Simple Nonlinear Rainfall-Runoff Model

A simple nonlinear conceptual model for simulating Hortonian rainfall-runoff phenomena is presented. The model is based on the concept of a nonlinear storage outflow relationship and assumes a nonlinear loss module. The abstractions can take the form of a constant or an exponential decreasing rate. The analytical model is derived from an approximate perturbation solution of the governing nonlinear ordinary differential equation and relates in an explicit fashion the runoff to the rainfall, the abstractions, and the watershed parameters. The model is function of few parameters that can be estimated efficiently using optimization techniques and nonlinear least-squares regression. The model has been applied to a very small semiarid watershed with considerable success. The proposed model can be considered as an improvement over the classical linear reservoir theory, and an attractive and useful substitute to the linear reservoir components in more complex conceptual rainfall-runoff models.