A technical evaluation on the mathematical attitudes and fitting accuracy of soil moisture retention curve models

Numerous mathematical equations have been formulated in the literature of different researchers for describing soil moisture retention curve (SMRC), which can be applied to simulate and solve soil hydraulic modeling problems. The primary concern lies in selecting an efficient model to simulate accurately the S-shaped curve or sigmoid-type of the SMRC for soils with different textures. Therefore, the objective of this study was a comprehensive and technical evaluation of 50 developed models of the SMRC based on the influence of parameters on the behavior of the curve and the ability of their fitting accuracy on 728 soil samples of the UNSODA dataset, that has not been investigated so far. Statistical criteria including corrected Akaike’s information criterion (AICc), root mean square error (RMSE) and coefficient of determination (R²) together with Duncan's multiple range test and cluster analysis were employed to assess the fitting accuracy of SMRC models to measured data. Results from fitting accuracy on the UNSODA dataset indicated that Brutsaert model provided the best fit to the measured data compared to other models in 14.6% of the soil samples with RMSE = 0.0125 and AICc = -94.18. This model was classified in the same cluster with Groenevelt and Grant (GG₁, GG₂ and GG₃), Dexter, Mualem, and Fredlund and Xing models and did not have a significant difference in terms of RMSE. Also, Brutsaert model had the highest fitting accuracy in 67% of different soil textural classes compared to other models. Finally, the technical evaluation in terms of accuracy, flexibility and simplicity of the fitting process showed that the Brutsaert, Mualem, Dexter and GG₃ models can be selected for better simulation of the SMRC in water and soil research.