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, Kalman filters and related smoothers, and adjoint (Lagrange multiplier) methods. The final chapters discuss a variety of practical applications to geophysical flow problems. Discrete Inverse and State Estimation Problems is an ideal introduction to the topic for graduate students and researchers in oceanography, meteorology, climate dynamics, and geophysical fluid dynamics. It is also accessible to a wider scientific audience; the only prerequisite is an understanding of linear algebra.

• Provides a comprehensive introduction to discrete methods of inference from incomplete information • Based upon 25 years of practical experience using real data and models • Develops sequential and whole-domain analysis methods from simple least-squares • Contains many examples and problems, and web-based support through MIT opencourseware

### Contents

Preface; Part I. Fundamental Machinery: 1. Introduction; 2. Basic machinery; 3. Extensions of methods; 4. The time-dependent inverse problem: state estimation; 5. Time-dependent methods (continued); Part II. Applications: 6. Applications to steady problems; 7. Applications to time-dependent fluid problems; References; Index.

### Reviews

From the author's previous book, The Ocean Circulation Inverse Problem: ' … written by an acknowledged master in the field.' The Times Higher Education Supplement

'Wunsch has met his objectives of producing an extensive discussion of finite-dimensional inverse methods applied to the ocean circulation inverse problem. Practitioners will find it an important contribution to their bookshelves … a unique introduction to inverse methods with a healthy dose of critical scientific method.' Philip Bogden, American Meteorological Society Bulletin

'Wunsch has been a pioneer in adapting statistical methods from other scientific fields to oceanography … A tremendous amount of experience is distilled in this book.' Kirk Bryan, Science