Estimating soil hydraulic conductivity by Inverse Laplace Transform

Multimodal soil pore structures introduce substantial challenges for deriving hydraulic properties, including the estimation of hydraulic conductivity from water retention data. Conventional models often have difficulty representing the complexity of multimodal pore systems, motivating the development of more flexible approaches. In a recent paper, we demonstrated that a new model based on the Inverse Laplace Transform (ILT) can be used to estimate the pore size distribution (PSD) from soil water retention curves (SWRC), providing a flexible alternative to traditional parametric models. The present study extends the ILT methodology to determine soil hydraulic conductivity in unsaturated soils. We derive a closed-form equation for the hydraulic conductivity function within the ILT–Gauss method and validate it using a dataset from the UNSODA database that includes paired soil water retention and hydraulic conductivity measurements. The results demonstrate that hydraulic conductivity was accurately predicted, yielding statistical performance comparable to conventional unimodal and multimodal van Genuchten models. The main advantage of the new method is its ability to implicitly capture multimodal pore systems when evaluating unsaturated hydraulic conductivity and, consequently, soil water dynamics in such soils.