, D.J., 290 Turner, D.B., 234 Uhlenbeck, G.E., 238 UK Meteorological Office, 295, 316, 342, 346, 347, 382, 384 Valcher, S., 187, 360, 361 Van Der Hoven, I., 206 Van Dop, N., 377 Van Leeuwen, H.P., 237, 258

Varshneya, A.K., 122 Vercelli, F., 289 Vincenzi, S., 111, 218 Vinnichenko, N.K., 377 Vittori, O., 108, 250, 253 Wagner, N.K., 206 Waldmann, L., 246 Waller, R., 155 Warke, P.A., 13 Warscheid, T., 14, 67, 127, 148, 169, 173 Wax, N., 238 Weast, R.C., 160, 352 Wei, W.W., 304 Wendler, E., 148 Wexler, A., 295, 342 White, D.R., 321, 338, 339 Wiederhold, P.R., 347 Willetts, B.B., 287 Winkler, E.M., 147, 177 Wittenburg, C., 169 Wolfe, W.L., 336, 340 Woodcock, A.H., 183 World Meteorological Organization, 295, 316, 324, 325, 342, 346, 347, 358, 381, 382, 384 Wright, H.L., 143 Wypych, G., 104, 124 Young, K.C., 137 Zardini, F., 210 Zehnder, K., 179, 181, 182 Zezza, F., 284 Zimon, A., 266 Zissis, G.J., 336, 340

411

Subject index absolute humidity, 55-58 absolute temperature, 9-10 absorbivity, 109 acid rain, 161-164 adhesive forces, 266 adiabatic (atmosphere, expansion, gradient), 93-96, 200-201 adsorption isotherm, 151-156 advection hoar frost, 79 aerodynamic deposition, 260-265 aerovane, 365 air-surface interactions, 30-37, 51-54, 353357 aliasing, 303 altitude of the sun, 110 anemometer location, 366-367 anemometry, 363-366 Archimedes hydrostatic balance, 254-255 artificial microclimate, 6-7 atmospheric stability, 198-205, 221, 332333 atmospheric variables needed for conservation, 296-298 averaging wind direction, 368-371 Avogadro number, 9 azimuth of the sun, 110 barometric formula, 134; particle distribution, 268-269 Bernoulli equation, 173 bimetallic thermograph, 318-319 biodegradation, 67 biological patina 2, 31-32, 167-169 black crust, 164-168 black surface, 267 boiling point, 144-146 Boltzmann constant, 9 Bouguer-Lambert law, 108-109 breaking white area, 169-170 Brookhaven stability categories, 230-231 Brown motion, 237-244 Brunt V~iis/il/i frequency, 206 bubbles, 143-146 bulk deposition sampler, 389-390 bulk IR reflection, 337 Cantor law, 151 canyon effect, 209 capillary force, 267; suction, 175-179 Carnot efficiency, 45 cellulose degradation, 66 church heating, 24-30

Clausius Clapeyron equation, 44-46 climate, 4 cloud condensation level, 100 cold light, 119 colour of natural light, 115-116; of sunlight, 116 colour temperature, 105 coning, 199, 201 constant stress layer, 226 contact charging, 257 contact sensors, 334-335 continuum regime, 236 corrasion, 284-285 corrosion, 65 Coulomb field of a drop, 141; attraction of particles, 266 crossings analysis of turbulence, 377-380 crusts (white, black, gray, soot deposit), 164-172 Cunningham slip factor, 240-241 cup anemometer, 363-364 Dalton law, 42, 267-268 daylight duration, 110 Deacon number, 227 declination of the sun, 109-110 degree of saturation of vapour, 58 deliquescent salts, 141, 185 density of water vapour, 55 deposition velocity, 236-237 dew, 76 dew point meter, 359; signaller, 359-361 dew point spread, 76, 145-147 dew point temperature, 74-79 diffuse solar radiation, 109 diffusion, 248-249; charging, 257; slip factor, 250 diffusiophoresis, 248-250 diffusivity (Brownian), 240-241 direct solar radiation, 109 donor-acceptor forces, 266-267 Doppler anemometry, 366, 375-377 drainage of large particles, 269 drizzle, 297 drunk's walk, 237-238 dry adiabatic atmosphere, 95-96 dry air (composition), 7-8 dry bulb temperature, 10 drying monuments, 174-175, 192-193 dynamic pressure, 173 eccentricity of the earth orbit, 110

412 eddies, 197 eddy diffusivity: coefficient, 353-354; heat, 214-215; momentum, 215, 353-354 eddy velocity, 211-212; viscgsity, 215 effective height, 229 effective radiation temperature, 340 Einstein equation, 103-104, 239-240 electric hygrometer, 346 electrical forces on a particle, 266-267 electrophoresis, 257-258 embryo, critical radius, 140 emissivity, 106-107, 338-340 enthalpy, 86, 137 entropy, 86-87, 98 Epstein equation, 239, 246-247 equation of state for perfect gases, 8-9 equilibrium moisture content, 61-64 equilibrium pressure (RH) over a solution, 179-181,351-352 equivalent temperature (isobaric), 92-93 equivalent-potential temperature, 99-100 error generated by uncorrect psychrometric readings, 350 Eulerian frame, 91 evaporimeter, 357 falling droplets, terminal velocity, 386 fanning, 199, 202 Fick equation, 249 film capacitor hygrometer, 345-346 fixed axis propeller, 364 flash light, 125 float type rain recorder, 383 floor heating, 25-27 foen, 100 fog, 297-298, dry fog, 162 free convection layer, thickness of, 263-264 freezing point depression (hygroscopic salts), 159-160; (Kelvin effect), 157-158 freezing-thawing cycles, 156-160 friction velocity, 212-213 fringe mode, 366, 376 frost (hoar, crystalline, white), 79 frost point temperature, 79 fumigation, 199, 202 gas constant, 9 Gaussian plume dispersion, 227-229 geopotential height, 134 Gibbs free energy of a surface, 132, 137 glass degradation, 65-66 glaze, 79 global climate, 3 globe thermometer, 315 Goldsmith equation, 253

granular disgregation, 12-13 Grashof number, 262-263 gravitational settling, 254-256 Great Sphinx, 287-290 ground ice, 79 gypsum (formation), 65 hail, hailstones, 297 hair hygrometer, 342-345 heat balance, 215-219 heat flux in atmosphere, 213-219, 353-354 heat flux into the ground, 216-219 heat island, 207-208 HVAC to avoid soiling, 270-279 heating buildings used at times, 24-30 height of the sun, 110 Helmoltz free energy, 138 Henry law, 180 heterogeneous nucleation, 141 Hettner formula, 259 hoar (frost, air), 79 H6gstr6m ratio, 225 homogeneous nucleation, 140-141 hot air heating, 27-29 hot wire anemometer, 373-374 hour angle, 110 humidifiers, 51-53, 281 humidity (deterioration mechanisms), 6467, 147-148; in rooms and show cases, 70-74; measurements, 341-361 hydration-dehydration cycles, 181-186 hydrometeor roses, 297-299 hygrometer, calibration, 351-352 hypsometric formula, 134 ice fog, 79 imaging instruments, 336 inertial impaction, 260 inertial interception, 260 ink-bottle pore, 150-151, 155 instrument location, 327-328 intensity of solar radiation, 111-115 internal boundary layer, 205-206 internal pore, 150-151 interstitial condensation, 187-190 inversion, 201 mviscid flow, 173 irradiation, 111-115 isentropic surface, 97-98 lsochoric lines, 87 isolines, 38-41 isothermy, 201 Kelvin equation, 130-138; paradox and experiment, 135-137

413 kinematic coefficient of eddy viscosity, 215 kinematic viscosity, 221-222 kinetic energy of gas molecules, 9; in sand blasting, 290-292 Knudsen number, 235 kytoon, 328-329 Lagrangian frame, 91 Lambert law, 107-108 Lambertian surface, 107-108 lamps, 117-119 Langevin equation, 238 Laplace pressure, 133-134 lapse rate, 198 laser Doppler anemometer, 366, 375-377 latent heat flux, 213-215, 216-219, 353-355 latent heats of vaporisation, fusion, sublimation, 44-48, 86 length of observations, 304-305 light (deterioration mechanism), 122-127 limits of HVAC, 7 liquid-film adhesion, 267 liquid-in-metal thermometer, 318 local climate, 3 lofting, 199, 202 logarithmic wind profile, 226 looping, 198-199 luminance, 107-108 macropores, 131 Magnus (or Tetens) formula, 42; coefficients for water or ice, 42 mantle heating, 29 Mason formula, 142-143 mass concentration of moist air, 54 mature droplet, 140 McVehil ratio, 223-224 mean Maxwell-Boltzmann velocity, 243244 mercury-in-glass thermometer, 316-318 microclimate (definition), 3-4 microclimate diagnostics, 30-37, 51-54; for conservation, 68-69 micropores, 131, 146-151 mixing ratio, 48-50 mode, 302 moisture capacity, 58; content of moist air, ",~\54 . moasture flux in atmosphere, 213-215, 21621'9, 353-355 mole, 9 molecular diffusivity, 354 molecular regime, 236 molecular temperature, 10 molecular viscosity, 211

Monin-Obukov length, 224-225 nanoclimate, 3 Neper number, 48 neutrons method to measure wall dampness, 358 non-imaging instruments, 336-337 normative on microclimate, 69, 295 Nyquist frequency, 304 occult precipitation, 381 open pore, 149-151 optical fibers, 122; filters, 121-122 optical path length, 111-113 osmotic pressure, 142 overpressure in a closed capillary, 178-179 particle diameter, 235 Pasquill Gifford diagrams, 233 Pasquill stability categories, 231-234 Peltier effect, 359 percentiles, 302 perfect gas, 8 pew heating, 25 pH of rain, 163, 171-172 photochemical smog, 126 photophoresis, 258-259 phototrophic organisms, 126-127 Pich6 evaporimeter, 355 picoclimate, 3 Pitot tube, 365 planetary boundary layer, 196 Plank formula, 103 platinum resistance sensor, 319-320 plume concentration, 228-229; dispersion, 227-229 Poisson equation, 95 position of light sources, 125-126; of paintings, 279-282 potential temperature, 96-99 Prandtl number, 262-263 precipitation measurement, 382-384 precipitation, 297, 381 pressure of a light beam, 258-259 pressure of water vapour, 42-44 propeller anemometer, 364 Pruppacher and Klett equation, 247-248 pseudo-adiabatic process, 100 psychrometer, 81, 346-351,355-356; coefficient, 82, 346-347 psychrometric chart, 83-89 Purkinje effect, 116 quartz thermometer, 324-325

414

R parameter, 227 radiant emission, radiance, 107-108 radiation laws, 103-105 radiometers, 336-340 radiometric temperature, 105-107 radiosionde, 328-331 rainfall, 297 rainout, 161 random walk, 237-238 Raolut law, 180 Rayleigh number, 262; distribution, 378 reflectivity, 107, 109 regional climate, 3 relative humidity, 58-60 remote sensing, 336-340 response time of a sensor, 305-312 Reynolds number, 222 Richardson flux number, 224; gradient number, 223 rime (soft, hard, fog), 79 roughness length, 226 rounding off of a number, 41 Rubinowitz formula, 259 runoff collector, 387-388 saltating granules, 286-287 sampling frequency, 302-304 sand blasting, 290-292 saturation pressure, 42 Schmidt number, 243 screen, 325-327 sea spray and salt damage, 181-186; and wind speed, 183 Seebeck effect, 323 sensible heat, 86 sensors with different time constant, 308 shearing stress, 210-211 show case (overheating), 21-24; lighting, 122 shower, 297 silica gel, 73-74, 155 similarity theory, 226 sine-cosine transducer, 367-368, 372 skewness, 371 snow, 297 soiling, 270-273 solar coordinates, 110 solar radiation on a surface, 109-114 sonic anemometer, 374-375 sound velocity, 374-375 specific free energy, 132 specific humidity, 54-55 speed of the free convection layer, 263-264 spread, 76 stable atmosphere, 201

statistical data representation, 298-302 stau, 100 Stefan Boltzmann law, 105-107 Stefan constant, 106 Stefan flow, 250-254 Stevenson screen, 326 Stevin law, 132-133 Stokes law, 239 Stokes-Einstein equation, 240-242 subadiabatic gradient, 200-202 sunrise and sunset, 110 superadiabatic gradient, 198-200 surface adhesion, 265-267 surface IR reflection, 337 surface layer, 226 surface temperature, 333-340 9surface tension, 132 Sutton turbulence index, 225-226 tafoni, 284 Talbot equation, 247-248 temperature (definition), 9-10; (deterioration mechanisms), 10-14; (habitat for biological life), 13-14 temperature cycles, 10-11; in a building, a room, 14-21; in a show cases, 21-24 temperature measurements, 315-340 Tetens (or Magnus) formula, 42 thermal, 198, 214 thermal conductivity, 216; diffusivity, 217; speed, 243 thermistor, 320-323 thermocuple, 323-324 thermophoresis, 245-248 thetered balloon, 330 time constant, 305-307, 314 time-of-wetness, 148, 296, 359-361 tipping bucket rain recorder, 382-383 transition regime, 236 transmissivity, 109 truncating a number, 41 turbulence, 219-221; turbulent transfer,211 two electrodes method to measure wall dampness, 359 ultrasonic pulses method to measure wall dampness, 358-359 uncertainty principle, 32 uplifting granules, 284-286 urban climate, 207-208 vacuum cleaners, 269-270 van der Hoven formula, 206 van't Hoff factor, 142 vane, 364-365

415 vapour tension, 42 ; over a solution, 179181 vertical fluxes of heat, moisture and momentum, 213-215 vertical temperature profile, 328-333 virtual temperature, 101-102 viscosity (molecular or dynamic), 211 Waldmann and Scmitt equation, 246 wall dampness, 357-359 Washburn equation, 177 washing white area 2, 30 washout, 161 water in capillary, 172, 177-178 water molecule, 8, 176 wavelength of solar radiation, 104 weighing-type rain recorder, 383 wet and dry deposition sampler, 388-389 wet bulb temperature (isobaric), 79-83; depression, 80-81

whashing white area, 164-171 Wheatstone bridge, 321-322 whiskers, 182 Wien displacement law, 105 Wildt anemometer, 365 wind drag, 174; lift, 174; shear, 202, 211, 367 wind erosion, 282-290 wind kinetic energy, 363; pressure, 365 wind measurement, 363-380 wind property of transmitting light, 366; sounds, 366; cooling power, 365; wind standard deviation, 227, 371-372 wind vector components, 197, 367-368 windscreen effect, 76 wood deformation (tangential, radial, longitudinal), 61-64 Wright formula, 143 zenith angle, 110