An iterative ensemble square root filter and tests with simulated radar data for stormscale data assimilation

An iterative procedure is designed to accelerate the ‘spin-up’ of ensemble square-root filter (EnSRF) data-assimilation cycles when starting from a poor initial ensemble. Referred to as the iterative EnSRF (iEnSRF), this iterative procedure follows the ‘running in place’ (RIP) concept developed for the local ensemble transform Kalman filter (LETKF) but because of algorithm differences is implemented differently. The iEnSRF is a three-step procedure: first, a backward EnSRF analysis is performed that updates the ensemble model states at an earlier time. Second, an ensemble of forecasts is run from these updated model states to the analysis time. These two steps are then repeated a prespecified number of times. The backward analysis is performed via an asynchronous ensemble Kalman filter (EnKF), which is capable of assimilating observations collected at times different than the analysis time. Like RIP, the iEnSRF uses the same observations repeatedly during the initial assimilation cycles, allowing for the extraction of additional information from observations when estimated ensemble mean state and ensemble covariance are poor. The iEnSRF algorithm is tested using simulated radar data for an idealized supercell storm. In experiments with a perfect model and the correct storm environment, as well as in the presence of model and environmental errors, the iEnSRF reduces the analysis error in the first few cycles more quickly than the regular EnSRF, leading to improved subsequent short-range forecasts. After the first few analysis cycles, continued use of iterations does not lead to further improvement. The better performance of the iEnSRF appears to be the result of improved background error covariance estimation as well as improved state estimation in the first few cycles, especially for correlations between observed and unobserved variables. Through iterations, the iEnSRF is also able to reach a steady level of state estimation error more quickly than the corresponding non-iterated version.