A Dynamical Estimation of Forecast Error Covariances in an Assimilation System

Abstract

The author uses an approximation of the extended Kalman filter to estimate the forecast and analysis error covariances of an operational assimilation system. The fundamental differences with Kalman filtering are the basic-state trajectory, which is kept close to the operational analyses, and the analysis weights, which follow the usual approximations of optimal interpolation with local data selection. The estimation error covariances for the model state are updated during the analysis and prediction cycles. Although no model error term is specified, the estimation error variances grow according to the dynamics on poorly observed areas. The unbounded error growth found in the Southern Hemisphere has to be limited by a representation of error saturation to account for nonlinearities in the atmosphere. A weak relaxation to climatology is introduced in order to improve the independence on the initial covariances. The behavior of the error variances and correlations is shown to be particularly interesting over and around the oceans, suggesting improvements to analysis schemes and forecast skill models. A comparison with observation minus analysis and forecast statistics provides an estimate of the model error, which is then introduced into the covariance estimation procedure.