An Economical Approach to Four-dimensional Variational Data Assimilation

Four-dimensional variational data assimilation (4DVar) is one of the mostpromising methods to provide optimal analysis for numerical weatherprediction (NWP). Five national NWP centers in the world have successfullyapplied 4DVar methods in their global NWPs, thanks to the increment methodand adjoint technique. However, the application of 4DVar is still limited bythe computer resources available at many NWP centers and researchinstitutes. It is essential, therefore, to further reduce the computationalcost of 4DVar. Here, an economical approach to implement 4DVar is proposed,using the technique of dimension-reduced projection (DRP), which is called``DRP-4DVar. The proposed approach is based on dimension reduction usingan ensemble of historical samples to define a subspace. It directly obtainsan optimal solution in the reduced space by fitting observations withhistorical time series generated by the model to form consistent forecaststates, and therefore does not require implementation of the adjoint oftangent linear approximation.To evaluate the performance of the DRP-4DVar on assimilating different typesof mesoscale observations, some observing system simulation experiments areconducted using MM5 and a comparison is made between adjoint-based 4DVar andDRP-4DVar using a 6-hour assimilation window.