Abstract
ABSTRACT In hydraulic and hydrologic modeling, the storage (S)-discharge (Q) relation is often represented by a straight line or a curve, although when plotted using field or experimental data it is found to be hysteretic or looped. The characteristics of this looped relation depend on geometric, hydrologic, and hydraulic conditions. Despite the widespread use of the storage-discharge relation, there does not appear to have been a mathematical treatment discussing what causes the relation to be looped or double-valued. The objective of this study, therefore, is to analyze the S-Q relation analytically for a catchment represented by a rectangular plane, considering rainfall excess (rainfall minus infiltration) and surface runoff or overland flow modeled by kinematic wave approximation. Depending on the duration of rainfall excess, two cases - equilibrium and partial equilibrium - are distinguished and for each case the looped relation is analyzed. It is shown that the loop is different for the two cases.
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