Abstract
An unconditionally mass conservative hydrologic model proposed by Talbot and Ogden provides an effective and fast technique for estimating region-scale water infiltration. It discretizes soil moisture content into a proper but uncertain number of hydraulically interacting bins such that each bin represents a collection of pore sizes. To simulate rainfall-infiltration, a two-step alternating process runs until completion; and these two steps are surface water infiltration into bins and redistribution of inter-bin flow. Therefore, a nonlinear dynamical system in time is generated based on different bin front depths. In this study, using rigorous mathematical analysis first reveals that more bins can produce larger infiltration fluxes, and the overall flux variation is nonlinear with respect to the number of bins. It significantly implies that a greater variety of pore sizes produces a larger infiltration rate. An asymptotic analysis shows a finite change in infiltration rates for an infinite number of bins, which maximizes the heterogeneity of pore sizes. A corollary proves that the difference in the predicted infiltration rates using this model can be quantitatively bounded under a specific depth ratio of the deepest to the shallowest bin fronts. The theoretical results are demonstrated using numerical experiments in coarse and fine textured soils. Further studies will extend the analysis to the general selection of a suitable number of bins.
Highlights
The recharge of groundwater [1,2] is critical in many aspects, for example, natural environments, industry, and agriculture
The convergence test for choosing a proper number of bins by Talbot and Ogden [23] is more rigorously analyzed in this work, and its physical meaning, a greater variety of pore sizes leading to a larger infiltration rate, can be naturally explained from this study
RMS1 /RMS2 values indicate that the coarser the soil texture is, the more sensitive the infiltration rate is to the change in the number of bins, especially at the beginning of this change
Summary
The recharge of groundwater [1,2] is critical in many aspects, for example, natural environments, industry, and agriculture. To avoid the drawbacks of the Green–Ampt model and rapidly determine how well ground water and aquifers are recharged only, the Talbot–Ogden model is proposed [23,24] for estimating large-scale surface water infiltration into various unsaturated soil textures [25] over long periods Valuable features of this model are the relatively low computational cost and the large-scale applicability. The convergence test for choosing a proper number of bins by Talbot and Ogden [23] is more rigorously analyzed in this work, and its physical meaning, a greater variety of pore sizes leading to a larger infiltration rate, can be naturally explained from this study It will be quantitatively estimated how an infinite water content discretization affects the flux variation through an asymptotic analysis by linearly fitting the wetting front.
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