Soil hydraulic properties estimation from one‐dimensional infiltration experiments using characteristic time concept

Abstract

Many different equations ranging from simple empirical to semi-analytical solutions of the Richards equation have been proposed for quantitative description of water infiltration into variably saturated soils. The sorptivity, S, and the saturated hydraulic conductivity, K s , in these equations are typically unknown and have to be estimated from measured data. In this paper, we use so-called characteristic time (t char) to design a new method, referred to as the characteristic time method (CTM) that estimates S, and K s , from one-dimensional (1D) cumulative infiltration data. We demonstrate the usefulness and power of the CTM by comparing it with a suite of existing methods using synthetic cumulative infiltration data simulated by HYDRUS-1D for 12 synthetic soils reflecting different USDA textural classes, as well as experimental data selected from the Soil Water Infiltration Global (SWIG) database. Results demonstrate that the inferred values of S and K s are in excellent agreement with their theoretical values used in the synthetically simulated infiltration experiments with Nash-Sutcliffe criterion close to unity and RMSE values of 0.04 cm h −1/2 and 0.05 cm h −1 , respectively. The CTM also showed very high accuracy when applied on synthetic data with added measurement noise, as well as robustness when applied to experimental data. Unlike previously published methods, the CTM does not require knowledge of the time

Choice of Pedotransfer Functions Matters when Simulating Soil Water Balance Fluxes

“…Finally, the so‐called characteristic time ( t grav ) was calculated according to Philip (1957), which determines the “time” t where gravitational forces become dominant ( t ≫ t grav ), while for t ≪ t grav capillary forces remain dominant over gravitational forces (Rahmati, Groh, et al., 2020; Rahmati, Vanderborght, et al., 2020): …”

Simplified characteristic time method for accurate estimation of the soil hydraulic parameters from one‐dimensional infiltration experiments

“…Following Rahmati et al (2020), the contribution of capillaryand gravity-driven components to the cumulative infiltration are temporally variable and is illustrated in Figure 1. The contribution of the capillary-driven component shows a maximum at the start of the infiltration process (t close to 0), whereas the contribution of the gravity-driven component is 0.…”

“…In general, two major approaches are used to estimate S and K s : linearization approaches (Sharma et al, 1980;Smiles & Knight, 1976;Vandervaere et al, 2000) and inverse estimation using curve-fitting method (Bonell & Williams, 1986;Bristow & Savage, 1987;Marquardt, 1963;Vandervaere et al, 2000). Both approaches usually result in very good agreement (R 2 > .9) between measured and predicted infiltration curves (Rahmati et al, 2020). However, linearization approaches suffer from substantial arbitrariness in deciding which part of the data fully meets linearity, leading to uncertainty in estimated infiltration parameters.…”

“…On the other hand, the curve fitting methods suffer from equifinality, the principle that the minimum of the objective function can be obtained by a broad set of parameter values (Beven & Freer, 2001), as well as possible nonrealistic parameter values when the optimization is unconstrained. Rahmati et al (2020) introduced a new procedure based on the use of the characteristic time (named characteristic time method, CTM) to predict S and K s from one-dimensional (1D) infiltration experiments. Their method uses an iterative procedure to ensure accurate predictions of S and K s regardless of the infiltration regime measured (i.e., the transient regime only or both transient and steady-state regimes).…”

“…Contrary to previously published methods, the CTM does not require knowledge of the time validity of the applied semi-analytical solution for transient infiltration and can be applied to any infiltration duration (from a few minutes to several days). Rahmati et al (2020) demonstrated the usefulness and strength of CTM in comparison with a suite of existing methods including classical methods of Sharma et al (1980) (SH) and curvefitting methods using two- (Haverkamp et al, 1994) (CF2) and three-term (Rahmati et al, 2019) (CF3) approximate expansions based on the quasi-exact implicit (QEI) formulation proposed by Haverkamp et al (1994). Note that the QEI model addresses the case of 1D water infiltration and was extended to the case of water infiltration through discs (three-dimensional [3D] axisymmetric geometry) by Smettem et al (1994).…”