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Conservation equations governing hillslope responses: Exploring the physical basis of water balance
Author(s) -
Reggiani Paolo,
Sivapalan Murugesu,
Hassanizadeh S. Majid
Publication year - 2000
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 - 10.1029/2000wr900066
Subject(s) - nonlinear system , shallow water equations , mathematics , soil water , water balance , scale (ratio) , independent equation , partial differential equation , hydrology (agriculture) , mathematical analysis , environmental science , soil science , geology , geotechnical engineering , physics , quantum mechanics
A unifying approach for the derivation of watershed‐scale conservation equations governing hydrologic responses has recently been introduced. The approach is based on space‐time averaging of the corresponding point‐scale conservation equations over an averaging region called the representative elementary watershed (REW). The conservation equations are supplemented by constitutive relationships needed for the closure of various mass and momentum exchange terms. In this paper, we present a summary of the resulting equations for a somewhat simpler problem and show how these equations can be employed to model the long‐term water balance of a single, hypothetical REW. The governing equations are formulated in terms of an average saturation and a flow velocity of the unsaturated zone soils and the average thickness of the saturated zone soils. The equations are coupled ordinary differential equations and are nonlinear. Their solution is carried out simultaneously for a variety of combinations of watershed geometry, soil type, and atmospheric forcing. We show how a similarity analysis of the governing equations can lead to a general classification of REWs in terms of meaningful dimensionless similarity variables. In addition, we investigate the long‐term water balance and show that the governing equations are able to provide a realistic picture of the impact of changing climate, soil, and topographic controls on long‐term water balance.