Physics of the marine atmosphere, Volume 7 (International Geophysics)

International Geophysics Series Edited by J. VAN MIEGHEM

Royal Belgian Meteorological Institute Uccle, Belgium Volume 1 Volume 2 Volume 3 Volume 4 Volume 5 Volume 6 Volume 7

BENO GUTENBERG. Physics of the Earth's Interior. 1959 JOSEPH W. CHAMBERLAIN. Physics of the Aurora and Airglow. 1961 S. K. RUNCORN (ed.). Continental Drift. 1962 C. E. JUNGE. Air Chemistry and Radioactivity. 1963 ROBERT G. FLEAGLE AND JOOST A. BuSINGER. An Introduction to Atmospheric Physics. 1963 L. DUFOUR AND R. DEFAY. Thermodynamics of Clouds. 1963 H. U. ROLL. Physics of the Marine Atmosphere. 1965

IN PREPARATION RICHARD A. CRAIG

.

The Upper Atmosphere: Meteorology and Physics

COPYRIGHT

© 1965, BY ACADEMIC

PRESS INC.

ALL RIGHTS RESERVED. NO PART OF THIS BOOK MAY BE REPRODUCED IN ANY FORM, BY PHOTOSTAT, MICROFILM, OR ANY OTHER MEANS. WITHOUT WRITTEN PERMISSION FROM THE PUBLISHERS.

ACADEMIC PRESS INC.

111 Fifth Avenue, New York, New York 10003

United Kingdom Edition published by ACADEMIC PRESS INC. (LONDON) LTD.

Berkeley Square House. London W.l

LIBRARY OF CONGRESS CATALOG CARD NUMBER:

PRINTED IN THE UNITED STATES OF AMERICA

64-21673

Preface Although a sufficient number of books exist that treat maritime meteorology as an applied science, I doubt that there is any book available that considers the subject as a pure science. In view of the particular emphasis now placed on the development of marine sciences, it is felt that works dealing with the physical approach are needed. It is hoped that this volume will fill this need and will prove useful not only to meteorologists and oceanographers but also to scientists working in the fields of atmospheric physics and geophysics. In this volume, marine atmosphere is regarded as that part of the atmosphere which has the sea surface as its lower boundary and which receives its peculiar characteristics from interaction with the ocean. The main object of this monograph is to discuss the influence exerted by the sea surface on the properties of the atmosphere as well as on atmospheric processes of small and medium scale. Particular consideration is given to the exchange occurring in the boundary layer between ocean and atmosphere. The discussions include the flow characteristics and thermodynamics, as well as the chemistry, electricity, and radioactivity, of the marine atmosphere. The particular difficulties inherent in meteorological measurements at sea are considered in an opening section. Emphasis is placed on the physical approach rather than on geographical aspects and those of application. The discussion of the empirical facts, regarded as fundamental, is followed by a theoretical interpretation. The extent of the representation and the details given therein are dependent on the amount of information available to me in the literature published up to 1961, and in some 1962 and 1963 publications. About 600 papers and books were consulted. It is interesting to note that the number of works published in the decade 1950-1960 is almost three times greater than the total number published in the previous five decades. I wish to acknowledge the support I received from the German Federal Ministry of Transport and from the German Weather Service who granted me additional leave for writing this monograph. I have had the advantage of working with a group of scientists who are particularly distinguished in the field of maritime meteorology and v

vi

PREFACE

thus I feel extremely indebted to my colleagues in the Seewetteramt who offered me helpful suggestions and constructive criticism. I am appreciative of the help of my secretary, Mrs. Franziska Petsch, who typed the manuscript with considerable devotion and reliability. Further, I am very much obliged to the Publisher for valuable assistance. Finally I want to address my sincerest thanks to my wife who never failed to encourage me in spite of the fact that I had to do the writing during my spare time. Without her understanding and her continuous linguistic assistance this book would never have been written. Hamburg November, 1964

H. U.

ROLL

Harmonious in their action, the air and sea are obedient to law and subject to order in all their movements; when we consult them in the performance of their manifold and marvelous offices, they teach us lessons concerning the wonders of the deep, the mysteries of the sky, the greatness, and the wisdom, and goodness of the Creator, which make us wiser and better men. M. F. Maury, The Physical Geography of the Sea, 1858.

1. Introduction and Basic Principles Since the very first meteorological observations and investigations at sea, maritime meteorology has mostly been considered and treated as an applied science, its chief purpose being to benefit shipping, fishing, and marine aviation. For this reason books dealing with this subject have generally been written with the intention of furnishing seamen with the necessary basic knowledge of meteorological phenomena and processes at sea as well as giving them some guidance on how to use the information received from the weather services with regard to improving both the security and economy of marine navigation. It goes without saying that any publication issued for this purpose must try to deal with the subject in a manner as elementary as possible and as practical as necessary. Neither is there a need to give a detailed and comprehensive account of the state of knowledge maritime meteorological science has reached so far, nor is it essential to discuss the inherent physical problems which have not yet been settled. For maritime application it is fully sufficient to restrict the treatment to describing the well-known facts and explaining those maritime meteorological phenomena, processes, and procedures which are of importance to shipping and flying. Looking back to the old days when Maury initiated the development of modern maritime meteorology, we notice a long line of excellent textbooks which have served and are still serving the purpose mentioned above. There is hardly a maritime country which has not tried to comply with the marine requirements in this way. Moreover, maritime interests and needs are still vivid and strong, which may be gathered from the fact that France, Germany, The Netherlands, 1

2

I

INTRODUCTION AND BASIC PRINCIPLES

Poland, the Union of Soviet Socialist Republics, the United Kingdom, and the United States of America, among others, have published textbooks on maritime meteorology for the use of mariners within the past ten years. (Titles and names of authors are given at the beginning of the list of references.) Having this in mind, I hope everybody will agree that there is no pronounced necessity for an additional publication of this kind, i.e., a meteorological textbook for mariners. But there are other aspects which should be dealt with. Turning to a more scientific approach and dropping the matter of application to shipping and flying, we should ask which publications of this kind are available at present. The result will be that there is a considerable number of monographs and handbooks chiefly devoted to general meteorology and/or oceanography and containing more or less detailed and complete sections on maritime meteorology. As an example of the first type, there may be mentioned Byers' widely known General Meteorology (1959), which-within a comprehensive treatment of all the important modern topics of meteorology -also deals with certain maritime meteorological problems such as energy exchange between ocean and atmosphere or tropical cyclones. The second type, giving a representation of oceanography from a purely scientific viewpoint and including maritime meteorology, is, of course, much more frequent than the first. Starting with the classical book by Maury (1858), where the modern concept of considering ocean and atmosphere as a whole certainly has its source, we meet with numerous relevant publications, of which only the books by Berget (1931), Bigelow (1931), Shoulejkin (1953) and Sverdrup (1943a) will be mentioned here. In each of these four publications attention is paid to the problems of maritime meteorology, although there are certain differences as to putting the question and handling the subject. Berget's contribution originates from lectures given on physical oceanography (without any references to other papers and publications). It contains a discussion of ocean and atmosphere which, however, must now be considered as superseded by new results. In Bigelow's book the chapter dealing with the relations between oceanography and meteorology, especially the section on seasonal weather forecasting on the basis of oceanographic data, may be of interest to meteorologists even today. Shoulejkin's work covers many meteorological aspects, although it is principally concerned with the physics of the sea. Sverdrup, finally, presented us with a treatment of oceanography that distinguished itself by a new tendency especially welcome to meteorologists: It was written particularly for them;

1

INTRODUCTION AND BASIC PRINCIPLES

3

they now can obtain information from it on the findings in physical oceanography that have bearing upon problems of the atmosphere. Taking these contributions into consideration we may state that they do not provide a complete scientific treatment of what we now understand by maritime meteorology. According to the International Meteorological Vocabulary-(World Meteorological Organization, 1959) maritime meteorology is defined as follows: "Branch of meteorology which is concerned with the study of atmospheric phenomena above the oceans, their influence on shallow and deep sea water, and the influence of the ocean surface on atmospheric phenomena." This definition clearly comprises more than the books on oceanography mentioned above contain. They are more or less restricted to describing the energy exchange between ocean and atmosphere or at least certain parts of it. A complete treatment of marine meteorology should, however, aim at investigating and characterizing all the atmospheric phenomena occurring above the sea and controlled by the sea surface as lower boundary of the air flow. Thus maritime meteorology is going to emerge from the "inferior regions" of applied science in order to enter the "sacred realm" of pure science. I realize quite well that this interpretation is liable to meet with criticism. The statement of Donn should be mentioned here. He said in the Preface to his excellent book Meteorology with Marine Applications (1951) that there is only one meteorology dealing with the atmosphere as a whole and that, consequently, there does not exist a marine meteorology, or any other kind, these being merely applications of the pure science to different fields of human endeavor. Nevertheless it is my opinion that there is evidence enough for the existence of a marine meteorology as a pure science. When we look at the known data on oceans we notice that there is not a small but rather a large number of meteorological phenomena that are closely related to or dependent on the sea surface and which do not occur on land. Without intending to be complete I would like to refer to such problems as the energy exchange between sea and atmosphere, which manifests itself not only in small-scale processes as, e.g., wind stress, heat transfer, and evaporation, but also extends its influence to phenomena of medium and large scale, eventually affecting the whole system of oceanic and atmospheric circulation and thermal interaction. Furthermore, there are the numerous problems connected with tropical cyclones, which originate at sea and spend the greatest

4

1

INTRODUCTION AND BASIC PRINCIPLES

part of their life history there, too. Even when summarizing meteorological data by means of statistical methods we encounter fundamental differences between land and sea not only with regard to the behavior of the climatological elements themselves but also as far as the methods and procedures used therein are concerned. Taking all these experiences together I feel we must agree that there exist special atmospheric phenomena at sea that have no analogs or that differ from similar processes on land. Therefore, particular studies must be carried out that form a special branch of basic research on meteorology. Certainly it would be clarifying to use another name for this pure science than the traditional phrase "maritime meteorology" which has already been used for the applications of this science to shipping. Therefore, we suggest referring to this part of meteorology as "physics of the marine atmosphere," indicating the intention of dealing with the subject from a purely scientific viewpoint and neglecting the traditional shipping aspect. A similar procedure is pursued in other fields of meteorology, e.g., the word "micrometeorology" is used for the basic studies and "agricultural meteorology" for the applied science. So the question is raised of where to fix the border lines of the "marine atmosphere." It is obvious that the sea surface forms the lower boundary, but the determination of the upper boundary is not so self-evident and clear. If we restrict the marine atmosphere to the layer affected by surface friction, a height of, say, 1500 meters might perhaps be sufficient. But there can also be observed at sea atmospheric processes which extend to much greater heights. Therefore, a general upper limit cannot be fixed. It will depend on the special problem under study. In principle all atmospheric properties, phenomena, and processes substantially influenced by the sea surface as lower boundary and investigated by meteorological measurements at sea should be considered as belonging to the marine atmosphere. With regard to the horizontal boundaries of the marine atmosphere, circumstances are even more difficult. Of course, the coast lines are clearly defined and sufficiently known. The difficulty is that the atmosphere does not respect these boundaries and that an intense and frequent exchange of air masses takes place across the coast lines, affecting weather and climate over large continental and maritime areas. The processes involved depend to some extent on the geographical situation and, consequently, call for a climatological treatment. The physical core of the problem in question, i.e., the modification of air masses by the sea surface, can, however, be studied in a general way.

I

INTRODUCTION AND BASIC PRINCIPLES

5

Apart from the connections the marine atmosphere has with meteorological processes on the continents there exist relations to other physical and biological phenomena. In the first place the interaction of ocean and atmosphere is considered important. Further, reference is made to the propagation of visible light, of radio, radar, and sound waves at sea, which strongly depend on meteorological conditions. Moreover we should mention the relations between meteorological disturbances and "atmospherics" as well as seismic waves originating from them. Expanding finally into the field of biology, we have come to believe that meteorological phenomena also affect certain parts of oceanic life. With respect to those relations, I would like to state that they belong to the physics of the marine atmosphere only as far as they have a bearing on the physical processes occurring in it. Primarily this is the case with the oceanic influence on the marine atmosphere. Originally I intended to attempt a review of the present state of our knowledge with regard to the physics of the marine atmosphere within the scope outlined above, i.e., including the interaction of air and sea, but leaving out the relations of other physical and biological processes within and above the oceans as well as the application to human activities such as shipping, fishing, and marine aviation. But realizing the considerable number of problems involved I had to confine myself to describing some basic concepts of the physics of the marine atmosphere. Regarding the characteristic features of that science, which were roughly sketched above, those fundamentals must necessarily and primarily comprise the influences exerted by the sea surface on the properties of the atmosphere and on atmospheric processes of small and medium scale. Thus this monograph is mainly concerned with maritime boundary layer problems which form an essential part of all physical processes in the marine atmosphere. The representation of the large-scale phenomena observed at sea must be left to further efforts which, I hope, will be undertaken by a scientist who can approach this work with more authority than I. In order to be as complete as possible within these limits I have laid stress on the inclusion of numerous references. They are to inform the scientific reader-especially the scientist working in that branch, or related branches, of geophysics to whom this monograph is addressed in particular-of the broad spectrum of scientific activity in this important field of the physics of the earth.

2. Meteorological Observations and Measurements at Sea 2.1

BASIC PROBLEMS

In maritime meteorology, as in any branch of natural science, suitable measurements are required as a basis for empirical investigations and as a touchstone for theoretical studies. Owing to the vastness, enormous energy, and variety of influencing forces by which the atmospheric processes are distinguished from others, there are at present only very few opportunities for enlarging our knowledge by experiments under completely controlled conditions. Therefore, the classical physical approach characterized by separating, dimensioning, and controlling the acting forces, and by measuring their effects, is generally not adaptable to meteorology. Meteorologists are rather forced to execute field measurements which must be representative, dense in time and space, and complete with regard to the influencing factors, all to such a degree as to achieve the success that is expected. These requirements can be fixed and written down much more easily than they can be fulfilled. This is especially true for meteorological measurements at sea. On the oceans it is very difficult to meet even a primary demand which can be easily provided for on land, namely, a fixed site for measuring. Even if we succeed in keeping a floating observing station always at the same point, movements of this float caused by the waves will raise new difficulties. Of course, these two handicaps could be overcome by using fixed constructions erected from the bottom of the sea (e.g., lighthouses, Texas towers) as bases for meteorological measurements. Since such maritime structures are only possible in shallow waters (in tidal flats or on the continental shelf), it is only in coastal waters that they can serve as useful and, therefore, welcome additional sites for meteorological activity. In view of the necessity of gathering meteorological data from deep sea areas also, we have to 6

2.1

BASIC PROBLEMS

7

face the difficulties inevitably connected with the use of floating bases for measuring. From the purely methodical viewpoint five possibilities are available at present. We can use anchored ships, drifting ships, moving ships, anchored buoys, or drifting buoys for obtaining meteorological observations near the sea surface. All of them have the disadvantage that they are exposed to the action of ocean waves, and consequently, make irregular motions. Taking a ship as base means further disadvantages. The body of the ship causes a considerable disturbance of the air flow and, furthermore, forms a source of convective and radiative heat. Therefore, it is to be expected that errors will occur in meteorological measurements on shipboard, owing partly to the presence of the ship and partly to its irregular movements in the seaway. The amount of these errors is very difficult to estimate and not exactly known. It will depend on various factors (size of the ship, site of measurement, apparent wind, sea spray, sea conditions, and others). There is some evidence (Dietrich, 1950; Hay, 1956a) that these errors are larger with ships under way than with anchored ships, e.g., lightships. However, in comparing humidity observations made on merchant ships and on ocean station vessels, Brown (1952) found satisfactory agreement between the corresponding monthly averages. The disturbing influence of the ship can be removed if the measuring equipment is installed on a buoy, whereas the disturbing effect of wave motion cannot. In spite of the latter handicap and although the construction and operation of telemetering and reporting buoys offer severe technical and economic difficulties, automatic ocean-based weather stations are to be considered as promising progress and will perhaps form an important part of the future meteorological network at sea. As long as the use of automatic weather buoys is still in the development and trial stage, measurements made on anchored, on drifting, and on steaming ships will constitute the bulk of maritime weather data. All these considerations refer to meteorological measurements near the surface of the sea. As regards aerological observations it should be stated here that these are not as dependent on sea conditions as the surface observations. On principle, the same methods may be used at sea as over land. This is true, above all, if land-based airplanes serve for weather reconnaissance purposes. Radiosonde and radar wind techniques need certain adaptations to the special requirements aboard ship.

8

2

METEOROLOGICAL OBSERVATIONS AND MEASUREMENTS

2.2

OPERATIONAL QUESTIONS

The principal difficulties connected with meteorological measurements at sea having been indicated, detailed consideration will now be given to the question of what bases and procedures are available for executing such measurements. We had better clarify this matter first before entering into a discussion of maritime meteorological instruments and observation methods, since the use of these devices will depend strongly on the operational systems available. 2.2.1 Mobile Stations Meteorological stations established on ship or aircraft whose motions are determined by man are defined as "mobile" stations.

2.2.1.1 Merchant Ships and Trawlers. In view of the vastness of the oceanic regions it seems quite hopeless that sufficient control of : maritime weather can be achieved through the use of only those observing stations managed by scientific institutions or weather services. The only possibility of getting meteorological observations from the sea somewhat regularly has been to ask the captains and officers of merchant ships for cooperation. This is a very natural request, since the chief practical aim of marine meteorology is to render assistance to shipping and fishing. This scheme of mutual assistance came into being at the very beginning of modern meteorological activity at sea more than 100 years ago. It is again Maury to whom is due the credit that the cooperation between shipping and maritime meteorology was started, organized, and coordinated internationally. From the first international conference at Brussels in 1853 onward, this scheme of mutual assistance has been further developed, especially by the Commission for Maritime Meteorology of the IMO (International Meteorological Organization), and later by that of the WMO (World Meteorological Organization). At present a fleet of 4000 ships under the flags of all seafaring nations is taking part in the weather-observing network at sea. These ships are classified into "selected ships," making full observations, "supplementary ships," sending weather messages in abbreviated form, and "auxiliary ships," which make additional observations by means of noncertified instruments of their own. In order to supply the seamen with the necessary meteorological knowledge, care has been taken that basic instruction in meteorology is included in the training curriculum at navigation schools. Furthermore, meteorological liaison officers in ports are prepared to check the meteorological

2.2

OPERATIONAL QUESTIONS

9

instruments on shipboard, to contact the weather observers on merchant vessels, and to give them any advice they may need. This traditional system, which has proved very useful for more than a century, may be characterized with regard to its effectiveness as follows: Advantages: It is an ideal system of cooperation on a nonprofit basis, devoted only to the security of life at sea. Since the meteorological observations are made by the ships' officers voluntarily and without payment, the weather services are merely charged with the cost of the instruments and for the transmission of coded weather messages. Therefore, the scheme is less expensive by far than it would be if meteorological services had to pay for every observation, or had to do the observing with their own personnel. Disadvantages: The observations are made not by specialists but by meteorological laymen who have received only brief training. Therefore, detailed checking of the observations is indispensable. Since the ships' officers do the observing work in addition to their other duties, only the limited routine observations and no special data can be expected from them. The instruments used must be robust, easy to maintain, and, also, easy to remove if observing is discontinued. Expensive installations are not feasible in general; they are possible only in cases in which the shipowners are willing to take over the costs. The observations from merchant vessels are more or less confined to the main sea routes. In order to extend the observations to other areas several countries have successfully recruited weather observers on trawlers, who furnish additional reports from the fishing grounds. A distribution picked at random is given in Fig. 1. It clearly shows that a sufficiently dense and quasiuniform coverage is attained only in certain parts of the North Atlantic Ocean and its adjacent seas. A similar random sample taken at a later date resulted in about 44 per cent of all observations being located in the North Atlantic. While 89 per cent were allotted to the northern hemisphere, only 11 per cent originated from the vast seas of the southern half of the globe. For climatological purposes a certain improvement of coverage can be achieved by taking meteorological observations from the log books of sailing ships, since the former sailing routes differed considerably from the tracks followed by modern powered shipping. 2.2.1.2 Special Ships. An important supplement to the scheme of voluntarily observing merchant vessels and trawlers is provided by

I

I

I

I

\

,

I

I

I

I

I

i~n--r;-r Uif

I

I

I

I! r b

I ---;--t--r-r-

I

I

-

y,

II I' Tl~ I I II I ;! - lII

hi

I .-

r-t-r-t-t

I I

! I

I',

FIG, 1. Distribution of ships making meteorological observations at 1200 GMT, November 1, 1957; total number 937. (From World Meteorological Organization, 1961.)

2.2

OPERATIONAL QUESTIONS

11

special ships which undertake scientific investigations or fulfil other duties at sea. Under this heading belong the following marine activities: Voyages and expeditions of research vessels with complete scientific outfit and collecting data and carrying out investigations for oceanography, maritime geology, biology, and/or meteorology. Expeditions of whaling factories making similar measurements incidentally, and to a smaller extent, than the above. Cruises of fishery protection vessels, coast guard cutters, ice breakers, and other special ships fitted out with meteorological equipment and staffed with experienced personnel. Voyages of transports, freighters, and tankers with radiosonde, pilot balloon, or radar wind equipment, and with the meteorological experts to make aerological measurements. Although all these undertakings were not, and are not now, carried out primarily for meteorological studies, and, consequently, the course, speed, and stops of the ships have almost never been determined by meteorological interests, they have contributed enormously to our knowledge of marine meteorology. An important advantage is that on research vessels and other special ships the handicaps of instrumentation mentioned before for merchant ships do not occur, since in general here it is possible to install the necessary meteorological equipment even if certain alterations in the ship's hull or superstructure are required.

2.2.1.3 Air-Borne Meteorological Reconnaissance. During World War II when meteorological observations were kept secret, weather reconnaissance flights over meteorologically unknown areas were regularly executed by both sides and supplied very useful, sometimes even vital, information. Since the war this technique has been successfully employed in polar meteorology and for detecting and tracking tropical cyclones. In the latter case especially, great advances in marine meteorological knowledge have been achieved. It is one unwelcome by-product of effective maritime storm-warning activity that the regions covered by tropical cyclones are nearly deserted, as all the ships do their best to avoid these dangerous areas. The consequence is that almost no surface weather observations are received at the maritime forecast centers from the regions in question. In this situation meteorological observations and measurements collected by aircraft are not only a necessary and useful substitute but, more than that, they furnish exact data on the location, the horizontal and vertical structure, and the

12

2

METEOROLOGICAL OBSERVATIONS AND MEASUREMENTS

movement of tropical cyclones-and this is much more than could be obtained from ships' reports. These airplanes are flying laboratories; they carry air-borne equipment specially developed for measuring winds, atmospheric pressure, air temperature and humidity, sea surface temperature, electric field, icing, turbulence, cloud-physics parameters, clouds, and other elements during hurricane reconnaissance flights (Hilleary and Christensen, 1957). The airplanes even penetrate the circular area of hurricane winds, thus reaching the "eye" of the cyclone, whereby they get the exact position of the center and are able to measure the minimum pressure at sea level by dropsonde. Releasing a tracer balloon, which is kept within the center by the cyclone's circulation, may then help in locating the moving cyclone for a certain time. The information provided by such ingenious and elaborate techniques is of great importance not only for the stormwarning service but also for research purposes. In recent years camera-carrying rockets and satellites have been launched successfully, offering us a foretaste of what maritime meteorology can expect from such new devices. At this stage of development it is rather difficult to estimate the real extent of the meteorological progress that will be reached in this way. Certainly these photographs will at least provide us regularly with global representations of cloud distribution, which will help us to detect disturbances in the so-called "sparse areas" of the oceans where there is no sea traffic, and which will give us new insight into atmospheric circulation patterns. Moreover, suitably instrumented rockets and satellites may be very useful tools for measuring and controlling the radiation budget of the earth. 2.2.2 Fixed Stations Meteorological stations operating more or less at the same location are referred to as fixed stations. 2.2.2.1 Fixed Constructions. Although lighthouses, Texas towers, and similar fixed maritime structures are erected in tidal waters or on the continental shelf and, consequently, belong more or less to the coastal zone, they may render good service not only to coastal meteorology but also to maritime meteorology in general. They represent the sole carriers of instruments in marine meteorology that are not liable to fluctuations in space and time, if seismic influences are left aside. Therefore, such maritime constructions are the most suitable bases for investigations of meteorological fluctuations at sea, e.g., wind structure, oscillations of air temperature, and humidity. Of

2.2

OPERATIONAL QUESTIONS

13

course, special care must be taken that the records of meteorological elements are truly representative of maritime conditions and not influenced by the land or the construction itself. 2.2.2.2 Lightships. Lightships are anchored ships with special nautical duties, including meteorological observations. Comparing them with merchant ships as far as weather observing is concerned, we may state that they offer the following advantages: (a) They are special ships managed by the government. Therefore, it is comparatively easy to equip them with additional instruments for research purposes. (b) Their position is more or less fixed, a fact enabling us to install recording instruments on shipboard (e.g., for mean wind speed), if the influence of the ship's movement is not decisive or can be ruled out. Since the observers on lightships are usually thoroughly experienced men and the instruments are under continuous control, the observations are, in general, of a high standard. In certain maritime countries meteorological observations on lightships have a fairly long tradition and may even be used for studies of climatic change. 2.2.2.3 Ocean Weather Stations. In all arrangements mentioned so far and concerned with ships, meteorological observing and measuring was considered as an additional and secondary task, the primary duties being shipping, fishing, whaling, oceanographic research, fishery protection, ice breaking, etc. Maritime meteorology was admitted or sometimes invited to take part-more or less as a guestand tried to do its best in utilizing the existing conditions for its own purposes, without having the opportunity of adapting these conditions to meteorological requirements. The situation changed gradually with the development of marine aviation which urgently needed meteorological information to an extent not available from mobile ships' stations. The first forerunners of the weather ships of today appeared in the early thirties when some countries, e.g., France and Germany, started to operate suitably converted merchant vessels in order to render assistance to Atlantic flying. Within the duties of these ships, meteorological and aerological measurements formed an important, if not the principal, part. The demand for such meteorological information increased rapidly during and after World War II, thus leading at first to a variable scheme of weather ships according to wartime emergencies and finally

14

2

METEOROLOGICAL OBSERVATIONS AND MEASUREMENTS

in 1946 to an international agreement for the North Atlantic. A fixed network of thirteen ocean stations was established by the International Civil Aviation Organization. This agreement was amended-mostly for economic reasons, in 1949 and 1954-reducing the number of stations to ten and finally to nine. Twenty-one ships are now engaged in this service, among them nine from the U.S.A., four from the U.K., three from France, two each from Holland and Norway, and one from Canada. Other nonoperating states contribute in cash. The share of each country depends on the number of its transatlantic crossings. In the North Pacific three ocean stations are operating. A Dutch weather ship was transitorily stationed in the Indian Ocean. The locations of the twelve weather ships of today may be seen on the map (Fig. 2). This representation clearly shows that the vast ocean areas of the southern hemisphere are not covered by a similar observing system. It will be a future task to find an adequate and economical solution for this region. The types of ships used for ocean station work are coast guard cutters (U.S.A.) or converted corvettes or frigates (U.K., Holland, Norway). In France two newly built vessels came into service in 1959. Since these ships are comparatively small and have to perform continuous duties frequently in regions of bad weather, ships and crews are subject to a heavy strain. The meteorological work of the ocean stations comprises an hourly routine program of surface observations as well as upper air ascents with radiosonde and radar wind techniques four times per day. In addition, scientific investigations, e.g., recording ocean waves, studies of boundary layer problems, and radiation measurements, are carried out according to circumstances. On two new U.S.S.R. weather ships, which are cruising or occupying stations in the North and Central Pacific, meteorological rockets are used to get upper air data up to a height of 80 km. For maritime meteorology the important state of progress reached with the ocean station network is due to the fact that the locations assigned, i.e., positions within a square of 10 nautical miles around the designated stations, are maintained whenever practicable, and that interruptions of observing routine will only happen in case of emergency (such as air-sea rescue work). Therefore, complete series of meteorological observations, which were not possible before, can be obtained for fixed locations in the oceans over long periods. The weather ships' data constitute material of eminent value for nearly all studies in maritime meteorology. Their

FIG.

2. Map indicating the positions of the ocean stations.

16

2

METEOROLOGICAL OBSERVATIONS AND MEASUREMENTS

importance will even be increased in future years when the available period, which now comprises 14-17 years, will be longer. 2.2.2.4 Floating Automatic Weather Stations. As already mentioned in Section 2.1 the great advantage of automatic weather buoys is that their disturbing effect on meteorological measurements may be much smaller than that of ships. Furthermore, there is a serious lack of meteorological information from certain parts of the oceans which are not fishing grounds, not crossed regularly by merchant ships, and not controlled by meteorological reconnaissance flights, and where establishing an ocean weather station is not considered feasible for economic reasons. In those areas floating automatic weather stations could render good service to marine meteorology. Several types of such weather buoys have been developed by the U.S. National Bureau of Standards (1956) after similar attempts had been made by other countries during World War II. The so-called Marine Automatic Meteorological Observing Station (MAMOS) can be anchored. Therefore it may be considered as a fixed station. It is a boat type of hull, 20 feet long anJ 10 feet wide, made of aluminum and nonmagnetic alloys; it has two masts and wind powered batteries; and it can be anchored even in water 12,000 feet deep if necessary (Fig. 3). It sends out coded broadcasts of air and water temperature, barometric pressure, and wind direction and speed at intervals of 6 hours with a nighttime range of 1500 nautical miles, the daytime range, however, being much less. The station can be left unattended for several months. Field tests have been conducted during the past few years in the Gulf of Mexico (U.S. Weather Bureau, 1959) to determine the durability of moorings, rigidity and performance of the station, and the effectiveness of the broadcasts. Encouraging results have been obtained. During the 1960 tests the automatic station broadcasts alerted forecasters to the development of hurricane Ethel, permitting warnings to be issued several hours earlier than would have been possible without such reports. The automatic station has survived hurricane winds and has been at its station up to 8 months before being returned to port for servicing. The tests were continued during the 1961 hurricane season, when the buoy experienced winds exceeding 100 knots as the center of hurricane Carla passed the station at a distance of less than 100 miles. Though some difficulty arose from high seas, extremely low pressure, and blowing spray, the moorings and the transmitter withstood the ordeal. In the future these weather buoys are expected to be equipped with solar cells for recharging the storage

2.2

17

OPERATIONAL QUESTIONS

AUTOMATIC WEATHER STATION

3/.

INCH CHAIN

THIMBLED' EYE AND SHACKLE

1875 FATHOMS

3/.

INCH DACRON CABLE (5,000 FEET)

3/.

INCH POLYPROPYLENE CABLE (1V.OOO FEET)

THIMBLED EYE AND SHACKLE

3/.

INCH CHAIN

500 POUND MUSHROOM ANCHOR

FIG. 3. Boat type of automatic weather station with deep-water slack-line anchorage. (From Corwin et al., 1959.)

18

2

METEOROLOGICAL OBSER VAnONS AND MEASUREMENTS

l-- --------------------~8

EN

Mast of aluminum

E u

o L[) r--

E

r

Buoy

u

o L[)

~ o

o

L[)

x

c

E

I

r. FIG. 4. Buoy for recording the vertical distributions of wind speed, temperature, and humidity near the sea surface. (From Brocks, 1959a.)

2.2

OPERATIONAL QUESTIONS

19

batteries which are now energized by wind driven chargers. With such an outfit these stations are supposed to operate for one year or more without any servicing. In addition to automatic weather buoys used for synoptic observations, special meteorological buoys have been constructed for scientific investigations, e.g., for air-sea transfer studies, in particular for recording the vertical wind, temperature, and humidity distributions in the first few meters above the sea surface (Shoulejkin, 1928; Brocks, 1959a, Fig. 4; Deardorff, 1962). Such studies require very accurate measurements taken in an airflow not disturbed by any obstructions and, therefore, they cannot be carried out on, or in the neighborhood of, a ship. 2.2.3 Drifting Stations Meteorological stations, established on bases whose motions are not determined by man but by natural forces, are defined as "drifting stations." 2.2.3.1 Drifting Stations in Air. The constant-level balloon technique, called "Transosonde," should be mentioned here. It collects upper-air meteorological data such as wind, atmospheric pressure, air temperature, and humidity during transoceanic flights and may serve to supply welcome information from oceanic areas (Corwin et al., 1959). 2.2.3.2 Drifting Stations in Water. The U.S. Navy has been developing three types of free-floating automatic weather stations (Corwin et al., 1959), all of which are able to transmit the following data: station identification, wind speed and direction, barometric pressure, air and sea temperature. (a) The "Transobuoy" was constructed as a means of gathering meteorological data on a transoceanic scale. It is 10 ft long, weighs about 600 lb, carries a 25-ft whip antenna, and can broadcast daytime transmissions from over 1000 to 2000 miles, while nighttime transmissions can be heard up to 4000 miles. It is expected to operate for approximately 6 months, transmitting coded radio signals of 3 minutes' duration on a 6-hour schedule. During preliminary testing the messages were received over a 10-day period at distances of up to 5000 miles. (b) The "Parachute Weather Buoy" is designed to be put into action by parachute in areas from where no weather information is available. Its characteristic feature is that it can be delivered and placed exactly at the desired location by aircraft in a comparatively

20

2

METEOROLOGICAL OBSERVATIONS AND MEASUREMENTS

short time. It is 10 ft long, weighs about 350 lb, has a 12-ft parachuteerected, telescoping antenna, and will operate for 2 months on a 6-hour schedule. Tests have indicated that parachute delivery of the buoy can be accomplished without damage to the equipment. (c) The "Hurricane Monitoring Buoy" was developed as an expendable automatic weather reporting instrument for tactical use in connection with forecasting tropical storms. It consists of a cylindrical buoy 6 ft in length supporting a 9-ft instrumented mast and a 7-ft whip antenna (Fig. 5). Furthermore, it carries an 8-ft counterpoise, thus making the overall length 30 ft. The buoy telemetered meteorological data every 6 hours for 2 months with a reliable operation range of from 800 to 1000 miles. Such buoys proved very useful during the 1955 and 1956 hurricane seasons. If we compare the drifting buoys with the anchored buoy MAMaS described in Section 2.2.2.4 it can be stated that the latter offers several advantages over the free floating buoys, among which there is the possibility of installing additional sensors for other quantities and of wind driven, thermo-electric, or nuclear power generators to enlarge the operation period. In addition, the problem of locating the buoy is eliminated. Although securing reliable operation of such buoys must be considered as very noteworthy progress in marine-meteorological observing technique, the full benefit of these devices will also depend on the quality of the measurements themselves, especially when severe weather conditions hamper the performance of the buoy. Bearing in mind that the measuring heads are very near the sea surface we may ask what disturbing influences are to be expected, for instance, on wind and temperature data from wave motion and sea spray. Up to now no information has been available with regard to these questions. 2.2.3.3 Drifting Stations on Sea Ice. Meteorological stations on drifting ice, as operated by the U.S.A. and the U.S.S.R. in the Arctic Ocean, must also be considered as maritime stations. On the basis of the experience gained from the famous drift of Nansen's polar vessel Fram from 1893 to 1896 and similar later expeditions (e.g., the Norwegian Maud 1918-25), in 1937 the U.S.S.R. established by airplane the first drifting station near the North Pole, which was then rescued near Scoresby Sound in East Greenland 9 months later. Further similar expeditions followed and in April 1959 the eighth Pole station was set up (Polar Record, 1959a). Reference should also be made to the drift of the Russian icebreaker Sedov 1937-40.

2.2

OPERATIONAL QUESTIONS

21

FIG. 5. Hurricane monitoring buoy measuring and transmitting station identification, atmospheric pressure, wind direction and speed, and air and sea temperature. (Official U.S. Navy Photo.)

22

2 METEOROLOGICAL OBSERVATIONS AND MEASUREMENTS

In addition to these manned ice stations, automatic weather stations measuring wind direction and speed, air temperature, and atmospheric pressure, were established on the polar ice by U.S.S.R. airplanes. There were 30 of these in the spring of 1959 (Polar Record, 1959b). The U.S.A. has been operating drifting stations on so-called "ice islands" in the North Polar Sea from 1952 onward; two stations, named "A" and "B," were set up as a contribution to the International Geophysical Year (Groen, 1960). At all manned stations surface weather observations and, to some extent, also aerological ascents were carried out according to international schedules. In addition to this routine service, micrometeoro logical investigations, as well as radiation measurements, were executed in order to study the thermal balance of the pack ice (Larsson, 1959). 2.3.

REVIEW OF INSTRUMENTS AND METHODS

Now that the operational considerations for meteorological measurements at sea have been described in some detail, we will discuss the meteorological instruments and methods themselves. It is not intended to give a thorough description of the different types involved; we shall rather confine ourselves to dealing with the particular aspects of maritime measurements, supposing that the principal facts on the relevant instruments and methods are known. Only those procedures that are used for routine observations at sea will be considered whereas special techniques developed for research purposes will not be dealt with here. These will be mentioned in the relevant sections of this monograph if necessary. A detailed discussion of meteorological instruments for use on ship-board has recently been published by Hahne (1963). 2.3.1 Surface Observations 2.3.1.1 Wind. The observation of wind speed and direction is usually made either by visual estimates or by means of anemometers or anemographs. Visual estimates are normally based upon the appearance of the sea surface under the action of the present wind. This traditional method is widely used at sea, as only special ships have anemometers at their disposal. The wind speed is estimated in the numbers 0-12 of the Beaufort scale using sea surface specifications attached to these numbers. These descriptive terms applied to the different Beaufort numbers

2.3

REVIEW OF INSTRUMENTS AND METHODS

23

originate from Petersen (1927). He transformed the specifications, originally given by Admiral Beaufort, and referring to the speed and sails of a full-rigged frigate at the beginning of the nineteenth century, into descriptions of the sea surface, basing these upon his long experience as a captain of sailing ships. Later on these specifications were slightly amended with regard to the requirements of modern shipping. There were many efforts to determine the correct wind speed equivalents pertaining to these Beaufort numbers. The values published by Verploegh (1956) are based on the results of all comparative studies so far available from the sea and may, therefore, be considered as the most suitable ones at present. They are given in Table I together with the specifications of the Beaufort numbers. It should be noted that these wind speed equivalents are valid for a height of 10 meters above sea level under indifferent atmospheric stability. Marked deviations from these equivalents may occur with other thermal stabilities (Roll, 1953-1954; Brooks and Brooks, 1958), winds colder than the sea producing higher and steeper waves than warm winds. Since the high Beaufort numbers, above and including 10, are based on comparatively rare cases, the relevant equivalents may not be considered as well established as those for the lower wind forces. The wind direction is obtained by observing the motion of wind driven waves. Estimating the wind visually is a matter of experience. Several disturbing effects have to be taken into account, e.g., the "lag" between the wind increasing and the sea getting up, and the influences of fetch, depth, swell, heavy rain, and tidal currents on the appearance of the sea. As shown by Otto (1961), the tidal effect, particularly in cases of low wind velocities, causes the estimation of an apparent wind force which corresponds to the air speed relative to that of the water. Even the plankton content may influence wind estimates at sea since the foaming of the sea water depends on it. Seilkopf(1955-l956) has found that in sea areas rich in plankton the foaming (as taken from estimated wind forces greater than 3 Beaufort) observed with smaller wind speeds is the same as that with higher wind speeds in areas poor in plankton. Consequently, there is a certain tendency to overestimate wind speeds in regions with high plankton content. When the sea surface is invisible, e.g., at night, estimation becomes questionable. To meet this difficulty Graham Millar and Macphail (1951) proposed a scale for estimating apparent wind from on board ship basing their conclusion on wind effects on persons, rigging, flags, and smoke plumes, but, so far, little use seems to have been made of this method.

TABLE I WIND SPEED EQUIVALENTSa AND SPECIFICATIONS FOR THE BEAUFORT NUMBERS OF WIND FORCE

Wind speed equivalents Beaufort number

knots

Descriptive term

Mean

meters/sec

Limits

Mean

Specifications

Limits

0 1

Calm Light air

0 3

28.2

Moderately high waves of greater length; edges of crests begin to break into the spindrift; the foam is blown in well-marked streaks along the direction of the wind High waves; dense streaks of foam along the direction of the wind; crests of waves begin to topple, tumble, and roll over; spray may affect visibility Very high waves with long overhanging crests; the resulting foam, in great patches, is blown in dense white streaks along the direction of the wind; on the whole, the surface of the sea takes a white appearance; the tumbling of the sea becomes heavy and shock-like; visibility affected Exceptionally high waves (small- and mediumsize ships might for a time be lost to view behind the waves); the sea is completely covered with long white patches of foam lying along the direction of the wind; everywhere the edges of the wave crests are blown into froth; visibility affected The air is filled with foam and spray; sea completely white with driving spray; visibility very seriously affected

26

2

METEOROLOGICAL OBSERVATIONS AND MEASUREMENTS

Measuring wind on board ship meets with certain difficulties, by which such measurements are restricted more or less to special ships. The instruments used should give both wind speed and direction. They should have a proper exposure and be capable of minimizing roll effects. With regard to the exposure of wind measuring instruments, the disturbance of the air flow produced by the superstructure of the ship must be taken into account. The obstruction of the air flow by the ship's hull is by no means negligible even with small vessels. Deacon et al. (1956), who studied this subject in the case of a small diesel schooner, obtained hull effect corrections ranging between 1 and 12 per cent. Similar values were reported by Brocks (1959a). Therefore, the position of the instrument should be as far forward and as high as practicable. The top of the foremast is generally thought to be the best site for an anemometer. Naturally, such an installation requires a distant reading instrument. This is the reason that anemometers are very rarely found on merchant vessels. Hand anemometers are no substitutes since they can hardly be given a representative exposure on board. Only an observer who knows the distribution and structure of the air flow over the ship under different conditions may be able to choose a place for measuring where he will arrive at satisfactory results. Some hints as to the errors caused by the ship's movement can be found in papers of Sanuki and Kimura (1954, 1955), who tackled this problem empirically by wind tunnel investigations. They arrived at the result that the readings of cup anemometers were increased by about 10 to 25 per cent by pitching and rolling motion. An increase was also reported by Ogata et al. (1958b) but it amounted only to from 2 to 3 per cent at a height of 11 meters. A more theoretical treatment of this subject was given by Langmaack (1938), who computed the wind speed error caused by the rolling of the ship by taking into account the angle between the wind direction and the direction of the ship's oscillation as well as the relation between the maximum velocity of the oscillating anemometer and the true wind speed. To correct the values given by a cup anemometer for the rolling effect Deacon et al. (1956) suggested the following formula (2.1) where u- = recorded wind speed, u- = corrected wind speed, h = anemometer height above the axis of roll, z/; = root mean square rolling amplitude, and T r = root mean square rolling period.

2.3

REVIEW OF INSTRUMENTS AND METHODS

27

Wind measuring equipment particularly developed for use on shipboard was described by Hohne (1960). On a moving ship it is only the apparent or relative wind that is given by such measurements. The true wind is obtained from it by allowing for the ship's course and speed. This can be done automatically by a computer, to be sure, but the amount of equipment needed for this simple correction would be considerable and is, at present, almost prohibitive for merchant vessels (Bell, 1951; Bell and Langham, 1952). The wind data generally refer to a period of 10 minutes. They are, therefore, mean values. The accuracy obtained in measuring mean wind at sea under fair conditions is estimated at present to be ± 5° in direction and ± 1 knot in speed. The approximate maximum error under bad conditions at sea may reach ± 15° and 5 knots, respectively. Since the influence of the ship's movements on measurements of instantaneous wind vector is very difficult to estimate and to compensate, only few possibilities can be seen at present for the use of anemographs for obtaining representative wind records on shipboard. An examination of wind records gained on British weather ships made it clear that a large proportion of the apparent gustiness was actually caused by the rolling of the ship. Therefore, investigations of wind structure at sea can only be carried out on fixed constructions or stabilized buoys.

2.3.1.2 Atmospheric Pressure. Pressure may be measured by either precision aneroid or mercury barometers. The main difficulties arising with barometric measurements on shipboard are caused by the effects of the wind and by the movement of the ship. The influence of the first source of error may be reduced by enclosing the instrument in a chamber connected with a static pressure vent. The second disturbing effect is particularly bothersome with mercury barometers. Certainly, the pressure variations caused by the lifting and sinking of the barometer in a rolling and pitching vessel are of less importance, since these marine barometers have an appropriate lag in order to reduce the pumping of the mercury column. Much higher errors may arise from the varying accelerations to which the barometer is subjected by the movement of the ship. Since the instrument is mounted in gimbals and can swing freely it will execute more or less regular oscillations due to the movement of the ship in the seaway. A barometer which is oscillating for 15 minutes or more

28

2

METEOROLOGICAL OBSERVATIONS AND MEASUREMENTS

with an amplitude of about 10° may read as much as 4 mb too high. This error would, however, be reduced to about 0.2 mb if the amplitude of the swing were only 2°. This difficulty and, furthermore, the necessity of applying four corrections (index error, temperature of the instrument, latitude, reduction to sea level) to mercury barometer data are the reasons that such instruments are gradually losing importance in routine meteorological work at sea. Now that the instrument industry has succeeded in constructing aneroid barometers that are sufficiently reliable and will also remain so for some time, these handy barometers may be considered as standard instruments for the use on shipboard, especially as far as merchant vessels are concerned. Aneroid barometers and barographs specially adapted for maritime purposes are distinguished by a builtin damping device and a relatively powerful control exerted by the actuating element in order to avoid frictional errors. They should be mounted on shock-absorbing material in a position where they are least likely to be affected by concussion, vibration, or movement of the ship. The best results are generally obtained from a position as near to the center of flotation as possible. Since nearly all aneroid barometers are compensated for temperature, corrections have to be applied only with regard to scale error and reduction to sea level, which in most cases can be allowed for by adequate adjustment during calibration. The accuracy of atmospheric pressure data obtained at sea may be estimated to ± 0.5 mb. Under bad conditions at sea, especially if no damping device is provided, the approximate maximum error may reach ± 3 mb.

2.3.1.3 Air Temperature and Humidity. In merchant vessels temperature and humidity observations are usually made by means of well-ventilated psychrometers with direct reading. Ventilation may be operated manually, electrically, or by clockwork. Special care must be taken that psychrometers are well exposed in an air flow that is not affected by the ship, such as is the case at the windward side of the bridge. Furthermore, they must be protected against radiation, precipitation, and sea spray. Exposure in a fixed single screen is not suitable. According to Walden (1952, 1953-1954) the increase in the air temperature measured in a fixed screen of an old-fashioned (varnished!) type on sailing vessels against the temperature value obtained from aspirated psychrometer readings to the windward side was as follows:

2.3

REVIEW OF INSTRUMENTS AND METHODS

29

Averaged over all hours and conditions +O.9°C Averaged around the daily maximum +2.7°C Averaged with screen in full sunshine +4.5°C Averaged at the daily maximum with screen in full sunshine Single cases with screen in full sunshine and ventilation speed near the screen below 1 knot up to + l1.3°C We should take note from these values that great caution is necessary when conclusions are drawn from temperature observations in old log books. If a screen is still used for temperature and humidity measurements, it should be at least a portable one and hung to the windward side. Although temperature 'and humidity measurements obtained by operating ventilated psychrometers at windward generally seem to be fairly satisfactory for routine purposes, it is rather certain-and it can be proved by comparative measurements-that the disturbing effect of the ship, manifesting itself by conductive and radiative heating, is not completely removed if observations are made quite near to the superstructure of the ship, e.g., on the bridge. Real improvement can only be made if the measuring head is installed as far away from the ship's hull as possible, i.e., on the top of the mast. Such exposure necessarily requires distant reading equipment which confines measurements of this kind more or less to weather ships, lightships, research ships, and other ships with special meteorological tasks and equipment. Some information on the differences between "conventional" readings of air temperature on the bridge or elsewhere near the superstructure of a vessel and measurements obtained on the mast is given in the following: On German shipboard weather stations staffed with trained meteorologists, comparisons have been made between air temperatures measured by (screened and naturally ventilated) resistance thermometers situated at the top of the fore mast (height from 18 to 22 meters) and simultaneous readings of sling psychrometers at the height of the bridge (from 6 to 9 meters). In order to exclude differences due to thermal stratification only the cases near indifferent equilibrium were selected, i.e., the absolute value of the difference between the potential air temperature at the top of the mast and the temperature of the sea surface was always smaller than or equal to O.4°C. If the difference in potential air temperature "mast minus bridge" was negative it was regarded as representing the heating effect

30

2

METEOROLOGICAL OBSERVATIONS AND MEASUREMENTS

of the ship s superstructure on the temperature reading on the bridge. The mean value for this difference depended in some way on the particular situation on the ship concerned. A fairly reliable average was estimated to be -0.03°C (number of cases: 558). Owing to varying insolation a diurnal variation of about ± O.13°C was indicated. In addition, the obvious influence of the (relative) wind speed on the potential air temperature difference "mast minus bridge" was present, as may be inferred from Table II. The warming effect of the ship's superstructure on the temperature reading on the bridge evidently decreased with increasing ventilation. With very high wind speed the measurement of the air temperature at the top of the mast, being obtained with natural ventilation, was even higher than the reading on the bridge. That can, perhaps, be ascribed to the influence of sea spray, which may be responsible for the apparent lowering of the air temperature measured at the height of the bridge. TABLE II INFLUENCE OF THE SHIP'S SUPERSTRUCTURE ON THE MEASUREMENT OF AIR TEMPERATURE

Relative wind speed (knots) 0-9.5 10-19.5 20-29.5 >30

Mean difference (oC)a

Number of cases

-0.09 -0.03 -0.00 +0.09

112 249 166 31

a Between the potential air temperature measured on the top of the mast and that read on the bridge (mast minus bridge) for indifferent thermal stratification and different values of relative wind speed.

Air temperatures on shipboard may be measured to an accuracy of about ± 0.3°C if serious errors are avoided. Beside the traditional psychrometrica1 determination of atmospheric humidity, the direct electrical measurement of dew point temperature by means of hygroscopic material was introduced on shipboard during the past few years and it seems to provide a promising method which, however, is also limited to special ships. 2.3.1.4 Temperature of the Sea Surface. There are two principal methods of obtaining this information: (a) Taking a sample from the sea surface by means of a bucket and measuring its temperature with a thermometer.

2.3

REVIEW OF INSTRUMENTS AND METHODS

31

(b) Reading the temperature of the sea water that enters the condenser intake of the ship with a fluid thermometer. Although no attempt has ever been made to standardize the bucket, the thermometer, or the technique, procedure (a) is to be regarded as the standard method, particularly if judged from the scientific point of view, since it is the surface temperature of the sea which is mainly of interest for meteorological purposes. Certainly, it is not possible to obtain the real skin temperature of the sea surface since the sample taken by the bucket will contain water from lower parts, too. This question was investigated by Ball (1954), who found a mean difference between the actual surface temperature and the bucket temperature of - O.25°C. Measurements with this bucket will therefore yield fairly satisfactory values for the sea-surface temperature if they are quoted to the nearest O.5°C. (Further remarks on the thermal stratification in water near the sea surface are made in Section 5.1.2.) Of course, we must take care when constructing and handling a bucket to eliminate or at least minimize all the errors that may affect the water sample within the bucket by heat exchange with its surroundings, including cooling by evaporation. These requirements have been fulfilled quite satisfactorily; e.g., the rubber bucket with an inserted thermometer as described by Goedecke (1951) showed a maximum variation in water temperature of ± O.2°C during the first minute after taking the sample under conditions such that the air-sea temperature difference ranged from + 5°C to - 5°C and the wind speed went up to 8 meters/sec (Roll, 1951b). From the practical viewpoint, however, it must be stated that the bucket method is difficult to apply on large and fast ships and also on small ships in stormy weather. This is the reason that method (b) has been gaining in importance and has now reached a state where it may be considered as the second standard procedure. Its chief disadvantages, however, are that, first, it is not the temperature of the sea surface which is determined but the temperature at a depth of somewhere between 5 and 12 meters, depending on the size of the ship concerned; and, second, the measured value is liable to varying errors due to the heating caused by the ship. Some information about these errors can be derived from comparative measurements using both the bucket and the intake method. This subject has been given close attention by various maritime services (e.g., Kirk and Gordon, 1952). A summary of the discussion was published by the World Meteorological Organization (1954) but no definite conclusion could be drawn as to which of the two methods, (a) or (b), deserved preference. Additional material is presented in the

32

2

METEOROLOGICAL OBSERVATIONS AND MEASUREMENTS

following discussion. Figure 6(a) shows a frequency distribution of 5689 differences between simultaneously measured water temperatures obtained by bucket (B) and at the intake (I) at 4.5 meters' depth in the engine room. The mean difference B-1 is -O.18°C, i.e., the average intake temperature is nearly O.2°C higher than the bucket temperature. In 62 per cent of all cases the absolute difference was smaller than or equal to O.3°C; in 6 per cent of all cases the absolute difference exceeded I.O°C. More detailed information on the different effects could be gained by investigating the annual and diurnal variations of the differences B-1 and by discussing the influences of wind force and thermal stratification on them. In addition, water temperatures

o

-I

20 1\

1\ 1\ I }"

I

I

I

I

I

I I I

~b

I

,

I I

* I

I I ,

~ :>

I

u u

o

'0 10

, I I

:

15

'"uc::

I

15

I I

,

iI

I

1

I

,

I I

10

I

I

,

I

I

I

I

\ ,~

II \

5

5

}" \ \

\ \

\

\

-I

0 Temperature difference (OC)

FIG. 6. Results of simultaneous measurements of sea surface temperatures: (a) frequency of temperature differences between bucket and intake method; (b) frequency of temperature differences between bucket and tank method.

2.3

REVIEW OF INSTRUMENTS AND METHODS

33

were measured at the depth of the condenser intake but outside the ship. According to these studies the mean value of the differences B-1 of -O.18°C roughly corresponds to the mean increase of the intake temperature caused by the heating originating from the ship. This value will, of course, depend on the ship concerned and vary according to circumstances. With high insolation and calm weather this temperature increase may even reach O.9°C. On the other hand, investigations carried out by Arnot (1955) and Benditskii (1958) have shown that the heating effect seems to be less serious under different conditions. In addition, results of a comparison reported by Kirk and Gordon (1952) indicated that the transfer of heat from the engine room to the intake pipe is smaller while the ship is under way than the value obtained while the ship is on station. Furthermore, the influence of thermal stratification in water results in compensating approximately the above-mentioned increase of the intake temperature owing to the heating by the ship in summer, since then the sea surface is warmer (in favorable cases up to 1.6°C) than the water below. In winter, with small but reverse stratification in water, both effects are working in the same sense, thus enlarging the absolute amount of B - [. Summarizing this information and that from other sources, and bearing in mind also that the effect of thermal stratification in water will be reduced by the movement of the ship, we may say that the intake method may be liable to varying errors due to the heating of the ship, whereas the fact that the temperature is not measured at the sea surface but at a certain depth of 5-10 meters is significant only if there exists a substantial thermal stratification in water, i.e., in areas or at times with light winds and high insolation. Realizing that these two standard methods are, on the whole, of only limited benefit, the maritime services are searching for better procedures. Methods which try to avoid the limitations mentioned above are the following: . (c) The intake method with distant reading. Here it is assumed that the distant-reading thermometer can certainly be installed more easily than the direct-reading thermometer at a site where the heating effect of the ship is small. Benditskii (1958), for example, found that 96 per cent of all differences between temperatures obtained by bucket and by telemetering equipment at the intake did not exceed ± O.5°C. (d) The skin method. Here the temperature of a copper block attached to the bare metal of the ship's hull inside the ship below the water line, and protected against radiative and conductive heating

34

2

METEOROLOGICAL OBSER VAnONS AND MEASUREMENTS

from within the ship, is measured electrically. This method takes advantage of the relatively great heat conductivity of iron and steel. (e) The tank method. Here the temperature of the water in a small tank below the water line, and connected with the sea water outside the ship by several holes, is measured with resistance thermometers. Results of comparative measurements between bucket and sea water tank are given in Fig. 6(b). This figure shows the frequency distribution of 1158 differences between simultaneously measured water temperatures obtained by bucket (B) and in the tank (T) at 2 meters' depth by distant reading. The mean difference B - T is + 0.04"C. In 80 per cent of all the cases the absolute difference was smaller than or equal to 0.3°e; only in 0.7 per cent of all the cases did the absolute difference exceed l.aae. This result is remarkably better than that reached by the similar comparison made with method (b). (f) The infrared radiation thermometer for measuring the seasurface temperature. This instrument is designed specifically to convert the long-wave radiation from the sea surface into a measure of temperature. Up to now some success has been attained with an airborne model which has proved very useful in getting a rapid survey of the geographical distribution of sea-surface temperature. More recently satisfactory results seem to have been obtained also on shipboard (U.S. Weather Bureau, 1961). The ART (airborne radiation thermometer) senses the temperature of a surface layer about 5 x 10-4 em thick. This implies that the results gained will deviate to a certain degree from those furnished by methods (a)-(e), which give the temperature of a deeper layer. Moreover, the measurement is affected by the amount of water vapor present in the air below the instrument. The accuracy of this method seems to be lower than that of the conventional methods (Richardson and Wilkens, 1958). The improved methods (c)-(e) are practicable but they require certain installations on shipboard which are rather expensive. Therefore it seems unlikely that these methods will be introduced into general use on merchant vessels at present. But they may and should be used on special ships in order to serve the accuracy and economy of meteorological measurements at sea. With a view to the fact that a simple, inexpensive, and fully effective device for measuring sea surface temperature on merchant vessels is still lacking, the efforts to modify and improve the bucket method are worthwhile and deserve attention. Finally it should be mentioned that, with a stationary vessel, there may exist an appreciable increase in sea temperature in the neighborhood of the ship corresponding to insolation and wind drift. Amot

2.3

REVIEW OF INSTRUMENTS AND METHODS

35

(1955) found a difference in sea temperature of about O.3°C between localities close to the ship's side and those farther distant. The accuracy obtained when the sea surface temperature is measured with methods (a)-(e) may be estimated at O.2°C provided that conditions are not too unfavorable and serious errors are avoided. 2.3.1.5 Visibility. Although visibility forms one of the most important weather elements in marine navigation the methods of observing it at sea are comparatively poor. The absence of suitable objects in most cases makes it impossible to estimate visibility as accurately as it can be done at land stations and, therefore, only a IO-figure code is used for determination. Some help can be obtained when landmarks or other ships are sighted, but naturally only if the distances are measured in other ways (e.g., on the chart or by radar). On the high seas, however, the appearance of the horizon, as observed from different levels, is the only basis for estimating visibility. The values obtained in this way are, of course, doubtful, particularly if the visibility is low. Visibility meters of the transmissometer type can be used only if they have been adapted to the relatively short base line or light path available on shipboard. Unfortunately, the smallness of the air sample, the effect of the ship's smoke, and the radiative and convective heating of the air near the ship are severe handicaps which may prevent the measurement from being representative. Hence a visibility meter which functions by measuring the light emitted by a pulsed-light system and back-scattered from the atmosphere may be more suited to shipboard use. In this case no base line is necessary, the back-scatter measurement being made to the side of the ship which results in the sampling of a sufficiently typical atmosphere. 2.3.1.6 Cloud Characteristics. Visual methods prevail when cloud characteristics are observed at sea. The complete absence of disturbing objects-even very near the horizon-is certainly a remarkable advantage over cloud observations on land. Therefore, type and amount of cloud can be observed at sea rather easily, supposing that the observers have the necessary training. Estimating the height of cloud base is, however, as difficult as on land and, bearing in mind that most maritime observers are volunteers, we should not expect too high an accuracy with these estimated values.

36

2

METEOROLOGICAL OBSERVATIONS AND MEASUREMENTS

The ordinary method of measuring the cloud height by means of a searchlight is only of very limited value as the base line available on a ship is relatively short. Preference should, therefore, be given to devices that do not require a base line, e.g., a pulsed-light cloud searchlight, which measures electronically the time required for the reflection from the cloud base of a pulse emitted vertically from the ship. The amount and cost of equipment necessary for such measurements, however, restrict the application more or less to special ships, e.g., research vessels and ocean weather ships. 2.3.1. 7 Precipitation. In spite of the importance of getting exact information on the oceanic distribution of the amount of precipitation, this meteorological element has been treated like a stepchild of maritime observing technique. The reasons for this regrettable fact are the particular difficulties connected with rainfall measurements at sea. The ideal solution would require a rain gauge well protected against spray, splashing, and evaporation and installed on a small float in such a way that its orifice is at the sea surface. Then there would be reason to hope that the amount of precipitation arriving at the sea surface could be measured quite accurately. Unfortunately, this method cannot be generally applied at sea, except on very rare occasions (e.g., from stationary ships if the sea is sufficiently quiet). Installing a recording and automatically reporting rain gauge on an anchored buoy may be considered as a good approximation to the ideal solution, but no information on such equipment in use is available at present. Therefore, employing a ship as a base for the rain gauge cannot be avoided and, consequently, the following influences inherent to this procedure must be taken into account: (1) The disturbing effects of the ship and of the rain gauge on the air flow. (2) The effect of the motion of the gauge caused by the ship's movement. (3) The effect of sea spray. Besides, the analysis of rainfall amounts obtained on shipboard is complicated if the measuring is done on a moving vessel. Several investigations were executed in order to study the influences mentioned above, to test the different types of rain gauges, and to find a site on shipboard where the effect of those disturbances is a minimum. Ocean station vessels and lightships provide good opportunities for such studies especially if suitable reference stations exist on land

2.3

REVIEW OF INSTRUMENTS AND METHODS

37

nearby for comparison purposes. Skaar (1955), Verploegh (1957), Spinnangr (1958), and Roll (1958a) published results of relevant investigations which may be summarized as follows (World Meteorological Organization, 1962): The best exposure is to site the shipborne rain gauge (or at least its collector) as high as possible, preferably at a height of 16 meters or more. Then both the disturbing effect of the ship on the air flow and the percentage amount of sea water in the catch (resulting from sea spray) are reduced to a minimum. The influences of roll and pitch are not easy to estimate since their effect depends upon three additional factors as well, namely the mounting of the gauge (rigid or in gimbals), the slant of the rain, and the heeling of the ship. A detailed-mostly theoretical-discussion, however, shows that, first, the rigid mounting should be preferred to the installation on gimbals and, second, that on the whole this effect will cause a total error of less than - 12 per cent in the majority of cases, which is acceptable for the time being, particularly when compared with the errors caused by other influences. The ideal type of rain gauge for use on shipboard has not yet been found. In particular, it is not yet clear what benefit can be obtained from solid or wire mesh wind shields if the gauge is installed high up on a ship. A fixed collector sited high up on the mast and connected with a receiver on deck by a plastic pipe seems to come very near to the best solution if the problem of cleaning salt deposits from the apparatus can be solved. Here special attention must be devoted to fixing the collector in such a manner that its orifice is horizontal when the ship is lying in still water. Furthermore, a telemetering rain gauge installed on a buoy or the use of radar in estimating precipitation amounts at sea may be developed into useful techniques in the future. Until better apparatus is available, the marine rain gauge (Roll, 1959) may be considered as a useful preliminary instrument. The accuracy achieved with such rainfall measurements on shipboard is hard to determine and rather uncertain. Comparisons between monthly precipitation values obtained with marine rain gauges on lightships and on small flat islands nearby (Roll, 1958a) have resulted in a mean percentage rainfall deficit of - 10 per cent for the lightships, the standard deviation of the precipitation differences being 32 per cent.

38

2

METEOROLOGICAL OBSERVATIONS AND MEASUREMENTS

2.3.1.8 Ocean Waves. Although ocean waves are not an atmospheric but an oceanic phenomenon, they depend closely on atmospheric influences and, besides, are very important for the security and economy of marine navigation. These facts may be the reason that the observation of ocean waves forms part of the marine meteorological observing procedure at present. Within this scheme mean values of wave direction, height, and period are reported separately for sea and swell waves. The bulk of these observations is obtained not by using instruments but by visual observing methods. With a view to the fact that the chief characteristic of the appearance of the sea surface is its irregularity, little benefit-from the scientific standpoint-may be expected from mean values of wave height and period obtained by visual estimation or observation. Information that is really useful can only be provided by ocean wave recorders which up to now have been more or less confined to special ships, e.g., research vessels or ocean weather ships. The methods of measuring and recording ocean waves are manifold and cannot be treated here. A summary of information and further references were given by Roll (1957). A more detailed and more up-to-date description can be found in the Special Publication on Oceanographic Instrumentation (U.S. Navy, Hydrographic Office, 1960). 2.3.1.9 Radiation. During the past few years radiation measurements have also been included in the observational program at sea. In 1956 radiation measuring equipment was installed aboard the four British weather ships as a contribution to the program of the International Geophysical Year. * Total radiation on a horizontal surface is recorded by a MollGorczynski thermopile solarimeter mounted on a gimballed compass. The site of the instrument must be suitably chosen so that it is least subject to obstruction. Net flux of radiation is measured by means of two ventilated fluxplate radiometers which are mounted on aluminum alloy booms projecting about 4.5 meters outboard on both sides of the ship in the vicinity of the bridge structure. In order to avoid the disturbing influences originating from the ship each radiometer is screened so that only the upper and lower half hemispheres away from the ship

* The details given in the following were taken from a personal communication for which the author is indebted to Cdr. C. E. N. Frankcom, Marine Superintendent, Meteorological Office, London.

2.3

REVIEW OF INSTRUMENTS AND METHODS

39

are used for measuring, giving a pair record on the recording potentiometer. To ensure strict similarity both radiometers are ventilated by one blower. The instruments are stabilized (by a simple undamped pendulum system) for roll but not for pitch. In practical operation some difficulties have arisen from corrosion, which caused electrical faults. Unfavorable weather conditions, such as rain, heavy spray, and high winds of Beaufort 7 and more impeded radiation measurements on shipboard. Further information can be found in the Special Publication on Oceanographic Instrumentation (U.S. Navy, Hydrographic Office, 1960). 2.3.2 Aerological Measurements 2.3.2.1 Historical Review. Until radio techniques permitted one to have meteorological sondes broadcast their measurements to the ground station, aerological work at sea was distinguished from similar measurements on land by certain characteristics related to the necessity of getting the instrument back after it had come down again. In this respect reference could be made to .the tandem balloon technique introduced by Hergesell (1905). In this procedure two balloons were linked together by an electrically controlled hook which released one of the balloons at a predetermined level. The second balloon-not being able to lift the instrument-carried it down gently and acted as a signal in order to facilitate its rescue. This method was used particularly for getting information from the upper troposphere, and possibly from the stratosphere. It required favorable wind conditions, continuous pursuit of the balloon with a theodolite, and a sufficiently powerful vessel, skilfully operated, if a successful sounding were to be achieved. All of these requirements have seldom been present; we have, therefore, only a few such measurements. Also the captive balloon and kite techniques were adapted for use on shipboard, the chief difficulty being in the handling of this apparatus in the disturbed flow around the ship. With the captive balloon technique it was possible to take advantage of the ship's ability to steam downwind at suitable speed, thus keeping the balloon always in a relative calm and simultaneously securing values of the upper wind. The latter method was successfully employed on the Lake of Constance for many years (Kleinschmidt and Huss, 1935; Huss, 1961). With kite ascents there was no such possibility of overcoming the wind turbulence in the neighborhood of the ship. Therefore, in the logs of research voyages, many notes on accidents are to be found, reporting kite and instrument lost. Nevertheless, kites had to be used,

40

2

METEOROLOGICAL OBSERVATIONS AND MEASUREMENTS

since they provided the only possibility of obtaining meteorological information from the lower troposphere up to 3000 meters as to air temperature, pressure, and humidity, as well as wind direction and speed. From 1900 to the early thirties this awkward technique was employed more or less regularly and successfully on many marine expeditions, thus serving as a good example of what can be accomplished in maritime meteorology with skill and tenacity. A detailed description was given by Reger (Kuhlbrodt and Reger, 1933). Turning now to pilot balloon ascents we also have to report on a special development for use on shipboard. The "mirror theodolite" was constructed by Wegener and Kuhlbrodt (1922a, b) and consists of a combination of a theodolite in gimbals and a sextant, thus enabling the observer to measure the elevation from the true horizon. This sounds easier than it has been in practice. Tracking a pilot balloon from a rolling and pitching vessel, which is subject to irregular variations of course, and where unfavorable clouds, parts of the ship's superstructure, and sometimes its own smoke try to interfere, may be indeed a "terrific job," and good luck is indispensable if a high and reliable sounding is to be accomplished. Of course, the ascent rate of the balloon had to be assumed to be constant if the height could not be determined by other means (range finder or radiosonde). A comprehensive account of the pilot balloon technique on shipboard can be found in the report of Kuhlbrodt and Reger (1933) on the ascents carried out during the German Atlantic Expedition 1925-27 on the research vessel Meteor. 2.3.2.2 Modern Equipment. Against this historical background we should see the new electronic methods which were developed and tested in the mid-thirties and which now have reached a remarkable degree of reliability. Only then will we realize what decisive progress has been achieved with regard to the extent, accuracy, and regularity of the soundings, as well as to the simplification of operation on shipboard. For measuring and reporting temperature, humidity, and pressure up to heights of 30 km, radiosondes are carried aloftgenerally twice daily-by means of a free flying balloon. A radar target is suspended from the balloon to allow it to be tracked and, consequently, to enable the upper winds to be measured by means of air search radar or fire control radar, which supply values of azimuth, elevation, and slant range. The latest outfits may even include Doppler radar, a device that directly senses the balloon's speed radial to the radar antenna and relative to the ship. A detailed description of the modern instruments for upper air observations can be found in the

2.3

REVIEW OF INSTRUMENTS AND METHODS

41

"Handbook of Meteorological Instruments," Part II, published by the Meteorological Office, London, in 1961. As far as possible the technique is the same as adopted at land stations, using the same apparatus but with certain modifications, such as gyro-stabilization, in order to conform with the necessities aboard a ship. Since most air search radar sets cannot scan above an elevation of 60° to 70°, it may become necessary during an upper wind sounding to direct the motion of the ship accordingly. Steaming downwind is, furthermore, required with strong winds in order to keep the balloon within radar range. One of the main scientific advantages of these new electronic techniques is the fact that the former "fine weather selection" of pilot balloon ascents, which was caused by the unavoidable influence of the weather, in particular of the cloud amount, on their practicability and maximum height, has now been eliminated. This is an indispensable supposition for every synoptic utilization or statistical evaluation of such measurements. Unfortunately the costs involved in the use of electronic equipment are rather high and confine the method more or less to special ships, e.g., ocean station vessels and research ships. For this reason the aerological network at sea is by no means satisfactory, particularly in the southern hemisphere. Therefore, great efforts are being made to intensify aerological observation on shipboard with the particular aim of executing regular measurements on suitable merchant vessels on the different sea routes. While remarkable success has been achieved in carrying out radiosonde observations on board merchant ships, considerable difficulties have been met with regard to radio wind measurements on shipboard in view of the expensive and complicated equipment needed for them. High priority has been given to the development of a simple, low-cost device which will yield satisfactory radio wind data on board merchant vessels. During recent years meteorological rockets have come into use also on research vessels in order to extend the measuring height up to about 100 km. The main meteorological quantities which can be measured by means of rockets are atmospheric pressure, air temperature and density, ozone content, solar radiation, and wind. In general the instruments used differ greatly from those applied to the balloon technique and are not yet out of the experimental stage. The measuring and reporting is mostly done during the descent of the instruments, which are released from the rocket at its maximum height and carried down by a parachute.

3. Composition and Properties of the Marine Atmosphere 3.1

GENERAL CONSIDERATIONS

Although the purpose of this monograph is to describe the physics of the marine atmosphere we shall now endeavor to summarize some facts which belong to the field of atmospheric chemistry, rather than physical processes. This will not mean a substantial deviation from our original way of presentation, but it should be regarded more as an effort to consider the characteristic properties of the "material" in question before starting with the intended interpretation of its kinetics and dynamics. Our atmosphere consists of the well-known mixture of nitrogen (76-78 per cent by volume), oxygen (20-21 per cent), argon (0.9 per cent), and some other rare gases (in very small percentages), and, additionally, of matter that-although small in volume and weightplays an important role in many meteorological processes. In the first place, of course, water vapor must be mentioned; it exists as a very variable component (up to 4 per cent), present in all three phases (gaseous, liquid, and solid matter) and, therefore, of particular interest. Furthermore, there are ozone, carbon dioxide, and other gaseous substances whose participation in atmospheric processes is not yet completely understood. It is quite obvious that, moreover, reference must be made to atmospheric nuclei which are partly of natural origin and partly produced by human activities. Numerous studies have been devoted to clarifying the nature and origin of the latter colloid constituents of the atmosphere and, in particular, to discovering their significance with regard to atmospheric processes such as the mechanism of cloud formation and precipitation. If these particles bear electrical charges they are called ions and are, if sufficiently small and mobile, of importance for atmospheric electricity. 42

3.2

ATMOSPHERIC NUCLEI ABOVE THE OCEANS

43

Also organic matter may be present and playa certain part in the interchange among ocean, atmosphere, and continent. Finally, radioactive substances originating from natural and artificial sources may be mentioned, although they seem to be more important as tracer substances for the study of atmospheric motion than as agents in such processes. Bearing in mind that we are only concerned with the marine atmosphere we shall attempt to present in the following a condensed review of those results regarding atmospheric nuclei, trace substances, atmospheric electricity, and radioactivity that were obtained by measurements in the marine atmosphere and that are or may become closely related to phenomena and processes in it. 3.2

ATMOSPHERIC NUCLEI ABOVE THE OCEANS

When speaking of the atmosphere as a colloid system wherein solid or liquid matter is suspended or dissolved we may refer to it as an aerosol. Today, we are accustomed to call the particulate substances themselves aerosols, thus deviating from the original notation. The two main classes of aerosol are the condensation nuclei and the freezing nuclei. Condensation nuclei are necessary for the formation of cloud droplets from water vapor in saturated or slightly supersaturated air. Freezing nuclei are assumed to take an active part in the process of ice nucleation in supercooled clouds by inducing supercooled cloud droplets to freeze and so provide the ice crystals necessary for the production of precipitation. Considering the nature of the condensation nuclei, a subdivision may be made between particles that are insoluble in water and those that consist of droplets of solutions. For the process of condensation water droplets are the most important. The significance ofthe insoluble particles depends upon whether they are wettable or not. In the latter case larger supersaturations are needed for condensation than are required for water droplets. Thus such nuclei are of less importance. Owing to coagulation various intermediate or mixed types exist (Junge, 1951). The natural aerosol is characterized by a wide range of particle sizes from about 10- 7 to 10-3 cm in radius and also by variations of nuclei concentrations which cover more than six orders of magnitude (from about 0 to 4 X 166 cmr"). Therefore, it is necessary and also useful to subdivide the whole nuclei spectrum into different parts which are distinguished by certain common features with reference to their nature, origin, and importance for meteorological processes.

TABLE III SUBDIVISION OF THE ATMOSPHERIC NUCLEI SPECTRUM WITH REGARD TO SIZE, ORIGIN, AND METEOROLOGICAL IMPORTANCE OF NUCLEl u

Nomenclature

I

.~

.c .. o ... 0 .c .... .~

~

....

I

Large nuclei

AITKEN nuclei

Giant nuclei

Cloud physics

Atmospheric optics

cD@

"" ....

!i~"

~

.....

electricity

I

Small ions

Large ions

Air chemistry Condensation and sublimation of vapors

:E""

s

:~ ...

S 0

.o ....... ~

'"

""

Particles which contain main aerosol mass

Mechanical disruption and disper-sal of matter

Formation of dust and sea spray

Z

Coagulation

Radius of particles (cm) 110-8 a

After Junge (1952) and Mason (1957a).

10- 7

10- 6

10- 5

10-
-------+----"..---...p.;~------+---1

1 ~:::;, ~\ _CLOUD

1000

I<X

+~ +

o

o

00

z

,

'0

"

TC

TOP

10-'

LOCAL CU +---BASES 20

25

Z <X

;: 10-2 f--:>...,__---+------+-~c_-~__+IT_-----+-----____::::J 0:

W

I<X W

0:

2740

(!)

...

'E 10-3>-------+--"----+--------+__+---"--~rt_-----__1 u

10- 1 2 >10- 11 >10- 10 >10- 9

1.4 1.2 2.0 4.7

2.0 4.4 14.5

124 397

Total amount of sea-salt

1.5

3.3

115

U

b

Computed from Fig. 7. Subscripts give heights in meters.

3.2

ATMOSPHERIC NUCLEI ABOVE THE OCEANS

55

(see Fig. 7). In view of these results it is not surprising that the vertical distribution of sea-salt nuclei also showed a marked dependence on thermal stability (Woodcock and Gifford, 1949), the rate of decline being great in thermally stable air, whereas little change with altitude was observed in well-mixed air flowing over warmer water. All these influences may contribute to the fact that the rate of decrease with height of the sea-salt particle concentration was found different by other authors and at other places; a decrease smaller than Woodcock's value, and approximately the same for all particle sizes, was observed by Lodge (1955), who measured the size distributions of sea-salt nuclei up to 3000 meters altitude over Puerto Rico under typical maritime conditions. He even found in four of his five flights that over the sea an increase in chloride particle concentration occurred between 30 and 150 meters altitude when the wind force was low and, therefore, the supply of sea salt from the ocean surface negligible. 3.2.2.4 Correlation with Wind Speed. Contrary to the behavior of the Aitken nuclei, sea-salt particles show a distinct correlation with wind speed which is not surprising for nuclei produced at the sea surface by wind action. As can be inferred from Fig. 8 increasing winds were associated with a rather consistent pattern of increase both in numbers and sizes of particles near the cloud base over the sea in the Hawaii area. Attention should be drawn to the curve for a wind force of 12 Beaufort, which was obtained during a tropical storm near Florida. It is highly impressive to see that the most energetic performance of the marine atmosphere is able to raise the number of largest giant sea-salt nuclei with m > 10- 8 gm from 1 per meters at 4 Beaufort to about 2 x 104 per meter". The remarkable increase with wind speed is particularly distinct if we consider the total amount of sea salt in the air as presented in Fig. 9. Adequate results for the relations between concentration of seasalt nuclei and wind speed were obtained by Moore (1952) on the ocean weather station Item for m > 10-11 gm up to wind speeds of 15 meters/sec. He also found a clear correlation between concentration of nuclei of m > 5 x 10- 9 gm and wave height, which showed a linear increase of the former with growing waves. Metnieks (1958), however, reported a somewhat different relation between concentration and wind speed characterized by a higher rate of increase with wind speeds from 5.1 to 6.7 meters/sec than with lower ones. An effort to explain this dependence of the concentration of seaspray particles on altitude and wind speed was made by Junge (1957a).

56

3

COMPOSITION AND PROPERTIES

Particle radius at 99 % rh (10- 4 em) 5.1

11.0

23.7 Wind force I

51.1 Number of sompling doys I

3

4

7

2

4 11 ~--~-..::----t---5f----+5----,j

1:

12

Ol

I

"w:;: 1 2 10- ~--"""'-t"""~

"0

a

.S:!

"0

.!:

§ 10-2 t - - - - - - t " £ ... 2a Q)

0, 10-3

t------t----),

r 10-13 (giant nuclei) were found only in concentrations of about 10/cm 3 in the marine atmosphere and it is quite obvious that they are not numerous enough to constitute a major source of cloud-forming nuclei, although they may be essential for initiating an efficient coalescence process such as Ludlam (1951) indicated was required for the production of showers. On the other hand, the possible assumption that there might exist much larger concentrations of salt particles, too small to be detected by the methods employed for sampling and measuring sea-salt nuclei, and that, consequently, such small particles might be found in an Aitken counter, does not fit in with the results given for Aitken nuclei in Section 3.2.1. In order to clarify the problem of production, one should refer to the following results: Moore and Mason (1954) investigated the rate of production of sea-salt nuclei with m > 2 x 10- 13 gm by breaking waves in a windwave tunnel and obtained a value of 40 cm-2sec-1 for the strongest winds which corresponded to a speed of 16 meters/sec at a height of 10 meters. This result is in good agreement with an estimate made by the same authors from their measured size distributions of large and giant nuclei over the ocean. For nuclei with m > 2 x 10- 14 gm a production rate of about 86 cm-2sec~1 was obtained. For a better insight into the mechanism of sea-salt nuclei production further investigation is necessary. If the wind over the sea is strong enough to create whitecaps, air is captured by the collapsing wavecrests and rises to the sea surface in the form of tiny bubbles. Moreover, all forms of precipitation particles are effective bubble producers when striking the sea surface, as was shown by Blanchard and Woodcock in 1957. When bursting at the surface these bubbles certainly cause a transport of sea water particles into the air which needs to be investigated in detail. Woodcock et al. (1953), Kientzler et al. (1954), Knelman et al, (1954), and also Moore and Mason (1954) studied, partly with the aid

60

3

COMPOSITION AND PROPERTIES

of high-speed motion pictures, the different phases of a bubble bursting at the surface of sea water, and they arrived at the following results: There are two phases when a bursting bubble has an opportunity to eject water particles into the air (Fig. 11): (1) The hemispheric cap of a bubble rising from below breaks the surface where it is thinnest, causing a disruption of the film, probably into many fragments which, however, have not yet been photographed. (2) After the bursting of the cap, a narrow unstable jet evolves from the bottom of the collapsing bubble and breaks up to form from one to five droplets which are ejected upward to heights that are great compared with the size of the bubble. The droplets are about 10-15 per cent of the corresponding bubble size (diameter between 3 x 10-2 and 4.3 x 10-1 em), They carry an appreciable electric charge which may be significant for electrification processes in the marine atmosphere (Blanchard, 1955) (see Sections 3.4.2.1 and 3.4.5.2). According to Mason (1957b) only the droplets produced by very small bubbles during phase (2) may become giant nuclei and so contribute to the supply of potential condensation particles. The droplets resulting from the bursting of bubbles larger than 5 x 10-2 cm in diameter will fall back quickly into the sea. Blanchard and Woodcock (1957), who investigated phase (2) of bubble bursting in greater detail showed that the great majority of the bubbles caused by breaking waves are < 2 x 10-2 cm. They concluded that most of the sea-salt nuclei are produced via the jet mechanism [phase (2)] and, assuming that only one of the droplets ejected from each bursting bubble remains air borne, they estimated the relevant production rate at 34 cm- 2sec-1, which corresponds to about 3 cm-2sec-1 if it is accepted that 10 per cent of the sea surface is active in nuclei production by white caps. In a later paper Woodcock and Spencer (1961) pointed out that enormous numbers of giant hygroscopic particles consisting mostly of sea salt are present in the steam clouds arising when molten lava encounters sea water. Since the rate of production of these nuclei is estimated to be from one to six million times greater than that produced from the sea surface on the average, they suggest that such an occurrence, although rather rare and confined to a very limited area, might even contribute a weight of sea-salt nuclei per unit of time that is equal to a considerable fraction of the total average production of all oceans. Mason (1957b) tried to get an idea of the number of nuclei produced by a bursting bubble in phase (1), which had so far escaped

FIG. 11. Ten consecutive stages of the bursting of an air bubble at a water surface. (From Kientzler et al., 1954.)

62

3

COMPOSITION AND PROPERTIES

detection by cinematography. Observations were made in an expansion chamber of air bubbles, ranging in diameter from 2.5 x 1O~2 to 2.15 x 10-1 cm, bursting in sea water. They led to an overall estimate of 300 ± 80 nuclei per bubble. Electron micrographs proved that the diameters of these particles were mostly between 2 x 10-5 and 5 x 10-5 em and that the smallest ones (10-5 em) contained about 10-15 gm of salt. Summing up all these results, Mason (1957b) came to the following conclusions: (a) Extrapolation of the measured distribution curves in Fig. 10 down to nuclear masses of 10-15 gm gave as an estimate for the total concentration of sea-salt nuclei with m > 10-15 gm 100/cm 3 (b) With (a) the share of sea-salt nuclei in the total nucleus concentration measured by Aitken counter (see Section 3.2.1.1) would be no more than about 20 per cent. Therefore, no strong reaction of the total nucleus concentration is to be expected with wind speed increasing (as observed). (c) Supposing that the concentration of salt particles in the lower layers of the atmosphere is more or less proportional to their rate of production at the sea surface, we arrive, according to (a), at an estimated total production rate of sea-salt nuclei with m > 10-15 gm of about 1000 cm-2sec- 1 since a production rate of about 100 cm- 2sec-1 was necessary to account for a concentration of 1O/cm3 with m > 2 x 10- 14 gm. (d) The result (c) would need a rate of bubble formation of about 3 cm-2sec-1 which seems to be reasonable and is also in agreement with the abovementioned estimate of Blanchard and Woodcock (1957) of the frequency of air bubbles produced by breaking waves. However, no consideration was given to other bubble-producing mechanisms such as the impact of raindrops or the melting of snowflakes. The figures in (a) and (c) estimated by Mason for both the total concentration and the total production rate of sea-salt nuclei account only for about 20 per cent of the quantities of condensation nuclei both needed for the formation of precipitating clouds and lost from the atmosphere by precipitation. This may also be gathered from a very rough evaluation (Mason, 1957b) starting from figures on the annual global rainfall and arriving at an estimate of the necessary production rate of condensation nuclei. This implies that about 80 per cent of

3.2

ATMOSPHERIC NUCLEI ABOVE THE OCEANS

63

the condensation nuclei must be supplied from the continents partly by combustion products and partly by dust particles from the earth's surface. Mason's estimate received some support from electron microscope measurements of nuclei found in cloud and fog droplets near the coast of Japan by Kuroiwa (1953) and Yamamoto and Ohtake (1953), which showed that nuclei produced by combustion amounted to 40 per cent of all droplets whereas both sea-salt and soil particles reached only 20 per cent of the total. A similar investigation by Isono (1957), carried out with residues of cloud droplets at the summit of a mountain, resulted in 30 per cent of the nuclei being mainly composed of sea salt. Mason's results as regards the number of sea-salt nuclei produced by bursting air bubbles were critically viewed by Rau (1956b), who was not able to confirm the production rate of 300 ± 80 nuclei per bubble, estimated by Mason, but found the process of bursting bubbles to be mostly ineffective for producing nuclei. According to his investigation the process of spraying is much more effective and may even account for concentrations of nuclei with m > 10- 15 gm of about 106jcm3 . Such a figure would, of course, considerably modify the outcome of the deliberations described above on the role that sea-salt nuclei play in condensation. There is some doubt, however, whether the level of efficiency of spraying achieved in the laboratory will also be reached in nature. Furthermore, reference should be made to an effect which was studied by Facy (1951) and later by Twomey and McMaster (1955). These authors examined the behavior of salt droplets when the environment humidity was lowered sufficiently (to around 70 per cent relative humidity for droplets of 10- 4 to 10- 3 em radius) for crystallization to take place, and they found that at least several hundred minute salt crystals with a mass range of from 10- 18 to 10- 14 gm were produced during the crystallization of each of the larger salt particles. These small salt crystals are effective condensation nuclei at moderate supersaturation. The process of crystallization should, therefore, also be taken into account when the nature and the origin of the condensation nuclei in the marine atmosphere are considered. Finally, it is worth mentioning that, beside the hygroscopic particles from the sea surface which are well known to be active nuclei for the condensation of water vapor to the droplet state, particles with icenucleating properties also are released from the ocean to the atmosphere, as preliminary tests of Brier and Kline (1959) have indicated. In air samples drawn in a laboratory from near the surface of agitated

64

3

COMPOSITION AND PROPERTIES

sea water they found an increase in concentration of ice nuclei of from about 0.5 to 300 per liter if the temperature was lowered from -15° to - 30°C. The nature of these ice nuclei is, however, not yet quite clear. According to Georgii and Metnieks (1958), who studied the activity of sea-salt particles in the process of ice nucleation of supercooled clouds on the west coast of Ireland during the summer of 1958, the concentration of freezing nuclei active above - 30°C showed no relationship to that of the sea-salt particles. There was even some indication that the most active freezing nuclei were particles of continental origin. Battan and Riley (1960), however, concluded from observations made on Mount Bigelow in southeastern Arizona that their data could be most readily reconciled with the hypothesis that the oceans are an important source of ice-crystal nuclei. After discussing the production of sea-salt nuclei at the ocean surface one might be tempted to trace their further life history, which is determined by transporting and distributing forces, by the processes of condensation, coagulation, and precipitation, and which would certainly show many interesting, sometimes even fascinating, features and problems. Such a review would necessarily have to include the continents, since we know from a paper of Junge and Gustafson (1957) that even large sea-salt particles may travel considerable distances in the atmosphere over the continents without being removed by precipitation. These considerations would, however, go far beyond the range of this monograph. 3.3

CHEMISTRY OF THE MARINE ATMOSPHERE

In the preceding section we dealt with the physical aspects of atmospheric nuclei. We studied their concentration and size, we tried to reveal their interrelation with meteorological elements and phenomena, and, finally, we even endeavored to clarify their nature and origin, as far as this was possible with purely physical and statistical methods. Looking back we realize that, although important and helpful information was gained, neither did we get to the "root of things" -namely, to the fundamental principles which govern those colloid processes and which we ought to know if we aspire to a thorough and full understanding of the phenomena-nor did we acquire sufficient knowledge on the real nature and origin of the substances involved. In this situation effective help and elucidating information can only be expected from atmospheric chemistry, a relatively new branch of meteorology which, however, is developing quickly and has already achieved promising results.

3.3

CHEMISTRY OF THE MARINE ATMOSPHERE

65

Basically, trace substances in the atmosphere can be present as solid or liquid particles, or as gases. It is, therefore, essential that, when dealing with air chemistry, we clearly distinguish between particulate matter and gaseous substances, both of which should be measured simultaneously but separately. Only then will we be able to describe completely and, perhaps, understand the natural process in question. Following these lines we shall deal separately with the composition of particles and gas traces in the marine atmosphere and then we will add some remarks on the carbon dioxide content of marine air, which deserves special attention. 3.3.1 Composition of Particles Relevant measurements were made by Junge in Florida (1956) and in Hawaii (1957b), and by Lodge et al. (1960) in the North Pacific on the ocean station November. The air samples were taken with particular care in order to avoid contamination resulting from human activities on shipboard or at the coast. Thus the results of the analyses can be considered as fairly representative of maritime conditions. While Lodge and his colleagues did not give separate values for the different types of atmospheric nuclei, Junge, by using a two-stage cascade impactor which separated the two radius ranges from 8 x 10-6 to 8 X 10-5 em and from 8 x 10-5 to 8 X 10- 4 em, was able to differentiate almost exactly between large and giant nuclei (see Table III). The analyses were confined to that matter which was soluble in distilled water. The amount of insoluble matter, which may become considerable at some continental locations, could not be measured. The places and periods of observation and the components analyzed are shown in the tabulation. Observer

Place

Date

Junge

Homestead, Florida

July 19-August 3, 1954

Junge

Hilo Harbour, Hawaii

October-November, 1954

Lodge, et

at. Ocean station

November 30° N, 140 W Ocean station November 30° N, 140 W

July 27-August 13, 1957

Components NH!, N03", Cl", S04", Nat NH!, NOi, ci-, S04" Chloride, sulfate

0

Lodge et

at.

0

July 31-August 28, 1958

Chloride, sulfate, nitrate, organic material

66

3

COMPOSITION AND PROPERTIES

Although the number of observations is comparatively small and also unevenly distributed, the results are of importance since very little is known about the composition of aerosols at sea. The results published by Junge are summarized in Table VII. From the concentrations measured in Florida, only the values with sea breeze were included. The figures give the average concentrations of the various components in micrograms (10- 6 gm) per meter" of air. The figures in parentheses are the average limits of detection. Their meaning is as follows: When a component did not show up in the analysis, it can only be said that it was not present above the limit of detection, which depends on the component and on the size of the sample in question. When the averages were computed, this limit of detection was taken in those cases in which the relevant component was too small to be determined by the analysis. Thus maximum values were obtained. The difference between the average value and the average limit of detection is the minimum value. Should both figures be equal, nothing was found above the limit of detection. Lodge and his colleagues published their findings in the form of a cumulative frequency distribution of analyzed components which is reproduced in Fig. 12. All results refer to sea level. The following information can be taken from Table VII and Fig. 12: NH4 was confined almost completely to large particles. That its amount was small, particularly in Hawaii, clearly indicates its continen tal origin. N03 was concentrated predominantly in giant particles. Its amount decreased with increasing maritime influence (Florida -+ Hawaii). This would point to a continental origin. On the other hand, Junge found N03 concentrations even lower than those measured in Hawaii in the giant particles of purely continental air masses on the east coast of the U.S.A., the nitrate also being concentrated in giant particles here. In this region the highest concentrations belonged to maritime air masses, while cities and industrial areas did not contribute substantially to the N03 amount. Junge finally arrived at the tentative conclusion that N03 might be formed by the oxidation of N02 to N03 when sea-salt nuclei mix with continental air masses, thus confining the source of N03 to coastal areas. This result requires further investigation. On some days the samples from Florida were also examined with regard to N02. No trace was found above the limit of detection. Referring to similar results at other continental places, Junge states rather definitely that no N02 is present in natural aerosols.

TABLE VII COMPOSITION OF MARITIME AEROSOLa, Place, kind, and number of data

Florida Average value Average limit of detection Number of values Hawaii Average value Average limit of detection Number of values a b

b

NH1

NO;

Cl-

Large Giant particles particles

Large Giant particles particles

Large Giant particles particles

SO~-

0.057 av

(4.7)

rectangular coordinates with x axis along direction of the mean wind, z vertical component wind velocities along x, z component mean wind velocities along x, z departures from the mean flow internal shear stress or vertical transport of horizontal momentum (dyn cm

E

50

Cl>

>

o .0 o

s:

20

0'

Cl>

I

10 f-------+-1,-----,f---+----/t---+---+-----i~----+--

200

400

600

Wind speed (em/sec) FIG. 37. Wind profiles over a water surface under near-adiabatic conditions. (After Roll, 1948a). The profiles are grouped according to wind speed.

even if a wide range of wave heights was considered. This result once more emphasizes the peculiar character of the sea surface as lower boundary of an air flow. Perhaps more success would be obtained if the "roughness factor" defined by Schooley (1961b) (Section 4.2.3) were used as representative of the sea surface characteristics. In this connection it should be mentioned that Miyazaki (1951a, b) theoretically attempted to relate the dynamic roughness of the sea surface to ocean wave elements by assuming that eddies are generated in the air-sea boundary layer and that the width of the eddy-generating

4.3

WIND FIELD IMMEDIATELY OVER SEA SURFACE

137

layer and the largest eddy diameter are determined-for large Reynolds numbers-by the height and the length of the waves, respectively. This concept appears to be based, however, on a rather theoretical idea of the airflow around moving water waves which by no means has been clarified up to now. Besides, mean values of wave height and length cannot be considered as truly representative characteristics of the irregular wave pattern. No verification of Miyazaki's formula has become known so far, apart from recent measurements of Vinogradova (1960) that seem to point to a relation between the dynamic roughness of the sea surface and the mean steepness of the surface waves. While the results concerning a possible relation between dynamic roughness and waves are rather uniform, although only in the negation, the statements are conflicting with regard to the variation of the dynamic roughness depending on the characteristics of the air flow. At first it must be decided which quantity of the air flow shall be taken as representative. The velocity of the wind, although it is often used as an independent variable, does not seem to be a suitable one since it varies with the altitude. It is more satisfactory to take the friction velocity u, as the quantity representative of the air flow. This was done by several authors. Their results may be summarized in two antagonistic statements as follows: (a) Roll (1948a) found that his wind profile measurements led to the relation (4.16) Zo = v!(2.lu*) This equation is in conformity with von Karman's formula [Eq. (4.15)] for the turbulent flow along a hydrodynamically smooth boundary, thus suggesting the conclusion that the air flow over the sea surface seems to obey the law of the hydrodynamically smooth flow, the pertinent dynamic roughness being about four times as high as for a smooth boundary. This is in good agreement with the results of Motzfeld (1937) who, in his wind-tunnel investigations, found that for round-crested (solid) waves Zo was a function of the maximum angle am of the wave profile, so that zn

= (v!3u*)

x

10 3.17(tan Gtm l u . >

(4.17)

It should be mentioned further that Rossby (1936) arrived at a similar

conclusion when considering the lower parts of the wind profile measurements of Wiist (1920) and Shoulejkin (1928). More recently Takahashi (1958) deduced, from his own wind profile data, that the

138

4

FLOW CHARACTERISTICS OF MARINE ATMOSPHERE

concept of the hydrodynamically smooth character of the sea surface holds true. (b) In contradiction to (a), Charnock (1955), discussing his own wind profile measurements and those of some other authors and after stating that the dynamic roughness Zo was comparatively independent of fetch or stability but largely determined by U*, suggested the relation Zo = u~/(ag), (4.18) the approximate value of the dimensionless constant a being 81.1. Equation (4.18) implies an increase of Zo with growing u; and, therefore, differs distinctly from Eqs. (4.16) and (4.17) which show a decrease. Charnock's relation was-at least qualitatively-confirmed by the wind profile measurements of Hay (1955) and Deacon et al. (1956), which also indicated an increase of zn with increasing u., The suitable value of the constant a was about 13 for the former measurements and 20 for the latter. In the range of friction velocities below 10 ern/sec Charnock's formula received some support from relevant results reported by Roll (1948a) and Bruce et al. (1961) and, to a minor degree, from the wind profiles measured by Portman (1960), who obtained extremely small values of the dynamic roughness Zo which, however, seem to be affected by the rather strong unstable stratification that existed there. The relationship advanced by Charnock cannot be interpreted in terms of a hydrodynamically smooth or rough flow. Much more, it may be regarded as an empirical result of the endeavors to find a suitable representation of the air flow over a water surface. A task which remains to be done is to interpret this empirical result in the light of our (as yet rather incomplete) knowledge of the characteristic processes near and in the sea surface. An illustration of the situation, particularly of the discrepancies between (a) and (b), is given in Fig. 38 where only wind profile measurements that are nearly logarithmic and that have been published in a suitable form are used. When looking at this diagram one may have the impression that-a certain scatter of the observations admitted-the data of Roll (1948a) are more or less covered by Charnock's curve, too. Apart from this argument we may further state that Charnock's concept (b) appears to be more realistic and, therefore, more adequate than (a) since it is very difficult to imagine that the roughness elements of the wavy and choppy sea surface should be small as compared with the thickness of the laminar atmospheric boundary layer (order of magnitude '" 0.1 em), which would be implied in the case of a hydrodynamically smooth flow.

4.3

WIND FIELD IMMEDIATELY OVER SEA SURFACE

139

Unfortunately, this perplexing situation appears by no means clarified when we refer to more recent profile measurements, e.g, to those which were most carefully executed by Brocks (1959b, 1962). He used a specially constructed buoy as carrier for the instruments. The profiles proved to be closely logarithmic under adiabatic conditions but the variation of the dynamic roughness seemed to be insignificant over a wind speed range of from 2 to 14 meters/sec, i.e., over a range of the X

# ~:

10- 1

\\0,

",0'\

\ 10- 2

,\

,,;

1ROII

"Q.', /'; u

c,"-

\\0,

\\

\~,o

E

V>

'"

c s:

C'

::>

e u

10- 4

o Bruce

E 0

er of. (1961)

c;

>-

0

10- 5

•• Ie Portman (1960) 10- 6

• • •

10-7

30 10 20 Friction velocity

40

50

u. (em/sec)

FIG. 38. Dynamic roughness =0 as a function of friction velocity 11*. Results of wind profile measurements over the sea surface and wind tunnel investigations.

140

4

FLOW CHARACTERISTICS OF MARINE ATMOSPHERE

friction velocity u.. from 12 to 50 cm/sec. The mean value of Zo amounted to about 0.004 em for the open North Sea whereas 0.025 em was obtained for the enclosed waters of-the western Baltic Sea. Thus we must state that this problem has not yet been satisfactorily settled but needs further study. More adequate and more exact measurements of the wind distributions over the sea are necessary, which is no easy task in view of the fact that, in order to provide sufficiently exact values, precision anemometry is required under difficult circumstances. In additions- theoretical efforts should be made to contribute to the solution of the problem of why the sea surface, owing to its characteristic properties, behaves neither as a rough nor as a smooth boundary, and how the complicated mechanism of surface friction works. Promising steps in this direction were made by Schmitz (1961; 1962a, b). It is realized quite well that-apart from wind profile measurements-there are other sources of information (measurement of the wind-induced tilt of the sea surface, for example) on such parameters as dynamic roughness and friction velocity. However, in order not to confuse the already complicated situation we have restricted the discussion in this section, devoted to the wind profile over sea waves, to the information gained from profile measurements. The other aspects will be dealt with later on (see Section 4.3.5).

4.3.4 Effect of Thermal Stratification on the Wind Profile over the Sea 4.3.4.1. Introductory Remarks. Hitherto, the treatment of the wind profile has been confined to adiabatic conditions. The turbulent processes involved in creating the peculiar vertical wind distribution reflected the nature of the lower boundary and of the flow itself, the turbulent energy being supplied by the kinetic energy of the flow. We are used to calling this turbulent motion dynamic or isotropic turbulence. The latter designation refers to the fact, already mentioned above, that the velocity fluctuations are of the same order of magnitude for all the components of the turbulent flow. No component is specially distinguished when compared with the others. Their turbulent fluctuations are equally suppressed in the vicinity of the ground. If, however, the thermal stratification is not indifferent but stable or unstable, conditions are modified, since buoyant forces, which influence the vertical flow components alone, are brought into play. This is the case of nonisotropic turbulence and we are now going to discuss its bearing on the wind profile over the sea surface.

4.3

WIND FIELD IMMEDIATELY OVER SEA SURFACE

141

In doing so we make use of the relevant knowledge of wind profiles over land. As is to be expected, the effect of thermal stratification is, roughly speaking, that under unstable thermal conditions the turbulent exchange in the vertical is intensified and the vertical wind speed gradient decreases more rapidly with height than in the adiabatic case. The reverse is true for thermal stability. The corresponding types of the wind profile are schematically indicated in Fig. 36. In a semilogarithmic system the nOJladiabatic wind profiles no longer follow straight lines but are bent into curves. Under unstable conditions their curvatures are convex to the u axis; in stable cases they are concave. This effect of thermal stratification diminishes with increasing dynamic turbulence, i.e., with growing wind speed. The influence of stability also decreases when the surface is approached. Very close to the ground the logarithmic law is found to be valid, the roughness parameter Zo having the character of a boundary condition. Although these expectations have been verified sufficiently for wind profiles over land, similar evidence is rather scarce for maritime profiles. As the effect is small, especially in the first few meters from the surface, the requirements, with regard to both instruments and exposure, are not easily fulfilled. This observational handicap, as well as the fact that the influence of thermal stratification must diminish with decreasing altitude or increasing wind speed, may explain why several authors [Roll, 1950; Hay, 1955; Goptarev, 1957 (for wind speeds above 15 meters/sec); Portman, 1960] also have reported nearly logarithmic wind speed distributions under nonadiabatic conditions. Wind profiles over the sea surface which showed the expected effect of stability were published by Bruch (1940), Deacon et al. (1956), and Fleagle et al. (1958). An example is shown in Fig. 39. 15,--------,-----,--------, 10

8 ~

~ 6

.§.

4

~A,.,..4

~4

.»

08 0.9 Relative wind velocity

FIG. 39. Profiles of relative wind speed over the sea surface under different thermal conditions. (From Deacon et al., 1956.) 0, unstable, Ri = - 0.07. x, adiabatic, Ri = +0.01. ~, stable, Ri = +0.18. The Richardson numbers refer to the levels 13 and 4 meters.

142

4

FLOW CHARACTERISTICS OF MARINE ATMOSPHERE

4.3.4.2 Profile Coefficients for Momentum. Since at sea, particularly in the first few meters above the surface, deviations from the adiabatic wind profile are relatively small, some benefit can be expected from approximations of the nonadiabatic wind distributions by means of logarithmic profiles. The vertical gradient of the mean wind speed may then be written in the form OU ruJia (4.19) az z + zo where the quantity

r

U

a

is defined by 1

au aIn(z + zo)

ru = - ---a

ii«

(4.20)

in analogy to Montgomery's (1940) evaporation coefficient. The expression I'U a is called profile coefficient (Brocks, 1956; Deacon and Webb, 1962) or profile contour number (Fleagle et al., 1958), a; being the mean wind speed at the height z = a. As shown by a comparison with Eq. (4.12), the form of Eq. (4.19) corresponds to a logarithmic profile where the product ruaUa has the same function as u,,jk in the adiabatic case. The difficulty now is that, unlike u", I'U a is not independent of the height variable z as might be inferred from Eq. (4.20). Consequently, Eq. (4.19) is valid-strictly speaking-only for z = a and approximately in the neighborhood of this height. In particular, it is neither possible to compute friction velocity and dynamic roughness from Eq. (4.19), nor is it admissable to integrate this equation over a substantial height interval as was pointed out by Brogmus (1958). It is only to adiabatic stratification that the following relations apply (4.21)

r., = (ln~

;0 ZO)-l

(4.22)

which permit the evaluation of u, and Zo if rU a and Ua are known. The difficulties mentioned above restrict the applicability of the profile coefficient in practice, as I'»; can only be computed from measured wind profile data if Eq. (4.19) is integrated. Therefore, the relevant results of different authors are only comparable under adiabatic conditions. Nevertheless, some benefit seems to have been obtained from the concept of the profile coefficient I'U a ' particularly when the observational material that has to be considered is large. Although

4.3

WIND FIELD IMMEDIATELY OVER SEA SURFACE

143

the former values of the profile factor r ua, as given by Brocks (1955) for different stabilities or Richardson numbers (see Section 4.3.4.3), disagreed with those of Fleagle et .al. (1958), even in the adiabatic case, later results obtained by Brocks (1959a) appear to be more in harmony with them. This question will be dealt with in greater detail in Section 5.2.5. 4.3.4.3 The Richardson Number. When attempting to account for the stability effect on the wind profile quantitatively we have to consider the contribution of the vertical heat flux H to the production of turbulent kinetic energy as compared with the share supplied by the shear stress. While the latter is Touloz per unit volume and per second, the additional energy provided by buoyancy forces may be written (gH)/cpTo

where g = acceleration of gravity Cp = specific heat at constant pressure To = mean absolute air temperature of the bottom layer The dimensionless ratio of these two expressions is introduced as the flux form of the Richardson number Rf=

-gH cpToT( ou! oz)

(4.23)

(The negative sign is taken in order to have negative Richardson numbers for positive heat flux values H, i.e., for unstable stratification.) Its relation to the more familiar gradient form of the Richardson number

.

Ri

g(oe!oz) To( ou! OZ)2

=----

(4.24)

where B = mean potential air temperature can be established by means of the proportionality of the fluxes T and H to the corresponding vertical gradients ouloz and oBloz according to Eqs. (4.7) and (5.1). We then obtain Rf = (KH!KM)Ri

(4.25)

where KH is the eddy conductivity. Rf equals Ri if the eddy transfer coefficient for heat (KH) is the same as for momentum (KM). The dimensionless Richardson number serves as an estimate for the energy transfer in a turbulent flow under nonadiabatic conditions. It indicates the energy supplied or consumed by thermal stratification

144

4

FLOW CHARACTERISTICS OF MARINE ATMOSPHERE

as compared with the energy furnished by eddy stresses. It is positive for inversional or stable stratification where the turbulent stresses have to work against gravity. Negative Ri numbers correspond to superadiabatic or unstable cases, whereas Ri equals zero under adiabatic conditions. Ri increases numerically with the height z. 4.3.4.4 The Diabatic Wind Profile in General. It seems reasonable that we should look for a solution where Eq. (4.12), which determines the vertical wind speed gradient under adiabatic conditions, is generalized by adding, on the right side, the dimensionless factor S, which represents the influence of stability and is a function of the flux Richardson number Rf: 8u, ~ SeRf) (4.26) 8z k(z + zo) k] S can then be considered as the generalized von Karman constant k" . For the adiabatic case Rf = the stability function S must equal unity. Applying Eq. (4.23) we eliminate 8a/8z in Eq. (4.26) and subsequently arrive at

°

gkH(z

S=

+ zo)

(4.27)

pCpTou~ Rf

Following Monin and Obukhov (1954) we introduce the quantity pCpTou~

L=----

(4.28)

gkH

which has the dimension of a length and may be called "stability length." Attention should be paid to the inverse relations between the heat flux H and the stability length L: Stable stratification: H < 0, L > Adiabatic stratification: H = 0, L --> ± 00 Unstable stratification: H > 0, L < 0. With Eq. (4.28), Eq. (4.27) takes the form

°

S =

z

+ L

Zo 1

-

Rf

k

k*M

(4.29)

We may consider (z + zo)/L as a dimensionless buoyancy parameter, which is particularly useful when the profiles of both wind speed and air temperature are to be expressed in a dimensionless form. The

4.3

WIND FIELD IMMEDIATELY OVER SEA SURFACE

145

basic assumption of the similarity theory advanced by Monin and Obukhov (1954) is that the deviations S from neutral stability in these two vertical distributions are universal functions of (z + zo)/L. Then, according to Eq. (4.29), the height dependence of Rfis entirely determined by L. For near-neutral conditions, S approaches unity and KH does not deviate much from KM. Thus, in that stability region, the three buoyancy parameters Rf, Ri and (z + zo)/L are nearly equal to each other. The same is valid for k'M and k. The parameter (z + zo)/L serves to clarify the differences in the vertical. Since S must tend to unity if L --+ ± 00, it is obvious that purely dynamic turbulence without appreciable thermal effects will predominate at heights (z + zo) with (z + zo) ~ ILl. Thus Eq. (4.26) approximates to the neutral expression as (z + zo) decreases and a certain fraction of ILl, probably a small one, may be interpreted as the height of the bottom layer with dynamic turbulence prevailing. According to Eq. (4.28), L increases as H approaches zero and/or with growing wind speed. Additional properties of L will be discussed in Sections 5.2.6.1 and 5.2.6.2. Combination of Eq. (4.7), (4.26), and (4.29) leads to a useful relationship between the eddy viscosity KM or the Austausch coefficient A = pKM and the flux Richardson number: KM = ku*LRf

A

=

(4.30)

pku*LRf

4.3.4.5 Approximative Solutions Proposed for the Diabatic Wind Profile. The attempts to determine the still unknown stability func-

tion Sin Eq. (4.26) can be divided into two classes: (a) Those which assume similar profiles for wind speed and temperature. (b) Those which do not presuppose that similarity. Case (a) implies that the stability function for wind speed (Su) differs from that for potential air temperature (So) only by the constant factor y so that Su = v So. Thus, according to Eqs. (4.26) and (5.26) (see Section 5.2.6.1), the ratio of the vertical gradients oil/8z and olJ/oz equals that of the corresponding turbulent fluxes multiplied by y: (4.31) oiljoz : o0j8z = yT : - Hjcp Consequently we have KH = yKM

and

Rf= yRi

(4.32)

146

4

FLOW CHARACTERISTICS OF MARINE ATMOSPHERE

Along this line the following formulae were suggested:

ou

-

oz

U".

= ----

k(z

+ %0)

(1

+

0"1

.

Rt)1/2

(4.33)

by Rossby and Montgomery (1935)

sa oz

1

u;

=----

k(z

(4.34)

._---

+ zo) (1- cr2Ri)I/2

by Holzman (1943)

ea

oz = k(z

,

( Z + Zo) + zo) 1 + rx~

U".

(4.35)

by Monin and Obukhov (1954) Here aI, a2, and o: are constants to be fixed empirically. By applying Eqs. (4.29) and (4.32) and assuming y = 1 (as done by Monin and Obukhov) the last formula can be transformed into ea u; 1 (4.36) oz k(z + zo) 1 - o: Ri For near-neutral conditions [i.e., at very small values of Ri ~ (z + zo)/L] the higher order terms of Ri and (z + zo)/L, respectively, can be neglected and the three formulae given above are reduced to the same approximative equation

ea

-

oz

U".

.

= - - - - (1 + const. Rt) k(z

+ zo)

(4.37)

which requires the constants to be connected by the relation 0"1

=

0"2

(4.38)

= 2rx

Integration can be easily performed for the near-adiabatic case + zo)/L ~ 1] by using Eq. (4.35). It yields the well-known "log + linear" profile [(z

_

U

=

u, (

k

Z + Zo

In - Zo -

rxZ)

+L

(4.39)

which contains the adiabatic case for L --)- 00 and describes the effect of stability by an additional term linear in z. Similar "log + linear" laws have been derived by various authors (see the instructive review given by Charnock, 1958a). It is easy to verify that the nonadiabatic modification of the adiabatic formula [Eq. (4.13)] is given in the right sense as indicated in Fig. 36.

4.3

WIND FIELD IMMEDIATELY OVER SEA SURFACE

147

Monin and Obukhov (1954) evaluated the constant o: at 0.60 ± 10 per cent by using wind profile data over land without simultaneous flux measurements. This value is, however, not consistent with Eq. (4.38) as al was determined to be about 9. It was also criticized by Taylor (1960a), who found that Monin and Obukhov (1954) had applied (Eq. (4.39) over too wide a range of (z + zo)/L, i.e., of thermal stability. In a later paper Taylor (1960b) could show that o: varies systematically with stability, and ranges between about 3 and 6 for the stability region - 0.03 < (z + zo)/L < 0 for which Eq. (4.39) does apply. Thus an average value of 4.5 results, which would be consistent with al = 9 and Eq. (4.38). Deacon (1962a), from unpublished data of vertical wind speed and temperature differences measured by Calder over a very level desert surface, derived values of 3.4 and 3.0 for the product rf.y. Since, for near-neutral conditions, any departure of y from unity has not yet been established with certainty, the product rf.y also provides a sound estimate for a: Summarizing, we can say that the "log + linear" wind profile is adequate only for a very narrow stability range which, on the lapse side, seems to be limited by I(z + zo)/LI = 0.03 and which corresponds more or less with the region where mechanical turbulence dominates, i.e., with the conditions of forced convection (see Section 5.2.6.2). In that region the constant y seems to assume values around unity (Taylor, 1960a). Bearing in mind that Eq. (4.39) was derived for near-adiabatic stratification, i.e., for small values of Ri, we cannot expect that this approach will prove useful also under conditions of great instability or stability. Therefore, let us now turn to a discussion of case (b), which is not based on the assumption of similarity as was (a). Consequently, = KHIKM = Rf[Ri is no longer constant but appears as an additional variable. With increasing instability (z/L < - 0.03) the flow enters a region where, in addition to dynamic turbulence, buoyancy forces begin to playa dominant role. If the instability is sufficiently great, the heat flux and buoyancy term is decisive whereas u ; becomes negligible. This is the region of free convection (see Section 5.2.6.2). Ellison (1957) suggested that, with high instability, y = KH/KM might approach a constant value which would again imply similarity between wind and temperature profiles. On this basis Taylor (1960a, b) tested the height dependence (Z/L)-l/3 y

148

4

FLOW CHARACTERISTICS OF MARINE ATMOSPHERE

which is well established for temperature profiles (see Section 5.2.6.2), also against three sets of wind profile observations in free convection, and he found a rather satisfactory agreement for zjl: < - 0.03. The corresponding y values (for two sets of observations) were 1.35 and 1.67. In the case of extreme stability (z/L}> 1) the existence of a limiting Richardson number Rfis assumed. When this Rfvalue is approached, KM no longer increases Wrth height but remains more or less constant, i.e., according to Eq. (4.30), proportional to u.L, Here the elements of turbulence do not explicitly depend on the distance from the ground. They are only of local character. Striving for a solution that would incorporate near-neutral conditions as well as strong instability and stability Ellison (1957) put forward a theory predicting that y = KH/KM would vary strongly with the flux Richardson number Rf, particularly under stable conditions. The variable quantity y tends to zero when Rf approaches a critical value Rferit. which thus appears as the maximum value of Rf for the maintenance of turbulence. The relationship proposed by Ellison reads

oa oz

u..

=

(

Rf A-(z + zo) 1 - Rferit.

)-114

(4.40)

The constant Rfen«. was estimated to be about 0.15. Panofsky et al. (1960) found Eq. (4.40) well confirmed by various wind profile data for unstable conditions if Rf/Rferit. was replaced by 18 Ri, a modification which is caused by the fact that the flux Richardson number Rf cannot be obtained from profile data alone, and which implies y = 18 Rferit. '" 2.7. Under near-adiabatic circumstances this result is consistent with the approximative relation Eq. (4.37), in particular with regard to the factor of Ri which should be 40t '" 4 x 4.5 = 18. If we combine Ellison's formula, Eq. (4.40), with Eq. (4.29), we obtain the following equation for the stability factor 5

1 z + Zo 54 - - - - - 53 = 1 Rferit. L

(4.41)

which serves as a useful link between the wind profile and the heat flux provided that Rfen«. is known. If the wind profile is given, the heat flux can be computed. Conversely, the wind profile can be determined if roughness length Zo, friction velocity u; and heat flux H are known.

4.3

WIND FIELD IMMEDIATELY OVER SEA SURFACE

149

With Eqs. (4.40), (4.29), and (4.28) we further arrive at a relation for the eddy viscosity KM (Panofsky et al., 1960) U~ (Oil KM = - - = U~ -

oil/oz

OZ

1 PCpTo Rfcrit.

gH +-

)1/3k

4 /3( Z

+

ZO)4/3

(4.42)

Here, u:( oilj8z) represents the production rate of mechanical turbulent energy (per unit mass" whereas gHjpcpTo gives the rate at which energy is created by buoyancy. The relation between the contributions of dynamical turbulence and convective forces to the vertical momentum transport is determined by IjRfcrit. Panofsky (1961) interpreted Eq. (4.42) in the light of Heisenberg's expression

where € is the rate of energy dissipation and I the eddy size. He suggested that, in the atmosphere, z takes over the function of I, i.e., the eddy scale is identified with the height above the ground. However, according to Panofsky this relation is unlikely to be valid with stable stratification where the turbulent elements seem to be independent of the distance from the ground, as was already mentioned. Further evidence on this case is needed. So far no investigation has become known in which, beside the determination of wind speed profiles, simultaneous measurements of wind stress and heat flux were carried out at sea so that the solutions of the diabatic wind profile, which in part are well established over land, could be examined with regard to their applicability to wind profiles over the sea surface. There is, however, the approach suggested by Deacon (1962a), who, by using Eqs. (4.28) and (4.31), transformed the second term «zujkl: of Eq. (4.39) into rxyzg(08joz)jTo(oiljoz). Hence, the wind stress T = PU.2 and the heat flux H are replaced by the vertical gradients of wind speed and potential air temperature. Consequently, if no fluxes are measured, profile data only permit the evaluation of the product rxy. Deacon (1962a) applied this amended form of Eq. (4.39) to the wind and temperature profile observations carried out over water by Fleagle et al. (1958). The differences between the wind speed measurements ill, il2 at the two levels Zl, Z2 were considered in terms of the wind velocity ile taken at a small height. In addition, the ratio of the gradients (oBjoz)j(oiljoz) was replaced by the ratio of the differences !:1Bj!:1il observed between two convenient heights. The relation derived

150

4

FLOW CHARACTERISTICS OF MARINE ATMOSPHERE

from Eq. (4.39) then reads ii2 - iiI

U"

Z2

- - - = -In - + ue ku; Zl

g

tiJj

IXy - - - ( Z 2 -

ueTo flu

zr)

(4.43)

u..lue is a constant, which, according to Eq. (4.39), implies that the stability term is considered negligible at that small height and that Zo is constant, too. The latter supposition, however, is somewhat questionable when applied to observations over the sea surface. With u,,/Ue taken as constant the first term on the right-hand side of Eq. (4.43) is constant, too. Thus IXy can be evaluated from observed values of Ul, U2, ue, flu, and flO in the near-neutral range. Deacon arrived at an average of IXy = 3.7 which agrees satisfactorily with the values obtained over land and suggests that the concepts developed for an air flow over a rigid boundary may also apply to conditions over a water surface.

It was assumed that

4.3.4.6 Other Wind Profile Formulae. In addition to the formulae given in the preceding section there must be mentioned two further approaches to the diabatic wind profile wherein the influence of stability is taken into account in a way somewhat different from Eq. (4.26), namely, so that the dimensionless factor S does not appear as an explicit function of the Richardson number. The power formula advanced by Deacon (1949, 1953) has been used with particular success. It reads

(Z

ZO)l-fJ

OU u" + OZ = k(z + zo) ~-

(4.44)

The exponent f3 is termed the "Deacon number." It is defined by the equation f3 = _ oln( oujoz) = _ _Z(_0_2u_j_oz_2) (4.45) oln Z (oujoz) Apart from a slight dependence on the height z, the Deacon number f3 is a function of the Richardson number, assuming values greater than unity under unstable conditions and less than unity for stable stratification. In the adiabatic case (f3 = 1) the power formula passes into the logarithmic profile. An analytical expression for the relation between f3 and stability was published by Panofsky et al. (1960). A disadvantage is that the dynamic roughness Zo, which normally is considered as a boundary condition, varies with stability. A similar power law was introduced by Laikhtman (1944).

4.3

151

WIND FIELD IMMEDIATELY OVER SEA SURFACE

A direct approach to the marine wind profile was published by Goptarev (1960). Using the observation that, under unstable thermal conditions, the fluctuations of the horizontal flow component decrease exponentially with height, and applying the concept that this decrease is connected in some way with the intensification of the vertical exchange motion, Goptarev derived the following relation for the height dependence of the mixing length in a stratified atmosphere I = k(z + zo)e-a 0 stable). In the last case the mixing length I increases with z near the surface until a maximum is reached at z + zo = t]«. Above that height the mixing length decreases. The integration of Eq. (4.47) is done by developing the e function into a series. It yields the wind profile in the form _

u

U"

= -

k

(

Z

+

Zo

In - - - + az + Zo

a2(z

+

ZO)2 -

2· 2!

z5)

)

+ ...

(4.48)

The first two terms of this solution correspond to Eq. (4.39) if a is assumed to equal «[L (which would be in accord with Eq. (4.28), at least as far as the sign is concerned). Provided that the higher terms are used, Eq. (4.48) is, however, reported to be valid also for strong deviations from adiabatic conditions, which is not the case with Eq. (4.39). Goptarev interpreted his equation by making use of his profile measurements on an oil drilling platform (Goptarev, 1957). From his results the following is paraphrased here: The dynamic roughness Zo cannot be considered as a direct characteristic of the geometry of the sea surface but as an aerodynamic quantity reflecting the interaction between wind and waves. According to Goptarev this is made evident in particular by his finding that the dynamic roughness Zo decreases with increasing wave height and with decreasing wind speed relative to that of the waves, i.e., with improved flow conditions around the moving waves. With a view to the difficulty inherent in fixing really representative wave

152

4

FLOW CHARACTERISTICS OF MARINE ATMOSPHERE

data these results should, however, be regarded with reserve. Furthermore, the dynamic roughness Zo was found to be greater with unstable thermal stratification than with indifferent or stable temperature distributions, a result which agrees with the observation that, at the same wind speed, the sea is rougher in cold air masses than with warm air over cold water. 4.3.5 The Wind Stress at the Sea Surface 4.3.5.1 Definitions and Designations. When discussing the vertical wind profile in the first few meters above the sea surface we have dealt so far only with the dependence of the dynamic roughness on other factors, e.g., wave height, wind speed, friction velocity. Nothing has been said up to now about the second important parameter of the air flow over the sea: the friction velocity u., According to Eq. (4.10) the friction velocity is closely connected with the vertical flux of the horizontal momentum or the turbulent shear stress T which was defined by Eq. (4.7) and which, as already mentioned, is generally considered as constant with height in the first few meters of the atmospheric boundary layer. Thus we can write T

=

TO =

pu..2

(4.49)

where TO is the tangential stress exerted by the wind on the sea surface = air density). This quantity is of considerable importance as it plays an essential part in all processes of momentum transfer across the air-sea boundary, including generation of ocean surface waves and drift currents by wind action, wind setup, and storm tides. Finally the entire ocean circulation, as well as the momentum balance of atmospheric circulation, is substantially affected by the shearing force of the wind acting on the sea surface. It is customary to express the surface drag TO of the wind at the sea surface in terms of the mean wind speed Uz at a certain height z

(p

(4.50) the factor of proportionality C z being a dimensionless constant, termed "resistance coefficient" or "drag," "shear-stress" or "friction coefficient," and depending on the height z. Usually z = 10 meters is taken as reference level. The problem of determining the surface stress TO is now reduced to ascertaining reliable values of ClO. The drag coefficient C10 can be easily related to the parameters of the vertical wind profile. By combining Eqs. (4.49) and (4.50) we get ClO

=

(U../UlO)2

(4.51)

4.3

WIND FIELD IMMEDIATELY OVER SEA SURFACE

153

Further, if adiabatic conditions prevail the following relation can be derived from Eq. (4.13) 10

+ ZO)2

ClO = k 2 j ( In-~

(4.52)

In the absence of thermal stratification ClO is, therefore, entirely determined by the dynamic roughness zoo With temperature distributions other than neutral ClO has to be computed from Eq. (4.39), which implies an additional dependence on IX/L.

4.3.5.2

Methods of Measuring. Estimates of the drag coefficient

ClO have been based largely on indirect evidence. The following

effects of the wind stress at the sea surface have been used. In air: (1) Vertical wind profile immediately above the sea surface (wind profile method). (2) Departure from the geostrophic wind in the atmospheric boundary layer (geostrophic departure method). (3) Simultaneous fluctuations of the horizontal and vertical components of the air flow from the mean over the recording period using Eq. (4.7) {eddy correlation method). In water: (4) Stationary tilt of the surface of enclosed bodies of water due to wind action (sea surface tilt method). At the sea surface: (5) Contraction of an insoluble monolayer on the water surface by the action of the wind (surface film method). The wind profile method (1) has already been described in Sections 4.3.3 and 4.3.4. Measurements of wind speed at two heights would, at least in an algebraic sense, be sufficient under adiabatic conditions in order to determine u; and/or zn, whereas such values would be necessary at three heights if stable or unstable stratification were present. Should values be available at more than three heights, additional information on the accuracy of the parameters can be obtained. The difficulty inherent in this method was clearly shown by Priestley (l959a), who compared wind stress values derived from wind profiles (over land) with simultaneous measurements of surface stress. Even the close fitting of the measured values to the profile curve did not assure sufficient accuracy in the results inferred therefrom. Evidence was given that values of surface wind stress of acceptable accuracy can only be gained from wind profile measurements "when Zo is

154

4

FLOW CHARACTERISTICS OF MARINE ATMOSPHERE

assigned in advance." This, of course, may be possible over land but offers nearly insurmountable difficulties at sea, where the dynamic roughness is not a constant but an aerodynamic quantity reflecting the interaction between wind and waves. Thus, values of the wind stress on the sea surface derived from wind profile data must be regarded with caution. Similar and further objections against the wind profile method were raised by Schmitz (1961). Since it is particularly difficult to obtain reliable wind profile data on shipboard, Gerstmann (1961) suggested the calculation of u; from measurements of the wind speed taken at one height and combined with values of the air-sea temperature difference. This procedure certainly requires some theoretical background. The computation is done by applying Eqs. (4.39) and (5.32) for the wind and the temperature profiles, respectively, under nonadiabatic conditions, and by using Charnock's relation [Eq. (4.18)] for the roughness parameter, zoo This method may be useful when shipboard observations are applied to the computation of vertical energy fluxes at sea. The weak side of this procedure, however, is that unestablished theoretical concepts have to be used. The geostrophic departure method (2) covers a region beyond the first few meters above the sea surface to which this Section is devoted and will, therefore, be dealt with in a later section. (See Section 4.4.1.1.) The eddy correlation method (3) offers severe difficulties when applied at sea, as the motion of the vessel will falsify the recorded fluctuations of the wind components. This handicap can only be overcome if the carrier of the recording instruments is fixed or completely stabilized. The stabilization might be achieved with the least expenditure if the sensing elements are mounted on a buoy. Apart from preliminary values obtained by McIlroy (1955), and Vinogradova (1959), on fixed near-shore constructions and by Deacon (1960) on a small vessel, no results of eddy flux measurements over the sea have become known so far. * The sea surface tilt method (4) is applicable if an enclosed body of water is available and the wind has blown for a sufficiently long period as to assure steady state conditions. Using Ekman's (1923) assumption that the surface stress then just balances the hydrostatic forces due to the tilt of the surface, the wind slope i can be expressed by the equation i =

TO

+ TB

~~

gpu;d

(4.53)

* Recently Brocks and Hasse (1963) reported the first results of eddy flux measurements executed by means of a gyro-stabilized mast installed on a buoy.

4.3

WIND FIELD IMMEDIATELY OVER SEA SURFACE

155

Herein T B denotes the frictional shear stress of the bottom return current on the bed of the lake, g the acceleration of gravity, pw the water density, and d the mean depth of the water. From Eq. (4.53) the surface stress TO can only be derived if the bottom stress is known. Theoretical considerations have shown that TB = To/2 is valid in the special case of laminar flow in water (Van Dorn, 1953) and that the values for TB generally lie between 0 and To/2 if turbulent flow is assumed (Hellstrom, 1941). Measurements of the bottom stress have indicated that, in most cases, TB is quite small compared with TO, e.g., Francis (1953) found TB '" 0.015 TO, and Van Dorn (1953) found T B ~ 0.1 TO. Consequently the bottom stress may be neglected in Eq. (4.53) and the surface wind stress TO is given by TO

= gPwdi

(4.54)

from which, for the drag coefficient ClO, we have the following: ClO =

Pwgdi pil 120

(4.55)

The tilt method has been applied both in laboratory and in field measurements. Examples of the former procedure were published, for instance by Francis (1951) and Keulegan (1951), whereas results of field investigations were reported by Neumann (1948), Van Dorn (1953), Hellstrom (1953), Keulegan (1953), Darbyshire and Darbyshire (1955), and others. The possibilities of achieving the necessary accuracy are somewhat different in laboratory and field investigations. Since the magnitude of the tilt of the sea surface is only of the order of 10- 7 at low wind speeds, the setup must be measured to at least 10-4, 1O~2, or I em for consideration of distances of 10 meters, I km, or 100 km, respectively. From these requirements it could be inferred that using rather large natural bodies of water would offer certain advantages as compared with laboratory tests, where the short distances available demand a hardly realizable exactness of the setup measurements, notwithstanding the fact that in the laboratory it is comparatively easy to establish controlled conditions and to secure the best possible precision in measuring. Even supposing that the required accuracy of 1 em could be fulfilled with water-level indicators in large lakes and seas, the determination of the effective mean depth would raise new difficulties, particularly if the density stratification is such that the wind effects of drift and slope are confined to the upper layer. In addition, tidal and seiche movements, as well as horizontal differences

156

4

FLOW CHARACTERISTICS OF MARINE ATMOSPHERE

in water density, may disturb the slope measurements, apart from the fact that a steady state of equilibrium between wind and setup will be guaranteed only rarely. Finally, near-shore effects due to waves can seriously affect determinations of wind setup if these, as is customary, are derived from water level records taken near the shore (Stewart, 1962). A workable compromise can be attained by investigating the wind effects on ponds which are small enough for an adequate control but large enough for the setup measurements to be done with sufficient accuracy. Therefore, the investigation carried out by Van Dorn (1953) on an artificial pond of about 240 meters length, in which an accuracy in the setup measurement of 5 x 10- 7 could be reached, deserves special attention. The surface film method (5) is a new approach which was practiced by Vines (1959) and seems to provide reliable stress values at very low wind speeds where the other methods are difficult to apply. Surface-active material was introduced into the water in the absence of wind. The resulting monolayer was retracted under the action of a wind until the surface stress exerted by the wind was exactly counterbalanced by the opposing film-pressure gradient. Simultaneous measurements of surface pressure (at the end of the tunnel) and of the extent of the film resulted in proving a linear relationship between these two, the surface-pressure gradient being a measure of the wind stress. 4.3.5.3 Resulting Drag Coefficients. A comprehensive and very useful compilation of the wind stress coefficients ClO determined by the different methods (1) to (4) was given by Wilson (1960). A total of forty-seven investigations are quoted therein. After having coordinated the different results, Wilson arrived at the conclusion that, for strong winds (.» 10 meters/sec, mean about 20 meters/sec), the mean value of ClO is 2.37 X 10- 3 with a standard deviation of 0.56 x 10-3 • For light winds « 10 meters/sec, mean about 5 meters/ sec) the scatter of ClO is particularly wide, the average value being 1.49 x 10-3 with a standard deviation of 0.83 x 10-3 • Greater accuracy is certainly needed for this wind speed range in order to establish reliable values of the drag coefficient. According to Wilson (1960) CI O increases between light and strong winds from about 1.5 to 2.4 x 10-3 , probably in a nonlinear manner, and there is some reason to assume that for very high wind velocities some value in the neighborhood of 2.4 x 10- 3 will be approached asymptotically (Francis, 1959), as is depicted in Fig. 40. The linear relation between drag

4.3

WIND FIELD IMMEDIATELY OVER SEA SURFACE

157

coefficient and wind speed proposed by Sheppard (1958) obviously does not fit the data in that region. When summarizing, Wilson gave equal weight to all the results listed by him. Consequently, his truly "democratic" resume does not show the peculiarities inherent in the data supplied by the five methods. 0003.--------------.:,....-----~

..........

o

<S

~ .;:

xx~~~---~--~--o-

x

s?9 . ' ~ ~;.. h). v = Measured profile of mean wind component normal to the surface-wind direction; Vg = vertical variation of corresponding component of geostrophic wind. The shaded area is proportional to the surface drag TO.

The situation is illustrated in Fig. 45. It should be noted that here the surface drag is computed from the integral of the geostrophic departure normal to the surface wind up to the level z = Zx and that at and above this height v is not necessarily equal to Vg as in (i). Thus the approach (ii) differs distinctly from the classical procedure. It is particularly suitable for use in the trade wind region as, owing to

4.4

WIND STRUCTURE IN MARITIME FRICTION LAYER

175

the opposing directions of pressure and thermal gradients, there is commonly a maximum in the profile of ii at a height of a few hundred meters. Additionally, the Trades constitute a relatively steady airflow and the path acceleration is quite small there. Relevant application of this method was reported by Sheppard and Omar (1952) as well as by Charnock et al. (1956). It is an advantage of method (ii) that the resulting value for TO is not greatly sensitive to the variation of Vg with height, which is difficult to ascertain. After the surface drag TO has been determined from Eq. (4.67) or Eq. (4.68), the turbulent stresses Txz and Tyz at other levels can be calculated from Eqs. (4.65) and (4.66). If, moreover, there exists a level z = Zy at which ov/oz = 0 and, consequently, Tyz = 0, then

I pl( o Zy

Ug) dz = 0

(4.69)

o

may serve as a useful constraint during the calculation. z

z

/

/ /v t

v

g

FIG. 45. Determination of surface wind stress from geostrophic departure if there exists a level z = Zx at which oujOz = 0 and, consequently, Txz = O. ii, v = measured profiles of mean wind component in the direction of the surface wind and normal to it; Vg = vertical variation of the geostrophic wind component normal to the surface wind direction. The shaded area is proportional to the surface drag TO.

Values of the Austausch coefficients A xz , A y z or the eddy viscosities Kee, K y z can finally be derived from Eqs. (4.60) and (4.61). The geostrophic departure method offers the advantage of furnishing average values of shear stress and eddy viscosity that comprise

176

4

FLOW CHARACTERISTICS OF MARINE ATMOSPHERE

the entire momentum transport over all periods of turbulent fluctuation. On the other hand, it suffers from the following two handicaps: (i) The necessity of excluding the influence of acceleration. Since, apart from turbulence, steady motion was assumed, the geostrophic departure method is only applicable to wind measurements averaged over a period which is long enough to allow the components of acceleration to be neglected. In general this will preclude the computation of the momentum balance for shorter periods, such as one day. In addition, the locality chosen for study must not have any marked topographical features (such as those of coasts and mountains) which could tend to interfere with steady flow. The open sea would be a site well suited to this approach. (ii) The difficulty of providing sufficiently accurate data regarding the geostrophic wind both at the surface and at upper levels. The most serious difficulty in applying the method is the practical one of estimating the geostrophic wind. Even on land where a relatively dense network of pressure-observing stations is available, the geostrophic wind may hardly be derived from the pressure distribution with an accuracy greater than 5-10 per cent. The possibility of getting sufficiently accurate values is obviously much smaller at sea than on land, as in general there exists no adequate network of pressureobserving stations and even if there are islands suitably situated the pressure readings may be disturbed by topographic effects. Sea stations are still less qualified. On the other hand, the requirements with regard to the accuracy of the pressure values must be higher at sea than on land, owing to the fact that the bottom friction and its effects on the flow are smaller there. The difficulties are augmented in the baroclinic case. Then the atmospheric density distribution has a horizontal gradient and, consequently, the geostrophic wind varies with altitude. In the absence of suitable measurements, which will generally be the case, a rough estimate of the vertical profile of the geostrophic wind in such a baroclinic atmosphere at sea can only be attained with the help of climatological data concerning the horizontal gradients of both air and sea temperature, a method that is subject to considerable uncertainty. In view of this unsatisfactory situation, some authors dropped the direct determination of the geostrophic wind from the pressure field but tried to derive this quantity from the measured wind profile, assuming that in the higher levels the wind may, on an average, be taken as approximating to the geostrophic wind. This procedure was applied, for example, by Sutcliffe (1936), but Sheppard et al. (1952)

4.4

WIND STRUCTURE IN MARITIME FRICTION LAYER

177

found it impossible to insert the corresponding component Vg of the geostrophic wind into their measured profile curves of v by inspection. Lettau (1957), however, subjected some of the wind profiles measured by Sheppard et al. (1952) to a new analysis, assuming that the Austausch coefficient is a scalar quantity, thus deviating from Eqs. (4.60) and (4.61) which ascribe to it a tensor structure. This constraint, which still has to be verified generally, served to fix values for the geostrophic wind and its vertical variation from the measured wind profiles with an accuracy considerably greater than attainable otherwise. 4.4.1.2 Eddy Correlation Method. This method is based on the right-hand portions of the basic Eqs. (4.60) and (4.61), which were not used by the geostrophic departure method discussed above. Two procedures have become known so far which enable us to obtain correlated values of the turbulent departures from the mean flow: (i) Series of pilot balloon ascents. Pilot balloons, which have been inflated in order to give them a low rate of ascent of about 1.5 to 2.5 meters/sec, are released at regular intervals of 10, 15, or 20 minutes and tracked by two or three theodolites installed on fixed sea stations, e.g., lighthouses or small, flat islands, a few kilometers apart. Synchronized readings are taken every 15 or 20 seconds. The balloons are followed for 10 minutes or so, until they have reached a height of from about 1000 to 1500 meters, after which they are abandoned. In order to secure the best possible accuracy the angles of bearing and elevation should be read at least to 0.01°. Then the displacement of the balloon, both in the horizontal and in the vertical, can be considered correct to about ± 1 meter and the accuracy of the corresponding component velocities of the balloon can be estimated at ± 5 em/sec. The evaluation of the readings of one ascent yields the actual velocity components of the balloon as measured along its trajectory. While the horizontal components can be taken as representatives for the components u, v of the air flow averaged over the different height intervals, the corresponding vertical components w of the wind are obtained by subtracting the mean vertical velocity of the balloon throughout the entire ascent, under study from the measured vertical velocities of the balloon during the different time or height intervals. When applying this procedure we assume, first, that the rate of ascent of the balloon relative to the air remains constant throughout every ascent and, second, that the air flow has no vertical component when averaged over a complete sounding. Thus, any vertical motion of the air lasting longer than one ascent (10-15 minutes) will escape detection.

178

4

FLOW CHARACTERISTICS OF MARINE ATMOSPHERE

Apart from the difficulty of determining correct values for the vertical component of the air flow, there are other peculiarities inherent in this method which should be examined. This method does not supply any continuous records of the instantaneous components of motion at fixed levels and at a fixed locality, as can be done near the surface, and the detailed structure of the vertical wind profile, as can be determined from photogrammetric measurements of the successive positions of a smoke trail left by a vertically rising missile (Tolefson and Henry, 1961), is not obtained. The pilot balloon technique rather furnishes samples of certain air flow data taken more or less at random every 15 or 20 minutes. Here, each wind value corresponds to an average taken over a time interval of 15 or 20 seconds and along an inclined path covering a height difference of from 25 to 50 meters. Thus, a considerable portion of the small-scale wind variation is filtered out. In addition, the measurements are taken visually and, therefore, confined to areas free of clouds; this will affect particularly the determination of the vertical flow component. It goes without saying that observational material of that kind is far from being ideal. Before the required turbulent departures u', v', w' from the mean flow can be computed, the components of the mean motion ii, '8, w have to be fixed. In most cases it will not be possible to gain a sound estimate of the real mean flow and so we have to confine ourselves to the departures from the observed mean flow, their products being regarded as contributions to the complete products related to the real mean flow. In this connection, the length of time available for averaging plays an important role as it determines the range of fluctuation periods, i.e., the section of the spectrum of turbulence that will become effective in the turbulent departures. In general, the pilot balloon technique will give information about fluctuations ranging from several minutes up to several days (medium scale turbulence), provided that the measurements comprise several weeks. Therefore, the momentum transport obtained by this method does not cover the entire spectrum of turbulent exchange but only a certain part of it which depends on the density of soundings as regards time and on the length of the observational period. The turbulent shearing stresses TXZ and Tyz as well as the corresponding values of the eddy viscosity can be computed from the turbulent departures and from the vertical gradients of the mean horizontal wind components with the aid of Eqs. (4.60) and (4.61). The pilot balloon technique was applied by Sheppard et al. (1952), Charnock et al. (1956), and Roll (l958b).

4.4 WIND STRUCTURE IN MARITIME FRICTION LAYER

179

(ii) Acceleration measurements in an airplane. One disadvantage of the pilot balloon method, namely the restriction of the measurements to cloud-free areas, can be avoided if an airplane is used for turbulence studies at sea, since such a carrier of instruments can be directed to measure within the clouds. When flying through turbulent air, the airplane experiences changes in the angle of attack and in the speed of the apparent air flow in rapid succession, resulting in irregular motions of the plane. For the determination of these effects there are installed in the airplane a pressure anemometer, a vertical accelerometer, a gyroscope, and a drift sight, which yield simultaneous records of the total air speed, vertical acceleration, and the attitude of the plane during short horizontal flights inserted into vertical soundings. After the airplanelift theory has been applied and after the characteristics of the particular type of aircraft have been accounted for, these records allow us to measure the vertical gradient of mean horizontal wind oil/oz as well as to evaluate the simultaneous fluctuations of the horizontal and vertical wind components u' and w'. Here, u designates the component in the direction of the upper wind. Shearing stress Txz and eddy viscosity K x z are computed according to Eq. (4.60). The phugoid oscillations of the airplane, a pendulumlike motion arising whenever a perturbation disturbs the balance between the lift of the airplane and the force of gravity, can be eliminated by computation, unfortunately at the cost of reducing to zero any contribution of wind fluctuations of larger sizes. Thus, also, the airplaneacceleration technique covers only a part of the turbulence spectrum and here particularly the short-period fluctuations are effective. The method described above was developed and applied over the North Atlantic Ocean by Bunker (1955, 1957, 1960). One-fifth-second averages of the observations were used to obtain a time series of the turbulent components. Most of the horizontal runs lasted 2 minutes. Since the speed of the airplane was about 110 knots (= 57 meters/ sec), the area swept out by the plane within 1/5 second amounted to about 360 meters-, which defined the lower limit of the horizontal dimensions of the gusts investigated. The upper limit was set by the procedure applied when eliminating the phugoid motion. This was done by subtracting values averaged over a quarter period (7 seconds) of the phugoid oscillation from the instantaneous values. Consequently, the contributions from the gusts greater than 350 meters in radius were lost. Thus the effective range of gusts measured was from 20 to 350 meters.

180

4

FLOW CHARACTERISTICS OF MARINE ATMOSPHERE

4.4.2 Variation of the Mean Wind with Altitude 4.4.2.1 Profile of Mean Wind Speed. In order to provide preliminary information on the wind field in the maritime friction layer, we shall first consider the vertical profile of the mean wind speed. Relevant results of Sheppard et al. (1952) are shown in Fig. 46, together with similar results obtained by the author. All these observations were taken during the regime of westerly winds. The remarkable fact is that there is no constancy of wind speed with increasing ~ 54

.. .57

...~~

800

:~·63

700

l64

600

'" " E Q;

'

,

19X

r

,r

•• 66

.' 11' ...

67

26X , ,, 26X

200

,,

671'

500

250

I

"

,

= 400

'" Q;

Q;

30X I

"0

150

,

31 ~



/ 33 X

';:

\

,x'"

f

50

............. x

100

33-;:....x Mean wind speed

4 0

100

If

200

" = -l

z15 r-

~

..... 00 VI

.-

00

01

.j:::.

"TI t""

o

~

TABLE XVIII FREQUENCY (PER CENT) OF WIND SPEED INCREASE (DECREASE) FROM THE SURFACE TO 600 METERS OVER THE SEA AS RELATED TO THERMAL STRATIFlCATIONa Air-sea temperature difference CF) Wind speed

> + 2

+1 to-2

Decreasing Unchanged Increasing

0 3 97

20 6 74

Number of cases a

Rearranged after Jones (1953).

67

176

258

45 7 48 166

:I:

~ ;I> o ..., tIl

-3 to -7 -8 to -12 -13 to -17 36 6 58

o

40 7 53 77

< -17

Number of cases

Per cent

32 8 60

247 47 490

32 6 62

40

784

100

~

VJ ...,

oVJ

o "TI

a::;I>

::c

Z tIl

;I> ...,

S VJ

"tl

:I: tIl

::c rn

4.4

187

WIND STRUCTURE IN MARITIME FRICTION LAYER TABLE XIX

FREQUENCY (PER CENT) OF WIND SPEED INCREASE (DECREASE) FROM THE SURFACE TO

600

METERS OVER THE SEA AS RELATED TO WIND DIRECTION a

Wind quadrant Wind speed

North

Decreasing Unchanged Increasing

45 8 47

36 11 53

23 4 73

28 66

247 47 490

201

53

263

267

784

Number of cases a

East

South

West

6

Number of cases

Rearranged after Jones (1953).

showed the wind speed at 300 meters as smaller than or equal to the surface wind. Thus the result should be taken as truly representing the real situation. It may, in part be attributed to the effect of thermal stratification as can be inferred from Table XVIII where the percentage of wind speed decreasing or remaining constant with height is only 3 per cent under stable conditions but attains more than 50 per cent with growing thermal instability. Table XIX, finally, gives us some hints as to the possible participation of thermal wind effects. Since the ocean stations considered are located in the northern and western parts of the North Atlantic, meteorological situations characterized by opposing surface pressure and air temperature gradients will be relatively frequent there. Such influences may, perhaps account for the conspicuously high percentage of wind speed decreasing with height that was observed with winds from northerly and easterly directions. The dependence of the vertical wind profile on the temperature gradient at sea was also studied by Gordon (l950a), who calculated mean values for the ratio of the wind speed at 15 meters to that at 600 meters for a number of soundings made on the ocean weather ship stations "I" (60° N, 20° W) and "J" (53° 50' N, 18°40' W) in the North Atlantic. The result is given in Fig. 50. We see that the ratio U15!U600 slowly increases from minimum values under inversion conditions to a primary maximum of 0.70 which occurs at the isothermal case. A secondary minimum is observed with a lapse rate of about - O.4°CjlOO meters. For higher lapse rates the ratio U15!ii600 resumes the increase. No explanation is offered for the strange behavior

188

4

FLOW CHARACTERISTICS OF MARINE ATMOSPHERE

between 0 and - 0.4°CjI00 meters. The over-all mean of U15/U600 calculated from 710 values taken at random was 0.71. The ratio showed a slight tendency to decrease with increasing wind speed (at 600 meters).

8

l~

.s" 070

°

~

-e

""~

0.65

-e c

~

060

055 -10

-0.5

o

0.5

Temperature gradient (OC/IOOmetersl

FIG. 50. Wind speed ratio fhs/iiaoo as a function of temperature gradient (measured between 15 and 600 meters) over the North Atlantic Ocean. (After Gordon, 1950a.) Figures indicate number of cases.

4.4.2.3 Vertical Variation of Mean Wind Direction. Proceeding from the classical concept of the frictional boundary layer we must expect that, in the northern hemisphere, the wind will veer with height until the direction of frictionless wind is reached. As far as the veer is concerned, the expectations, on the average, are fulfilled, which can be inferred from Fig. 51 where the results obtained by Charnock et al. (1956) in the northeast Trades are combined with similar data referring to the westerlies. We can make the general statement that although, it is true, the mean wind direction veers with altitude, in other respects its vertical variation, in part, deviates substantially from the attributes of the profile for a barotropic friction layer. Apart from this, there also exist considerable differences between observations at different localities. While in the Trades the veering averages nearly 20° at 1000 meters, and a mean value of 15° may be reached with westerly

4.4

WIND STRUCTURE IN MARITIME FRICTION LAYER

189

winds off the German North Sea coast, west winds under really oceanic conditions seem to be characterized by very small values of veer which seldom surpass a few degrees, as is shown by the results obtained at the Scilly Isles and in the German Bight during a heavy gale. The latter profiles of wind direction apparently come nearest to the barotropic boundary layer conception. 1400

1200

1000

E800 " ~ :2"

s:

'"\ '"\.

r '1-

/

~

~

600

f,t

400

~J

200

0

0

5

10

15

20

25

Veer of wind direction (degrees)

FIG. 51. Veer of mean wind direction with height relative to the surface wind as measured in different maritime regions. D- -0, Scilly Isles, January 1951, averaged over 2 days with westerly winds. Number of cases 58 at the lower levels decreasing to 6 at the top (Sheppard et al., 1952).0--0, Anegada, West Indies, 1953, averaged over fifteen days with northeast trade wind. Number of cases about 400 to 280 (Charnock et al., 1956). x .... x, German Bight, 1954, averaged over 4 days with westerly winds. Number of cases 69 (below) decreasing to 41 (above). German Bight, 1954. averaged over one day with a westerly gale. Number of cases 19 (below) decreasing to 5.

*--*,

Naturally, the thermal wind will come into play if the geostrophic wind blows toward lower or higher temperatures. In the former case, the geostrophic wind will veer with altitude, whereas it will back in the latter. It is relatively easy to give qualitative examples for this behavior but quantitative evidence is much more difficult owing to the uncertainty about the horizontal temperature gradients at sea. Nevertheless, some illustration to this phenomenon will be given here.

190

4

FLOW CHARACTERISTICS OF MARINE ATMOSPHERE

In Fig. 52 two average wind direction profiles are presented that were obtained in the German Bight under opposite conditions. Curve A refers to a southeasterly flow transporting very warm air over colder water, resulting in an air-sea temperature difference of + 5.5°C. In this case the geostrophic wind should veer with altitude. That it did do so can actually be concluded from the very pronounced veer of wind direction with height as exhibited by curve A. 1000

'" ~



600

400

:'

800

,

,x

,,I

600

r

x \ x,

,

200

0

1000

1

800

] l

,,

~

... ,

8

400

'x,

"

- ' , --x ___

---

200 <x /

-100

-75 Mean

-50

-25

I

0

25

50

75

0

wind direction relative to surface wind (degrees)

FIG. 52. Vertical variation of mean wind direction at sea with geostrophic wind blowing toward lower (A) and higher (B) air temperature (Northern Hemisphere).

A Temperature difference, air-sea Surface wind direction (at 40 meters height) Geostrophic wind direction (at the surface) Number of ascents

B

+ 5.5°C 1500

13T 20

Contrary to case A, curve B represents conditions occurring when a northeasterly flow passes over warmer water. Here the wind strongly backs with altitude above a bottom layer of about 100 meters, a fact that might obviously be interpreted as caused by the backing of the geostrophic wind blowing toward higher temperature. Unfortunately, nothing is known of the temperature distribution at the altitudes concerned.

4.4

WIND STRUCTURE IN MARITIME FRICTION LAYER

191

If we go into greater detail, we are confronted with the remarkable experience that there is an almost symmetrical spread of the variation in wind direction on either side of the frequency maximum for heights up to 500 meters or more, if single flights are considered. Evidence for this fact was given by Westwater (1943), Sheppard et al. (1952), and Roll (1958b). Frequency distributions for the variation of wind direction at different levels in westerly winds are presented in Fig. 53. Frequency of occurrence (%)

I

900

~ 600

+-

+

I

3

7

12

T

25

54+,4+2

I

4I

T

t-

57

+t-++ 14

48

-

I

T T-

49

::l

t- 12 +2 +- + - 66 '0u

63 ~

10

46

+- + + + 67 ~~ +t-+-25 60:t-+-++-- 69 ~E + +- +29- 46+ +- + + 69 39

+ +28

T

500 r-

"400 ;;'

46 1 15

T-. T 26

700-+++

5. ~

5

2

+

800 ~

I 27

+ + t:39 47+ +-

f-

I

60

I

300 f-

9

3

7

•

2

I

+ +- • +28 f-41 + +- + + 3

200 l100 f2

t-

6

+-

I 10

16

I

+- +- +31 I

+-27

-20 -15 -10 -5

5

14

7

14

0

5

10

10

3

.L, I

15 20

3

69 51 25

Vertical variation of wind direction (degrees) Backing

I

Veerrng

FIG. 53. Frequency distribution of the variation of wind direction with height over the sea. Summary of pilot balloon ascents carried out in the German Bight on 4 days with westerly winds in 1954. Each frequency number refers to the layer and to the direction range indicated by the limits of the relevant square. Positive direction means veer relative to the direction at the lower level of the two levels concerned.

The frequency maxima are always on the positive side and the mean values range between +0.5° (900/800 meters) and +2.6° (200/100 meters). On the average the wind veered with altitude, as mentioned before; but there is an appreciable fraction of cases (from 26 to 45 per cent) in which the wind direction at the higher level was backed on the lower one. A similar figure was given by Sheppard et al. (1952), who, when measuring the wind structure at Scilly Isles in winter time, found that over 30 per cent of the flights showed the wind at 300 meters backed on the surface wind. These findings support the interpretation that medium-scale eddy motions of a couple of kilometers in horizontal extent and in time intervals of several minutes may substantially participate in the momentum exchange at sea.

192

4

FLOW CHARACTERISTICS OF MARINE ATMOSPHERE

In Fig. 53 the relative minimum of the spread of the variation in wind direction observed in the layer between 400 and 500 meters is of particular interest. One has the impression that, in the cases considered, the layer in question acted as the upper limit of the eddying motion originating from the sea surface, whereas the increase in directional variability above that layer was caused by the mediumscale eddy motion mentioned above. The influence of thermal stability on the variation of wind direction with height was investigated by Gordon (1952a), who derived mean values for the angles of deviation between the winds at 15 meters and 600 meters over the North Atlantic Ocean as a function of the temperature gradient, using soundings made at the ocean weather ship stations "I" and "J." His results are given in Fig. 54. They agree with what we should expect. The upper wind is veered on the surface wind, the angle of deviation becoming smaller with decreasing thermal stability. The decrease appears to level off for lapse rates greater than the dry adiabatic. The over-all mean of the angles of deviation, calculated from 699 values, amounts to 10.5°.

64 co

.g o

15

s

"

-e

'0

g, 10


+ zo)

(5.19)

which is analogous to the adiabatic expression [Eq. (4.14)] and passes into this relation for SeRf) = 1. Similar equations can be derived for the eddy transfer coefficients KH and KE for which different generalized von Karman coefficients k u" and ke" may be assumed. Thus the equality of the eddy transfer coefficients that was supposed in the preceding section now has been dropped. When we apply Eqs. (5.13), (5.14), and (5.19) to Eqs. (5.1) and (5.2) we obtain H = CppkH*f ea«(jO - (ja)U. (5.20) E = pkE*fqa(ijo - ija)U. (5.21) The equations can be modified if we subject the vertical eddy transfer of momentum T to the same procedure. Combination of Eqs. (4.19) and (5.18) results in T = p(kM*f ua)2iia2 (5.22) or

U* = kM*fuau a

268

5

THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE

a formula which could serve as a basis for the discussion of the influence of stability on the wind stress (see Section 4.3.5.4). With this relation, Eqs. (5.20) and (5.21) finally take the form

H = CPpkM*kH*rUaroa(Bo - Ba)ila E = pkM*kE*rUarqaCiio - ija)ila

(5.23) (5.24)

It must be emphasized that the profile coefficients in the nonadiabatic transfer formulae [Eqs. (5.20)-(5.24)] are different from those appearing in the adiabatic flux equations [Eqs. (5.16) and (5.17)]. For adiabatic stratification (L --+ ± 00) the relations of Eqs. (5.22) and (5.24), .however, are transformed into those of Eqs. (5.17) and (5.16), respectively. The formulation employed in the above relations is rather general and its applicability to practice depends entirely on whether suitable values for the k*'s and P's are available. Unfortunately, our knowledge is still very defective in that respect. However, if we confine ourselves to near-neutral conditions, i.e., to very small values of Rf ~ Ri ~ (z + zo)/L, a more serviceable solution is reached. Then we can combine Eq. (4.30) with Eqs. (4.29), (4.26), and (4.35) in order to obtain the following approximate form of the eddy viscosity

ku/z + zo) 1 + IX(Z + zo)/L

(5.25)

KM=------

Under the supposition of equal transfer coefficients for momentum, heat, and moisture, the generalized von Karman coefficients ku", k u", and k E * in Eqs. (5.22)-(5.24) can then be substituted for by k/[l + IX(Z + zo)/L]. Likewise the "generalized" profile coefficients r have to be replaced by the "adiabatic" profile coefficients from Eqs. (5.16) and (4.22) respectively, multiplied by the factor

z + Zo) In z + zo/ ( In z + Zo + ( 1 + IX L Zo zn

z)

IX-

L

The resulting values for Hand E are equal to those given in Section 5.2.7.1 and will be described later.

5.2.5.4 Observational Results. Numerical values for the profile coefficients are mostly derived from Eqs. (4.19), (5.13), and (5.14) by means of data on wind speed, potential air temperature, and specific humidity measured at different levels. This procedure involves an integration over a certain height range which is, strictly speaking, not

5.2

THE TEMPERATURE AND MOISTURE FIELD

269

permissible unless under adiabatic conditions. Hence only the profile coefficients rU a and rq a in Eqs. (5.16) and (5.17) can be correctly evaluated in this manner. Of course they will depend on the reference level chosen. . On the other hand, it is customary to apply Eqs. (4.19), (5.13), and (5.14) also if the thermal stratification deviates from the neutral case. In addition to their depending on the reference height, the profile coefficients obtained in this way will be influenced by the character of turbulent motion, i.e., they will vary with stability and wind speed. Following a suggestion of Fleagle et al. (1958) we had better term them "apparent profile coefficients." Relevant results have been reported, for instance, by Brocks (1955, 1956), who computed profile coefficients by using the humidity profile measurements of Wiist (1937), Montgomery (1940), and Sverdrup (1946), and also on the basis of wind profile data of Roll (1953-1954). His values are summarized in Table XXVI. In spite of the considerable uncertainties inherent in those computations the agreement between the ru's and re's is not as bad as it could be. Nevertheless, it does not seem feasible to draw very far-reaching conclusions from such not very representative material. However, the dependence of the profile coefficients both on stability and-to a minor degree-on wind velocity appears to be sufficiently established. The variation with wind speed is confirmed by some I'u. values given by Deacon and Webb (1962) (which increase from 0.090 at U6 = 2 meters/sec to 0.123 at U6 = 14 meters/sec) and-although only qualitatively-by a few r q values reported by Das and Dhar (1954). In addition, the laboratory experiments executed by Okuda and Hayami (1959) must be quoted here. They determined the evaporation from a wavy water surface in a wind-water channel of about 20 meters length by measuring profiles of both wind speed and vapor pressure up to about 30 em height under nearly stationary conditions. Since these profiles proved to be nearly logarithmic, the profile coefficients r q could be correctly evaluated from Eq. (5.14). When adapted to a height of 8 meters they showed a rather slow increase from about 0.09 at Us = 2 meters/sec to about 0.11 at Us = 15 meters/sec. For still greater wind speeds a sudden rise of r a, to 0.20 or more was observed, which might be attributed to the effect of spray. Profile coefficients for wind speed, air temperature and water vapor density were also published by Fleagle et al. (1958). In Fig. 85 their results have been plotted against the Richardson number. They show a distinct increase of the profile coefficient with the Richardson number, thus being in qualitative agreement with Brocks (1955, 1956).

270

5

THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE

TABLE XXVI PROFILE COEFFICIENTS

rei AND r

IN RELATION TO WIND SPEED AND AIR-SEA TEMPERATURE DIFFERENCEa,b

U4

Profile coefficients from humidity profilesWind speed at 6 meters (meters/sec)

-3

-2

-1

0

+1

2 4 6 8 10

(0.02) (0.03) (0.07) (0.11) (0.12)

0,03 0.05 0.08 0.12 0.15

0.05 0.08 0.10 0.13 0.15

0.06 0.11 0.13 0.14 0.15

(0.07) (0.14) (0.14) (0.14) (0.16)

Profile coefficients from wind profiles"

2 4 6 8 10 12

-4

-2

-1

0

+1

0,03 0.06 0.07 0.08 0.09 (0.11)

0.03 0.06 0.07 0.08 0.10 (0.11)

0.05 0.07 0,07 0.09 0.10 (0.12)

0.08 0.10 0.10 0.11 0.11 (0.12)

0.12 0.12 0.12 0.12 0.12 (0.13)

Reference level, a = 4 meters. Doubtful values in parentheses. After Brocks (1955, 1956). c Column headings are temperature difference, air (at 6 meters) - sea, in deg. C. d Column headings are temperature difference, air (at 16.5 meters) - sea, in deg. C.

a

b

This behavior appears to be particularly pronounced with I' 8. and rea which, within the limits of observation, are almost identical. Contrary to Brocks, a significant secondary dependence of the profile coefficients on wind speed could not be detected in the speed range encountered (3-9 meters/sec). On the whole, the values of Fleagle et al. (1958) are lower than the results reported by Brocks (1955, 1956); they do, however, closely agree with the profile coefficients that can be deduced from the measurements of Takahashi (1958). Summarizing, we may say that the profile coefficients are useful

5.2

THE TEMPERATURE AND MOISTURE FIELD

271

tools for describing the vertical profiles of atmospheric quantities near the sea surface, on the condition that they are employed with regard to their inherent limitations. Their numerical values, however, need confirmation and completion. "' Q; Oi 0.16 E

co

2

0.14

C

012

'"u

'" u 0

'"

•

~ ~ ~

ib.

00

C

004

0

II

0

0.02 f-

er

o 00

•

Ii

o

-

~o· 0

XXX

x

xx

x x x

.••

x 'Ix o 0 x

0.08 006

a. a.

0

010

'2a. ~

•

• 0

•

0

__-'------' 0.04 005

L---"~--'--~---"---~--'--~L------'-~--'-

-0.02 -0.01

000 001

0.02

0.03

Richardson number Ri at 80 cm

FIG. 85. Profile coefficients for wind speed, air temperature, and water vapor density (at 8 meters) against Richardson number (at 80 cm). (From Fleagle, et al., 1958.) x, Wind speed; 0, air ternperatureg, water vapor density.

5.2.6 Further Theoretical Approaches to Temperature and Humidity Profiles The intention underlying the bulk aerodynamic method and the application of profile coefficients was to provide simple procedures for computing the vertical eddy fluxes based on measurements at a certain height above the sea and on the surface data. Consequently, these efforts were mainly directed toward practical application and had to bear the unavoidable shortcomings of such undertakings. Now we are going to tackle the subject in a more theoretical way without caring too much about observational possibilities. 5.2.6.1 Diabatic Temperature and Humidity Profiles. A fairly general approach to the problem in question starts from the following equations for the vertical gradients of the mean potential air temperature B and the mean specific humidity ij, which are similar to the relevant relations for the vertical distribution of wind speed [Eqs. (4.26)].

8B 8z

0* --SeCRf) Z

+

ZQ

(5.26)

272

5

THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE

oij

q*

- = --Sq(Rj)

oz

z + Zo

(5.27)

The quantities 8* and q* correspond to u*/k in Eq. (4.26) and are defined as follows 1 H (5.28) 8* = - - ku; cpp

q*

=

1

E

--ku; p

(5.29)

The dimensionless factors SIJ and Sq represent the influence of the thermal stability and are functions of the flux Richardson number Rf Their indices 8 and q indicate that,in the general case, the stability function describing the transfer of heat is assumed to be different from the functions affecting the turbulent transport of momentum and humidity. Under adiabatic conditions the stability functions must be equal to unity. Considering that observational evidence is still insufficient for a complete determination of the stability functions we have to be content with approximative solutions. In this respect the similarity principle advanced by Monin and Obukhov (1954) has proved rather useful. With the particular form in which this principle was applied by these two authors it is assumed that the stability factors S are functions of (z + zo)/L and are equal for the profiles of wind speed, temperature, and humidity. Consequently y = 1 is accepted, and, according to Eqs. (4.31) and (4.32), this implies the equality of the eddy transfer coefficients and of the Richardson numbers Rf = Ri. With these simplifications, Eqs. (5.26) and (5.27) take the form

00

oz oij

oz

8*

z +

q*

Zo

S(Z + Zo)

(5.30)

s(Z + Zo)

(5.31)

z + zo

L

L

If we further follow Monin and Obukhov (1954) and restrict our considerations to small values of (z + zo)/L, i.e., to the near-adiabatic case, S may be approximately expressed by the linear term [1 + ex (z + zo)/L,] similarly to Eq. (4.35). After integrating Eqs. (5.30) and

5.2

THE TEMPERATURE AND MOISTURE FIELD

(5.31) we obtain the well-known "log air temperature and humidity _

{)z -

110 =

()*

(

In

ijz - ijo = q, ( In

z

+ linear" profiles for potential

az) L + -az)

+ zo + -

(5.32)

+

(5.33)

Zo

z

273

zn

zn

L

The sea-surface values are attained for z = O. The adiabatic case is represented by (). = 0 and L ~ 00. With regard to the value of the constant a, reference is first made to the discussion given in Section 4.3.4.5. As stated there, Taylor (1960b) found that a ranges systematically with stability, assuming values between 3 and 6 for -0.03 < (z + zo)/L < O. In addition, we should mention that an analysis of wind, temperature, and humidity profiles, combined with simultaneous measurements of evaporation (Pasquill, 1949), was carried out by Brogmus (1959), resulting in a = 3.67. Deacon and Webb (1962) fitted together temperature profiles at the boundary between the layers of forced and free convection (see Section 5.2.6.2) and arrived at a = 4.5. On the whole it can be stated that the "log + linear" profile has been confirmed also for temperature and humidity. Its limit of application, on the lapse side, appears to be around I(z + zo)/LI = 0.03, i.e., it applies to the zone of "forced convection," which will be described in the next section. In view of the assumed equality of the S functions for momentum, heat, and moisture exchange, the corresponding transfer coefficients must be calculated from Eq. (4.30), which, by application of Eqs. (4.29) and (4.35), can be transformed into Eq. (5.25). All these statements refer to conditions over land because no relevant results have been reported from the sea. Although it is most likely that in this respect there are no substantial differences between land and sea, conclusive confirmation, based on reliable simultaneous determination of gradients and fluxes over the sea, is still lacking and would be very welcome. So far there are available only some preliminary results which were derived from simultaneous measurements of wind speed, temperature, and humidity profiles above the sea, as well as of evaporation, carried out by Takahashi (1958). Assuming equality of the stability functions S for wind speed and humidity (which implies KM = KE), Roll (1963) calculated corresponding values of Sand Ri from the differences in wind speed, air temperature, and humidity observed

274

5

THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE

between the levels of 50 and 200 em, using Eqs. (5.27), (4.26), and (4.24). For the computation, twenty-six measured values of evaporation were selected out of the material published by Takahashi. These data are distinguished by a good temporal coordination with the corresponding 196 profiles. The measured evaporation values were reduced by the factor 0.54, following Deardorff (196Ia) (see Section 5.2.7.2). Unfortunately, there is no information on the heat flux H and hence the stability length L and the flux Richardson number RI cannot be taken as independent variables. Consequently, we are forced to assume y = I. The results so obtained are represented in Fig. 86 and can be compared with the stability functions S suggested by Monin and Obukhov (1954) [Eq. (4.36)] and by Ellison (1957) [Eq. (4.40)]. While the former relationship is reproduced for two values of the constant o: (0.6 and 4.5), the latter function is given in the form applied by Panofsky et al. (1960) with Rlerit = y/18 which, in our case, implies Rlerit = 1/18. I .5 rrr-,------,-----,---,------,------,----,-------,-------,

c

5? o c

"

J:>

a (j,

05

'---~0--_-;c:0'::o.2---c0~A;:-----;:0:'-::.6;------;;0'::o.8---.:"c1.0;;---1:'-2;----' ::. I~

- 1.6

Richardson number Ri

FIG. 86. Stability function S versus Richardson number Ri (reference height 125 em). Circles: Mean values computed from Takahashi's (1958) measurements of wind speed, air temperature, and humidity profiles as well as of evaporation; standard deviation indicated by vertical stretches. Figures: Number of averaged evaporation data used. Curves: Theoretical relationships of Monin and Obukhov (1954) and of Ellison (1957) with constants indicated.

5.2

THE TEMPERATURE AND MOISTURE FIELD

275

If the whole Ri range is considered, the interpolation formula proposed by Ellison (with the constant Rfcrit according to Panofsky et al.) seems to represent the empirical S values best. In view of the rather crude method of investigation, in particular with regard to the determination of evaporation, the result should be considered as a preliminary one. Further study is necessary.

5.2.6.2 Convective Layers. Under lapse conditions, the vertical exchange of momentum, sensible heat, and moisture is effected partly by purely dynamic turbulence and partly by buoyant forces. When both agents are effective, the wind, and in particular the wind shear, must exercise a certain control on the size and structure of buoyant elements besides its direct contribution to vertical exchange. We then speak of forced convection, thus indicating the dominating influence of wind shear on the thermal effects. When, however, the purely dynamic turbulence is negligible as compared with buoyant forces, the resulting exchange motion is termed free convection. It would be of great interest to get some further information on the characteristics of these two regimes of transfer. In particular, their dependence on the height above sea level is of importance. Assuming buoyant motions with local similarity and negligible effect of wind shear, Priestley (1954) derived the following relations for the profile of mean potential air temperature 88/8z ~ Z-4/3 and 8 ~ Z-1I3 (5.34)

respectively, which was verified observationally by Webb (1958) and by Taylor (1960a) up to a height z that is approximately equal to the absolute value ILl of Monin and Obukhov's stability length. A relation similar to Eq. (5.34) had already been suggested years ago by Prandtl (1932). In this height region the dimensionless heat flux H (5.35) H* = pcp(g/O)1I2(80/8Z)3/2 Z2

is constant with a value of about 0.9. Priestley (1955) further showed that the lower boundary of the regime characterized by the temperature profile Eq. (5.34) and by H* ~ 0.9 is at z ~ 0.03 ILl which corresponds approximately to Ri ~ - 0.03. Below that level, forced convection, i.e., mechanical turbulence, is dominant and the dimensionless heat flux H* is a function of the Richardson number given by H* = k21Ril-1I2 (5.36)

276

5

THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE

which implies that H* decreases with altitude. Here the height functions of wind speed, air temperature, and humidity are, with sufficient accuracy, represented by the "log + linear" relationships, Eqs. (4.39), (5.32), and (5.33). Above the upper boundary of the layer with H* '" 0.9, the gradient of potential air temperature 80/8z vanishes and the profile (5.34) no longer holds true. From z '" ILl upward, a homogeneous region with neutral or slightly subadiabatic stratification extends to a considerable height. This is the layer of essentially free convection where buoyancy is the governing factor. This motion will be treated in greater detail in Section 5.3.2.1. As was pointed out by Webb (1962) the vanishing of 80/8z at the height z '" ILl [which according to Eq. (4.28) drops when u, decreases] indicates that in the intermediate height region 0.03 < z/[L[ < 1, the wind shear is not completely negligible. In fact, the presence of some mechanical turbulence seems to be even more necessary for the diffusion of heat from the rising buoyant elements into the environment. Thus the temperature profile (5.34) must be connected with the existence of a certain wind shear. Consequently, the name "composite convection" appears to be appropriate for the intermediate height region,0.03 < z/ILI < 1, as was suggested by Webb (1962), who also advanced a theoretical approach on the basis of the consideration outlined above. After the foregoing remarks it seems rather obvious that the comparatively shallow maritime bottom layer with superadiabatic temperature gradients, about which some preliminary information was supplied in Table XXV (Section 5.2.4.4), might be identified with the regions of forced and composite convection up to a height of about z '" IL[. In order to illustrate the functional dependence of the stability length L on Hand U*, some numerical values, according to Eq. (4.28), have been graphed in Fig. 87. From this diagram it can be taken that the thickness of the bottom layer comprising forced and composite convection grows with decreasing heat flux and increasing wind shear, contrary to its apparent growth with increased instability as indicated in Table XXV. Thus the existence of the superadiabatic bottom layer is more a consequence of wind shear than of unstable stratification. The merging across the transition level,z '" 0.03[L[, between the layers of forced and composite convection, i.e., between a "log + linear" temperature profile and the height dependence [Eq. (5.34)], was studied by Webb (1960), who suggested taking a two-sided linear smoothing factor, thus ensuring continuity of the first, second, and third derivatives of O(z) at z = 0.03[LI.

5.2

TIlE TEMPERATURE AND MOISTURE FIELD

277

60 , - - - - - - - - - - - - - - - - - - - - - - - - = 0 , - - - - - - - - - ,

50

r'u

~

2

3

4

5

6

7

8

9

FIG. 87. Stability length ILl as a function of vertical eddy flux of sensible heat Hand friction velocity u* [computed after Eq. (4.28)].

5.2.6.3 Inversion Conditions. Since, on the greater part of the oceans, the sea surface is warmer than the overlying air, lapse conditions predominate at sea and so the profile data obtained during stable stratification are rather scarce. The same impression can be obtained by examining Figs. 82 and 83. Although the profiles presented therein were measured in coastal regions, where with warm continental air flowing over cold water, particularly in spring and early summer, stable conditions are more frequently encountered than on the open sea, the share of stable stratification is small. So, with regard to temperature and humidity profiles, little of importance can be added to the corresponding explanations given in Section 4.3.3 for the wind profile. There is, however, one interesting and important feature that seems worth mentioning: Fleagle (1956b), when applying the optical refraction method to the measurement of the vertical temperature gradient above a cold water surface, discovered an anomaly with regard to this gradient at a height of about 10 em, which obviously must be interpreted as a real feature of the temperature distribution under stable conditions. The rather high accuracy of refractive measurement revealed at that height a cooling which is too small to be detectable by ordinary thermometry. The winds were slight (1-5 knots) and the air (at 3-4 meters above the surface) was 4-8°C warmer than the sea. These are exactly the conditions under which the effect of radiative exchange might become significant.

278

5

THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE

Accordingly, Fleagle attributed this cooling to the interaction of convective and radiative processes. If warm air is flowing over a cold sea surface, heat is transferred to the sea by turbulent and molecular exchange. The resulting temperature profile shows a gradient which is very steep close to the surface, but decreases monotonically with increasing height. Radiation tends to modify this profile in such a way that the equilibrium between convective and radiative processes is attained at each height. If the rate of radiative temperature change is computed from the measured temperature distribution on the basis of the emissivity distribution discussed later in Section 5.3.5.4, a radiative warming at a rate of about lOoCjhr is found for the sea surface whereas at about 10 em height the result is a cooling of 6°Cjhr. Above 30 em height the radiative cooling rate remains constant and equals 3°Cjhr. Thus it seems sufficiently established that the anomaly reported by Fleagle (1956b) is due to radiative cooling. This effect may become important in the formation of fog (see Section 5.3.5). 5.2.7 Heat Flux and Evaporation 5.2.7.1 General Relations. It was the purpose of the bulk formulae (Section 5.2.2.3) and of the profile coefficients (Section 5.2.5) to relate the fluxes of sensible heat H and moisture E with the differences in temperature and humidity measured between a single height (e.g., at the ship's bridge) and the sea surface. The shortcomings of such an approach have already been mentioned. They are mainly caused by a complete neglect of the transfer characteristics that are found close to the sea surface, although the models used included those layers. There are two possible ways to overcome these difficulties:

(a) We might avoid the inclusion of the layers next to the sea surface by confining the analysis to levels well above that region. (b) We might apply suitable flow models, taking into account the peculiarities dominating at the sea surface. Dealing first with (a), and limiting our consideration to the nearneutral case, we can well employ Eqs. (5.28)-(5.33) and (4.39), fixing two levels Z2 and zi with Z2 > Zl and assuming that, for L -+ co and 8* = 0, adiabatic conditions are present. We then obtain: (adiabatic stratification) (5.37) Had = 0 2 pk (iiI - t]2)(tl2 - Ul) (5.38) Ead = {In [(Z2 + ZO)/(Zl + zo)]}2

5.2

THE TEMPERATURE AND MOISTURE FIELD

(near-adiabatic stratification) c p pk 2(01 - 02)(il2 - ill)

H=--------------E =

{In [Z2 + ZO)/(Zl + zo)] + «(I.(L)(Z2 - Zl)}2 pk2(ijI - ii2)( U2 - U1) {In [(Z2 + ZO)/(Zl + zo)] + «(I./L)(Z2 - Zl)}2

279

(5.39) (5.40)

After having examined these equations one might argue that the aim described in (a) has not been reached because the relations still contain the roughness parameter Zo which is closely connected with the aerodynamic properties of the sea surface. In order to counter this argument we could say that, in the light of the results given in Section 4.3.3.3, Zo cannot be considered as an actual roughness length, but merely as an empirical factor characterizing the air flow above the sea surface, which is neither rough nor smooth. Thus no possible later interpretation of zo is anticipated. Besides, since Zo is small as compared with Zl and Z2, it can be neglected in most cases. With the help of Eq. (4.39), Eqs. (5.39) and (5.40) can finally be transformed into (5.41) (5.42) in which they apply to adiabatic conditions, too, and are particularly suitable if the wind stress is known. As the equations of Monin and Obukhov (1954), which were used above, are only applicable in the region of forced convection, i.e., for Z ~ 0.03[LI, care should be taken that the levels Zl and Z2 of the measurements concerned fall within that height range. Equation (5.40) is not very appropriate for practical application, because the stability length L is not directly accessible to measurement. It will be noticed that the quotient of Eq. (5.40) over Eq. (5.38) E { In [(Z2 + ZO)/(Zl + zo)] }2 (5.43) = F2 = E ad In [(Z2 + ZO)/(Zl + zo)] + «(I./L)(Z2 - Zl)

-

serves as a link between adiabatic and nonadiabatic moisture transfer. For ease of application the conversion factor F can be written in the form (Brogmus, 1959): g(02 - 01) F = 1 - (I.---(Z2 - Zl) (5.44) TO(U2 - U1)2

280

5

THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE

Comparison with Eq. (4.24) shows that the structure of the factor of is similar to that of the Richardson number. Thus this factor can be considered as a stability parameter. From comparison with Eqs. (4.36) and (4.26) we further infer that the whole conversion factor F approximates to the reciprocal of the stability function S. Turning now to (b), we may remember that for the flow over the sea surface the following two models have been suggested: The flow may be assumed as aerodynamically smooth or rough (see Section 4.3.3.2). Since at present there is not available any convincing evidence as to which of the two models is true, or whether there is still another model that might be applied, we shall abstain from going into detail but merely present the resulting formulae. This is done in Sections 5.2.7.2 and 5.2.7.3. (X

5.2.7.2 Aerodynamically Smooth Flow. Following Montgomery (1940), we can characterize the aerodynamically smooth boundary by a very thin layer of laminar flow (of the order of 1 mm thick) immediately over the sea surface wherein the transfer of momentum, sensible heat, and moisture is effected by the molecular coefficients of viscosity (v) conductivity (ve), and diffusivity (D). Numerical values are given in the List of Physical Constants (p. 250). Sverdrup's (1937) conception of this laminar layer was that it must be considered as a statistical quantity representative of the average conditions which comprise a large number of processes where air parcels come into contact with the sea surface and remain so for a certain time, exchanging heat and vapor content by molecular conduction and diffusion. As the derivations are similar for heat and moisture transfer we may restrict our consideration to the latter. Montgomery (1940), after taking into account molecular and turbulent transfer (under neutral conditions) and fitting together the two regimes at the top of the laminar boundary layer, arrived at the following expression for the evaporation from an aerodynamically smooth sea surface:

E=

pk(qo - qa)u* (>"vk/D)

+ In [(ku*a)/ D]

(5.45)

Here a is the level where qa is measured and>" is a dimensionless constant defined by >.. = uJ)/v (5.46) (8 = thickness of the laminar boundary layer). It will be noticed that Eq. (5.45) is equivalent to Eq. (5.21), thus providing an interpretation of kE* rqa • There are, however, considerable discrepancies as

5.2

THE TEMPERATURE AND MOISTURE FIELD

281

regards the numerical value for A, which ranges between 7.8 (Montgomery, 1940) and 27.5 (Sverdrup, 1937), the value for an aerodynamically smooth surface being A = 11.5 according to von Karman (1934). This is not surprising since the assumption of a laminar boundary layer, as well as its thickness and its dependence on wind speed, is completely hypothetical and can only be verified by indirect evidence. An attempt in this direction has recently been made by Deardorff (1961a), who first compared the evaporation rate of an artificial square pond of smooth water with a side length of 1.2 meters, where the evaporation was assumed to be unaffected by the 5 mm rim of this pond, with that from a small pan situated upon it. After having determined the average ratio of these two values to be 0.54, which clearly shows that the evaporation from the pan is increased by the turbulence caused by the upwind portion of its rim, Deardorff measured the evaporation from the same pan located upon a larger water surface, 'thus deducing values for the constant A in Eq. (5.45) pertaining to a smooth water surface. The result was that A appeared not to be constant but ranged between 4 and 6 for low wind speeds and amounted to about 7 for higher ones. Wind tunnel investigations under strictly controlled conditions will be needed before these results may be interpreted in terms of the theoretical model.

5.2.7.3 Aerodynamically Rough Flow. For heat and moisture transfer in the case of an aerodynamically rough flow, a rather large number of different models have been proposed. Sverdrup, in his 1951 review, describes five different approaches. In four of them a true diffusion layer next to the sea surface is assumed while above that laminar layer different concepts of the transition zone between the laminar flow and the fully turbulent one are applied (Sverdrup, 1937; Montgomery, 1940; Norris, 1948; Bunker et al., 1949). In one model (Sverdrup, 1946), the existence of a laminar boundary layer is denied. The results reached by these five methods diverged widely (the discrepancy in prediction being more than four to one) and, since empirical evidence was not sufficient, it was impossible to decide which assumption might be acceptable. Since then some progress has been made. In the first place, it now seems widely agreed that, at the sea surface, there must exist a significant difference between the exchange of momentum and that of other properties such as sensible and latent heat. As was pointed out by Swinbank (1960), molecular viscosity does not playa decisive part, if any, in the momentum exchange, since this

282

5

THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE

is brought about by pressure forces acting on the roughness elements. However, this model cannot be applied to the transfer of heat and moisture at the sea surface because, in this case, there is no equivalent to the pressure exerted on the waves. Similar conclusions are reached if we consider the model suggested by Stewart (1961) (see Section 4.3.5.6) in which the momentum is supposed to be transferred to the waves not by turbulence but by an organized and wave-like motion in the layer close to the surface. According to Stewart, also, these motions will presumably contribute only little to the transport of sensible and latent heat. Thus we are led to believe that the final exchange of heat and moisture between air and sea can only be effected by molecular processes. (Some observational evidence for this conclusion has already been mentioned in Section 5.1.2.1). Consequently, the proper representation of evaporation and heat transfer must include the molecular coefficients of conductivity (ve) and diffusivity (D). A suitable approach has been described by Sheppard (1958). It has the advantages of both simplicity and freedom from unknown constants. Sheppard used the basic equations [Eqs. (5.1) and (5.2)] in the following modified form: (5.47) H = - Cpp(ve +.KH)(88j8z) (5.48) E = -p(D + KE)(8ijj8z) Thus there is no longer assumed a distinct layer of exclusively molecular transfer; molecular and turbulent exchanges are rather supposed to exist simultaneously. Since the K's increase linearly with height, Ve and D, respectively, preponderate close to the surface. Sheppard took (5.49) thus neglecting Zo on the argument that the aerodynamic roughness is of more importance for the momentum transfer than for the exchange of sensible and latent heat as was explained above. Integration yields cppk(80 - 8a)u* (5.50) H=------In [eve + ku*a)jve] pk(ijo - ija)u* (5.51) E= In [(D + ku*a)/ D] where the subscripts 0 and a refer to the heights z = 0 and z = a. The equations are confined to near-adiabatic conditions or to the first layer above the sea, where dynamic turbulence dominates.

5.2

THE TEMPERATURE AND MOISTURE FIELD

283

5.2.7.4 Comparison with Observations. We now dispose of quite a number of relations for the determination of heat flux and evaporation at sea. Everything considered, their number may amount to eight for each of the two quantities. However, some of these formulae are related to each other since we may also interpret the equations for H and E derived in Section 5.2.7 in terms of profile coefficients I' 8 and r q by making use of the corresponding equations [Eqs. (5.16), (5.20), (5.21), (5.23), and (5.24)] given in Section 5.2.5, thus furnishing theoretical formulae for the T''s. However, we shall not proceed in this direction. We feel we had better investigate the question of which of the equations given in Section 5.2.7. describes reality best. For such an examination simultaneous profile and flux measurements are required. There is still a serious lack of suitable and reliable measurements taken at sea. In the case of humidity, the only study providing humidity profiles, as well as evaporation measurements, was published by Takahashi (1958). It has already been used in Section 5.2.6.1. No corresponding temperature profile and heat flux measurements have become known up to now. In the case of heat exchange, an additional difficulty arises from the fact that the transfer of radiant heat was not considered in the above deliberations; hence the formulae for H do not include its effect which, however, may become noticeable if the turbulent transfer is small, as with high stability and light winds. In our attempt to use Takahashi's profile and evaporation measurements for the purpose of comparing theory with observation, we undertook an examination of Sheppard's equation [Eq. (5.51)], which does not involve any adjustable constant. Out of Takahashi's series we selected those data where the time periods corresponding to the evaporation values were sufficiently covered by profile measurements. Bearing in mind the deviations from the log profile at the higher levels-caused by internal boundaries owing to short fetches or by thermal stratification-we confined the computation to the lowest 50 em, i.e., the friction velocity u, was evaluated from the wind speed measurements at 25 and 50 em and the air-sea humidity difference referred to the level of 50 em. Air density p and molecular diffusivity D were computed for the intermediate level of 25 cm. The results for-fifty-five cases of comparison are given in Fig. 88A. First there will be noticed the considerable scatter which clearly indicates the deficiencies inherent in such a manipulation. On the average the observed evaporation values seem to be higher than the theoretical ones, a fact that is quite understandable if the work of Deardorff (196Ia) (see Section 5.2.7.2) is taken into account. When

284

5

THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE

comparing the evaporation from a pan with that from a small artificial pond, for which the disturbance caused by the rim is assumed to be negligible, he obtained a correction factor of 0.54, i.e., the evaporation from the pan was increased considerably by an eddying motion originating from the rim of the pan. Similar effects must be expected with Takahashi's evaporation measurements because they, too, were obtained by means of a pan mounted on a small wooden float and moored at nearly the central point of a floating square frame with 2 meters side length. Applying the pan-correcting factor determined by Deardorff (1961a), to Takahashi's evaporation values, we obtain the results given in Fig. 88B. Here the agreement between observed and computed evaporation is more satisfactory than in Fig. 88A, although the scatter is still substantial. Apart from this fact, we may say that Takahashi's evaporation measurements appear to be represented by Sheppard's formula [Eq. (5.51)] with appreciable reliability. It should be mentioned that Takahashi (1958) himself compared his evaporation measurements with Eqs. (5.16), (5.38), and (5.45), but he did not establish sufficient agreement. In order to give an idea of the magnitude of the evaporation rate at sea, Fig. 89 has been computed on the basis of Eq. (5.51). 2

2

s:

o o o

o 00

0

0

00

o o

o

~

B

A

0

o

o

o o

x

x

x

2 EObserved (mm/6hr)

0

x x

x

x x x

"0

~

E o

'x xxx \ x x

~

;/x x x:

o

0

o

x

x

x

E E

I

x

2

0 Eobserved (reduced) (mm/6 hr)

FIG. 88. Comparison between evaporation values computed after Eq. (5.51) (Sheppard 1958) and those observed by Takahashi (1958). (A) Observed values as given by Takahashi. (B) Observed values of Takahashi reduced by 0.54 according to Deardorff (1961 a).

5.2.7.5 Effect of Sea Spray. So far we have said next to nothing about the effect that sea spray might exert on evaporation, apart from the remark that this influence must be present at higher wind

5.2

THE TEMPERATURE AND MOISTURE FIELD

285

velocities. It is indeed very difficult to get any quantitative information on this subject because field measurements of evaporation taken at the sea surface can only be made with slight winds where there is no appreciable sea spray and, on the other hand, the problem seems hardly approachable by means of theoretical studies. 25

20

s:

15

""

N

E

~ 10

'"

FIG. 89. Evaporation rate in millimeters per 24 hours as a function of wind speed and water vapor differences computed after Sheppard's formula (5.51). eo - eso = Water vapor difference between the sea surface and 50 em height. Uso - u 2S = Wind speed difference between the levels 50 and 25 em. Tv = 290°K. Diffusivity D = 0.250 cm 2 sec-I.

Montgomery (1940) remarked that sea spray must release water vapor and thus cause an increase of I'q in the layer between the sea surface and the level of measurement. With moderate instability, he estimated this increase at about 40 per cent for a wind speed of 4 meters/sec and at about 100 per cent for 6.5 meters/sec. These figures appear to be rather high in view of the moderate wind velocities concerned (compare Table I). As they were determined in such a way that observational deviations from the theoretical values were more or less interpreted as an effect of sea spray, they can only be considered as a very rough approximation. In accord with the difficult nature of the subject in question, quantitative information can best be expected from laboratory studies. Relevant investigations have been carried out by Okuda and Hayami (1959). They used a wind-water channel of about 20 meters in length and, among other quantities, they observed the sprayed water drops by means of a suitable filter paper exposed vertically to the spray for

286

5

THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE

about 5 to 10 seconds. The diameter of the sprayed drops observed was less than 1.5 mm but the lower limit of the drop diameter could not be determined. The vertical distribution of horizontal transport by sprayed water drops is exhibited in Fig. 90. From this diagram it can be taken that, above a height of 10 em, sea spray is negligible with wind velocities below 10 meters/sec. (Unfortunately the exact height of the corresponding wind speed measurements is not given but it must have been approximately 30 cm.) In the wind speed range of 12-13 meters/sec the water transport by spray at 10 em height increases rapidly. A strong decrease is found with height, the water transport by spray at 30 em being only about 10 per cent of its value observed at 10 em height. In conformity with these findings Okuda and Hayami (1959) ascertained that the influence of sea spray on the profile coefficient I'a, was substantial only for a wind speed U8 above, say, 15 meters/sec.

FIG. 90. Vertical distribution of horizontal water mass transport by sprayed drops. (From Okuda and Hayami, 1959.)

This result complies well with the descriptive terms of the Beaufort wind force numbers (Table I) wherein appreciable effects of spray and foam are assigned to wind forces above 7, i.e., to wind speeds of about 15 meters/sec and more. The laboratory measurements did not show any noticeable effect of (mechanically generated) swell waves on spray and on evaporation. Whether or not the results of these wind flume experiments can be applied to field conditions remains an open question, though.

5.2.7.6 Influence ofa Monomolecular Film. Some substances, such as cetyl alcohol, spread spontaneously on water to produce a surface film only one molecule thick. The special structure of such a monolayer is of importance for the transport of water through it, i.e., for

5.2

THE TEMPERATURE AND MOISTURE FIELD

287

evaporation. For instance, cetyl alcohol is a waxy material having a terminal alcohol group attached to a saturated paraffin chain of 16 carbon atoms. The transport of water through a compressed and, therefore, oriented monolayer is not an ordinary diffusion process which involves a small energy barrier but is to be considered as a process in which the water molecule must pass along a molecular pathway between paraffin chains, thus requiring a substantially higher amount of energy (La Mer, 1962). Consequently, a compressed monolayer results in a retardation of evaporation. The resistance to evaporation increases with the length of the chain and with the reciprocal of the absolute temperature. The retarding effect is much smaller if the surface film consists of multilayers of molecules oriented at random. In recent years the effect of a monomolecular film in suppressing evaporation has received increased attention in view of the practical problem of conserving water in lakes and reservoirs (see, e.g., La Mer, 1962). Although in maritime areas this viewpoint is not of as much interest as in arid zones, the subject will be briefly touched upon here because we have seen (d. Sections 3.3.1, 3.3.2, and 4.2.4) that surface films consisting of organic matter or originating from artificial contaminat\on can be found on the sea surface too. Field measurements indicating the reduction of evaporation by natural surface films have been reported by Deardorff (1961b). He compared the evaporation rates of two pans floating at the sea surface. One of these two pans was filled with subsurface sea water while special care was taken in filling the second so that any surface film which might have been present would have been retained. The pans were exposed to light winds and the evaporation rate was determined from the increase of salinity observed. The results of six sets of measurements showed a distinct reduction of evaporation, of the order of 20 per cent, which was obviously caused by natural surface films. Deardorff (1961b) believes that the amount of reduction found in these measurements was even somewhat smaller than that actually occurring, owing to the following circumstances: At the natural water surface the differences of evaporation between clean areas and film-covered areas are liable to be larger than those indicated by the two pans, because the surface roughness is greater under natural conditions than within the corresponding pan. In addition, the surface film, if captured by the relevant pan, may not cover the entire surface area but cling to the interior walls of that pan, thus reducing the effect of the film on the evaporation observed.

288

5

THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE

When these results are applied to practice, the areal extent and the frequency of occurrence of natural surface films must be estimated if their effect on evaporation is to be taken into account. This, however, is by no means an easy task. For artificial films it has been shown by Grundy (1962) that a monolayer is carried across the water surface by the wind, its rate of movement being about 400 meters/hr with wind speeds between 4 and 20 knots. Besides, the film may be damaged by waves. For these reasons it is difficult to estimate the portion of the surface covered by a monolayer as well as to maintain an artificial film at full pressure over the whole of a reservoir surface. Field investigations on reservoirs covered by artificial films resulted in evaporation reductions which ranged between 40 and 60 per cent (Grundy, 1962). In Section 5.1'.2.1 it was mentioned that, according to laboratory studies, such a surface film reduces or even prevents evaporation but does not substantially impede the exchange of heat. This would account for the fact that the cool skin which is attributed to evaporation is not always observed at the sea surface. Laboratory investigations (Mysels, 1959) further revealed interesting details of the transfer processes that occur at a quiescent water surface covered by a monolayer. The technique adopted was quite simple because the color change of a filter paper, impregnated with cobaltous chloride and held just above the water surface for a few minutes, gave a good, although only qualitative, indication of the marked effect a monolayer exerts on the pattern of thermal convection and evaporation. Since a monolayer offers hysteretic resistance against extension and contraction, convective motions rising to or sinking from the surface of the water are impeded and can only develop over greater distances and with larger forces present. Thus the convective heat transport from deeper layers to the surface is necessarily affected and localized. However, when the surface is clean the convection pattern is unlike that described above, the local differences being much smaller. 5.2.8 Temperature and Humidity Fluctuations near the Sea Surface As was already indicated in Section 5.2.3.3, at present very little can be said about turbulent fluctuations of temperature and water vapor in the first few meters above the sea surface. The only information as yet available originates from Staley (1960), who recorded from 2- to 30-second-period fluctuations of water vapor in a stable atmosphere over a lake surface by means of a microwave refractometer (Magee and Crain, 1958) and a bead thermistor. The index of

5.3

THERMODYNAMIC PROCESSES OF MEDIUM SCALE

289

refraction for microwaves being particularly sensitive to fluctuations in water vapor pressure, the combination of a refractometer (which is not in itself an absolute instrument) with a bead thermistor, having equal response time constants of about t second, allowed the magnitude of the water vapor fluctuations to be derived. Staley has obtained simultaneous records of refractive index and air temperature taken at different heights up to 13.8 meters over a cool lake surface, which showed coincident peaks of high water vapor content and of low temperature. Thus these records are consistent with the measurements of temperature and humidity fluctuations performed at a much greater height (134 meters) in maritime air by Charnock and Ellison (1959) (see Section 5.2.2.2). Since simultaneous wave records led to the supposition that the fluctuations in air temperature and moisture are closely related to the wave motion, it seemed possible to consider these eddies as air parcels forced up from the wave crests. Applying this model, and using the vertical profiles of temperature and vapor pressure for environment and rising parcels measured by himself, Staley (1960) arrived at some estimates of the mixing length for water vapor. They amounted to about 190 em at 4.6 meters height and increased to 765 ern at 13.8 meters. Unfortunately, no wind profiles were measured simultaneously and thus the conclusion must be considered preliminary. The study, however, clearly shows the advantages and possibilities of that new technique. 5.3

THERMODYNAMIC PROCESSES OF MEDIUM SCALE IN THE MARINE ATMOSPHERE

5.3.1 General Outline It is certainly true that the meteorological phenomena occurring in the immediate neighborhood of the sea surface hold a key position among all the physical processes in the marine atmosphere that we have defined as being controlled by the sea surface as lower boundary. Hence it is quite understandable that the air-sea boundary layer problems have called for a thorough treatment in this monograph, as has been given them in Sections 4.3 and 5.2. Nevertheless there are thermodynamic processes in the marine atmosphere that reach considerably higher than a few meters above the sea surface but, in spite of this, may be claimed to be typically maritime. We are referring here to such processes as convection, condensation, and air mass transformation which involve thicker layers, as well as larger areas

290

5

THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE

and bigger air parcels, than we considered when treating the layer next to the sea surface. Consequently, if the latter phenomena can be characterized as small-scale interactions between air and sea, the subject of this section may be termed processes of medium scale. The subdivision which lends itself most readily to this description is the separate representation of lapse and inversion conditions. At sea, the significance of stability is particularly pronounced, both as a characteristic feature and as a directing agent, even at higher altitudes. Thus, it seems justified to take stability as an index of classification. In addition, it would be rewarding and also of rather great interest to treat this subject from the viewpoint of temporal dependence, i.e., to separate the steady state phenomena from the transient processes. But considering "the fact that, even in the trade wind region, truly stationary operation can be secured only rarely, and that, owing to horizontal differences in sea-surface temperature and to dynamic features of the wind field, most of the atmospheric motions at sea involve advective and dynamic transformation of air masses, the principle mentioned above cannot be applied in a strict sense. The particular difficulties inherent in the theoretical treatment of transient processes should also be regarded. Having all this in mind, we decided to subdivide the topic into "general" facts and "transformation" processes. Hence, we will first attempt to describe the general features of the atmospheric motions under different stratifications. In this description the weights cannot be distributed evenly between the two components since, as to the frequency of occurrence, horizontal and vertical extension, and importance, much more can be said about processes under lapse conditions than about those occurring in air masses warmer than the sea. Thereafter, in a separate section, the aspects of air mass modification will be dealt with, i.e., special attention will then be given to the transformation processes. 5.3.2 Lapse Conditions Even a short glance at the climatic charts representing the air-sea temperature difference will reveal the fact that, on the greater portion of the oceans by far, and also during the greater part of the year, the sea surface is warmer than the air above it. The reverse is only found in certain, mostly coastal, regions where upwelling occurs or cold currents dominate. During the early summer months those comparatively small areas show, it is true, a temporary tendency to extend, but on the whole the picture is not changed. Even if we take

5.3

THERMODYNAMIC PROCESSES OF MEDIUM SCALE

291

into account that, to a certain degree, the observed preponderance of the situation "water warmer than air" might be biased by the method normally applied to the measuring of the sea-surface temperature which does not furnish values of the actual (probably lower) skin temperature, we can state that, in general, lapse conditions dominate at sea. Thus the study of this case deserves, and has received, particular attention. With lapse conditions prevailing at sea the fluxes of sensible and latent heat pass from the ocean to the atmosphere, thereby initiating the powerful mechanisms of mass exchange and mesoscale convection which may affect considerable portions of the atmosphere. As we are mainly interested in the processes influencing or transforming the maritime atmosphere by energy exchange with the sea, we shall now add a supplement to our description of this energy transfer, which, in the preceding sections, was entirely confined to the layer next to the sea, by discussing how the energy absorbed at the sea surface is transported upwards and how it gives rise to convective motion, cloud formation, and kindred phenomena. The procedure adopted in our discussion is first to describe the main observational facts and afterwards attempt to summarize the existing concept of the mechanism of the processes concerned. 5.3.2.1 The Structure of the Homogeneous Layer. From the treatment given in Section 5.2.6.2, we know that, under lapse conditions, there is, next to the sea surface, a superadiabatic layer extending to about z = ILl. Within this bottom layer "forced convection" or dynamic turbulence dominates up to z = 0.03jLI, whereas wind shear effects are of minor importance in comparison with buoyant forces in the intermediate layer, 0.03 ILl < z < ILl, the layer of "composite convection." It has already been indicated that the vertical gradient of the potential temperature vanishes at the top of the superadiabatic bottom layer. Various measurements executed by means of captive balloons (Roll, 1939, 1950; Deacon et al., 1956) and by airplanes (Craig, 1946, 1947; Bunker et al., 1949; Malkus, 1958) have given evidence of the existence of such a layer which begins above the superadiabatic bottom layer and, within the accuracy of the observations, is roughly characterized by an adiabatic temperature gradient and by vertical constancy of the specific humidity. In this height region, the air thus seems to be completely mixed or homogeneous. An example is given in Fig. 91. This sounding was made in the Caribbean Sea and represents the conditions in the trade-wind zone. There is some indication

292

5

THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE

that the homogeneous layer can also be found in other regions, and so it seems to form an essential feature of the vertical temperature and moisture structure under lapse conditions. As most of the knowledge originates from investigations in the Trades, we shall base our description on the findings obtained in that region. In particular, the results of two expeditions performed by scientists of the Woods Hole Oceanographic Institution will be mentioned. These two expeditions are distinguished by the fact that, although both were carried out in springtime, they encountered rather 9

10

II

12

15gm/kg

13 14

1000

1000

--x 900

(

~

900

~x,

x x'

800

Transitional ...~ x.... __ layer

x,f x...

Mixing ratio

x.: k

700

'~~ •

-;;

:E

'xI 600

"x,>

Q;

Q;

.5

700

x)

600

800

500

E 500 :: s:

'"

\x

'"

q;

,)

I

400

300

200

Homogeneous layer

.'"

Q;

0q; I

400


Rerit - -

gKd4

(5.52)

gKd4 8~

R=-vcv 8z

is the so-called Rayleigh number and Vc = the thermometric conductivity [ern- sec:"] v = the kinematic viscosity [ern- sec-I] K = the coefficient of thermal expansion [OC-l] g = the acceleration of gravity [em sec-2 ] d = the depth of the liquid [ern] The critical Rayleigh number depends on the character of the boundaries but is independent of the geometry of the cells. On the other hand, the geometry of the cells does not depend on the physical parameters. A summary of the data concerned is given in Table XXVIII. The quantity b designates the side of a square cell, the width of a strip cell, or the side of a hexagonal cell, respectively. It should be noticed that in Rayleigh's theory the coefficients of conductivity and viscosity were considered as constant. ' In liquid layers the circulation is directed upward in the center of the cells and downward at their boundaries. The reverse is true for gaseous layers. Up to now no theoretical explanation of this difference has been given. It is only in recent years that a particular form of cellular convection has become known and investigated. We refer to the toroid convection cells for which theoretical evidence was found by Zierep (1958) and for which experimental evidence was given by Tippelskirch (1959). Contrary to Benard's cellular convection, which is

296

5

THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE TABLE XXVIII THEORETICAL FIGURES FOR CONVECTION CELLS a

Cell shape Character of boundaries Square Two free One free, one rigid Two rigid a

R c rlt

b[d

4.00 3.28 2.8

Strip 2.83 2.34 2.00

Hexagon 1.89 1.56 1.34

657.5 1100.7 1707.8

After Stommel (l947a).

initiated by a heat source uniformly distributed over a plane, the toroid convection originates from a point source of heat. The resulting convective motion consists of concentric annular cells around the point of instability. Below the critical temperature gradient (according to Rayleigh's formula) this pattern depends on the horizontal temperature differences; above that value it is transformed into the normal Benard form of cellular convection. The significance of this new convective motion for practical application is not yet fully understood. Turning to marine applications, we should endeavor to find out whether the convective motions described above can also be observed in the marine atmosphere. In general, meteorologists are not in such a privileged situation as are hydrologists, who have occasionally been favored in their efforts toward observing convection cells in water by pure chance, e.g., by a melting ice cover (Woodcock and Riley, 1947) or wet snow squash (H. G. Neumann, 1958) on ponds which thus readily revealed convective structures. In the marine atmosphere, however, ingenious observational techniques had to be applied before any relevant results could be obtained. Woodcock (1940), for instance, interpreted the flight tactics of herring gulls off the New England coast of the United States in terms of convective motion. With cold air over warmer water the birds usually soared in circles when the wind speed ranged from 0 to about 7 meters/sec. This soaring routine seemed to indicate that cellular convection cells were present under such circumstances. For wind speeds between 7 and 13 meters/sec linear soaring prevailed, i.e., the birds soared straight to windward, gaining altitude rapidly. This technique argues in favor of longitudinal roll vortices, the up-moving currents at the striplike cell boundaries being used by the birds. At still greater wind speeds and, in general, for air warmer than water, no continuous

5.3

THERMODYNAMIC PROCESSES OF MEDIUM SCALE

297

free soaring could be observed. Thus the regular mesoscale convection pattern apparently does not exist either with high winds or with stable stratification. An interesting additional observation was that the birds did not appear at great distances from the coast until fall, when cold continental air begins to flow out over the warmer sea. In order to get more quantitative results, Woodcock and Wyman (1947) subsequently undertook special investigations, using chemical smoke released from ships and airplanes. The lateral and vertical displacements of the smoke plumes were considerable, so that one portion of the smoke plume changed its direction with respect to another by as much as 47°, although the surface wind direction fluctuated by no more than 5°. All thesedisplacements could easily be reconciled with the concept of convection cells although some difficulty arose from the fact that the orientation of the smoke plume relative to the convection cells was not exactly known but had to be deduced from the observations. The side length of these cells was of the order of 500 meters; the average height was estimated at about 300 meters and seemed to coincide with the height of the homogeneous layer. Thus the ratio between side length and height of the cells appears to be in rough conformity with the theoretical values of Table XXVIII. The vertical motion reached speeds of about 1 meter jsec. In addition to the medium-scale motions caused by cellular convection, small scale turbulence was present and made visible by the diffuse expansion of the smoke plumes. Cellular convection is, however, not confined to the subcloud layer. Quite recently cellular cloud patterns over the Atlantic and Pacific Oceans were revealed by photographs from the Tiros meteorological satellites. Krueger and Fritz (1961) related pictures taken by Tiros I to conventional meteorological observations and found that the cellular cloud formations reported by the satellite occurred in regions where there was a homogeneous layer of about 1500 meters thickness with little variation in wind speed and direction. Superimposed over this convective layer was another one of greater stability which impeded the convection. Although the pictures showed many similarities between the observed cloud organization and the classical Benard convection, there were, however, many important physical differences. Since the diameter of the cells ranged between 20 and 50 nautical miles, the ratio of diameter to depth was about ten times as large as those given in Table XXVIII. It should be noticed that the physical parameters on which Table XXVIII is based are of molecular scale. According to Rayleigh's theory, it is true, the geometry of the cells

298

5

THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE

does not depend upon the physical parameters. But in this derivation there are not taken into account several features that are essential in turbulent atmospheric motions, for example, the fact that the horizontal eddy transfer coefficients are large when compared with the vertical ones if a comparatively shallow homogeneous layer is topped by a well-defined inversion and a statically stable layer. Priestley (1962) suggested that such conditions would occur mainly over the oceans, in particular with shallow polar outbreaks, and might be responsible for the geometrical distortion of the convection cells as observed by Tiros 1. Thus, the theory needs some relevant refinement before it is properly applicable to atmospheric convective motions at sea. In addition to the differences in scale there were differences in structure. Contrary to the simple circulation observed in Benard cells, the Tiros I pictures indicated several scales of motions, the cell walls often being made up of individual cloud elements. On the other hand, it is not entirely unreasonable to assume that the theoretical approach, by which Langwell (1951) attempted to provide an explanation of the "clear areas" within the trade wind cloud layer (see Section 5.3.2.4), might serve as a successful model for the cellular cloud pattern observed from Tiros 1. Langwell derived the characteristics of a two-dimensional convection cell within the cloud layer, the particular problem being to investigate whether cool moist pockets under an inversion, in a conditionally stable atmosphere, could initiate cellular, convective circulation. Applying the equations of motion, continuity, and the first law of thermodynamics, Langwell found, in theory, that large, slow-moving cells with diameters of about 10-20 km were possible and could persist for from I to 2 hours, thus constituting a semipermanent feature of atmospheric motion.

5.3.2.3. The Transitional Layer in the Trade Flow. As can be seen in Fig. 91 the trade wind homogeneous layer is topped by another layer wherein the moisture lapse rate is one order of magnitude greater than in the mixed layer below. The temperature profile, however, is much more stable than in the homogeneous layer while, owing to rapid drying, the virtual temperature lapse rate is usually rather steep and similar to that of the cloud layer above. For the latter reason the layer described is termed "transitional layer" since it forms a zone of transition between the homogeneous layer below it and the cloud layer above it. In general it is a rather narrow stratum just below or above the height of the cumulus base. Some figures characteristic of the transitional layer have been summarized in Table XXIX.

5.3

THERMODYNAMIC PROCESSES OF MEDIUM SCALE

299

Examination of the data found with a strong trade regime in 1946 reveals that in clear zones the transition layer was always present and had a mean depth of about 200 meters, the lapse rate of the mixing ratio being 22.5 times that rate in the homogeneous layer below. The lapse rates of temperature and virtual temperature amounted to 47 per cent and 70 per cent of the dry-adiabatic gradient, respectively. In cloudy regions there was no transitional layer in about 55 per cent of the cases. However, in about 44 per cent of this portion a layer of either somewhat more stable temperature lapse rate or somewhat steeper moisture gradient intervened between the top of the homogeneous layer and the main body of the cloud layer, thus leading-in combination with 'the 45 per cent of the cases where a transition layer was clearly recognizable-to an average depth of about 140 meters. With a weak trade wind regime (1953), the transition layer as found in clear areas was shallower (125 meters) and distinguished by a markedly greater moisture and virtual temperature lapse rate than in the case of a strong trade flow. In cloudy zones the transitional layer was almost completely missing. Summarizing, we may say that the transition layer seems to be sharply defined in clear spaces whereas in cloudy areas it is either missing or spreads out over the lower 400 meters or so of the cloud layer. Thus we may regard the transition layer as the manifestation of the compensatory subsidence in the clear areas. 5.3.2.4 The Characteristics of the Trade Wind Cloud Layer. The cloud layer extends from the condensation level up to the base of the trade inversion. This definition is valid for both clear and cloudy regions, without any regard to the actual vertical extension of the clouds which, in a considerable part, do not reach the trade inversion. For quantitative information Table XXX has been compiled from data published by Malkus (1958). From this tabulation we may infer that-contrary to the results obtained for the homogeneous and transition layers where pronounced differences existed between clear and cloudy areas as well as between strong and weak trade flow-the conditions within the cloud layer appeared to be rather uniform and that, in particular, no strong deviations were observed between the two measuring periods or between clear and cloudy zones. Bearing in mind the distinct differences of cumulus convection noticed between 1946 and 1953 we might thus be led to assume that the formation of oceanic cumulus clouds is controlled largely by processes in the subcloud layer.

300

5

THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE TABLE

XXIX

CHARACTERISTIC FIGURES OF THE TRANSITIONAL LAYER OVER THE CARIBBEAN SEAa

Lapse rate of Trade wind regime

Depth (meters)

Relative humidity

co

Strong (April, 1946) Clear Cloudy Average

197 138b 177.

Weak (MarchApril, 1953) Clear Cloudy Average

125 Missing Missing

81 88 84

80 Missing Missing

Mixing ratio

Temperature

Virtual temperature (oC/100 meters)

(100 metersrt

eC/lOO meters)

-14.4 x 10-4 - 5'.0 x 10-4 -12.6 x 10-4

-0.47 -0.79 -0.57

-0.70 -0.995 -0.80

-24.5 x 10-4

-0.51 Missing Missing

-0.88

From Malkus (1958). Effectively or totally missing in five cases out of nine. Average given for eight cases out of nine. a b

TABLE

XXX

CHARACTERISTIC FIGURES OF THE CLOUD LAYER OVER THE CARIBBEAN SEA a

Lapse rate of

Trade wind regime

Strong (April, 1946) Clear Cloudy Average Weak (MarchApril, 1953) Clear Cloudy Average a

Depth (meters)

Relative humidity

co

76 79 1328

77

77

1343

From Malkus (1958).

81 79

Height of Mixing ratio Temperature Virtual trade wind (100 metersr! (oC/100 temperature inversion (meters) meters) (oC/100 meters)

-2.4 x 10-4 - 5.2 x 10- 4 -3.5 x 10-4

-0.63 -0.61 -0.62

-0.69 -0.71 -0.70

2080

- 3.1 X 10- 4 -4.6 x 10-4 -3.6 x 10- 4

-0.63 -0.52 -0.58

-0.69 -0.60 -0.65

1932

5.3

301

THERMODYNAMIC PROCESSES OF MEDIUM SCALE

The picture is somewhat changed if we examine the moisture structure of the cloud layer in greater detail. An upward decrease of moisture that is somewhat faster in cloudy regions than in the clear can be noticed in Table XXX. For further investigation of this subject the lapse rates of the mixing ratio were computed separately for each third of the cloud layer (Table XXXI). Marked differences appear there. They occur not only between clear and cloudy areas but also between strong and weak trade flow. In particular, it should be noted that in most cases the in-cloud lapse rates are considerably in excess of the moist-adiabatic rate. TABLE XXXI MOISTURE STRUCTURE OF THE CLOUD LAYERa

Trade wind regime

Lapse rate of mixing ratio? (100 meters)-l in the cloud layer Lower third

Middle third

Upper third

Strong (April, 1946) Clear Cloudy Average

-2.9 x 10- 4 -8.8 x 10- 4 -5.6 x 10- 4

-0.5 -4.8 -2.5

X

10-4 10- 4 10- 4

+0.8 -0.3 +0.2

X

Weak (MarchApril, 1953) Clear Cloudy Average

-3.5 x 10- 4 -4.7 x 10- 4 -3.6 x 10- 4

-2.3 -5.1 -3.6

X

10- 4 10- 4 10- 4

-5.8 -5.9 -5.8

X

a b

X X

X X

X X

X X

10-4 10-4 10- 4

10- 4 10- 4 10- 4

From Malkus (1958). Saturated adiabatic lapse rate of mixing ratio --2.4 x 10- 4 •

These observational findings can be interpreted as follows: The strong trade wind regime of 1946 was distinguished by a large upward moisture gradient (nearly four times the moist-adiabatic one) in the lower third of the cloud layer in cloudy areas. It was nearly halved in the middle third and almost vanished in the upper third. An explanation of the rapid moisture decrease in the lower third was provided by cloud photographs' which showed that medium- and large-sized clouds were mostly surrounded by great numbers of small cloudlets, only a few hundred meters in diameter and thickness and confined to the lower cloud layer. Observations further suggested that the big clouds were formed from an aggregation of these cloudlets.

302

5

THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE

In contrast to this situation the average upward moisture gradient in the cloud layer during the weak trade wind regime of 1953 was rather uniform in the vertical and actually increased by a substantial amount from the middle to the upper third of the layer. In cloudy areas there was even observed a continuous increase from the bottom to the top of the cloud layer. Cloud photographs reveal that cumulus formation was poor in general but that a certain fraction of the cumuli penetrated the upper cloud layer and spread out below the trade inversion, thus providing a nearly constant vertical distribution of moisture throughout the entire upper part of the cloud layer (in cloudy areas as well as in clear ones). To a minor degree the same phenomenon could be also observed during the period of strong trade flow. But here a pronounced difference was found between cloudy and clear areas. In cloudy regions the upward moisture decrease became very small near the trade inversion but did not vanish since moisture was permanently supplied from below by cloud activity. In clear zones this supply was lacking, injections from cloudy areas being the only source of moisture at upper levels. The cloud form that can be considered as typical for the trade wind region is the "oceanic trade cumulus," which may be characterized by the following specifications (Malkus, 1958): Horizontal extension = 100 meters-2 km Vertical thickness = 300 meters-3 km Updraft = 0.5-5 meters/sec Since generally the vertical development of these clouds is limited by the trade inversion they often have a "blocklike" appearance. Oceanic trade cumuli commonly appear in irregular groups or clusters of about 10-50 km across and separated by somewhat wider clear areas. Apparently this structure does not alter from day to night. Other types of cumulus clouds can also be found at times, e.g. : "Cumulus humilis" or "fracto cumulus" if the moist layer is shallow and subsidence prevails; "Chimney clouds" if the trade inversion is weak, thus allowing the penetration of the cloud tops through it; "Cumulus congestus" if the cloud tops reach a considerable height, roughly more than 3-4 km, and the resulting cumulus massif presents a mountainous appearance; "Cumulonimbus" if synoptic-scale convergence leads to condensation processes extending far above the freezing level and occasionally reaching the height of the tropopause.

5.3

THERMODYNAMIC PROCESSES OF MEDIUM SCALE

303

Showers of different intensity and duration according to the cloud form may fall from nearly all types of cumulus clouds, except fracto cumulus. Some disturbance was caused by the observational evidence, frequently obtained, that cloudy areas were colder than clear zones nearby, in spite of the fact that cloudy regions are considered equivalent to convergence and to ascending motion due to buoyancy. This paradox proved to be a sampling effect. The growing and decaying clouds could not be treated separately. Intensive and detailed investigation (Malkus, 1958; Bunker, 1959) showed that a cloudy region contains only a small fraction (5 per cent) of actively buoyant, rapidly rising updrafts, a similarly small portion (5 per cent) of strongly sinking downdrafts, about 40 per cent of decaying, inactive, and slowly subsiding cloud matter, and around 50 per cent clear spaces between clouds. From this, the following space averages result: Draft + 5 ern/sec Mixing ratio anomaly (vs. clear) = + 1.5 gm/kg Virtual temperature anomaly (vs. clear) = - 0.14°C which show a negative anomaly of virtual temperature although the few active clouds of the group were virtually 2.0°C warmer than their nearby surroundings. Thus, previously divergent statements could be reconciled. The influence of wind shear on cumulus development was studied by Malkus (1952a, 1958). In one of her studies (1952a) it is shown how the slopes of cumulus clouds are related to external wind shear. In particular, the slant of the clouds is considered representative of the interaction between convective elements and the surrounding air. In the latter study the effect of wind shear on cumulus formation was investigated by combining the double theodolite pilot balloon runs made in 1953 by Charnock et al. (1956) near Anegada in the Caribbean Sea together with the aircraft temperature and moisture soundings obtained during the 1953 expedition of the Woods Hole Oceanographic Institution in an observing area that was, for the most part, within 20 miles of Anegada. Some relevant figures have been assembled in Table XXXII, from which we may infer that cumulus development seems to be related to the height of the maximum wind and, in particular, to the wind shear in the lowest 100 meters of the cloud layer. On days with good convection the wind maximum was usually near or well above the cloud base so that the lower part of the cloud layer was only subject to small wind shear. On poor convection days, however, the wind maximum was found considerably below the cloud

304

5

THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE

base, resulting in a strong negative wind shear in the lower cloud layer. This evidence might lead us to believe that cumulus development is probably impeded by strong wind shear. TABLE XXXII INFLUENCE OF WIND SHEAR ON CUMULUS DEVELOPMENTa

Mean wind speed

Mean wind shear

Height of maximum wind

(meter secr-)

(meter sec" km")

(meters)

Good convection days Poor convection days Overall average

a

5.8 3.8 4.8

3.1 3.4 3.2

699 524 611

Wind shear in the lowest 100 meters of the cloud layer (meter sec'< krrr') 1.5 4.7 3.1

From Malkus (1958).

5.3.2.5 The Mechanism of the Trade Wind Moist Layer. The trade wind moist layer comprises the four layers described in the foregoing paragraphs, namely the superadiabatic bottom layer, the homogeneous layer, the transitional layer (these three combined forming the subcloud layer), and the cloud layer. Thus the moist layer extends from the surface of the sea, where it gains its moisture by evaporation, up to the trade inversion. The schematic diagram given in Fig. 92 illustrates the situation and also indicates the function that the trade wind moist layer has to perform. This function may be roughly outlined as follows: From the sea surface, sensible and latent heat is transferred to the overlying air by the processes of heat flux and evaporation which, initially, are of molecular scale. Dynamic turbulence and thermal buoyant forces provide for vertical (and horizontal) spreading while the air is transported to the intertropical convergence zone by the trade flow. Thus larger and larger scales of motion come into play. Below the condensation level, i.e., within the subcloud layer, unsaturated convective turbulence dominates. Above that height some of the turbulent eddies condense to small cloudlets which grow and join to form larger trade cumuli. These clouds, by expansion and by interaction with their environment, try to distribute the moisture

5.3

THERMODYNAMIC PROCESSES OF MEDIUM SCALE

305

over the entire cloud layer. If the updraft is sufficiently strong, they may occasionally be able to penetrate into the dry air above the trade inversion, thus gradually raising and weakening this upper boundary of the moist layer. Finally, in the downstream parts of the trade flow Dry, stobie, sinking air

>000

o

~-

-

--

117'' ' ' '- -----

2000

Claud layer

1500

1500

~

Q;

0;

5

:;:

s:

a>

~

a>

1000

(

r----~"~~. -r-~~~;~~;'~ICumulus base

500

-

-

----

-

layer

1000

iU

I

500

Evaporation

_1_ ~p~a'::io~a~ ~y~

[

_

Sea surface Cloudy area

o

Clear area

FIG. 92. The trade wind moist layer over the Caribbean Sea (schematic vertical cross section).

near the equatorial convergence zone, the inversion disappears and the trade cumuli grow into enormous cumulonimbus clouds carrying latent heat up to the tropopause, from where the released heat is transferred aloft to the middle latitudes, thus contributing to the maintenance of the general circulation. This crude and sketchy description already shows that the trade wind moist layer forms an important link in the chain of the atmospheric

306

5

THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE

energy transport and supply. The question of what consequences would occur arises, e.g., in the trade flow, in the equatorial convergence zone, or even in the Westerlies, if the amount of moisture supplied by evaporation to the trade wind moist layer were, by some cause, substantially reduced. How can we explain the altogether different trade flow conditions experienced over the Caribbean Sea in the spring of 1946 and in the spring of 1953? Shall we attribute these variations in cumulus development to fluctuations in the subcloud layer or to fluctuations in the cloud layer? It is quite clear that a thorough knowledge of the mechanism effective in the trade wind moist layer would bring us nearer to the solution of the problems indicated above. In this monograph, which is only concerned with the marine atmosphere, we do not intend, though, to embark on questions of the general circulation. The latter represents a global problem, and hence it can only be treated globally. We shall rather limit our consideration to describing the mechanism of cumulus generation in the trade wind moist layer without, however, dealing in detail with the physics of the condensation process, which is a general problem and not a specifically maritime one. For further information on the subjects not treated here see, for example, Riehl (1954) and Malkus (1958). Within the scope of this monograph the following question is of major importance. What is the function of the homogeneous layer as regards the formation of the trade cumuli in the cloud layer above it? Does the homogeneous layer furnish the "roots" of the cumuli? The observational evidence is not easily understood. When gathering some information on turbulence in the trade wind moist layer from accelerometer records of the vertical motions of the airplane employed for their investigation, Bunker et al. (1949) experienced no significant differences in turbulence in the homogeneous layer when the plane was flying under the clouds and in clear areas. This comes out very distinctly in Fig. 93. Similarly, the fluctuations of water vapor, which were rather strong in the mixed layer, did not show any pronounced differences between cloudy and clear areas. Moreover, the fluctuations of temperature and moisture as observed in the homogeneous layer tended to be out of phase while in convective layers coincidence of phase is prevalent. Further evidence can finally be taken from Fig. 94, which exhibits the maximum accelerations observed at different heights of the moist layer in clear areas as well as in cloudy ones. The clear air curve, which Bunker et al. (1949) chiefly ascribed to dynamic turbulence originating from surface friction, has a maximum of 0.2 g at about 300 meters and decreases

5.3

THERMODYNAMIC PROCESSES OF MEDIUM SCALE

307

continually to a value of 0.025 g at 2000 meters. The vertical motions attributed to cloud development start at about 600 meters, i.e., at the top of the homogeneous layer. They are supposed to be clearly separated from this layer. Clouds

Clear areas

10.IOq

Homogeneous layer

055 0

5 10 15 20 3040 50 60 5 10 15 20 25 TIme (seconds)

FIG. 93. Accelerometer records taken in the homogeneous layer and in the cloud layer (From Bunker et al., 1949.) Unreduced tracings. Zero acceleration line coincides with height at which the run was made. Double-headed arrow indicates displacement equivalent to 0.10 g.

From these findings, Bunker et at. (1949) concluded that the convection which is effective in the cloud layer is obviously not related to any recognizable increase of vertical turbulence in the homogeneous layer below it. The convective motions in the cloud layer neither originate in thermals of the mixed layer nor do they extend an appreciable distance down into that layer. This agrees with the observational fact, mentioned in Section 5.3.2.1, that stability is increased in the upper part of the mixed layer which would damp out any convective motion generated at lower levels before the cloud base is reached. Consequently, organized thermal-convective circulations, e.g., cellular convection, in the homogeneous layer can be excluded as a possible cause for cumulus generation in the cloud layer. Occasional turbulent eddies hitting the condensation level at random can only be responsible for the formation of small cloudlets

308

5

THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE

but they do not explain the existence of cloud groups. Furthermore, we may leave aside such causes of updraft as differential heating due to islands, flow over barriers, and synoptic-scale convergence, bebecause these phenomena are irrelevant to the formation of the normal trade cumuli.

OJ.

2000 1900 1800 1700 1600

. ..

1500 1400 1300

'"

~

!

s:

'"

Q; I

1200 1100 1000 900 800 700 600

• In clouds

500

x In clear

400 300 200 100 0

0.1

0.2

0.3

0.4

05

Accolorat;ans 19)

FIG. 94. Maximum accelerations measured at different heights in clear air and in clouds in the trade wind moist layer. (From Bunker et al., 1949.)

Bearing in mind that the height of the homogeneous layer was found distinctly greater in cloudy areas than in clear regions, we should rather seek the origin of the trade cumuli in gradual variations of the thickness of the mixed layer. A corresponding mechanism has been suggested by Langwell (1953), who studied the oscillations of the boundary between the homogeneous layer and the stable-and sometimes even isothermalstratum above it. Unstable gravitational waves were found physically plausible. If a depth of 600 meters was assumed for the mixed layer, the upper limit of unstable wavelengths was calculated to be 2 km. Thus these oscillations would permit the air in the lower mixed layer

5.3

THERMODYNAMIC PROCESSES OF MEDIUM SCALE

309

to reach saturation in limited areas provided that the oscillating interface is then located at or above the lifting condensation level. In this way, moisture and latent heat could be transferred from the mixed layer to the cloud layer whereby trade cumuli are formed over the ocean. The calculated cloud diameter seems rather low, however, particularly if one considers that oceanic trade cumuli commonly appear in groups about 10-50 km in diameter and are separated by somewhat larger clear areas. Therefore the processes which are at work below clouds should permit rather large numbers of moist air parcels to reach the condensation level in particular localities simultaneously. When searching for inhomogeneities on a 10-50 km scale, Malkus (1957) encountered sea-surface temperature anomalies which seemed to be closely related to the pattern of cumulus clouds. Some details of the "warm spots" and "cold spots" of the sea surface have been given in Section 5.1.3 and need not be repeated here. We can confine ourselves to describing their effects on the air structure. A remarkable example of an association of cumulus clouds and turbid water has been reported by Isaacs (1962) from the Gulf of Bengal. He observed a circular mass of cumulus clouds, about 60 miles in diameter and reaching, in the center, up to about 7.5 km in altitude, which was situated directly above an equally circular region of turbid water originating from the river Ganges. The phenomenon was attributed to the turbid water being excessively heated by its high solar absorption, thus giving rise to evaporation and convection. Observations from the Trades also showed that oceanic cloud groups were always associated with warm spots and frequently developed at their downwind boundary. In general they were slightly displaced downwind relative to warm spots, thus being very similar to clouds generated over an island or a hill. Therefore, Malkus (1957) was able to apply the island model of differential heating as a first approximation to the horizontally convergent circulation across a warm spot at the sea surface and to the accompanying updrafts above it. Naturally, in the case of the warm spots concerned, the magnitude and scale of circulation superimposed upon the mean wind flow will be strongly reduced as compared with those over an island. A quantitative relation between the observed temperature excess at the sea surface and the main features of the heat-produced circulation across a warm spot could be derived in this way. The relations ascertained in this way were tested satisfactorily for three islands of different sizes in the Atlantic trade wind zone.

310

5

THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE

When this model was applied to an oceanic warm spot of 0.2°C in amplitude and of 10 km horizontal extent downwind the following circulation resulted: The average horizontal wind difference at the surface amounted to 0.7 meters/sec, and if the trade wind speed is 6.7 meters/sec the circulation reverses at the height of 1350 meters. The air takes about 25 minutes to cross the warm spot and the updraft at the cloud base (650 meters) is 4.3 em/sec. Thus a streamline starting at that height at the upwind edge is estimated to have risen about 65 meters at the downwind boundary. Ma1kus (1957) further showed that if the inflow air has the typical moisture distribution of a clear area (see Tables XXVII and XXIX and if, in order to satisfy continuity, the amount of air and water vapor entering per second at the upwind side equals the outflow per second through the top of the subcloud layer and through the downwind boundary, then the moisture distribution at the latter place is consistent with that gained in cloudy zones. On the whole, a remarkable upward moisture transport seems to be effected by motions of the scale considered which thus contribute substantially to the upward pumping of water vapor from the sea surface through the homogeneous layer into the cloud layer of the Trades. Small-scale turbulence alone would require rather high values of the Austausch coefficient (see Bunker et al., 1949) if it were held responsible for that moisture transport. Therefore this is no sufficient explanation of the moisture distributions found in the trade wind moist layer. Eddy turbulent transport is of importance mainly as a brake upon convection and in describing the exchange between the clouds and their surroundings. A complete discussion of this subject would, however, necessitate an examination of the circulation occurring both in the cloudy and in the clear areas. This was attempted by Malkus (1958), who advanced a physical model describing the processes at work in the trade wind moist layer. In this paper there were chiefly discussed the following two alternative concepts: (1) Individual cloud groups are stationary or very slowly moving downwind; thus the trade flow passes through them, undergoing rise and subsidence. (2) No relative motion occurs between individual cloud groups and the trade flow while new cloud groups generate and vanish in the latter at random. There was not sufficient observational evidence to be found and

5.3

THERMODYNAMIC PROCESSES OF MEDIUM SCALE

311

so it was impossible to decide which model would come nearest to reality. Of course, the real situation may lie between the two extremes. If we adhere to the "warm spot" scheme described above, the cloud group as a whole would remain in nearly the same location for at least 3 to 4 hours, despite a wind speed of 5-7 meters/sec. Individual clouds will form after the air flow has crossed the upwind boundary and will dissipate some 30 minutes later, shortly after passing the temperature step down, several kilometers downwind. Summarizing, we may say that trade wind cumuli and cumulus groups are thermally direct circulation systems, driven by buoyancy obtained from release of latent heat. It is their function to distribute the moisture supplied by evaporation over the entire cloud layer. Cloud groups seem to be associated with weakly convergent flows superimposed upon the mean trade wind and set up by inhomogeneities of the sea-surface temperature on a 10-30 km scale. The discussion given so far has dealt chiefly with the temperature and wind conditions which may lead to convection and condensation. A related question is whether there is a subcloud humidity structure which could be made responsible for certain features of the trade flow, such as the sequence of orographic showers, for example Woodcock (1960) reported that thirty-four showers passed over one rain gauge station on Hawaii while 105 km of air passed in the same period. This could be explained if the humidity structure of the air mass in question varied appropriately with an average wavelength of 3 km. According to Bunker (1962) observations of the mixing ratio were made simultaneously at three levels in the subcloud layer of the trade wind east of the Bahama island of Eleuthera with the particular aim of investigating whether there are similar-sized moist and dry parcels of about 2 km in diameter in the mixed layer. Spectral analysis of the humidity records showed that roughly 75 per cent of the variance of the mixing ratio was contributed by wavelengths longer than 3.75 km, and 22 per cent by the wavelengths between 3.75 and 1 km. Although the concentration lay in longer wavelengths, the moisture variations corresponding to wavelengths between 3.75 and 1 km were of such a magnitude [mean standard deviation 0.14 grn/kg (maximum 0.42 gm/kg) ; mean temperature difference generated by the condensation of the excess water vapor 0.23°C (maximum 0.67° C); that many of these variations appeared to be capable of producing shower cells if the air was forced up a mountain slope. Of course, there may be other effective mechanisms, such as gravitational waves, flow instabilities, and random turbulent gusts. Hence, final evidence as to

312

5

THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE

the cause of the sequence of orographic showers in the Trades is sti11lacking.

5.3.2.6 Models of Cumulus Formation and Maintenance. In the foregoing paragraphs the subject of cloud formation was treated in a rather summary manner. The properties of the trade wind moist layer were described, and an attempt was made to arrive at a physical interpretation of the processes inherent. Almost nothing has been said either on the nature of the cumulus clouds themselves or on the forces acting in them. This point is going to be tackled in the following. We are now interested in the formation and structure of the convective elements themselves. A detailed and complete treatment of cloud dynamics must, however, not be expected. It would lie outside the scope of this monograph which is only concerned with the maritime aspects of atmospheric processes. Regarding the general and basic fact of cloud dynamics, as well as of cloud physics, reference is made to the representations given by Moller (1951b), Austin (1951), Malkus (1952b), Riehl (1954), and Ludlam and Mason (1957). Hence, we can content ourselves with briefly reviewing the principal features of cloud formation. In the simplest approach there is assumed a buoyant air parcel which does not mix with its surroundings. In addition, no compensating motions are supposed to occur in the environment. This noninteracting, buoyant parcel first rises dry-adiabatically, then, after passing the condensation level, it is saturated and, provided that the surroundings are cooler, it follows the moist-adiabatic lapse rate until its path intersects the sounding representing the environment. The buoyancy acceleration B is then given by Tv - Tv' B = g (5.53) Tv' where Tv is the virtual absolute temperature within the parcel and Tv' is the corresponding temperature of the surroundings (g = acceleration of gravity). This well-known parcel model meets with severe difficulties. First, the acceleration provided by it is much more powerful than is usually observed. Secondly, the lapse rate inside the clouds is not moist-adiabatic, as required by the model, but considerably steeper (compare Section 5.3.2.4). Furthermore, the tops of trade wind cumuli are generally much below the level which the cloud air could reach if it rose moist-adiabatically from the cloud base (Stommel, 1947b). Finally, the liquid water content in cumulus clouds without precipitation is considerably smaller (about one-fifth) than

5.3

THERMODYNAMIC PROCESSES OF MEDIUM SCALE

313

that predicted by the parcel method, which agrees with the fact that the existence of "holes" or regions of apparent zero liquid water content has been verified inside cumuli (Squires, 1958). The latter observation indicates that the mixing in of dry air is a normal feature of these clouds. The deficiencies of the parcel model must be ascribed to the disregard of the following effects: (1) The mass continuity. (2) The interaction between the buoyant parcel and its surroundings. The continuity of mass can be secured if both the upward and the downward motions are taken into account within a limited area (slice model; Bjerknes, 1938). In the absence of divergence or convergence, the upward and downward mass transport across a reference level must be equal. Small areas of strong updrafts will thus be accompanied by weak downdraft in large areas, for instance, by a compensatory sinking of the environment which causes a substantial reduction of the excessive buoyancy given by the parcel method. The interaction between the rising parcel and its environment can be accounted for in different ways. The entrainment model advanced by Stommel (1947b, 1951) rests on the hypothesis that the clouds entrain air from their surroundings as a jet of rising air embedded in relatively quiescent environment does. The major reduction of vertical momentum as compared with that of the noninteracting parcel arises from buoyancy decrease by dilution. Steady state is assumed as well as complete horizontal mixing within the cloud. The entrainment model has been of value mainly in relating observations of buoyancy, updraft, and mixing, as well as in describing the influences of environmental properties on the structure of the cloud. In spite of this there remain the following difficulties in our understanding of cloud dynamics: (1) The downward force due to the weight of the condensed water is neglected. (2) The frictional and turbulent drag forces exerted by the environment on an element of rising air are not taken into consideration. (3) The steady state model says little about the mechanism of entrainment and nothing about the early or late phases of the life cycle of a cloud. The time dependence, missing in the entrainment model, is introduced with the bubble model (Scorer and Ludlam, 1953), which may

314

5

THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE

be considered as the next logical step forward from the entrainment model. Time-lapse cloud films, as well as a comparison of these with experiments on bubbles in water, suggest the interpretation of a convective element as a bubble of rising air (also called "thermal") with a characteristic diameter ranging between 100 meters and 2 km. The outer face of such a bubble is eroded by the relative descent of the outside air, thus generating a "wake" in which the surrounding air is mixed with the air of the bubble itself. Above the condensation level the bubble loses cloud material to its en.vironment, and the "wake," behind the rising bubble, is formed of a mixture of cloud and environment. (Fig. 95.) It should be emphasized that, in contrast to the entrain.ment model, no dilution of the bubble cap is assumed.

,

~,

, ,, I

I

~I

,,

, ,,,

~

, ,,, I

I

FIG. 95. Bubble model of cumulus formation. Velocity field around a rising bubble. Left side: Dry ascent; velocity upward at the edges of the wake; upward displacement of the environment. Right side: Condensation in the bubble; sinking motion at the edges of the wake caused by chilling due to evaporation; downward displacement of the environment. (From Scorer and Ludlam, 1953.)

The reduction of vertical momentum is merely caused by the form drag which implies the erosion of the bubble. By this process the bubble is wasted at last, leaving the turbulent mixed wake which causes the environmental air above the original cloud mass to be enriched with

5.3

THERMODYNAMIC PROCESSES OF MEDIUM SCALE

315

moisture and which facilitates further convective motion by diminishing the erosion of the subsequent bubble. Consequently, this bubble may penetrate farther than the first one. Successive rising bubbles result in the gradual upward extension of cloud mass. Hence the cumulus cloud can be interpreted as an aggregation of buoyant bubbles of saturated air and their wakes. A cloud penetrating to great heights is generally built up by the successive release of single bubbles. If the vertical wind distribution is subject to shear, the higher winds above the original cloud carry the wake, produced by preceding bubbles, downstream relative to the parent cloud mass. Consequently, the following bubbles, whose development is favored by an environment enriched with moisture, will also tend to appear farther downwind. Thus, the growth of a cumulus is greatest on its downshear side. With strong wind shear present, successive bubbles may even be unable to interact, with the result that the formation of cloud towers would be impeded. The bubble theory was supplemented by Squires (1960), who attributed particular stress to downdrafts of dry air originating at the top of the cloud and assisted by evaporative cooling. It is suggested that these downdrafts penetrate the cloud to a significant depth, thus providing a negative feedback mechanism of vertical mixing which limits the liquid water content of the cloud. Considered qualitatively, the bubble concept conforms well to observation. For instance, time lapse movies of overwater trade cumuli taken by Harrington (1958) indicated that the rise of cloud tops was not continuous, but in steps, which supports the bubble model. Similar conclusions can be drawn from the cross sections through trade-cumulus clouds executed by means of a slow-flying aircraft (Malkus, 1954). The measured draft structures of two cumuli have been summarized in Fig. 96 (A and B). The vertical velocities indicated therein were obtained by integration of the records of an accelerometer in a manner similar to that described by Bunker (1955) (see Section 4.4.1.2). The aggregation of several small neighboring updrafts or bubbles into a large cloud is clearly visible particularly in the lower altitudes. The upper portions of the two clouds, or the towers, belonged to widely differing phases of their life cycles. Cloud A was still in a very active phase with substantial updrafts dominating. On the contrary, cloud B represented a more mature stage characterized by strong downdrafts at its top. Further support for the bubble model was provided by a comparison of cumulus observations and simultaneous soundings made

HEIGHT (KM ABOVE SEA LEVEL)

2.0

A

1.8

1.6

2.0

!2MPS

1.8

WIND (MPS)

1.6

24

1.4

14 1.2

38

1.2

4.9 1.0

1.0

2.0

HEIGHT(KM ABOVE SEA LEVEL)

WIND (MPS) 1.6

1.6

2.0

B

2 MPS

1.8

5:3 ~

1.6

----.;::------=;;:;<W~~+_-----'''''"'''''~---':::-.-----=_-__i

1.4

1.4

i{ (-:-

6.2 1.2

1.2

6.6 1.0

0.6

6.9 0.6

6.7 6.4

0.6

0.6 -200-

-DISTANCE ,METERS---.

FIG. 96. Draft structure of two trade cumuli in different phases of development, combined from airplane records and cloud photographs. (From Malkus, 1954.) Curves represent vertical draft velocities (running averages over 150 meters distance) at relevant altitudes, their origin being thin horizontal lines at each level. Winds obtained by double drift of aircraft are shown at the extreme left. Calculated slopes of clouds are given by heavy curved lines.

5.3

THERMODYNAMIC PROCESSES OF MEDIUM SCALE

317

over the North Atlantic (Ludlam and Scorer, 1953). With large clouds, the tops were nearly always found very close to the equilibrium level of the parcel theory. These results suggest that with large clouds the bubbles seem to be rather well protected against dilution when rising through the cloud mass, and that dilution and evaporation are only effective after the bubbles have emerged at the top. Although nothing is said on how the bubble motion is initially created by buoyancy, the bubble concept contains considerable advantages as compared with the other approaches mentioned above, because it attempts to describe the mechanism of entrainment, i.e., the interaction of cloud elements with one another as well as with their environment. 5.3.2.7 Quantitative Treatment of the Bubble Model. A quantitative approach to the bubble model was attempted by Malkus and Scorer (1955), who described the rise of a single, isolated, and saturated bubble by the following differential equation: dwjdt + Kw 2 = B (5.54)

where w = ascent velocity of the bubble K = drag coefficient B = buoyancy acceleration given by Eq. (5.53) minus a correction for suspended hydro meteors According to Eq. (5.54), the acceleration of the bubble cap equals the resultant of the forces (per unit mass) acting upon it, i.e., the buoyancy minus the drag. If these two are balanced, the acceleration of the bubble becomes zero and its limiting velocity WL is given by WL =

(BjK)1I2

(5.55)

The drag coefficient K can be related to the radius R of the curvature of the rounded bubble cap by K = 9j4R

(5.56)

if it is supposed that bubbles in the atmosphere can be treated in a manner analogous to air bubbles in a liquid. Further, it is assumed that the radius of curvature of the bubble cap decreases with the time t in the following manner: (5.57) R = EB( -t) (t is taken negative during the bubble's lifetime, R being zero for t = 0). Since Eq. (5.57) describes the erosion of the ascending bubble, E is called the erosion parameter. After combining Eqs. (5.54),

318

5

THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE

(5.56), and (5.57) we arrive at an expression for the erosion parameter E which only depends on the time, on the bubble's ascent velocity, its acceleration, and its buoyancy. In other words: The remarkable result is obtained that the life cycle of the isolated bubble, once it is formed, does not, in the first approximation, depend on environmental parameters except lapse rate. Observations of a number of relatively isolated cumulus bubbles, ranging in diameter from 100 meters to about 1 km, were taken both in the trade wind region and in the middle latitudes. They confirmed the theoretical findings within the limits of measurement. The erosion parameter E was found to be about 50 ± 10 seconds, The same laws seem to apply when a composite bubble is formed at cloud base by amalgamation of several small bubbles into a large one. The theoretical approach is, however, different if several cloud bubbles are present and interact with one another and with their environment. In this case the life cycle of individual bubbles must depend on such environmental factors as wind shear and dryness. The life of each bubble may be divided into two sections: first, there is the "protected range," i.e., the section where the bubble rises within the cloud from its level of origin to its emergence at the cloud top. During this period the bubble is protected from the cooling effects of evaporation by the surrounding inactive cloud mass. When the bubble penetrates the inactive cloud top the "unprotected range" starts where the bubble is in contact with clear air and hence is subject to evaporation and erosion. Malkus and Scorer (1955) found that the maximum bubble radius at its emergence from the cloud approximately equals the unprotected height range, whereas the total range covered by each bubble, according to Ludlam and Scorer (1953), corresponds to the width of the cloud body from which the bubble has emerged. Later on, Saunders (1961) succeeded in relating the diameter of bubbles emerging at the tops or at the flanks of cumulus clouds to the heights penetrated by them. A linear relationship was found between the upper limit of that diameter and the relevant height with a coefficient of proportionality of 0.40. Thus the ascent of a bubble is always accompanied by a corresponding increase of its lateral dimensions, which results from the entrainment of the wakes and residues of former bubbles lying in its path. 5.3.2.8 Origin of Bubbles at Sea. Now the question arises of where the main source of bubbles or thermals is to be sought at sea. In principal, bubbles may generate at the sea surface and enter the cloud layer through the cloud base as well as form entirely within

5.3

THERMODYNAMIC PROCESSES OF MEDIUM SCALE

319

the cloud layer. Theoretical examples for the evolution of a convective element near the ground were given by Malkus and Witt (1959). As the initial organization of convection is a basically nonlinear process, such an approach could only be accomplished with the help of electronic computers. The calculation showed that, within a few minutes, the initial perturbation acquires a mushroom-like shape surrounded by a vortex ring circulation at its edges. Two phases of development can be distinguished: First, there is an "organization phase" characterized by the formation of the bubble cap and of the vortex ring and exhibiting only slight upward motion. The second phase comprises the actual ascent of the bubble. These numerical calculations were confirmed by laboratory experiments (Woodward, 1960). Conclusive observational evidence obtained at sea seems to be lacking as yet. Bearing in mind that Bunker et al. (1949) were not able to verify thermals, i.e., bubbles, in the mixed layer which could be regarded as "roots" of the cumuli, we might be led to assume that at sea the bubbles chiefly generate within the cloud layer, usually at any level up to that where the environmental lapse rate becomes more stable than moist-adiabatic (Scorer and Ludlam, 1953). In a later paper, Bunker (1959) concluded from observational studies that the air within the buoyant elements originated in the vicinity of the 100-200 meter level, i.e. within the mixed layer. Its transport to the cloud level could be performed by a lifting motion due to mesoscale convergence, possibly induced by inhomogeneities of sea-surface temperature (compare Section 5.3.2.5). In addition, other effects, e.g., turbulent motion, buoyant acceleration, and pressure variations, could be involved. In this respect it may be worth mentioning that, although no significant increase in the vertical turbulence was found under trade wind cumuli, a distinct increase of the horizontal turbulent component did occur (Bunker, 1955). Further work on this point will be necessary. 5.3.2.9 Structure of Oceanic Cumulonimbus Clouds. In Section 5.3.2.4 it has been mentioned that cumulonimbi are found at sea in synoptic-scale convergence zones, e.g., cold fronts, troughs, easterly waves, and in the region of the intertropical convergence. After the success with which the bubble model has been applied to oceanic cumuli in the Trades it seems worthwhile to focus our attention upon the cumulonimbi and to investigate whether this approach is also suitable for the considerably larger cloud masses of this kind. An example of such a study was given by Malkus and Ronne (1954), who reported observations taken by means of time lapse

320

5

THERMODYNAMlC PROCESSES IN MARlNE ATMOSPHERE

photography during the passage of a strong polar trough near the West Indian island of Anegada. Some extremely large oceanic cumulonimbus clouds extended upwards of 12 km into a region of strong vertical wind shear. The interpretation of the measurements was done in terms of the bubble model. The main results were that the same erosion parameter E as obtained for trade wind cumuli was found to be valid for the penetrative towers and that a certain minimum cloud dimension was required for the development of such vigorous convection. In conformity with the statement of Ludlam and Scorer (1953) on the correspondence between the total range of a bubble and the width of the parent cloud body we may assume that a large aggregation of cloud mass is necessary to protect the innermost core from dilution so that it is able to retain sufficient buoyancy up to altitudes of 12 km. A cloud mass with a diameter of about 9 km produced undiluted bubbles, 2 km in diameter, which emerged every 20 minutes from the cloud top, rising at a velocity of about 11 meters/sec. The conditions for penetrative cumulonimbus development have been investigated more recently by Malkus (1960), who based her study on the improved bubble model advanced by Levine (1959). The characteristics of this model are the following: An isolated bubblelike element is furnished with an internal circulation similar to that of a vortex ring, it is continually turning inside out during its ascent and, at each cycle, it exchanges a constant portion of its mass with the environment. From this short description it can already be taken that the model of Levine incorporates some essential features of the entrainment model into a new bubble model which, in its original form, involved no dilution of the bubble cap at all. The corresponding differential equation is similar to Eq. (5.54), except for the drag term which has to be adapted to the mass exchange mechanism described above, with the result that it is split up into a "form drag" and a "mixing drag." The important result of the computation was that a relationship was established between the entrainment rate and the diameter of the convective element. For bubbles of 500 meters across (trade cumulus size) entrainment rates of the order 0.5-1.0 x 10-5 ern"! were found, whereas for elements of 5 km across (thunderstorm size) the entrainment rate was one order of magnitude smaller, namely 0.05-0.1 x 10- 5 cm". In this connection it should be pointed out that the dilution of clouds is insignificant with entrainment rates ~ 0.1 x 10- 5 crrr ! under saturated conditions; ~ 0.05 X 10- 5 cm- l under fairly dry conditions. Herewith, we have gained a better understanding of the idea of the "protective cores." Confirmation is obtained for the necessity of a critical dimension that the cloud must

5.3

THERMODYNAMIC PROCESSES OF MEDIUM SCALE

321

have for a penetrative tower of a given height to develop. Explanation is also provided for some surprising observations, for example, that, except for the lower layers, a temperature lapse rate steepening beyond the moist-adiabatic one was by no means found indicative of a higher readiness for the development of penetrative towers or thunderstorms, or that spectacular cumulonimbi generated in spite of a relatively dry atmosphere above 3 km. It can be concluded that the problem of penetrative cumulonimbus is essentially reduced to that of element size. Malkus (1960) applied the improved bubble model of Levine to hurricane cumulonimbus towers which, by radar measurements, were found to have reached altitudes of about 18 km. The aim was to examine the theoretical relation between size and maximum height of each convective element, which appears as a single tower when emerging from the top of the cloud mass. As can be inferred from Fig. 97, the agreement is rather satisfactory. The measured data lie 15

-:

Hurncane Daisy

14

Aug 27, 1958

13

,-

12

~

II

~ s:

10

E

9

;


4km)

x Measured

Diameter (km)

FIG. 97. Relation between diameter and maximum height of active cumulonimbus towers. Comparison between theory and photogrammetric measurements from aircraft nose camera films. (From Malkus, 1960.)

mostly between the two theoretical curves calculated for saturated environment and for a relative humidity of 70 per cent above 4 km. It can be noticed that reducing the humidity of the cloud environment is much less effective with larger bubble diameters than with smaller ones. Further evidence, not reproduced here, shows that reduction in

322

5

THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE

environment humidity is most effective at low levels and the less inhibitory the higher it starts. It is almost certain that the larger elements penetrate the tropopause although their buoyancy is negative. This penetration, which seems to be affected only little by the static stability of the lower stratosphere mainly varies with the ascent velocity at the tropopause. For every kilometer of penetration into the stratosphere, an ascent velocity of 20 meters/sec is required at that level. Since the model provides for a maximum updraft of 2.5 times the ascent rate of the element and since, according to reconnaissance reports, updrafts of 50 meters/sec seem to occur in the eye walls of hurricanes, an ascent velocity of 20 meters/sec at the tropopause level can be accepted as sufficiently authentic. Thus, in contrast to the earlier bubble theories, but in agreement with observation, the improved bubble concept of Levine permits an element to overshoot its level of zero buoyancy. 5.3.2.10 Cumulus Organization at Sea. One of the most interesting aspects of maritime cloud distribution is the degree of organization on so many different scales. We have already mentioned the fact that oceanic cumuli are normally to be found in groups of from 10 to 50 km in diameter and separated by somewhat wider clear areas. Attempts were made to connect this rather irregular form of organization with the thermal patchiness of the sea surface (Section 5.3.2.5). We further referred to cellular cloud patterns as revealed by pictures taken by meteorological satellites (Section 5.3.2.2). From aircraft investigations there was obtained the information that the individual cumuli frequently line up into rows which may extend for several hundreds of kilometers. It seems necessary and useful that these different modes of cloud regime should be correlated with the atmospheric flow pattern. Although the larger scales of cloud regime can better be examined by means of suitable satellite pictures, relevant studies on the smaller scales of organization have been carried out during aircraft flights over the tropical Pacific Ocean (Riehl et al., 1959; Malkus et al., 1961a). These aircraft investigations proved that the orientation of the cumulus rows is mostly parallel to the low-level flow. Occasionally, however, another mode of organization, called the "normal" mode, was found which produced cloud lines at a substantial angle to the wind. Preliminary results reported by Malkus and Ronne (1960) showed that the "parallel" mode is related to convective disturbances of

5.3

THERMODYNAMIC PROCESSES OF MEDIUM SCALE

323

synoptic scale but it seems to be weak or absent (replaced by random cumuli) in the inversion-dominated regions of the upstream and poleward portions of the Trades. Figure 98 gives a schematic representation of the cloud organization in the neighborhood of a wave trough in the Easterlies. The windinduced orientation is clearly visible. The spacing between the cloud rows amounted to about 4 km at greater distances from the trough line and increased to 25 km as the wave trough was approached. Just west of the disturbance, spaces of 30 km were found. Similar experiences were reported by Bunker (1959), who, in the Atlantic Ocean, observed lines of cumulus clouds that were lying roughly parallel to and under a line of cirrus clouds. It is suggested that the two phenomena were related or possessed a common origin. Further, a lowlevel disturbance was found with lines of cumuli which clearly resulted from the convergence of two wind systems. ~IOOkm-

i?

()

If ()

t;:;l

o 0 r.

o.

g/ f}IO If (/'/0

Clear

AI

~

II

r)

CJ f:-/

,1

o

0

V () () '6 Trough

FIG. 98. Schematic distribution of cumuliform clouds near a wave trough in the North Pacific Ocean at 10° N, 170° E. (From Malkus and Ronne, 1960.) Orientation of cloud rows, spacing between them, and distances between the amplified cloud groups (denoted schematically in the figure as a single large cloud) were measured by timelapse photography from an aircraft. Individual clouds are not drawn according to scale.

According to Riehl et al. (1959), there was some indication that the "normal" mode, which occurred only rarely, was influenced by wind shear. The clouds were found to line up with the shear vector between the trade wind layer and the flow above. Later studies (Malkus et al., 1961a) allowed the authors to give a more detailed description of the factors favoring each mode of organization. They summarized their findings as follows:

324

5

THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE

A. Parallel mode Factors favoring 1. Airflow over warmer ocean 2. Strong low-level wind 3. No wind turning with height 4. Unstable cloud layer 5. Synoptic-scale convergence Factors inhibiting 1. Airflow over colder ocean 2. Weak low-level wind 3. Rotation of wind at low levels 4. Inversion domination-e-stable and/or dry cloud layer 5. Synoptic-scale divergence 6. Very pronounced normal mode (?) B. Normal mode Factors favoring 1. Cloud layer penetrating into upper shear 2. Abnormally low shear superimposed on trade cumulus layer 3. Disturbance (convergence) 4. Strong shear confined to narrow vertical layer Factors preventing: Uniform wind throughout troposphere. With parallel mode dominating, the spacing of the cloud rows appears to be directly related to the depth of the moist layer, i.e., the distance between the rows increases when a disturbance is approached (see Fig. 98). The spacing of the normal mode was 75-95 km in all cases studied so far. The frequency of occurrence of cloud organization seems to be highly variable, at least in the area concerned, i.e., the tropical Pacific. For instance, during the flight investigated by Riehl et al. (1959) organization was absent for 9 per cent, weak for 30 per cent, moderate for 33 per cent, and strong for 28 per cent of the time while, for the flight studied by Malkus et al. (1961a), the corresponding figures were: absent 32 per cent, weak 40 per cent, moderate 28 per cent, and strong 0 per cent. Thus, cloud organization was present for 91 per cent and 68 per cent of the time, respectively. A thorough investigation of the cloud pattern in a hurricane (Daisy, 1958) was made by Malkus et al. (1961b). It revealed a remarkable persistence of the cumulonimbus rows and of the cirrus shield which, for more than two days, held nearly the same position with regard to the center of the hurricane. Apart from this persistence, a

5.3

THERMODYNAMIC PROCESSES OF MEDIUM SCALE

325

slow and gradual development toward a symmetrical structure around the center was observed. Studies of this kind will certainly be activated and also facilitated by photographs from meteorological satellites. Some preliminary results in this line were described in Section 5.3.2.2. Further observations were given by Fritz (1961) who, in the relatively dry and cold central parts of a mature cyclone over the North Atlantic, found very narrow streets of cumuliform clouds several hundred miles in length and lying closely parallel to the contour lines of the 500 mb chart. Up to now the results have been more or less restricted to describing . the phenomena and to suggesting some qualitative critera for the occurrence of each rhode. Theoretical models appear to be lacking so far.

5.3.3 Inversion Conditions The importance of atmospheric processes in air warmer than water is generally inferior to that attached to phenomena connected with lapse conditions, since at sea the latter occur much more often than inversional cases. Relevant evidence can, for example, be obtained from frequency distributions of the air-sea temperature difference as measured at North Atlantic weather ship stations, In Fig. 99 such distributions are exhibited for the ocean stations "C," "D," and "I" whose positions are indicated in Fig. 1. As can be derived from Fig. 99, the percentage of occurrence of inversion conditions (air warmer than water) during the period in question was: "C" = 37.7 per cent "D" = 25.3 per cent "I" = 9.7 per cent These figures are similar to those given by other authors (see, for example, Brocks, 1956) and clearly show that, in general, inversion conditions are not very frequently found at sea and that, in particular, their frequency of occurrence seems to depend on the locality concerned and its meteorological and oceanographic implications. For instance, a station like "C" situated at the southern outskirts of the cool mixed waters in the northwestern part of the Atlantic Ocean (Rodewald, 1952) is liable to experience warm air flows relative to the sea more often than station "I," which lies in the northwestern branches of the eastern part of the warm North Atlantic drift current. Apart from the differences in occurrence between inversion and lapse conditions, there are dynamic reasons that one should attach more importance to lapse situations. In the latter cases dynamic

326

5

THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE

turbulence and convection operate in one and the same sense and therefore ensure a quick, intensive stirring of the air mass in question. The joint effect of these two powerful mechanisms is that a quasistationary state is approached comparatively soon, thus justifying the general treatment of this case as given in Section 5.3.2. 18

18

~

16

16

~

14

14

§

12

12

'0

10

10

"g o

/

4

2

a

_x_x_x-x.....

x"

x-x" xvx_!-~\x D \ x" x

x_x.. . x-rx

x-x-x-x ;...

"0 a..

5 0 _5

ySaturat;on curve

,,'

for ice

FIG. 100. Taylor diagram applied to air mass modification over the sea. A, Air mass, originally stable, flowing over a cold sea surface; B, homogeneous air mass flowing over a warmer sea surface. T. = sea/surface temperature.

Two (assumed) examples of that kind are exhibited in Fig. 100. Case (A) shows an air mass, originally stable, which flows over a cold sea surface of 15°C temperature, whose cooling influence is clearly recognizable up to point (4). In case (B) an originally homogeneous air mass of constant potential temperature and potential vapor pressure [note the cluster of points at (B)] passes over a warmer sea surface of 30°C resulting in a superadiabatic layer reaching from the sea surface up to point (3). In reality, the points (3) and (4) would correspond to certain altitudes, thus indicating the vertical range of influence of the sea surface. In this way the Taylor diagram serves as a useful aid for investigating air mass modification by the sea surface. It may even be used for extrapolating the value of the sea-surface temperature, in case this was not measured.

330

5

THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE

Besides, the slope of the characteristic curve of a sounding is qualitatively significant as an indicator for transfer processes, if radiation is neglected. For example, the flux of sensible heat goes up, is zero, or goes down if the lapse rate of the potential temperature is positive, zero, or negative. Thus the deviation of the slope of the sounding in the Taylor diagram from the horizontal isotherms of potential temperature indicates the direction of the transport of sensible heat. Similar criteria can be given for the eddy fluxes of aqueous vapor and of sensible and latent heat combined, as well as for the hydrostatic equilibrium (Montgomery, 1950). If the observational evidence at sea, particularly in the upper air, is poor, some benefit can be obtained from indirect aerology, which, however, implies the application of a theoretical model. Relevant experience and theoretical knowledge are then needed for describing the conditions in the upper air and their changes, whereas the actual values are mostly the result of surface observations. Naturally, such methods can be very useful when forecasting has to be done on a routine basis, since, for such purposes, the necessary aerological information at sea will generally be incomplete. 5.3.4.3 Some Observational Facts. Before discussing the theoretical background of air mass transformation, let us cast a glance at the results of some relevant measurements. Craig (1946) and Emmons (1947) were the first and-as far as I can see-the only ones who tackled this difficult task systematically by making series of airplane soundings up to 300-500 meters along the trajectories of flowing air masses. Since this investigation was carried out above coastal waters east of the U.S.A. in summer and fall, and since it was chiefly concerned with air masses crossing the coast and moving out over the sea, the great majority of the soundings gathered provided information on the cooling of a warm air mass by a colder water surface. A typical sample of this kind has been taken from Craig (1946) (Fig. 101). The first sounding was made over land and shows nearly homogeneous air up to at least 300 meters. Note the cluster of points representing the measured stratification in the Taylor diagram. After traveling 4 miles over water, the air is cooled and moistened up to a height of 46 meters, the largest gradient being confined to the lowest 6 meters. The Taylor diagram displays the characteristic modification curve as a straight line starting from the cluster of points and intersecting the saturation curve for salt water at the sea-surface temperature. The third sounding was made at a distance of 19 miles (measured

feet

!

1000

\

~

[)£W

PT

50 0

."""

'1

TEMP

;

38

,

40

feel 100 0

42

i'

44

46

~

50 0

100m

'\ ~

!

500

K I

I

I

72

i

,

56F

7

-\

5C

48 ,

50

i

52

'

54

~

56

\

62F

13

I~mb

60F

1\

58F

\

56F

19

~

\

i

20C \

7 72F

\

TEMP

70F

'\

68F 66F

f\

8

9

10

:1 ~

64F

\

C

-,

60 62 64 iii ,

15C

l\-

60F

12

r-,

58F \

./

"

56F

68

70

72

I lit 20e

tqrnb

r-,



2.1

1.9 x 10'

10

17

1.5 x la'

10

1.4

1.9 x 103

15

200

.!1 400

w

300

40 X

° -

9~

=2

0%

20

mi

Measured

Model

200

° °

100 0 400 300

40

~

20

0%

x: 2 mi

° -

Measured Model

200 100 0

40

.s-:° 20

0% Proportional

change

FIG. 105. Modification of warm air by a colder sea surface. Comparison between observed profiles of the "proportional change" and computed ones at different distances x from the shore. (From Craig, 1949.) The measured values are averages based on the soundings presented in Fig. 102. The parameters used for the computation are given at the right side. KE = Constant value of eddy diffusivity applied for z ;;. h; h = height of the bottom layer with KE increasing linearly; Uk = wind speed at z = h.

346

5

THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE

only be performed by turbulent motion but also by radiative processes, Eqs. (5.59) and (5.61), which represent the modification of the vertical temperature distribution, are not suitable for the determination of turbulent transfer coefficients. Hence, there remain Eqs. (5.60) and (5.62) from which numerical values for the eddy diffusivity at different levels may be derived. Results reported by Lettau (1944) and Craig (1949) may be considered relevant if sporadic data, which, in part, where already quoted above, are disregarded. The eddy transfer coefficients for humidity KE presented by Lettau refer to a vigorous outbreak of arctic air characterized by very strong instability and powerful convection. The values for KE were obtained from estimates of the water-vapor flux E and the pertaining vertical gradients of the absolute humidity, in accord with Eq. (5.2), and an attempt was made to allow for the precipitation that had occurred. The values of KE published by Lettau are given in Fig. 106. They are extraordinarily high, which can be explained by the strong instability. After an initial increase up to 750 meters, their vertical variation shows a decrease with height. In general, but not in detail, this result is in conformity with the vertical variation of the eddy viscosity, as depicted in Figs. 67 and 68. 5000

t>.-J. 'lI... c

''II.

2000 1000 ~

-

c -e

0.1

'"

=

~

0

\

\

\

x,

x, !

!

!

12

16

20

X_X-X'j 24

Local time (hours)

FIG. 113. Diurnal variation of mean air temperature in tropical and extratropical regions of the Atlantic Ocean. (After Kuhlbrodt and Reger, 1938.) Ti, from thermograph records taken in a screen on the wheel house; T2, from resistance thermometer records taken on the top of the mast. Difference of daily averages (Tl - T2) = 0.09° C.

temperature that amounts to 0.45°C if the temperature was measured in a screen on the wheelhouse. On the other hand, the diurnal range was reduced to O.28°C if the distant reading thermometer installed at the top of the mast was used. This result is of considerable interest when compared with the diurnal range of the mean temperature of the sea surface. Bearing in mind that the latter was determined by Kuhlbrodt to be O.26°C for nearly the same maritime regions (see

5.4

TIME VARIATIONS

369

Section 5.1.4.1) one could, similarly to Kuhlbrodt, be inclined to conclude that the diurnal variation of air temperature above the sea is primarily controlled by the processes of convection and turbulence and thus chiefly depends on the diurnal course of the sea-surface temperature. This would imply that direct absorption and emission of radiation by the air does not play more than an insignificant role in producing the diurnal variation of mean air temperature above the sea surface. There are, however, other facts not to be overlooked before a final conclusion can be drawn. First it must be pointed out that in the measurements of Kuhlbrodt the average air temperature wasat all hours and in all oceanic regions-well below (-o.rq the mean temperature of the sea surface. Hence, the average convective heat flux was directed upward from the sea to the air and the determinative influence of the sea, which was stated by Kuhlbrodt, is explained well enough if we assume that the measured values of the sea temperature were really representative for the sea surface. Certainly the case "air colder than water" applies to the majority of the thermal conditions occurring at sea. Nevertheless it would be interesting to know how the diurnal courses of temperature in the air and at the sea surface are related in the admittedly rare cases when the air is warmer than the sea. Up to now no pertinent information has been available. But even if we restrict our discussion to the case "air colder than water," there are still some arguments left advocating the significance of radiative processes for the diurnal variation of air temperature at sea. For instance, evidence was given by Wegener (1911), Braak (1914), and Roll (1939) that the diurnal range of air temperature in the boundary layer above the sea increases with altitude contrary to its behavior on land. [A more recent result, reported by Harris et al. (1962) and stating that the amplitude of the diurnal temperature wave over the Azores decreases with height (from 1.12°C at the surface to 0.14°C at 700 mb) need not contradict the former findings because the lower part of the soundings made on the Azores may not be strictly maritime, but could be influenced by the island of Terceira.) In addition, Roll (1939) furnished observations showing that at sea the daily temperature maximum occurred earlier at higher levels than at lower ones. The phase difference between the height of 150 meters and the lowermost layer amounted to about 1 hour. The observed changes with height of amplitude and phase agree well with the interpretation of the diurnal temperature variation in the planetary boundary layer as given by Schmidt (1920), who assumed

370

5

THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE

the phenomenon to be composed of a convective and a radiative component. Above the sea surface, these two partial waves act in the opposite sense, resulting in a diurnal temperature variation that was found to be considerably smaller than that on land. From a comparison of Figs. 78 and 113 we can further derive that the daily temperature maximum occurs considerably earlier in the atmospheric boundary layer (at about 1200 hr) than at the sea surface (at 1500 hr), and that, consequently, during a certain period of time, a decrease of air temperature is accompanied by an increase of sea temperature. All these facts can only be explained if some importance is also attached to radiative processes in the lower atmosphere above the sea. 5.4.1.2 Some Findings on the Basis of Routine Observations of Air Temperature. Besides the laborious study carried out by Kuhlbrodt (Kuh1brodt and Reger, 1938), other investigations on the same subject have been performed more recently. They are based, in part, on observations made on merchant vessels (Bintig, 1950), and, in part, use was made of the temperature measurements obtained on ocean weather ships in the North Pacific Ocean (Koizumi, 1956a, c), as well as in the North Atlantic Ocean (Rosenthal and Gleeson, 1958). Since all these studies deal with routine observations, it is understandable that their results differ from the findings obtained by Kuhlbrodt during a special expedition, particularly as regards the diurnal range of air temperature which, in the more recent publications, is considerably higher than the value of 0.28°C found by Kuhlbrodt and which, hence, must be considered as questionable. Nevertheless, the comprehensive new material allows us to study the influences of latitude, season, wind, cloudiness, and air pressure on the diurnal temperature variation, considerations which could not be discussed in detail when only Kuhlbrodt's older results were available. The latitudinal and seasonal changes in the range of the diurnal variation of air temperature are clearly indicated in Table XXXVI, which was compiled by Rosenthal and Gleeson (1958). The diurnal temperature range is smallest in winter, greatest in summer, and increases with decreasing latitude. Thus these changes reflect the influence of insolation. The same authors also presented evidence for the seasonal change of the time of the daily temperature maximum. In summer it occurs later than in winter. The time lag between the temperature maximum and the true solar noon ranges from 2t to 4 hours in early

TABLE PERIODIC DIURNAL RANGE OF AIR TEMPERATURE

Stations

M,A I, B

C, J D E,H

a

Average latitude 64.0 oN 57.9 52.65 44.0 35.85

From Rosenthal and Gleeson (1958).

XXXVI

(OC) AVERAGED OVER NORTH ATLANTIC WEATHER SHIPS' STATIONS OF SIMILAR LATITUDEa

January February 0.22 0.31 0.33 0.61 0.75

March April

May June

July August

0.47 0.53 0.64 0.83 1.06

0.61 0.81 0.72 1.06 1.36

0.61 0.69 0.75 1.22 1.47

September October 0.36 0.42 0.42 0.89 1.03

November December 0.17 0.22 0.33 0.50 0.72

372

5

THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE

summer, whereas it varies from 0 to 2 hours in winter, which is also a radiation effect. In order to study the temperature minimum, Rosenthal and Gleeson (1958) formed bimonthly averages of the zone time of sunrise minus the time of minimum temperature for all the weather ships' stations in the North Atlantic Ocean and obtained about 2t hours in winter and only t hour in summer for that difference. As an explanation of the temperature minimum occurring considerably before sunrise, as it does in winter, the authors offered the conclusion that there must exist a heat source which is capable of exceeding the radiative heat loss of the air during those night hours. It seems quite obvious that this heat is mostly supplied by convective and turbulent transports from the sea surface, whose temperature excess over the lower atmosphere is much greater in winter than in summer. Similar results were published by Koizumi (1956a) for two weather ships' stations in the North Pacific Ocean. The effects of wind speed and cloudiness on the diurnal range of air temperature were studied by several investigators, particularly by Bintig (1950), who found some indication of a decrease of the diurnal temperature range with increasing cloud amount, as well as with growing wind velocity. With zero wind force, it was about 2.6°C. It dropped to 0.9°C if the wind force rose to 8 Beaufort. This wind effect may be qualitatively interpreted in two ways: First, we can state that the higher wind speed is associated with stronger mechanical turbulence, thus causing the heat gained from the sea to spread over a layer of air which, in this case, is thicker than with lower wind velocities, and, consequently, resulting in a decrease of the diurnal temperature variation. On the other hand, the vertical spreading of water vapor by turbulence can be taken into consideration, as was suggested by Rosenthal and Gleeson (1958). With low wind speed, the moisture is mostly concentrated in the lowest atmospheric layer. A relatively high amount of incoming radiation reaches this layer, and is absorbed there, thus giving rise to strong radiative heating and, in connection with an intense outgoing radiation during the night, to a considerable diurnal variation of air temperature. With high wind speed, however, water vapor is distributed over a thicker layer of air and, so, in the bottom layer, we observe a reduction of the radiation effect, as well as of the diurnal temperature variation. Comparing these findings with the results described in Section 5.1.4.1 on the diurnal variation of the sea surface temperature, we

5.4

TIME VARIATIONS

373

can say that, on the whole, there are distinct parallels between these two phenomena. It may be expected that the relation between the diurnal temperature course in the air and that at the sea surface is particularly close when the sea is warmer than the air. So far, no relevant study has been published dealing with that influence of thermal stratification. One difference, which was pointed out by Koizumi (1956a, c) should be mentioned. He obtained diurnal variations of mean air temperature which showed a somewhat more complicated shape than those of the sea-surface temperature, namely, a characteristic swelling occurred at around 0900 hr local time, becoming comparable with, or even surpassing, the primary maximum in the early afternoon. The explanation offered by Koizumi was that the diurnal oscillation of atmospheric pressure might be considered as one of the possible causes of the effect observed. If the variation of the atmospheric pressure progresses adiabatically, the air temperature will rise when the pressure increases and vice versa. Quantitative estimation showed that in most cases the curve of mean air temperature was favorably corrected if the effect of atmospheric pressure variation was taken into account. Naturally, this effect, which in general is much smaller than 0.2°C, deserves attention only at sea where the diurnal range of air temperature is very small. 5.4.1.3 Evaluation of Humidity Records. In conclusion, a few remarks will be added on the diurnal variation of humidity, although the information available is very scanty, owing to the particular difficulties inherent in humidity observations at sea. Perhaps the best study on this subject is still that given by Reger (Kuhlbrodt and Reger, 1938), who discussed the humidity records obtained during the South Atlantic expedition of the German research vessel Meteor in 1925-27. Since these records were taken in a screen fixed just above the wheelhouse, the results must be considered with reserve, though. The diurnal variations of relative and absolute humidity, as computed by Reger by subjecting the records to harmonic analysis, are given in Fig. 114. The two graphs refer to the equatorial zone and to the trade regions, respectively. In both diagrams the diurnal variation of the relative humidity is represented by a single wave with a minimum at 1300 or 1400 hr and a maximum around 0400 hr. In general, this course is inverse to the diurnal variation of air temperature. Of particular interest is the diurnal variation of the absolute humidity which was obtained from the relative humidity by means of

374

5

THERMODYNAMIC PROCESSES IN MARINE ATMOSPHERE

the corresponding temperature data. Here, a distinct double wave appears in the equatorial zone. Its extreme values coincide completely with those of the diurnal double wave of the atmospheric pressure. %

o

-- --- --'\.

-I

-2

A

"-t'......

..-/

I

/ " , V

"

,,

Relot,ve humidity

o

4

--- --- --,