Watershed Environmental Hydrology (WEHY) Model Based on Upscaled Conservation Equations: Hydrologic Module

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Abstract
The Watershed Environmental Hydrology model presents a new approach to the modeling of hydrologic processes in order to account for the effect of heterogeneity within natural watersheds. Toward this purpose, the point location–scale conservation equations for various hydrologic processes were upscaled in order to obtain their ensemble averaged forms at the scale of the computational grid areas. Over hillslopes these grid areas correspond to areas along a complete transect of a hillslope. The resulting upscaled conservation equations, although they are fundamentally one-dimensional, have the lateral source/sink terms that link them dynamically to other hydrologic component processes. In this manner, these upscaled equations possess the dynamic interaction feature of the standard point location–scale two-dimensional hydrologic conservation equations. A significant computational economy is achieved by the capability of the upscaled equations to compute hydrologic flows over large transactional grid areas versus the necessity of computing hydrologic flows over small grid areas by point location–scale equations in order to account for the effect of environmental heterogeneity on flows. The emerging parameters in the upscaled hydrologic conservation equations are areal averages and areal variances/covariances of the original point-scale parameters, thereby quantifying the spatial variation of the original point-scale parameters over a computational grid area, and, thus, the effect of land heterogeneity on hydrologic flows. Also, by requiring only the areal average and areal variance of parameter values over large grid areas, it is possible to achieve a very significant economy in parameter estimation.

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