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The flow of water on a watershed is usually unsteady and spatially varied, but can be adequately portrayed by the equations of momentum and continuity, commonly referred to as the unsteady flow equations. Because these equations are quasi-linear, hyperbolic, partial differential equations, they are not easily amenable to solution. Analog computer model~ of surface runoff generally have been based on simplified forms of these equations. As an improvement of those models, an analog computer solution is presented here for the unsteady flow equations. The solution involves the conversion of the partial differential equations in to a differential-difference system, and a consideration of the stability of the difference approach was performed. The analog computer solution is then used to develop a model of surface runoff generated from rainfall on a watershed. Spatial distribution of the watershed parameters is accounted for by dividing the drainage basin into a number of subzones according to its physiography and the rainfall input was made to each subzone. Both the overland and channel flow components are considered in the surface runoff process. Preliminary testing and verification of the model have been made by simulating two runoff events on a subwatershed of the Walnut Gulch experimental watershed near Tombstone, Arizona.


This work made publicly available electronically on April 2, 2012.