Approximate analytical solution and parameter estimation for one‐dimensional horizontal absorption based on the van Genuchten–Mualem model. Issue 2 (19th March 2021)

• Record Type: Journal Article
• Authors: Su, Lijun; Hou, Linfang; Zhou, Beibei; Shan, Yuyang; Duan, Manli; Sun, Yan; Ning, Songrui; Wang, Quanjiu
• Is Part Of: Soil Science Society of America Journal. Volume 85:Issue 2(2021)
• Page Start: 217
• Page End: 234
• Publication Date: 2021-03-19
• Subjects: Soils -- United States -- Periodicals; Soil science -- Periodicals; Periodicals; 631.4973
• DOI: 10.1002/saj2.20185
• Languages: English
• ISSNs: 0361-5995

Abstract

Abstract: The van Genuchten–Mualem (VGM) model is used to describe the absorption of water by soil. The model is highly nonlinear, so developing a simple analytical or approximate method to predict the movement of soil water via the VGM model then estimating the model parameters is necessary. We present a approximate functional extremum solution (FES) for the problem of one‐dimensional horizontal absorption (1DHA) of water in soil under constant saturated boundary conditions and uniform initial conditions based on the least action and the variational principles. Simple linear relationships between the infiltration characteristics (distribution of soil water content, cumulative infiltration, infiltration rate, wetting front distance, and infiltration time) and the VGM model parameters were obtained. We developed a simple approximate analytical method for estimating the VGM model parameters by testing 1DHA. Numerical data simulated by HYDRUS‐1D were compared with the analytical results and used to verify our method's feasibility. The results indicated that the FES could accurately predict the infiltration characteristics, with relative errors between the approximate analytical and numerical solutions of 0.8 to 8.5% for the distribution of soil water content, 0.1 to 0.8% for cumulative infiltration, 1.1 to 6.4% for infiltration rate, and 0.1 to 6.9% for wetting front distance. Estimates of the parameters indicated that errors ranged from 3.2 to 28.3% for α (inverse of the mean pore diameter) and 0.4 to 8.0% for n (pore size distribution index). The proposed methods can be used to predict 1DHA and to estimate α and n in the VGM model. Core Ideas: The functional extremeum solution of soil water movement was developed The solution was obtained by the least action and the variational principles The relationship between infiltration rate & soil hydraulic parameters was linear An approximate analytical method was used to estimate the van Genuchten parameters