Comparison of empirical, semi-empirical and physically based models of soil hydraulic functions derived for bi-modal soils

The accelerated flow in soil pores is responsible for a rapid transport of pollutants from the soil surface to deeper layers up to groundwater. The term preferential flow is used for this type of transport. Our study was aimed at the preferential flow realized in the structural porous domain in bi-modal soils. We compared equations describing the soil water retention function h(θ) and unsaturated hydraulic conductivity K(h), eventually K(θ) modified for bi-modal soils, where θ is the soil water content and h is the pressure head. The analytical description of a curve passing experimental data sets of the soil hydraulic function is typical for the empirical equation characterized by fitting parameters only. If the measured data are described by the equation derived by the physical model without using fitting parameters, we speak about a physically based model. There exist several transitional subtypes between empirical and physically based models. They are denoted as semi-empirical, or semi-physical. We tested 3 models of soil water retention function and 3 models of unsaturated conductivity using experimental data sets of sand, silt, silt loam and loam. All used soils are typical by their bi-modality of the soil porous system. The model efficiency was estimated by RMSE (Root mean square error) and by RSE (Relative square error). The semi-empirical equation of the soil water retention function had the lowest values of RMSE and RSE and was qualified as “optimal” for the formal description of the shape of the water retention function. With this equation, the fit of the modelled data to experiments was the closest one. The fitting parameters smoothed the difference between the model and the physical reality of the soil porous media. The physical equation based upon the model of the pore size distribution did not allow exact fitting of the modelled data to the experimental data due to the rigidity and simplicity of the physical model when compared to the real soil porous system. On the other hand, the “optimal” unsaturated conductivity equation was obtained for a model based on the pore size distribution where the additional fitting parameters allowed a good agreement between the model and the reality of the measured data. We denoted this equation as semi-physical.