A four-dimensional asynchronous ensemble square-root filter (4DEnSRF) algorithm and tests with simulated radar data

A four-dimensional ensemble square-root filter algorithm (4DEnSRF) is designed to assimilate high-frequency asynchronous observations distributed over time. Given the serial nature of the EnSRF, the 4DEnSRF algorithm pre-calculates observation priors from ensemble model states at observation times and updates the observation priors at asynchronous observational times using the filter. These updated observation posteriors are used to update model state variables at the analysis time. Such an algorithm is able to utilize more observations collected over time with fewer analysis cycles, thereby reducing computational costs and potentially improving filter performance. The 4DEnSRF algorithm is tested using simulated Doppler radar data for a convective storm. The radar data are simulated elevation-by-elevation, grouped into batches with different time intervals and then assimilated with analysis cycles of the same lengths. Parallel sets of experiments using 4DEnSRF and the regular EnSRF are performed for comparison, with varying data batch or cycle lengths of 1 to 20 min. For longer time intervals, EnSRF either assumes that all data collected within the time window are valid at the same analysis time, or uses only elevations collected within a shorter time interval centered at the analysis time. Results show that 4DEnSRF outperforms EnSRF when the cycle length is more than 1 min. Observation timing error is the main cause of the performance degradation with EnSRF for both analysis and forecast; the longer the cycle length, the worse the degradation. For long cycle lengths, 4DEnSRF improves the analysis by utilizing more data whereas the EnSRF performs well only when data far away from the analysis time are discarded. Assimilating only a couple of scan elevations at a time using EnSRF with very short cycles can introduce imbalances into the model state that degrades the subsequent analyses and forecasts. Copyright (c) 2012 Royal Meteorological Society