Scaling Parameters of the Lewis-Kostiakov Water Infiltration Equation Across Soil Textural Classes and Extension to Rain Infiltration

Abstract

A recent study showed that the pore-size distribution index (k) of the Brooks-Corey equation related and scaled cumulative infiltration (I) across eleven textural classes under different rainfall and initial conditions using normalization of the Green-Ampt equation or implicit empirical relations. The initial objectives herein were to (1) explore if more explicit, easy to use, and compact scaling could be achieved through relationships between the parameters of the empirical Lewis-Kostiakov (L-K) infiltration equation (I = cumulative infiltration = kt α ; t = time; a, k = constants) and or the effective saturated hydraulic conductivity (KS ) across eleven soil types for instantaneous incipient (zero-head) ponding cases; and (2) in the process, look for a more physical interpretation of the parameters and their dependence on initial soil water content. The Green-Ampt infiltration method in the Root Zone Water Quality Model (RZWQM) was used to generate simulated values for instantaneous zero-head infiltration at two initial pressure heads (-1500 and -100 kPa) in eleven homogeneous textural-class mean soils for 5 h, using the detailed Brooks-Corey hydraulic parameters for each soil. The two L-K parameters (a, k) were shown to have fairly strong explicit relationships with (r 2 = 0.78 to 0.88) and stronger relationships with K S (r 2 = 0.94 to 0.99) across the eleven textural classes. Additionally, a was essentially the same for the two initial pressure heads, and its value varied from 0.5 for clay soil to 0.58 for sand, indicating the dominance of sorptivity for clay and the increasing gravity effect for lighter textures, as expected from the theory. The intercept k varied with the pressure head condition but was related to the initial soil water deficit in the same way as sorptivity. Upper time limits for the L-K equation (t b ) to be applicable were also more strongly related to Ks (r 2 = 0.99) in all soils. A larger-time (beyond t b ) extension of the L-K equation proposed in the literature was also shown to be valid, thus making it more valuable. The L-K equation was then extended to non-instantaneous ponding infiltration for several rainfall intensities (I - Ip = k (t - tp)α'; Ip = I at incipient ponding time tp). The new parameters α' and k for each rainfall intensity were again found to be strongly related to K s or λ, and their variation with respect to initial pressure head was similar to that of a and k. This study provides a simple new method to quickly estimate the variation of infiltration with soil type on a landscape, scale up infiltration from small to large areas, and estimate effective average parameters for modeling large areas. The study also establishes a more physical basis for the L-K equation parameters and shows that it can be extended to large times and to infiltration of rainfalls, just like the Green-Ampt equation.