Inverse Estimation of the Hydrodispersive Properties of Unsaturated Soil Using Complex-Variable-Differentiation Method under Field Experiments Conditions

Because soil hydraulic properties are indispensable for determining soil water retention and soil solute movement, their input for simulation models is essential. Many of these parameters cannot be estimated directly at the scale of interest, but can only be derived through inverse modeling. During this process, the parameters are generally adjusted using least-squares approach with Levenberg–Marquardt (LM) algorithms in which numerically simulated models are fitted to measured data. In this study we used a new inverse method to estimate the unsaturated soil hydro-dispersive properties from in-situ experiments. The method employs complex-variable-differentiation method (CVDM) to accurately predict of the hydraulic properties of the van Genuchten–Mualem models (θ_r, θ_s, α, k_s, n). To the knowledge of the authors, it is first study use CVDM in soil physics. The optimization procedure was performed by using a continuous data set of daily in situ soil water content and bromide concentration measurements. Estimated parameters during the inversion showed high correlation (R² = 0.88, RMSE = 0.013 and the model efficiency CE = 0.77) by using the CVDM-methods with the actual field measurements, compared with the traditional LM-algorithm (R² = 0.81, RMSE = 0.021 and CE = 0.626). The results show that the new inverse analysis in the present work has the high accuracy, validity, uniqueness, and higher inversion efficiency. Meanwhile, the convergence and stability of the modified LM-algorithm are improved. Overall, it was concluded that the CVDM is promising method to estimate hydro-dispersive parameters in soil physics.