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The problems of making inferences about the natural world from noisy observations and imperfect theories occur in almost all scientific disciplines. This 2006 book addresses these problems using examples taken from geophysical fluid dynamics. It focuses on discrete formulations, both static and time-varying, known variously as inverse, state estimation or data assimilation problems. Starting with fundamental algebraic and statistical ideas, the book guides the reader through a range of inference tools including the singular value decomposition, Gauss-Markov and minimum variance estimates,...

This book addresses the problem of inferring the state of ocean circulation, understanding it dynamically, and forecasting it through a quantitative combination of theory and observation. It focuses on so-called inverse methods and related methods of statistical inference. The author considers both time-independent and time-dependent problems, including Gauss-Markov estimation, sequential estimators and adjoint/Pontryagin principle methods. This book is intended for use as a graduate level text for students of oceanography and related fields. It will also be of interest to working physical...

This book provides a comprehensive presentation of the underlying oceanography and mathematics necessary to understand and develop such a system. It covers the forward and inverse tomography problem, as well as numerous models for data interpretation. It also includes an epilogue outlining the history of tomographic techniques.