The Kernel function of linear nonstationary surface runoff systems

Adopting a linear nonstationary model for the surface runoff system gives a better fit to a set of observed direct surface runoff hydrographs than adopting a stationary linear model. The kernel of this model, which is a function of two time variables, can be considered to be an assembly of impulse response functions for unit pulses acting at various time intervals after the beginning of the storm. Each of these impulse response functions must have the properties of an ordinary instantaneous unit hydrograph. The kernel function is evaluated by an optimization procedure that seeks to minimize the sum of squared deviations between the observed and computed hydrographs for a number of independent storms, subject to given constraints. The procedure is based on a discretization scheme for the functions involved. The set of equations for the unknown kernel values can be partitioned into independent subsets, each of which is solved individually. The complete equation set need be considered only when area constraints of the kernel function are imposed.