Employ multi-model ensemble background error covariance in four-dimensional ensemble data assimilation

Most Ensemble Kalman filter (EnKF) DA schemes were built on single model ensembles. Although many efforts have been put into estimation and representation of the model errors in the EnKF schemes, accurate estimate of such model errors is inherently limited by the ability of a single model ensemble to sample the model uncertainties and forecast errors (forward propagation). This limitation becomes more serious on mesoscale model EnKF because atmospheric physics and dynamics, and the model lateral boundary conditions and underlying forcing play great roles in mesoscale weather processes, whereas the uncertainties in these model components are typically large. In this paper, we study the background error covariance computed based on the NCAR mesoscale Ensemble Real-Time Four-Dimensional Assimilation and forecasting (E-RTFDDA) system, and use it in the NCAR 4-Dimensional Relaxation Ensemble Kalman Filter (4D-REKF) data assimilation and forecasting system (Liu et al. 2013, this conference). E-RTFDDA, which has been running for over 4 years at the Army Dugway Proving Ground, exhibits considerably enhanced ability to estimate the PDF of the forecast fields. However, multi-model ensembles tend to produce multi-mode signals and unwanted noises that should be carefully taken care of. In this paper, we 1) discuss the features of the background error covariance computed based on E-RTFDDA forecasts, and compare it with those from single model ensemble EnKF runs; 2) assess these multi-model background-error-covariance in the traditional EnKF scheme (with NCAR DART) system to show value added by E-RTFDDA; and 3) integrate the multi-model background-error-covariance in the NCAR 4D-REKF system. Algorithms for localization, approximation, and spatiotemporal interpolations of the background error covariance in 4D-REKF will be discussed, and evaluation using the perfect-model-perfect-observations framework and the real-weather-real-data cases is conducted.