Spatial averaging of ensemble‐based background‐error variances

It is common to compute background‐error variances from an ensemble of forecasts, in order to calculate either climatological or flow‐dependent estimates. However, the finite size of the ensemble induces a sampling noise, which degrades the accuracy of the variance estimation. An idealized 1D framework is firstly considered, to show that the spatial structure of sampling noise is relatively small‐scale, and is closely related to the background‐error correlations. This motivates investigations on local spatial averaging, which is here applied to ensemble‐based variance fields in this 1D context. It is shown that a spatial averaging, manually optimized, helps to significantly reduce the sampling noise. This provides estimates which are as accurate as those derived from a much bigger ensemble. The dependencies of this optimization on the error correlation length‐scale and on the heterogeneity of the variance and length‐scale fields are also illustrated. These results are next confirmed in a more realistic 2D problem, by considering the current operational version of the Arpège background‐error covariance matrix. Finally, the possibility to objectively and automatically optimize the filtering is explored. The idea is to apply the usual linear estimation theory and to use signal/noise ratios in order to calculate an optimal filter. The efficiency of this objective filtering is illustrated in the idealized 1D framework. Copyright © 2008 Royal Meteorological Society