Random fractional partial differential equations and solutions for water movement in soils: Theory and applications

Su, Ninghu (2023) Random fractional partial differential equations and solutions for water movement in soils: Theory and applications. Hydrological Processes, 37 (3). e14844.

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Abstract

This paper analyses a set of random fractional partial differential equations (rfPDEs) for water movement in soils. The rfPDEs for both rigid and swelling soils are solved for both a random flux boundary condition (BC), and random concentration BC. Solutions from a random flux BC are presented for the large-time and small-time situations with the large-time solution as a very simple method for determining the flux through the surface of the soil. The equation of cumulative infiltration is presented with random parameters of the rfPDE subject to a random concentration BC. The simulations using the results of the rfPDE for the two types of BCs yielded encouraging and stable results based on two sets of field data: the first set of the data was measurements at a single site while the second set was from 26 measurements in a small catchment. The results suggest that the presented procedures are very useful methods for the interpolation, extrapolation, and prediction of hydrological variables and parameters such as water content, hydraulic conductivity or the flux through the surface of the soil. The methodologies presented in this paper are able to reveal and reproduce the realistic hydrological processes in nature which are often stochastic and random.

Item ID: 78366
Item Type: Article (Research - C1)
ISSN: 1099-1085
Keywords: random flux boundary, random fractional partial differential equations (rfPDEs), random soil parameters, soils, water movement
Copyright Information: This is an open access article under the terms of the Creative Commons Attribution-NonCommercial License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited and is not used for commercial purposes. © 2023 The Author. Hydrological Processes published by John Wiley & Sons Ltd.
Date Deposited: 30 May 2023 00:45
FoR Codes: 37 EARTH SCIENCES > 3707 Hydrology > 370799 Hydrology not elsewhere classified @ 35%
49 MATHEMATICAL SCIENCES > 4901 Applied mathematics > 490199 Applied mathematics not elsewhere classified @ 30%
41 ENVIRONMENTAL SCIENCES > 4106 Soil sciences > 410605 Soil physics @ 35%
SEO Codes: 18 ENVIRONMENTAL MANAGEMENT > 1806 Terrestrial systems and management > 180605 Soils @ 50%
18 ENVIRONMENTAL MANAGEMENT > 1806 Terrestrial systems and management > 180603 Evaluation, allocation, and impacts of land use @ 50%
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