Comparison of Sequential Ensemble Square-Root Filter (EnSRF) and Four-Dimensional Asynchronous EnSRF Algorithms for the Assimilation of Simulated Radar Data

Effective utilization of frequent observations such as those from radars for model initialization poses a significant challenge. The assimilation of radar data using the ensemble Kalman filter (EnKF) method often groups data collected over a period of time and assimilates them in batches. An alternative is to use four-dimensional (4D) algorithms designed to deal with observations distributed over time. These include the 4D-EnKF and 4D-LETKF algorithms and the so-called ‘Asynchronous EnKF' algorithm (AEnKF). It has been shown that for a perfect model and linear dynamics (including observation operators), and perfectly initialized ensembles, many of these algorithms are equivalent. For the convective-scale radar data assimilation problem, the linearization assumption is, however, not necessarily valid. This paper examines the relative performance of standard sequential batch-based EnSRF algorithm and an Asynchronous implementation of the EnSRF algorithm (AEnSRF). We further compare the accuracy of regular EnSRF and its variant that is used by AEnSRF, which pre-calculates the ensemble observation priors from the initial background ensemble forecasts then updates them using observations. The latter was used by Anderson and Collins (2007) in their scalable parallel implementation of EnKF. We refer to this particular implementation for EnSRF as PEnSRF, where P refers to parallel or pre-calculation of H(x), the observation priors. OSSEs are performed for a simulated fast-moving supercell storm using simulated radar observations. The radar data are collected elevation by elevation, completing a volume scan every 5 minutes. The observations are grouped into 1, 3, 5, and 10 minute batches and assimilated using regular EnSRF at 1, 3, 5 and 10 minute intervals (called time windows), and using the AEnSRF for the corresponding intervals. The results show that when the assimilation window length is short (~1 minute), EnSRF and PEnSRF produce very similar results. The regular EnSRF with 1-minute assimilation windows produces the most accurate analyses, because of the lack of linear approximation (with the observational operators and model dynamics at least) while the AEnSRF produces results close to short-time-window EnSRF. When the assimilation window length is increased to 10 minutes, the observation timing error causes significant deterioration with the regular EnSRF algorithm. More detailed results will be discussed at the conference.