Linear time‐varying model of rainfall‐runoff relation

Abstract

The linear time‐varying system model of the rainfall‐runoff relation can be represented by a first‐order, linear differential equation with time‐varying coefficients that depend on two parameters. The model does not require the time‐variance assumption necessary in the conventional unit hydrograph method. The long‐ and short‐term trends for a hydrologic system to change with time can be considered and described with the technique developed. Analysis of historical data for the rainfall‐runoff relation of a basin used for an experimental study indicates that the response of the basin to rainfall significantly changes with months during a year, although the yearly variation is not significant. The developed model and techniques used in the experimental study to describe and predict the rainfall‐runoff relation have proved satisfactory.