Modified expression for hydraulic conductivity according to Mualem-van Genuchten to allow proper computations at low-pressure heads

Water retention and hydraulic conductivity characteristics are key input data in studies on soil water dynamics in the vadose zone. The most well-known analytical functions to describe these characteristics are those given by Mualem and van Genuchten, where van Genuchten showed that both can be described by a limited set of shared parameters. Analytically, there are no restrictions on the range of pressure heads for which these characteristics can be used. Experience, however, has shown that for certain sets of parameters, the hydraulic conductivity cannot be computed accurately at low-pressure heads. This is due to the accuracy of (double precision) floating point operations in computer code. It is shown that for low-pressure heads, the Mualem function approaches a power function. An adapted version of the Mualem-van Genuchten (MvG) expression for the hydraulic conductivity is proposed: between saturation and a soil-dependent critical pressure head, the classical Mualem expression is valid and below this critical pressure head a power function is used. The power function is defined such that it matches the Mualem value at the critical pressure head. No accuracy problems will occur when using the power function until the result approaches the smallest possible (double precision) floating point value that significantly differs from zero. Computer calculated hydraulic conductivities K can show anomalous behavior at low-pressure heads h.Double precision floating point constraints are the main cause.The Mualem-van Genuchten K expression can be approximated by a power function at low h.An extended expression for the Mualem-van Genuchten K(h) equation is proposed.With the extended expression, K can be computed to values as low as floating point precision allows.