DistanceDependent Filtering in a 4DVar Based on Historical Forecast Ensemble

An economical approach to implement the variational data assimilation (4Dvar) using the technique of Historical Sample Projection (HSP) is proposed, it is based on dimension reduction using an ensemble of historical samples to define a subspace, directly obtains an optimal solution in the reduced space and does not require implementation of the adjoint of tangent linear approximation. But the ensemble is composed of far fewer members than both the number of observational data and the degrees of freedom of the model variables, which would lead to many spurious correlations between observation locations and model grids. More practical and easier way to deal with this problem is through localization technique. Three groups of experiments have been done, the results show that the localization can effectively ameliorate the spurious long range of correlations. And the Schur product tends to reduce and smooth the analysis increments. In addition, the rootmeansquare errors of the 6h and 12h forecast are smaller after the localization.