Closed-form hydraulic conductivity equations for multimodal unsaturated soil hydraulic properties

Closed-form expressions of the hydraulic conductivity function for linearly superposed subretention (multimodal) functions were derived for arbitrary sets of the Brooks and Corey (BC), van Genuchten (VG), and Kosugi (KO) water retention models. The generalized Mualem hydraulic conductivity model was evaluated using the mathematical approach of Priesack and Durner. Three types of modification to the multimodel were also proposed. Firstly, the derived conductivity equations can be simplified when the submodel parameters, hbi for the BC model, alpha i-1 for the VG model, and hmi for the KO model have the same (common) value (denoted as CH). Secondly, as in the case of the modified single VG and KO models, a hypothetical air-entry head near saturation can be introduced for the multimodal VG and KO models to prevent unrealistic reductions in the hydraulic conductivity near saturation when the VG n parameter approaches its lower limit of n = 1. Furthermore, the multimodal hydraulic conductivity functions become a simple sum of conductivity subfunctions when the exponent r is unity (such as for Burdine's model), which leads to independent tortuosity effects for each submodel. The models are illustrated for two soils: a highly aggregated Kumamoto Andisol and a relatively unimodal dune sand. The dual-(BC, VG, KO) and the VG(1)BC(2) models equally represented the water retention data of the Andisol, with similar hydraulic conductivity curves. The dual-BC-CH, dual-VG-CH, and VG(1)BC(2)-CH models fitted the water retention data of the dune sand well, with the hydraulic conductivity curves of the dual-porosity model being similar to those of the Fayer and Simmons (FS) model.