4D-VAR: four-dimensional variational assimilation
4D-VAR: four-dimensional variational assimilation
In this chapter, four-dimensional variational assimilation (4D-VAR) is described in the context of statistical linear estimation, in which it defines the best linear unbiased estimate (BLUE) of the state of the observed system from the available data. It consists in minimizing a scalar objective function that measures the quadratic difference between the estimated state and the data, weighted by the inverse covariance matrix of the data errors. 4D-VAR can be extended heuristically to the case of nonlinear models or observation operators. It is made possible in practice through the use of the adjoint equations, which allow explicit computation of the gradient of the objective function at a non-prohibitive cost. 4D-VAR is used operationally in a number of major meteorological centres, where it has brought significant improvement in the quality of the forecasts. 4D-VAR, together with the ensemble Kalman filter, is one of the two most powerful assimilation methods currently available.
Keywords: four-dimensional variational assimilation, 4D-VAR, statistical linear estimation, best linear unbiased estimate, BLUE, objective function, adjoint equations
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