Estimate of the soil water retention curve from the sorptivity and β parameter calculated from an upward infiltration experiment

Abstract

The water retention curve (θ(h)), which defines the relationship between the volumetric water content (θ) and the matric potential (h), is of paramount importance to characterize the hydraulic behaviour of soils. Because current methods to estimate θ(h) are, in general, tedious and time consuming, alternative procedures to determine θ(h) are needed. Using an upward infiltration curve, the main objective of this work is to present a method to determine the parameters of the van Genuchten (1980) water retention curve (α and n) from the sorptivity (S) and the β parameter defined in the 1D infiltration equation proposed by Haverkamp et al. (1994). The first specific objective is to present an equation, based on the Haverkamp et al. (1994) analysis, which allows describing an upward infiltration process. Secondary, assuming a known saturated hydraulic conductivity, Ks, calculated on a finite soil column by the Darcy’s law, a numerical procedure to calculate S and β by the inverse analysis of an exfiltration curve is presented. Finally, the α and n values are numerically calculated from Ks, S and β. To accomplish the first specific objective, cumulative upward infiltration curves simulated with HYDRUS-1D for sand, loam, silt and clay soils were compared to those calculated with the proposed equation, after applying the corresponding β and S calculated from the theoretical Ks, α and n. The same curves were used to: (i) study the influence of the exfiltration time on S and β estimations, (ii) evaluate the limits of the inverse analysis, and (iii) validate the feasibility of the method to estimate α and n. Next, the θ(h) parameters estimated with the numerical method on experimental soils were compared to those obtained with pressure cells. The results showed that the upward infiltration curve could be correctly described by the modified Haverkamp et al. (1994) equation. While S was only affected by early-time exfiltration data, the β parameter had a significant influence on the long-time exfiltration curve, which accuracy increased with time. The 1D infiltration model was only suitable for β < 1.7 (sand, loam and silt). After omitting the clay soil, an excellent relationship (R2 = 0.99, p < 0.005) was observed between the theoretical α and n values of the synthetic soils and those estimated from the inverse analysis. Consistent results, with a significant relationship (p < 0.001) between the n values estimated with the pressure cell and the upward infiltration analysis, were also obtained on the experimental soils.