Time-Expanded Sampling Approach for Ensemble Kalman Filter:Experiment Assimilation of Simulated Soundings

In the Ensemble Kalman Filter（EnKF） data assimilation-prediction system,most of the computation time is spent on the prediction runs of ensemble members.A limited or small ensemble size does reduce the computational cost,but an excessively small ensemble size usually leads to filter divergence,especially when there are model errors.In order to improve the efficiency of the EnKF data assimilation-prediction system and prevent it against filter divergence,a time-expanded sampling approach for EnKF based on the WRF（Weather Research and Forecasting） model is used to assimilate simulated sounding data.The approach samples a series of perturbed state vectors from Nb member prediction runs not only at the analysis time（as the conventional approach does） but also at equally separated time levels（time interval is △t） before and after the analysis time with M times.All the above sampled state vectors are used to construct the ensemble and compute the background covariance for the analysis,so the ensemble size is increased from Nb to Nb＋2M×Nb=（1＋2M）×Nb） without increasing the number of prediction runs（it is still Nb）.This reduces the computational cost.A series of experiments are conducted to investigate the impact of △t（the time interval of time-expanded sampling） and M（the maximum sampling times） on the analysis.The results show that if t and M are properly selected,the time-expanded sampling approach achieves the similar effect to that from the conventional approach with an ensemble size of（1＋2M）× Nb,but the number of prediction runs is greatly reduced.