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

By Seon Ki Park, Liang Xu

This booklet includes the newest growth in information assimilation in meteorology, oceanography and hydrology together with land floor. It spans either theoretical and applicative facets with a number of methodologies comparable to variational, Kalman clear out, ensemble, Monte Carlo and synthetic intelligence equipment. along with info assimilation, different very important issues also are coated together with concentrating on remark, sensitivity research, and parameter estimation. The publication can be valuable to person researchers in addition to graduate scholars for a reference within the box of knowledge assimilation.

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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.

10) To summarize the algorithm is the following: i. 4) to get X and P ii. 9) to compute Q and R iii. 10). 1) dt X(0) = U. 2) where C is the pollutant’s concentration and S is a function of space and time and represents the production of pollutant. -X. Le Dimet et al. The first task is to retrieve the fields from observations Xobs ∈ obs corresponding to the state variable X and Cobs ∈ obs associated with the concentration C of the pollutant. 3) where E is an operator from the space of the state variable toward the space of observations and D from the space of concentration toward the space of observations of concentration.

The model and the error are characterized by: ????u ???? ????u ????u + u − (???? ) + E = F, ????t ????x ????x ????x u(0) = ????. 46) Variational Data Assimilation: Optimization and Optimal Control 21 ???? ????E ????E − (???? ) = 0, ????t ????x ????x E(0) = ????. 48) The problem is to determine ???? ∗ , ???? ∗ , ???? ∗ minimizing the cost function J defined by: J(????, ????, ????) = T 1 T 1 1 1 1 1 1 1 (u − uobs )2 dxdt + E2 dxdt + ???? 2 dx + ???? 2 + ???? 2 . 49) For sake of simplicity we have chosen the simplest form with a complete observation, identity observation operators and ignoring the statistical information.

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