A hybrid EnKF-fsolve model for simultaneous dynamic soil moisture simulation and hydraulic parameters prediction

The challenge of inversely estimating hydraulic parameters and determining Soil Water Retention Function (SWRF) from time-sequenced, real-world soil moisture data is exacerbated by the limitations of existing optimization techniques and methods for solving the Richards equation. To address this, a hybrid method — the ‘EnKF-fsolve’ model is proposed and tested. The EnKF-fsolve model incorporates the fsolve function with the Ensemble Kalman Filter (EnKF) to simultaneously simulate sequenced soil moisture and predict hydraulic parameters of the van Genuchten–Mualem (VGM) model at multiple soil depths. When implemented to compute 100 daily soil moisture and weather data for three field sites, the EnKF-fsolve model demonstrated superior convergence, computational efficiency and simulation accuracy compared to HYDRUS-1D, a widely used soil–water modelling program. The outstanding performance of the EnKF-fsolve model was attributed to the EnKF’s dynamic optimization procedure, parallel computational operation, and consideration of model and observational uncertainty in the highly nonlinear soil water system. The highly effective solver, fsolve function, in the EnKF-fsolve model addresses the non-convergence issue of solving the Richards equation in the HYDRUS-1D model to ensure 100% successfully completed computations. Despite persisting dependencies on reasonable prediction of the initial VGM parameter values, the EnKF-fsolve model improved the capability of predicting multi-depth five VGM parameters and SWRFs. • A hybrid model combines the fsolve function and ensemble Kalman filter (EnKF). • fsolve solves Richards equation efficiently with strong convergence features. • EnKF enables dynamic optimization and parallel parameter estimation. • Shows superior convergence, computational efficiency, and simulation accuracy. • Improves prediction accuracy of multi-depth SWRFs using field soil data.