Discharge predictions of a rainfall‐driven theoretical hydrograph compared to common models and observed data

Abstract

A theoretical hydrograph based on Darcy's law and the diffusion equation has been extended into a predictive model for the discharge of diffuse springs and small rivers from a detailed rainfall record, using only a single free parameter, the basin time constant b. The model accurately predicts the flow variations of natural hydrographs, including the magnitude and timing of peak flow, total flow volume, inflection points, and recession rate, all as a function of effective rainfall amounts, basin area, and the time constant b. Predicted hydrographs for a sharp storm event in an unimpounded basin are compared to results for two common transfer functions, and our more parsimonious model is statistically superior. Modeling of a long‐term record in proximal basins illustrates the effect of variations in b. Potential applications of the model include flood prediction, comparative studies of basin response in a regional context, and estimation of actual evapotranspiration.