Abstract
From a viewpoint of overall grasp of response characteristics of a basin to rainfall, an integral form of expression such as the unit hydrograph, the Volterra series, and the Wiener series is superior to differential equation type expressions. However, hitherto, response or runoff kernels have been derived from empirical data or at the most from numerical simulation data. In this paper the runoff is represented by the Wiener‐Hermite orthogonal functional expansion. By application of the Galerkin technique a set of ordinary nonlinear differential equations for the expansion coefficients of kernel functions are derived from the basic equation of motion. The differential equations are solved by the Runge‐Kutta‐Gill scheme to obtain the runoff kernels. Various features of the theoretical linear and nonlinear runoff kernels thus derived compare well with the empirical ones.
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