Empirical determination of the covariance of forecast errors: an empirical justification and reformulation of Hybrid covariance models

Abstract

<p>The replacement of climatological background error covariance models with Hybrid error covariance models that linearly combine a localized ensemble covariance matrix and a climatological error covariance matrix has led to significant forecast improvements at several forecasting centres. To deepen understanding of why the Hybrid&#8217;s superficially ad-hoc mix of ensemble based covariances and climatological covariances yielded such significant improvements, we derive the linear state estimation equations that minimize analysis error variance given an imperfect ensemble covariance. For high dimensional models, the computational cost of the very large sample sizes required to emp..