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Entropy theory for movement of moisture in soils
Author(s) -
Singh Vijay P.
Publication year - 2010
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/2009wr008288
Subject(s) - moisture , water content , soil water , soil science , entropy (arrow of time) , tsallis entropy , maximization , environmental science , mathematics , hydrology (agriculture) , geology , geotechnical engineering , thermodynamics , mathematical optimization , physics , meteorology
An entropy theory is formulated for one‐dimensional movement of moisture in unsaturated soils in the vertically downward direction. The theory is composed of five parts: (1) Tsallis entropy, (2) principle of maximum entropy, (3) specification of information on soil moisture in terms of constraints, (4) maximization of the Tsallis entropy, and (5) derivation of the probability distributions of soil moisture. The theory is applied to determine the soil moisture profile under three conditions: (1) the moisture is maximum at the soil surface and decreases downward to a minimum value at the bottom of the soil column (it may be near the water table); (2) the moisture is minimum at the soil surface and increases downward to a maximum value at the end of the soil column (this case is the opposite of case 1); and (3) the moisture at the soil surface is low and increases downward up to a distance and then decreases up to the bottom (this case combines case 2 and case 1). The entropy‐based soil moisture profiles are tested using experimental observations reported in the literature, and properties of these profiles are enumerated.