Titlebook: Data Assimilation; The Ensemble Kalman Geir Evensen Book 2009Latest edition Springer-Verlag Berlin Heidelberg 2009 Data assimilation.Ensem

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Analysis scheme,is particular time. It is assumed that error statistics of the model prediction as well as the measurements are known and characterized by the respective error covariances. Based on this information the so-called analysis scheme used in linear data assimilation methods is presented in some detail. F

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Free-Radical

Nonlinear variational inverse problems,odels will be treated extensively in the following chapters, but an introduction is in place here. The focus will be on some highly nonlinear problems which cannot easily be solved using the representer method. Examples are given were instead, so-called direct minimization methods are used.

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Probabilistic formulation,sent a mathematically and statistically consistent formulation of the combined parameter and state estimation problem. The starting point is Bayes’ theorem which defines the posterior probability density function of the poorly known parameters and the model solution conditioned on a set of observati

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Generalized Inverse,ian statistics for the priors. This was previously demonstrated by . (1996) using the results from . (1970). We will now derive the generalized inverse formulation for the combined parameter and state estimation problem starting from Bayes’ theorem. Further, the resulting Euler–Lagrange equations ar

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Ensemble methods,KF). They belong to a general class of so-called particle methods which use a Monte Carlo or ensemble representation for the pdfs, an ensemble integration using stochastic models to model the time evolution of the pdfs, and different schemes for conditioning the predicted pdf given the observations.

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Statistical optimization,elihood estimate. Many solution methods, e.g. gradient methods, search only for the minimum of the cost function, and do not provide information about the uncertainty of the solution. The uncertainty can be estimated using statistical sampling based on the Metropolis or hybrid Monte Carlo methods fr

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