Empirical determination of the covariance of forecast errors: An empirical justification and reformulation of hybrid covariance models

Abstract

During the last decade, the replacement of static climatological forecast error covariance models with hybrid error covariance models that linearly combine localised ensemble covariances with static climatological error covariances has led to significant forecast improvements at several major forecasting centres. Here, a deeper understanding of why the hybrid's superficially ad hoc mix of ensemble-based and climatological covariances yields such significant improvements is pursued. In practice, ensemble covariances are not equal to the true flow-dependent forecast error covariance matrix. Here, the relationship between actual forecast error covariance and the corresponding ensemble covarianc..