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

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.