A geomorphologic synthesis of nonlinearity in surface runoff

Abstract

The geomorphic approach leading to a representation of an instantaneous unit hydrograph (iuh) which we developed earlier is generalized to incorporate nonlinear effects in the rainfall‐runoff transformation. It is demonstrated that the nonlinearity in the transformation enters in part through the dependence of the mean holding time on the rainfall intensity. Under an assumed first approximation that this dependence is the sole source of nonlinearity an explicit quasi‐linear representation results for the rainfall‐ runoff transformation. The kernel function of this transformation can be termed as the instantaneous response function (irf) in contradistinction to the notion of an iuh for the case of a linear rainfall‐runoff transformation. The predictions from the quasi‐linear theory agree very well with predictions from the kinematic wave approach for the one small basin that is analyzed. Also, for two large basins in Illinois having areas of about 1100 mi 2 the predictions from the quasi‐linear approach compare very well with the observed flows. A measure of nonlinearity, α naturally arises through the dependence of the mean holding time K B ( i 0 ) on the rainfall intensity i 0 via K B ( i 0 ) ∼ i 0 −α . Computations of α for four basins show that α approaches ⅔ as basin size decreases and approaches zero as the basin size increases. A semilog plot of α versus the square root of the basin area gives a straight line. Confirmation of this relationship for other basins would be of basic importance in predicting flows from ungaged basins.