Extension of the Gardner exponential equation to represent the hydraulic conductivity curve

The relative hydraulic conductivity curve K_r(h) = K/K_s is a key variable in soil modeling. This study proposes a model to represent K_r(h), the so-called Gardner dual (GD) model, which extends the classical Gardner exponential model to h values greater than h_o, the suction value at the inflection point of the K_r(h) curve in the log-log scale. The goodness of fit of GD using experimental data from UNSODA was compared to that of the MVG [two-parameter (K_ro, L) Mualem-van Genuchten] model and a corresponding modified MVG model (MVGm). In 77 soils without evidence of macropore flow, GD reduced the RMSE errors by 64% (0.525 to 0.191) and 29% (0.269 to 0.193) in relation to MVG and MVGm, respectively. In the remaining 76 soils, GD generally was less accurate than MVG and MVGm, since most of these soils presented evidence of macropore flow (dual permeability). GD has three parameters and two degrees of freedom, like MVG. Two of them allow the calculation of the macroscopic capillary length, a parameter from the infiltration literature. The three parameters are highly dependent on the K_r(h) data measurement in a short wet suction range around h_o, which is an experimental advantage.