Data Assimilation: Mathematical Concepts and Instructive Examples

Preface 1 Introduction through historical perspective 1.1 From Gauss to Kolmogorov 1.2 Approaching the meteorological system 1.3 Numerical Weather Prediction models 1.4 What, Where, When 2 Representation of the physical system 2.1 The observational system and errors 2.2 Variational approach: 3-D VAR and 4-D VAR 2.3 Assimilation as an inverse problem 3 Sequential interpolation 3.1 An effective introduction of a Kalman Filter 3.2 More Kalman Filters 4 Advanced data assimilation methods 4.1 Recursive Bayesian Estimation 4.2 Ensemble Kalman Filter 4.3 Issues due to small ensembles 4.4 Methods to reduce problems of undersampling 5 Applications 5.1 Lorenz model 5.2 Biology and Medicine 5.3 Mars data assimilation: the General Circulation Model 5.4 Earthquake forecast A Appendix A.1 Hadamard product A.2 Differential calculus A.3 The method of characteristics A.4 Calculus of variations A.5 The solution for the simplified equation of oceanographic circulation

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