A new kinematic–dispersive wave van Genuchten (KDW-VG) model for numerical simulation of preferential water flow in soil

Abstract

Preferential water flow in soil macropores such as underground channels formed by worm activity and plant root growth, can move a large volume of water and contaminants to groundwater resources in a short time. To describe these types of water flow in soil, Di Pietro et al. (2003) developed and proposed kinematic–dispersive wave (KDW) model. They suggested this model by adding a dispersive term to the kinematic wave (KW) model that was severely convective and was presented by Germann in 1985. The fundamental assumption of this model is that the water flux (u) is exclusively a function of the mobile water content, but in the KDW model, considering its additional dispersive term, it is assumed that the water flux is a non-linear function of the mobile water content and its first-time derivative. The first term of this assumption is a power function where the water flux depends on the mobile water content. This equation is just a mathematical equation and has no significant physical meaning. In this research, this power function is substituted by the shape of van Genuchten model that has an acceptable physical meaning, and thus the kinematic–dispersive wave van Genuchten (KDW-VG) model is introduced for the first time as the innovation of this research. The models were calibrated and validated with observations of four different rainfall intensities that were applied on the surface of a soil column with artificial preferential pathways. The output water fluxes from the bottom of the soil column versus the soil mobile volumetric water content in the column were recorded at set times. First, both the KDW and KDW-VG models were calibrated and their indefinite coefficients were determined by minimizing the error function between the observed and modelled water fluxes versus mobile volumetric water content using particle swarm optimization (PSO) algorithm. Next, both models, which are second-degree non-linear partial differential equations, were solved using numerical finite difference method with the MATLAB programming language, and were validated by experimental observations of rainfall hydrograph that was passed through the preferential routes of a physical model and was recorded from the bottom of the soil column. Root-mean-square error (RMSE) comparison of the models predictions and observations indicated that the proposed model (KDW-VG) could predict the observations more accurately compared with the KDW model, and also had better performance in the calibration stage.