Optimal ensemble size of ensemble Kalman filter in sequential soil moisture data assimilation

The ensemble Kalman filter (EnKF) has been extensively applied in sequential soil moisture data assimilation to improve the land surface model performance and in turn weather forecast capability. Usually, the ensemble size of EnKF is determined with limited sensitivity experiments. Thus, the optimal ensemble size may have never been reached. In this work, based on a series of mathematical derivations, we demonstrate that the maximum efficiency of the EnKF for assimilating observations into the models could be reached when the ensemble size is set to 12. Simulation experiments are designed in this study under ensemble size cases 2, 5, 12, 30, 50, 100, and 300 to support the mathematical derivations. All the simulations are conducted from 1 June to 30 September 2012 over southeast USA (from similar to 90 degrees W, 30 degrees N to similar to 80 degrees W, 40 degrees N) at 25 km resolution. We found that the simulations are perfectly consistent with the mathematical derivation. This optical ensemble size may have theoretical implications on the implementation of EnKF in other sequential data assimilation problems.