Data Assimilation for Atmospheric, Oceanic and Hydrologic by Seon Ki Park, Liang Xu

By Seon Ki Park, Liang Xu

This ebook includes the newest development in facts assimilation in meteorology, oceanography and hydrology together with land floor. It spans either theoretical and applicative features with a variety of methodologies akin to variational, Kalman filter out, ensemble, Monte Carlo and synthetic intelligence equipment. along with information assimilation, different very important subject matters also are coated together with focusing on commentary, sensitivity research, and parameter estimation. The booklet can be important to person researchers in addition to graduate scholars for a reference within the box of information assimilation.

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Then we will show how to solve related variational problems in the framework of a systematic classification of the reviewed work. This classification will permit us to review different variational methods as well as the context in which they were performed. The last section will be devoted to future developments and potential applications of variational methods in meteorology. 1 Definition of a Variational Method In the most condensed way a variational method may be defined as a search, amongst all the possible solutions of a model, of the solution closest to a given observation.

Let F(X, K) = 0 be the direct model. We introduce its adjoint: [ ]∗ ????G ????F ⋅P= , ????X ????X [ ]∗ ????F ????F where ????X is the adjoint operator of ????X . Then the gradient is given by: ∇G = [ ]∗ ????G ????F ⋅P − ????K ????K The advantage of this method is that the sensitivity is obtained by only one run of the adjoint model. The price to be paid is the derivation of the adjoint code. -X. Le Dimet et al. 2 Sensitivity in the Presence of Data In geophysics a usual request is the estimation of the sensitivity with respect to observations.

A consequence was that of rendering obsolete the optimal interpolation methods, mainly because the retrieved fields where not in agreement neither with the physics of the models nor with their dynamics. At the end of this period variational methods were successfully introduced in many national operational centers. 2 Variational Methods in Meteorology: A Perspective There are two main approaches employed when modeling a system described by a state variable, X. The first approach consists of finding a set of equations F such that X is the unique solution of the state equation F(X) = 0.

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