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Mathematical Models in Environmental Problems *STUDIES IN MATHEMATICS AND ITS APPLICATIONS, VOLUME 16* Editors: J. L. Lions, Paris; G. Papanicolaou, New York; H. Fujita, Tokyo; H. B. Keller, Pasadena *NORTH-HOLLAND-AMSTERDAM NEW YORK OXFORD TOKYO* G.I. Marchuk Academician, Head of the Computer Mathematics Department, U.S.S.R. Academy of Sciences, Moscow, U.S.S.R. *Matematicheskoye Modelirovanye v Probleme Okrazhayouschey Sredy* *Nauka. Moscow. 1982* Publishers: F.I. Seviek Science Publishers B.V., P.O. Box 1901, 1000 BZ Amsterdam, The Netherlands S. D., strikethroughs for the U.S.A. Elsevier Science Publishing Company, Inc., 52 Van de Rhilt Avenue, New York, N.Y. 10017 U.S.A. Library of Congress Cataloging-in-Publication Data Marchuk, G.I. (Guri I.) 2. Mathematical models in environmental problems / G.I. Marchuk. – Amsterdam ; New York : North-Holland, c1986. Includes bibliographical references and index. ISBN 0-444-87965-X PREFACE In the past few years, environmental protection has become a challenging scientific task whose importance is highlighted by ever-increasing pace of technological progress throughout the world. The swift industrial development resulting in increased level of industrial pollution of the environment has already begun disturbing the ecological equilibrium in many regions of the globe. Meanwhile industry continues to develop at unprecedented rates, giving a powerful impetus to research associated with the location of new industrial plants and complexes exerting minimum impacts on the environment. The problem of environmental contamination by industrial plants whose maximum permissible level of safe pollution is still inconsistent with current requirements has become even more pressing. All this refers equally to the processes occurring on land and in the ocean. Environmental protection problems have been taken up in a series of investigations carried out in the Soviet Union, specifically at the Chief Geophysical Observatory of the State Hydrometeorological Committee, as well as abroad. Selective information on such investigations can be gained from the references at the end of this book. In the present monograph, special attention is paid to mathematical modelling of optimization problems associated with environmental protection. These problems were first posed by the author in 1970 at the International Environmental Protection Symposium, which was held in Czechoslovakia (RudohoGi). The author's talk at this Symposium served a starting point for his further research in the field, which was reported subsequently at international symposia in Italy (Rome, 1973), France (Nice, 1975), and FRG (Würzburg, 1977). These findings provided the basis for the monograph. A substantial amount of research along these lines has been accomplished by staff of the Computer Center of the Siberian Division of the USSR Academy of Sciences. An active role in these efforts belongs to V.V. Penenko, N.N. Obraztsov, V.I. Kuzin, A.E. Aloyan, E.A. Tsvetova, and some other scientists. Much work has been done by the research probationer A.Yu. Sokolov, who computed examples illustrating the opportunities provided by the methods. Besides, the monograph draws on the calculations conducted by A.E. Aloyan, A.A. Kordzadze, V.I. Kuzin, N.N. Obraztsov, and V.A. Sukhorukov, to whom the author expresses his deep gratitude. In the present book, the author restricts himself to the study of direct environmental impact, leaving aside the problem of climatic fluctuations caused by manmade factors, which seems to be of interest in its own right. This latter issue is expected to be treated in a specific monograph which is being prepared at the Computer Center of the Siberian Division of the USSR Academy of Sciences. Preface Much of the monograph's text was edited by N.N. Obraztsov, to whom the author pays special tribute. The book was primarily written by the author during his staying on vacation in the Turkmen Soviet Socialist Republic, where the environmental protection problems are being intensely studied in connection with major industrialization and irrigation projects for desert and arid regions of the republic. The author is grateful to M.G. Gaporov, Ch.S. Karriyev, and A.G. Babayev for many helpful discussions of these issues. G.I. Marchuk Introduction The rapid industrial development all over the world has posed an acute problem before mankind striving to preserve the ecological systems that have formed historically in various regions of the globe. Local pollution caused by industrial emissions in many cities of the world have long surpassed the maximum permissible values of safe standards. The gigantic scale of work associated with the mining of coal, ferrous ores, non-ferrous metals and other mineral resources has resulted in erosion and contamination of vast expanses of land. Freon discharges from industrial and domestic refrigerators exert adverse effects on the environment. 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