• ensemble of assimilations;
  • Ensemble Kalman Filter;
  • sampling noise;
  • linear estimation


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