Deriving physical and unique bimodal soil Kosugi hydraulic parameters from inverse modelling

Hydraulic parameters define the water retention, theta( psi), and the unsaturated hydraulic conductivity, K(theta), functions. These functions are usually obtained by fitting experimental data using inverse modelling. The drawback of inverting the hydraulic parameters is that they suffer from non-uniqueness and the optimal hydraulic parameters may not be physical. To reduce the non-uniqueness, it is necessary to invert the hydraulic parameters simultaneously from observations of theta( psi) and K(theta), and ensure the measurements cover the full range of theta from saturated to oven dry. The challenge of using bimodal theta(psi) and K(theta) compared to unimodal functions is that it requires double the number of parameters, one set for the matrix and another set for the macropore domain. The objective of this paper is to address this shortcoming by deriving a procedure to reduce the number of parameters to be optimized to obtain a unique physical set of bimodal soil Kosugi hydraulic parameters from inverse modelling. To achieve this, we (1) derive residual volumetric soil water content from the Kosugi standard deviation parameter of the soil matrix, (2) derive macropore hydraulic parameters from the water pressure head threshold between macropore and matrix flow, and (3) dynamically constrain the Kosugi hydraulic parameters of the soil matrix. The procedure successfully reduces the number of optimized hydraulic parameters and dynamically constrains the hydraulic parameters without compromising the fit of the theta(psi) and K(theta) functions, and the derived hydraulic parameters are more physical. The robustness of the methodology is demonstrated by deriving the hydraulic parameters exclusively from theta(psi) and Ks data, enabling satisfactory prediction of K(theta) even when no additional K(theta) data are available.