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 arbitrary sets Brooks and Corey (BC), van Genuchten (VG), Kosugi (KO) water retention models. The generalized Mualem model was evaluated using mathematical approach Priesack Durner. Three types modification to multimodel also proposed. Firstly, equations can be simplified when submodel parameters, h b i ${h_{{{\rm{b}}_i}}}$ BC model, α − 1 ${{\alpha}}_i^{ - 1}$ VG m ${h_{{{\rm{m}}_i}}}$ KO have same (common) value (denoted as CH). Secondly, in case modified single models, a hypothetical air-entry head near saturation introduced multimodal models prevent unrealistic reductions n parameter approaches its lower limit = 1. Furthermore, become simple sum subfunctions exponent r is unity (such Burdine's model), which leads independent tortuosity effects each submodel. are illustrated two soils: highly aggregated Kumamoto Andisol relatively unimodal dune sand. dual-(BC, VG, KO) VG1BC2 equally represented data Andisol, with similar curves. dual-BC-CH, dual-VG-CH, VG1BC2-CH fitted sand well, curves dual-porosity being those Fayer Simmons (FS) model.