A nonlinear analysis of the relationship between rainfall and runoff for extreme floods

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Abstract
The watershed response to heavy rainfall was considered as a hereditary process. A nonlinear system model was developed in terms of a Volterra integral series of the first kind, which satisfies the principle of dissipation of hereditary action as well as the requirement of time invariance. A workable and practical method was developed to compute optimal response functions or kernels of the two‐term truncated Volterra series. A Galerkin‐type method was used, whereby the kernels were approximated by an orthogonal function expansion in terms of Chebyshev polynomials. The kernels evaluated from historical data for the Cowanesque watershed in the Chemung River basin were tested by reconstituting the hydrograph of an unrelated and unusual flood event caused by tropical storm Agnes of June 1972. It was found that the nonlinear watershed model yields a better prediction of the hydrograph of an exceptional flood than the linear model. The performance of both nonlinear and linear models is sensitive to the assumed value of the rainfall loss rate.