Abstract
The developed nonlinear time varying model of a hydrologic system that relates the rainfall and the runoff is represented by a pair of nonlinear ordinary differential equations with time varying coefficients. The model does not require the linearity and time invariance assumptions necessary in conventional unit hydrograph methods. The nonlinear and time varying characteristics of the system are incorporated into the model through four basic system parameters. These parameters can be determined by the procedure developed without using the equations of the model. The nonlinearity and long‐, medium‐, and short‐term time varying trends of a rainfall‐runoff system can be determined and described by analyzing the parameters. The model is empirical and its field application procedure is feasible and simple, since its derivation is based on the physical system response observed. In an illustrative field application the model and procedure proved effective, relative to other linear and/or time invariant models, in predicting the rainfall‐runoff relation, especially when the rainfall excess occurred during a very short time interval.
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