A Hybrid Ensemble Kalman Filter / 3-Dimensional Variational Analysis Scheme

Abstract

A crucial aspect to improving the accuracy of initial conditions for numerical weather forecasts is a more accurate specification of errors of the first guess, or "background." Most existing operational schemes have made assumptions about the statistics of background errors, assuming that the errors are stationary (don't change with time) or isotropic (don't change with direction from the observation).

In this talk we will demonstrate an assimilation method that can produce improved initial conditions even with small-sized ensembles. The assimilation method is a hybrid ensemble Kalman filter / 3-dimensional variational analysis scheme; the background error statistics are defined as a weighted sum of anisotropic, flow-dependent statistics derived from the ensemble and stationary 3D-Var error statistics. This scheme was tested in a quasigeostrophic channel model under perfect-model assumptions. A variety of observational networks were tested for ensembles of size 25, 50, and 100. For ensembles of size 25, it was found that a moderate contribution of error statistics from 3D-Var covariances produced the best analysis. For ensembles of size 50 and 100, the analysis was best when very little of the 3D-Var covariances were used. Errors were reduced from 25 to 50 percent relative to a full 3D-Var analysis, with more reduction in error for relatively sparse observational networks.

Further improvement in analysis error is demonstrated by applying a distant-dependent weighting to the ensemble-based background error covariances. This forces the covariances to zero at finite distance from the observations. A justification for the use of distance-dependent filters is given, based on the properties of sample covariance matrices and how they vary as correlations between grid points are changed.

This general approach to data assimilation may have considerable appeal to the operational community because very little code modification may be required to integrate it into existing 3D-Var systems.