Extension of the Gardner exponential equation to represent the hydraulic conductivity curve: inclusion of macropore flow effects

Abstract

In soil hydraulics, it is crucial to establish an accurate representation of the relative hydraulic conductive curve (rHCC), K_r(h). This paper proposes a simple way to determine K_r(h), called the Modified Gardner Dual model (MGD), using a logarithmic extension of the classical Gardner exponential representation and including mac ropore flow effects. MGD has five parameters which are hydraulic constants clearly identified in the bilogar ithmic representation of K_r(h). Two of them are related to the main inflection point coordinates of rHCC; from them, it is possible to determine the macroscopic capillary length of the infiltration theory. The model was tested in the suction interval 0 < h < 15,000 cm with a total of 249 soil samples from two databases, and employing a flexible representation of the Mualem-van Genuchten (MVG) equation as a reference. Using the RMSE statistics (with log base) to measure the fitting errors, we obtained a 31% reduction in errors (RMSE_MGD = 0.27, RMSE_MVG = 0.39). In 74% of the soils, including samples from the two databases, the reduction was 53% (RMSE_MGD = 0.19, RMSE_MVG = 0.40); the rHCC data fitting of this group was accurate over all the suction h intervals, with RMSE_MGD < 0.32 in each soil sample. In the remaining 26% of the samples, the quality of the MGD fitting degraded due mainly to the presence of multiple rHCC data inflection points. Therefore, in soils without this structural peculiarity, the proposed model revealed to be quite accurate in addition to being analytically simple. Another advantage of MGD is that its parameters depend mainly on the data with h around and lower than the main inflection suction value, which, in turn, never exceeded the 300-cm limit in this study. Hence, in soils that do not have multiple inflections, the extrapolations of the model in drier intervals (1000 cm < h < 15,000 cm) are reliable. The MGD parameter optimization software has been called KUNSAT. It is available in the Supplementary Material or from the corresponding author on request.