Intended to fill a void in the atmospheric science literature, this self-contained text outlines the physical and mathematical basis of all aspects of atmospheric analysis as well as topics important in several other fields outside of it, including atmospheric dynamics and statistics.

The last few decades have seen a spectacular growth in the use of variational methods, one of the most classic and elegant methods in physical and mathematical sciences, as powerful tools of optimization and numerical analysis. The tremendous accumulation of information on the use of variational methods in the area of the geosciences, which includes meteorology, oceanography, hydrology, geophysics and seismology, indicated the need for the first symposium on Variational Methods in Geosciences to be organized and held in Norman on October 15-17, 1985. The value of this symposium was enhanced by the number of stimulating and informative papers presented.

This volume explores and evaluates the development, multiple applications, and usefulness of four-dimensional (space and time) model assimilations of data in the atmospheric and oceanographic sciences and projects their applicability to the earth sciences as a whole. Using the predictive power of geophysical laws incorporated in the general circulation model to produce a background field for comparison with incoming raw observations, the model assimilation process synthesizes diverse, temporarily inconsistent, and spatially incomplete observations from worldwide land, sea, and space data acquisition systems into a coherent representation of an evolving earth system. The book concludes that this subdiscipline is fundamental to the geophysical sciences and presents a basic strategy to extend the application of this subdiscipline to the earth sciences as a whole.

This book contains the most recent progress in data assimilation in meteorology, oceanography and hydrology including land surface. It spans both theoretical and applicative aspects with various methodologies such as variational, Kalman filter, ensemble, Monte Carlo and artificial intelligence methods. Besides data assimilation, other important topics are also covered including targeting observation, sensitivity analysis, and parameter estimation. The book will be useful to individual researchers as well as graduate students for a reference in the field of data assimilation.

New statements of problems arose recently demanding thorough ana lysis. Notice, first of all, the statements of problems using adjoint equations which gradually became part of our life. Adjoint equations are capable to bring fresh ideas to various problems of new technology based on linear and nonlinear processes. They became part of golden fund of science through quantum mechanics, theory of nuclear reactors, optimal control, and finally helped in solving many problems on the basis of perturbation method and sensitivity theory. To emphasize the important role of adjoint problems in science one should mention four-dimensional analysis problem and solution of inverse problems. This range of problems includes first of all problems of global climate changes on our planet, state of environment and protection of environ ment against pollution, preservation of the biosphere in conditions of vigorous growth of population, intensive development of industry, and many others. All this required complex study of large systems: interac tion between the atmosphere and oceans and continents in the theory of climate, cenoses in the biosphere affected by pollution of natural and anthropogenic origin. Problems of local and global perturbations and models sensitivity to input data join into common complex system.