EFSR: Ensemble Forecast Sensitivity to Observation Error Covariance

Abstract

Data assimilation (DA) methods require an estimate of observation error covariance [Formula: see text] as an external parameter that typically is tuned in a subjective manner. To facilitate objective and systematic tuning of [Formula: see text] within the context of ensemble Kalman filtering, this paper introduces a method for estimating how forecast errors would be changed by increasing or decreasing each element of [Formula: see text], without a need for the adjoint of the model and the DA system, by combining the adjoint-based [Formula: see text]-sensitivity diagnostics presented by Daescu previously with the technique employed by Kalnay et al. to derive ensemble forecast sensitivity to observations (EFSO). The proposed method, termed EFSR, is shown to be able to detect and adaptively correct misspecified [Formula: see text] through a series of toy-model experiments using the Lorenz ’96 model. It is then applied to a quasi-operational global DA system of the National Centers for Environmental Prediction to provide guidance on how to tune the [Formula: see text]. A sensitivity experiment in which the prescribed observation error variances for four selected observation types were scaled by 0.9 or 1.1 following the EFSR guidance, however, resulted in forecast improvement that is not statistically significant. This can be explained by the smallness of the perturbation given to the [Formula: see text]. An iterative online approach to improve on this limitation is proposed. Nevertheless, the sensitivity experiment did show that the EFSO impacts from each observation type were increased by the EFSR-guided tuning of [Formula: see text].