This IMA Volume in Mathematics and its Applications STOCHASTIC MODELS IN GEOSYSTEMS is based on the proceedings of a workshop with the same title and was an integral part of the 1993-94 IMA program on "Emerging Applications of Probability." We would like to thank Stanislav A. Molchanov and Wojbor A. Woyczynski for their hard work in organizing this meeting and in edit ing the proceedings. We also take this opportunity to thank the National Science Foundation, the Office of N aval Research, the Army Research Of fice, and the National Security Agency, whose financial support made this workshop possible. A vner Friedman Willard Miller, Jr. v PREFACE A workshop on Stochastic Models in Geosystems was held during the week of May 16, 1994 at the Institute for Mathematics and Its Applica tions at the University of Minnesota. It was part of the Special Year on Emerging Applications of Prob ability program put together by an organiz ing committee chaired by J. Michael Steele. The invited speakers represented a broad interdisciplinary spectrum including mathematics, statistics, physics, geophysics, astrophysics, atmo spheric physics, fluid mechanics, seismology, and oceanography. The com mon underlying theme was stochastic modeling of geophysical phenomena and papers appearing in this volume reflect a number of research directions that are currently pursued in these areas."

The extraordinary growth and development of atmospheric sciences during the last dec ades, and the concern for certain applied problems, such as those related to the environ ment, have prompted the introduction of college and university courses in this field. There is consequently a need for good textbooks. A few appropriate books have appeared in the last few years, aimed at a variety of levels and having different orientations. Most of them are of rather limited scope; in par ticular, a number of them are restricted to the field of dynamics and its meteorological applications. There is still a need for an elementary, yet comprehensive, survey of the terrestrial atmosphere. This short volume attempts to fill that need. This book is intended as a textbook that can be used for a university course at a second or third year level. It requires only elementary mathematics and such knowledge of physics as should be acquired in most first-year general physicS courses. It may serve in two ways. A general review of the field is provided for students who work or plan to work in other fields (such as geophysics, geography, environmental sciences, space research), but are interested in acquiring general information; at the same time, it may serve as a general and elementary introduction for students who will later specialize in some area of atmospheric science."

'Ibis volt.nne contains the proceedings of a \\Orkshop on "Acid Deposition" held on September 9, 1982 at the Reichstag in Berlin. 'Ibe \\Orkshop was organized within the frame\\Ork of project COST 61a bis* of the Commission of the European Communities (CEC), as a satellite meeting to the joint meeting of WOrking Parties 4 (Pollutant Cycles) and 5 (Transport and Modelling - Field Experiments) which was held on September 7 - 8 at the Federal Environmental Agency in Berlin. 'Ibe organisation of the scientific \\Orkshop programme was in the hands of a CEC Acid Deposition Task Force consisting of nine scientists actively participating in projects COST 61a or COST 61a bis : Beilke (Federal Republic of Germany), Brosset (Sweden), Elshout (The Netherlands), Graven- horst (France), Liberti (Italy), ott (CEC, Belgium), Penkett (United Kingdan), Sandroni (CEC, Italy) and Zephoris (France). 'Ibe \\Orkshop progrcmne consisted of the presentation and discussion of five invited review papers covering different areas of the acid deposition problem and of ongoing \\Ork on topics which are relevant to acid depo- sition. Emphasis was placed on new scientific ideas and on indicating the most important areas of uncertainty, including the specification of a series of key research needs in the field of acid deposition. 'Ibis was done out of concern for danage to forest and freshwater ecosystems in various European regions attributed at least in part to acid deposition originating fran air pollution.

In this volume, we present the lectures given during the 1984 OHOLO Conference, held in Zichron Yaacov, Israel. The Conference was organized by the Israel Institute for Biological Research, Department of Mathematics, which is involved in Environmental Risk Evaluation, and in Projects Estimating the Potential of Wind Energy. The lectures cover a broad spectrum of mathematical models, ranging from those that deal with the solution of atmospheric conservation equations, and to those models that yield empirical estimates based on real time measure ments and thus are unique to the locale where measured. The goal of the Conference was to allow scientists from various countries to meet and discuss topics of mutual interest, including the following: 1. Structure of the boundary layer - primarily models dealing in the understanding of the various processes of atmospheric energy transfer, and their influence on the size and composition of the boundary 1 ayer. 2. Advanced mathematical techniques for describing flow and diffusion - lectures on approximations and techniques for solving the diffu sion and transport equations. 3. Flow over complex terrain - research into various aspects of the problem - mathematical models, physical models, experimental results. 4. Models of pollution transport and deposition."

Little more than ten years have passed since spaceprobe-borne instruments con clusively demonstrated the existence of the solar wind. These observations con firmed the basic validity of a theoretical model, first proposed by E. N. Parker, predicting a continuous, rapid expansion of the solar corona. The subsequent decade has seen a tremendous growth in both the breadth and sophistication of solar wind observations; the properties of the interplanetary plasma near the orbit of the earth are now known in great detail. The theory of the coronal ex pansion has also been highly refilled both in the sense of including additional physical processes, and of treating more realistic (time-dependent and non spheri cally-symmetric) coronal boundary conditions. The present volume is an attempt to synthesize the solar wind observations and coronal expansion models from this decade of rapid development. The ultimate goal is, of course, the interpretation of observed solar wind phenomena as the effects of basic physical processes occurring in the coronal and interplanetary plasma and as the natural manifestations of solar properties and structures. This approach implies an emphasis upon the "large-scale" features revealed by the observations. It requires extensive use of the concepts and methods of fluid mechanics."

Radiative heat transfer is a fundamental factor in the energetics of the terrestrial atmosphere: the system consisting of the atmosphere and the underlying layer is heated by the Sun, and this heating is compensated, on the average, by thermal radia tion. Only over a period of 1-3 days from some specified initial moment can the dynamic processes in the atmosphere be considered to be adiabatic. Global dynamic processes of long duration are regulated by the actual influxes of heat, one of the main ones being the radiative influx. Radiation must be taken into account in long-term, weather forecasting and when considering the global circulation of the atmosphere, the theory of climate, etc. Thus it is necessary to know the albedo of the system, the amount of solar radiation transmitted by the atmosphere, the absorptivity of the atmosphere vis-a-vis solar radiation, and also the effective radiation flux, the divergence of which represents the radiative cooling or heating. All these quantities have to be integrated over the wavelength spectrum of the solar or thermal radiation, and they must be ascertained as functions of the determining factors. The relation ships between the indicated radiation characteristics, the optical quantities directly determining them, the optically active compo nents of the atmosphere, and the meteorological fields will be discussed in this book."

This volume is based on a workshop on "Effects of accumulation of air pollutants in forest ecosystems'; held in GOttingen, Federal Republic of Germany, from May 16-18, 1982. This work'shop was initiated and sponsored by the Environmental Agency of the Federal Republic of Germany (project officer: Dr. J. Pankrath) as part of a research contract (project leader: Dr. B. Ulrich). THE PROBLEM SEEN UNDER THE ASPECT OF ADMINISTRATION The problem of forest damage caused by air pollution is not new in Europe. Already in 1983 a comprehensive report from Schroeder and Reuss about vegetation damages by fume in the Harz mountains was published. In 1923, Prof. Dr. Julius Stocklasa of the Bohemian Technical Highschool in Prague was concerned with research of toxical effects of sulphur dioxide in his publication "The damage of vegetation by flue gas and exhalations of facili ties". This comprehensive and instructive work concludes with the sentence: "It is already high time for the governments of all cultural states to take legal, police and private measures in order to prevent damage by flue gases". In the neighbourhood of industries with high gaseous and dust emissions damages have been shown to occur for a long timei these deleterious effects have influenced the growth of trees and in extreme cases have even caused their early death.

This book is an ordered collection of tutorial lectures on the physical processes in the polar upper atmosphere given at the NATO Advanced Study Institute (ASI) on "The Exploration of the Polar Upper Atmosphere" held at Lillehammer, Norway, May 5-16, 1980. The polar cap is an important part of the high latitude atmosphere not only because of circulation and horizontal trans port in the neutral atmosphere and convection in the ionosphere, but also because of its unique energy sources and sinks. In addition, solar wind plasma is led into-the upper atmosphere by the geomagnetic field at the poles, and the polar cap is, as stated by Tutorial Leader Roederer in this volume, "the place where outer space meets earth". The atmosphere at lower latitudes is well-known to the ground-based observer, and the advent of satellite observations was simply the beginning of a new perspective. The exploration of the atmosphere at polar latitudes, however, proceeded in quite the opposite manner, and satellite maps of the polar caps may be compared with a relatively meagre set of ground-based data. Recent efforts to extend the polar observations from the ground have resulted in the need for a review of the physical principles and processes occurring in the polar upper atmosphere. The interdisciplinary nature of these efforts led to the emphasis here on a tutorial program.

Our motivation for calling a conference on climatic change was to stimulate interdisciplinary exchange between researchers in various fields concerned with climatic research, which include meteorology, oceanography, limnology, palynology, glaciology, dendrochronology, and climate modeling. The philosophy behind this attempt at cross- fertilization is much the same as that of previous conferences on cli- matic change in the NATO-series ("Climatic variations and variability, facts and theories", Berger, 1981; "Milankovitch and climate", Berger et al., 1984). The past is the key to the range of future possibilities. It is for this reason that we stressed history and case studies in convening the present symposium on abrupt climatic change, without however forget- ting that modeling, conceptual and mathematical, ultimately provides the understanding necessary for prediction. We attempted to strike a bal- ance between these complementary aspects of current climatological re- search, aiming at a symposium situated in scope about halfway between "Climate in Earth history" (Berger and Crowell, 1982) and "Climate pro- cesses and climate sensitivity" (Hansen and Takahashi, 1984). We con- centrated, therefore, on the last 20,000 years, where the time-scales are potentially good enough to document rapid change.

Unique properties of laser radiation including its monochromatic properties, polarization, high spectral intensity, coherence, narrow beam divergence, the possibility of controlling the pulse duration and radiation spectrum and, finally, the fact that extremely high power and energy create very favorable conditions for the extensive application of lasers to communi cation systems, systems for the lidar sensing and ultra-high-precision ranging, navigation, remote monitoring of the environment, and many other systems operating in the atmosphere. The operative efficiency of the above systems depends significantly on the state of the atmosphere and the corresponding behavior of laser radia tion propagating through it. This circumstance has stimulated the studies of the above regularities during the passt 10-15 years. For the investiga tions to be carried out the scientists were forced to develop new theories and methods for studying the problem experimentally. Moreover, during such investigations some previously unknown phenomena were observed, among them the nonlinear effects accompanying high-power laser radiation propagating through the atmosphere are of paramount importance. Among the nonlinear effects caused by high-power laser radiation inter action with the atmosphere, the effects accompanying the propagation of high-power radiation through the atmospheric aerosols are of particular interest. Aerosols always occur in the atmosphere. It should be noted that the microphysical and optical characteristics of atmospheric aerosols vary widely, this fact causes a great variety in the features of their inter action with radiation."

2Vlanuals of mineral dressing or more precisely those of comminution-classifi cation treat in particular the mechanics of the machines, and generally their handling. In this way the plant engineer becomes acquainted with the equip ment but is given no help in learning something of the processes taking place in the material to be comminuted even though the purpose of the operation is to enhance wanted and to avoid unwanted physical or physico-chemical processes. Neglecting the description or representation of generally used and well known equipment the object of this monograph is to supply information on the processes taking place in grinding installations. It explains the sometimes complicated phemonena by applying quite simple means; it requires only an elementary knowledge of mathematics, mechanics and physical chemistry. The ideas are applicable to the grinding of all brittle raw materials or semi finished industrial products. The special problems of cement grinding and thm;e of hall mills are explained in more detail; in cement grinding we have to meet special requirements with regard to ball mills apart from other con siderations -, since these now demand the greatest overall energy consumption. Currently disputed problems are dealt with, and naturally the views of the author are given in detail, but contrary views are also mentioned and the ample list of references ensures that these opposing views can be considered.

Geysers. What makes them work? Many who have seen a geyser in action know only that it spouts hot water into the air. Many others have never seen one. Chapter 1, Geysers of the World, delineates their distinguishing features, locates the geyser regions of the world, and places investigations by world travelers and scientists in historic perspective. One of the quickest ways to become acquainted with a geyser is to observe it. The descriptions of several well known geysers, some based on past observations by others, but frequently by me, do not neces sarily portray current behavior. They do, however, represent general features. Geysers exist as a result of a delicate and unique interplay among the heat, the water, and the rocks of the earth. In essence, heat and water must be available, transported, distributed, stored, and finally released. Chapter 2, The Geologic, Thermal, and Hydrologic State of the Earth, especially that close to its surface, sets the stage for Chapter 3, Fundamentals of Geyser Operation. The geyser is treated here as a simple system consisting of three major interacting elements: a source of water, a source of heat, and a reservoir for storing water. The discus sion centers around the actions occurring within idealized columnar and pool geysers, and more complex systems. Some of the more workable geyser theories are evaluated."

The effects of meteorological phenomena upon forest produc tivity and forestry operations have been of concern for many years. With the evolution of system-level studies of forest eco system structure and function in the International Biological Program and elsewhere, more fundamental interactions between forest ecosystems and the atmosphere received scientific atten tion but the emphasis on meteorological and climatological effects on forest processes remained. More recently, as recogni tion has developed of potential and actual problems associated with the atmospheric transport, dispersion, and deposition of airborne pollutants, the effects of forest canopies upon boundary-layer meteorological phenomena has come under scientific scrutiny. Looking to the future, with rising atmospheric con centrations of C02 and increasing competition for the finite fresh-water resources of the earth, interest in the role of forests in global C02 and water balances can also be expected to intensify. Thus, the nature of forest canopy-atmosphere interac tions, that is to say, the meteorological phenomena occurring in and above forest canopies, are of importance to a wide variety of scientific and social-issues. Demands for forest meteorological information currently exceed levels of knowledge and given the economic constraints of science in general and environmental sciences in particular, chances for major improvements in scien tific support in the near future are slim. Unfortunately, studies of environmental phenomena in and above forests are costly and logistically difficult. Trees, the ecological dominants of forest ecosystems, are the largest of all terrestrial organisms."

The development of numerical integration techniques and the pioneering efforts of Von Neumann and his associates at the Institute for Advanced Studies (Princeton) have spurred the renewed interest of many leading fluid dynamicists and meteorologists in the theory and numerical simulation of planetary atmosphere and oceans circulations. Their work during the last 15 years, now culminating in the Global Atmospheric Research Program, has led to the possibility of vastly improved weather forecasts as wei I as the development of a ful I fledged branch of the physical sciences: geophysical fluid dynamics. Simultaneously, great strides have been made in developing new instruments, operating from earth orbiting satel I ites, to powerful observe the meteorological phenomena and to determine the state of motion of the atmosphere. Centre National d'Etudes Spatiales (CNES) of France has very significantly contributed to this effort by developing the EOLE navigation and data collection satell ite, launched on 16 August 1971 to interrogate 500 instrumented platforms measuring meteorological para meters. It is fitting then, that CNES should have brought together lead ing scientists in the field of dynamic meteorology, to participate in its 1970 Summer School on Space Physics.

In the micrometeorological literature, reference is sometimes made to the 'Businger-Dyer Profiles' or the 'Dyer-Businger profiles/relations' without referring to the origin of these relations. For example, in the textbook on 'Atmospheric Turbulence' by Panofsky and Dutton (1984) on p. 134, reference is made to the 'Businger-Dyer formula'. To add to the mystery, these authors refer on p. 141 to the Businger-Dyer-Pandolfo empirical result (Businger, 1966; Pandolfo, 1966) that in unstable air * Z r (1) Ri=-== ... L So it seemed to me that it would be appropriate for this issue of Boundary-Layer Meteorology which is dedicated to Arch Dyer, to go back to 1965 and describe the circumstances that led to the above mentioned profiles as I remember them. 2. Aspendale, 1965 In the academic year 1965-1966 I found myself in Australia on a sabbatical leave. The first part of this leave was spent at the CSIRO Division of Meteorological Physics in Aspendale, Victoria. It was in many ways a good choice. The fall is exchanged for spring, SE Australia is a pleasant place to be in spring and summer, and the scientists in the division were hospitable and stimulating. Priestley, Swinbank, Dyer, Webb, McIlroy, Taylor, Clarke, Deacon and several others carried out an active research program.

Collected articles in this series are dedicated to the development and use of software for earth system modelling and aims at bridging the gap between IT solutions and climate science. The particular topic covered in this volume addresses the major coupling software developed and used in the climate modelling community.

In this book the author has succeeded in presenting the many facets of the globel problems and hazards for our climate and thei r i nterdi scip l inary aspects, as we II as maki ng these under- standable for the non-specialist. In doing this, the author has not restricted himself to an analysis of the difficult problems but has indicated the necessity and the possibilities for ratio- na l so lutions. The book, therefore, can be a va lueb le deci si on- aid for all those who directly or indirectly are in positions of responsibi lity at various levels of administration or in industry end busi ness. We ll-timed precauti onary measures agai nst a g loba l deteri o- ration of cLimate are not only necessary for reasons of environ- mental protection. They are also an economical end political necessity. The measures include the reduction of the combustion of fossi l fue ls, a more rati one l energy uti l ization, as we II as the establishment of a global equilibrium between forest loss and reforestati on. The Federal German Government takes these potential anthro- pogenic climate changes very seriously. In order to obtein better scientific information, the Federal Government has ini- ti ated an i nterdi sci p l i nary nati one l Climate Programme. At the same time, the Federal Republic of Germany supports the relevant activities within the frame of international cooperation.

This was the fourth postgraduate summer school on remote sensing to be held in Dundee. These summer schools were originated by, and continue to remain in, the programme of EARSel (European Association of Remote Sensing Laboratories) Working Group 3 on Education and Training in Remote Sensing. The first of these summer schools was held in 1980 on "Remote Sensing in Meteorology, Oceanography and Hydrology." This was followed in 1982 by a more specialised summer school on "Remote Sensing Applications in Marine Science and Technology" which built on the foundation laid in 1980 and then concentrated on the marine applications of remote sensing techniques. The present summer school was another follow-up of the original 1980 summer school but this time concentrating on the atmospheric rather than the marine applications of remote sensing techniques. The 1984 summer school had not specifically involved atmospheric and marine applications but had been involved with the use of remote sensing in the field of civil engineering. This year's summer school was extremely successful. First of all, this was due to our sponsors, for without their very significant material contributions there would have been no summer school. These sponsors included the Scientific Affairs Division of NATO, together with the European Association of Remote Sensing Laboratories, the Council of Europe, the European Space Agency, the German Aerospace Establishment (DFVLR) and the Natural Environment Research Council.

This book gives a general picture of research-driven activities related to location and map-based services. The interdisciplinary character of the topic leads to a variety of contributions with backgrounds from academia to business and from computer science to geodesy. While cartography is aiming at efficient communication of spatial information, the development and availability of technologies like mobile networking, mobile devices or short-range sensors lead to interesting new possibilities of achieving this aim. By trying to make use of the available technologies, a variety of related disciplines looks specifically at user-centered and context-aware system development, especially in wayfinding and navigation systems.

The content of this book are lectures and research papers presented at the NATO Advanced Study Institute on -Chemistry of the Unpolluted and Polluted Troposphere-held from September 28 to October 10, 1981, on the Island of Corfu, Greece. The realization of the scientific event was made possible by the sponsorship of the NATO Scientific and Environmental Affairs Division. We must express our gratitude first to this Institution for the important assistance and cooperation we received. For additional assistance we are much obliged to our distinguished co sponsors: Carl Zeiss Werk, Oberkochen, FRGj Biotronik GmbH, Frankfurt, FRGj Bodenseewerk Perkin Elmer u. Co GmbH, Ueberlingen, FRGj and TSI Deutschland Inc., Aachen, FRG. To Mr. Dimitris Bouas, the Director of the Grand Hotel Glyfada, we would like to express our thanks and appreciation for the excellent services. The Center of Environmental Protection of the University of Frankfurt, FRG, conducted the NATO Advanced Study Institute because of the rapidly increased interest in the problems of air chemistry and air pollution. This development has contributed in recent years to a significant expansion of knowledge in the field of atmospheric chemistry, where several of the classic disciplines like meteorology, physics and chemistry have joined in combined research. The Advanced Study Institute offered an ideal opportunity to give a comprehensive survey of the present knowledge in this relatively new field of atmospheric science.

The contents of this volume are based largely on a symposium on cloud dynamics held in Hamburg, Germany, as a part of the Third General Assembly of the International Association of Mete- orology and Atmospheric Physics (IAMAP), 17-28 August-1981. Plans for this symposium were initiated by the Cloud Dynamics Group, appointed through the International Commission for Dynam- ic Meteorology (ICDM), IAMAP. Members of this group are Bruce Morton - Chairman, Australia; Tomio Asai - Secretary, Japan; E. M. Agee, USA; V. Andreyev, Bulgaria; K. Fradrich, FRG; M. W. Moncrieff, UK; R. S. Pastushkov, USSR; J. P. Chao, PR China; Bh. V. Ramanamurti, India; W. Roach, UK; J. Simpson, USA; J. T. Steiner, New Zealand; M. Yanai, USA. E. M. Agee served as con- vener of the symposium in Hamburg. Dynamic meteorology has grown rapidly and covered a great variety of fields since the foundation of ICDM, making it increas- ingly difficult for the Commission to manage all activities. In order to improve this situation, some ad-hoc Working Groups within ICDM were organized at the 1977 IAMAP meeting in Seattle. Each of these working groups, such as the one in Cloud Dynamics, deals with a particular sub-field of dynamic meteorology.

These proceedings are based upon the review lectures, the re search talks and the accompanying discussion from the NATO Advanced Study Institute on "The Dynamical and Chemical Coupling of the Neutral and Ionized Atmosphere" held at Spatind, Norway April 12-22, 1977. In recent years, in spite of the many subdivisions of atmospher ic physics it has become clear that a complete understanding of the subject matter requires an interdisciplinary effort of the scien tists working on a variety of atmospheric phenomena. This Advanced Study Institute was organized in order to meet this demand. A number of eminent scientists were invited to review the major subfields in atmospheric physics and expose the areas where the coupling between the neutral and ionized atmosphere is evident. These review papers were supported by current research results. However, the material covered here is by no means complete con sidering the range of subject matter covered by the title. The re sponsibility for this inadequacy lies with the editors and the pro gram committee, rather than with the individual contributors. Oslo, June 1977. B. Grandal J.A. Holtet. PARTICIPANTS Max-Planck-Institute for Nuclear Physics Arnold, F. P.O.Box 1248, D-0069 Heidelberg F.R.G. Bj centsrn, L. Uppsala Ionospheric Observatory S-755 90 Uppsala Sweden The Institute for Mathematical and Physical Brekke, A."

Solar and geomagnetic variability are of considerable interest for scientists of many different persuasions and indeed one has the distinct impression that for the sun at least, there is direct relevance for mankind in general as the interrelation between solar and terrestrial phenomena is starting to be appreciated. From the vast time scale of interest in the variability field, attention was confined to the last 10,000 years in a NATO Advanced Research Workshop held from April 6 - 10, 1987 in Durham, England, and the present publication comprises the lectures given there. Such a Workshop was very timely in view of the impressive new data available from 14C analysis in dated tree rings and lOBe in polar ice cores, from natural palaeomagnetic records in lacustrine sediments and from archaeomagnetic material. Also to be mentioned are new studies of historical accounts of naked-eye sunspots and aurorae. All the data have contributed to improvements in under standing the relative variations of solar properties, the geomagnetic field and climate and it is hoped that this volume will convey the flavour of these advances in knowledge. A feature of the Workshop was the lively discussions which followed so many of the papers. There were several instances of healthy disagreement and this is reflected in the opposing views presented inanumber of the papers published here."

This self-contained text/reference provides a basic foundation for practitioners, researchers, and students interested in any of the diverse areas of multiscale (geo)potential theory. New mathematical methods are developed enabling the gravitational potential of a planetary body to be modeled using a continuous flow of observations from land or satellite devices. Harmonic wavelets methods are introduced, as well as fast computational schemes and various numerical test examples. Presented are multiscale approaches for numerous geoscientific problems, including geoidal determination, magnetic field reconstruction, deformation analysis, and density variation modelling With exercises at the end of each chapter, the book may be used as a textbook for graduate-level courses in geomathematics, applied mathematics, and geophysics. The work is also an up-to-date reference text for geoscientists, applied mathematicians, and engineers.