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Open AccessArticle

A Sensitivity Analysis of Simulated Infiltration Rates to Uncertain Discretization in the Moisture Content Domain

by Lulu Liu 1 and Han Yu 2,3,*
1
Department of Mathematics, School of Science, Nanjing University of Science and Technology, Nanjing 210094, China
2
School of Computer Science and Technology, Nanjing University of Posts and Telecommunications, Nanjing 210023, China
3
Division of Physical Science and Engineering, King Abdullah University of Science and Technology, Thuwal 23955-6900, Saudi Arabia
*
Author to whom correspondence should be addressed.
Water 2019, 11(6), 1192; https://doi.org/10.3390/w11061192
Received: 25 April 2019 / Revised: 31 May 2019 / Accepted: 4 June 2019 / Published: 7 June 2019
(This article belongs to the Special Issue Rainfall Infiltration Modeling)
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. View Full-Text
Keywords: infiltration; moisture content discretization; uncertain; bin infiltration; moisture content discretization; uncertain; bin
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Liu, L.; Yu, H. A Sensitivity Analysis of Simulated Infiltration Rates to Uncertain Discretization in the Moisture Content Domain. Water 2019, 11, 1192.

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