Sampling Error in Ensemble Kalman Filter for 2-D Groundwater Flow

Data assimilation is useful to determine key hydrogeological parameters, and EnKF proved to be an effective method. Sampling error exists in the EnKF if the sample size is not sufficiently large. This article tested the capability of the cubature-based EnKF based on the 2-D groundwater flow problem. The sensitivity of EnKF to Monte Carlo-based sampling techniques and the performance of the cubature-based EnKF were further analyzed. The results show that it is hard to decide which Monte Carlo-based sampling technique is with the least estimation variability when taking the same ensemble size. The cubature-based EnKF provides deterministic estimation result and effectively reduces the sampling error.