## The Ocean Circulation Inverse ProblemThis 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 oceanographers. |

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### Contents

Introduction | 1 |

Physics of the Ocean Circulation | 17 |

Basic Machinery | 92 |

The Steady Ocean Circulation Inverse Problem | 212 |

Additional Useful Methods | 297 |

The TimeDependent Inverse Problem | 324 |

405 | |

427 | |

435 | |

### Common terms and phrases

adjoint algorithms assumption average boundary conditions Chapter coefficients column computed conservation Consider constraints correlation covariance decibars density field depth derivatives determined diagonal discussion dynamical eddy eigenvectors Ekman flux Ekman layer elements error example Figure Florida Straits flow field fluid forecast Gauss-Markov estimate geostrophic grid points Gulf Stream heat flux hydrographic interior inverse problems Kalman filter known Lagrange multipliers least-squares least-squares solution linear mass flux matrix mean measurements minimum noise nonlinear norm North Atlantic nullspace vectors objective function observations ocean circulation oceanographic physical probability density produce property fluxes reference level reference-level velocity residuals result Riccati equation salinity sample scale seasurface shows simultaneous equations singular values singular vectors smoother solved spatial squares statistical Stommel structure Suppose Sverdrup balance temperature flux thermal wind time-dependent tion tracer transport uncertainty underdetermined unknown variables variance vertical wavenumber Wunsch zero zonal