A LINEAR SPATIALLY DISTRIBUTED MODEL FOR A SURFACE RAINFALL-RUNOFF SYSTEM

This paper presents a linear, spatially distributed model for the rain fall-runoff process based on a system analysis approach. A watershed i s treated as a system that consists of a number of subwater-sheds, eac h of which is assumed to be approximately uniform in terms of rainfall excess and geographic conditions. An ordinary differential equation r epresenting the relationship between the input, output and function of the subwatershed is derived based on the mass balance principle and a storage-release equation. A number of ordinary differential equations for subwatersheds in series or parallel are assembled to form an over all equation for the watershed system. The rainfall excess process of each subwatershed is represented by a unit-step function. The Laplace transform of rainfall excess was taken and substituted into the waters hed system equation to obtain the Laplace transform of the outflow hyd rograph of the watershed. The analytical solution for calculating the outflow hydrograph was finally obtained by taking the inverse Laplace transform. This model, with a much simpler form than numerical convolu tion, is capable of predicting runoff from non-uniformly distributed r ainfall and geographical conditions over an entire watershed.