Estimation of Unsaturated Soil Hydraulic Parameters Using the Ensemble Kalman Filter

The parameters of soil hydraulic functions are essential to the accurate simulation of soil moisture based on the Richards equation. Optimal values of these parameters can be calibrated by inverse modeling, in which the incomplete consideration of various errors may influence the parameter estimation results, thus further limiting the accuracy of modeling and forecasting. The ensemble Kalman filter (EnKF) is believed to be a flexible and effective sequential data assimilation method that provides a framework of explicit consideration of the various sources of uncertainty and is suitable for real-time, updated observations. The objective of this study was to extend the use of the EnKF to parameter estimation in vadose zone hydrology to improve the treatment of uncertainty in the calibration process. The parameters of soil hydraulic functions were estimated by assimilating observations of soil water pressure dynamics using EnKF with an augmentation technique. The results of the synthetic experiments on 12 soils with different textures indicated that EnKF estimates can quickly approach stable estimates. In contrast to the batch calibration process that used a simple least squares objective function, the EnKF reduced the risk of obtaining suboptimal estimates. The EnKF also performed well in the multi parameter estimation scenarios with synthetic observations and in its application in a heterogeneous soil profile with in situ field observations from a previous study. We further explored the factors that may influence estimation results, including the initial estimate, the ensemble size, the observation error and the model error, the assimilation interval, the water regime, and the variability of the estimated parameters. The result of this study indicates that the EnKF scheme is an effective method for parameter estimation in vadose zone hydrology.