Validation of finite water‐content vadose zone dynamics method using column experiments with a moving water table and applied surface flux

Abstract

Data from laboratory experiments on a 143 cm tall and 14.5 cm diameter column, packed with Wedron sand with varied constant upper boundary fluxes and water table velocities for both falling and rising water tables are used to validate a finite water-content vadose zone simulation methodology. The onedimensional finite water-content Talbot and Ogden (2008) (T-O) infiltration and redistribution method was improved to simulate groundwater table dynamic effects and compared against the numerical solution of the Richards equation using Hydrus-1D. Both numerical solutions agreed satisfactorily with time series measurements of water content. Results showed similar performance for both methods, with the T-O method on average having higher Nash-Sutcliffe efficiencies and smaller absolute biases. Hydrus-1D was more accurate in predicting deponding times in the case of a falling water table, while Hydrus-1D and the T-O method had similar errors in predicted ponding times in the case of a rising water table in six of nine tests. The improved T-O method was able to predict general features of vadose zone moisture dynamics with moving water table and surface infiltration using an explicit, mass-conservative formulation. The advantage of an explicit formulation is that it is numerically simple, using forward Euler solution methodology, and is guaranteed to converge and to conserve mass. These properties make the improved T-O method presented in this paper a robust and computationally efficient alternative to the numerical solution of the Richards equation in hydrological modeling applications involving groundwater table dynamic effects on vadose zone soil moistures.

Numerical Solution of Richards' Equation: A Review of Advances and Challenges

“…Fluxes calculated using the SMVE advection-like term agree very closely with the numerical solution of Richards' equation (Ogden et al, 2015a), data from column experiments (Ogden et al, 2015b) and exact analytical solutions (Ogden et al, 2017). Results in all cases show that the diffusion-like term in Eq.…”

A new general 1‐D vadose zone flow solution method

“…Since 2008, we have continued to improve the T-O method, testing it against analytical and numerical solutions of RE as well as laboratory data. In every test, the performance of the improved T-O methodology described in this paper was similar to the RE solution, and by some measures better, when compared against laboratory [Ogden et al 2015b] data. This led us to hypothesize that the finite water-content method of Talbot and Ogden [2008] is actually an approximate general solution method of the unsaturated zone flow problem for infiltration, falling slugs, and vadose zone response to water table dynamics in an unsaturated porous medium that includes gravity and capillary gradients, but neglects soil water diffusivity, which is emphasized in Richards' [1931] equation [Germann, 2010].…”

“…Talbot and Ogden [2008] included the influence of a static near-surface water table in terms of its effect on groundwater/surface water interactions, but had not developed the equation to describe the effect of water table dynamics on the vadose zone water content distribution. We developed and verified this equation [Ogden et al, 2015b] using data from a column experiment that was patterned after the experiment by Childs and Poulovassilis [1962].…”

“…Ogden et al [2015b] demonstrated using experimental data that when the water table velocity was 0.92 K s this cross partial-derivative term is negligible. In the case of finite water-content bins on the left where there are significant deviations from equilibrium conditions, this cross partial-derivative term is multiplied by a very small value of K(h), which makes this term small.…”

Shallow water table effects on water, sediment, and pesticide transport in vegetative filter strips – Part 1: nonuniform infiltration and soil water redistribution

“…However, RE does not have a general analytical solution and its application in real-world systems requires computationally intensive numerical approximations that can result in mass-balance and instability errors in some cases (e.g., for coarse soils and highly dynamic boundary conditions) (Celia et al, 1990;Paniconi and Putti, 1994;Miller et al, 1998;Vogel et al, 2001;Ross, 2003;Seibert et al, 2003). As a result, soil infiltration is often modeled in field and watershed models using simpler physically-based approaches (Jury et al, 1991;Smith et al, 1993;Haan et al, 1994;Singh and Woolhiser, 2002;Talbot and Ogden, 2008;Ogden et al, 2015). One of the most often used approaches in hydrologic modeling is the Green-Ampt (1911) model adjusted to account for variable rainfall (Mein and Larson, 1973;Chu, 1978;Skaggs and Khaleel, 1982).…”