A gaussian process-based iterative Ensemble Kalman Filter for parameter estimation of unsaturated flow

Abstract

Water flow in the unsaturated zone is an important component of the water cycle. Accurate estimation of soil hydraulic parameters ensures precise simulations of water flow in the unsaturated zone. In this study, a Gaussian Process-based Iterative Ensemble Kalman Filter method (GPIEnKF) is proposed and applied for estimating soil hydraulic parameters for two-dimensional soil water flow. The method involves a surrogate model for two-dimensional soil water flow that is based on the Gaussian Process method. The accuracy and efficiency of the GPIEnKF method are validated using two synthetic cases and a real dataset involving a field experiment with drip irrigation. The impact of the layout of observation points as well as the number of training base points and observation points on the estimation of parameters are also analyzed. The results show that the surrogate model can accurately predict pressure heads at observation points. The layout of observation points that precisely describes infiltration water movement allows the surrogate model to better emulate the original model, thereby improving the accuracy of parameter estimation. The number of training base points is found to have only a small influence on parameter estimation. The accuracy of parameter estimation and pressure head predictions can be further improved by increasing the number of observation points. However, the accuracy of predictions is affected by the uncertainty of boundary conditions and the soil spatial heterogeneity. The GPIEnKF method can effectively estimate multiple parameters characterizing water flow in layered soils. As compared with the standard Iterative Ensemble Kalman Filter, the GPIEnKF method can greatly improve computational efficiency while obtaining comparable results. The GPIEnKF method is an efficient tool for parameter estimation of multi-dimensional soil water flow.