Comment on “Identification of a constrained nonlinear hydrological system described by Volterra Functional Series” by J. Xia

Abstract

In his recent paper Xia [1991] presents an interesting penalty function technique for the identification of kernel functions for watershed systems which are represented by Volterra series. It is unfortunate that the published results of research that has been carried out in hydrology on rainfall­ runoff modeling by means of Volterra series in the last 13 years were not taken into account. Hence, there are some errors and misconceptions in the paper. It is silently assumed in the paper by Xia that the water­ shed system can be represented by a lumped nonlinear operator P, which maps a space of lumped rainfalls into a space of corresponding flood waves at a measuring station on a river. If this unknown operator P is differentiable as many times as may be required in the Frechet sense, and the system is deterministic, time invariant, initially relaxed and nonanticipating, then its behavior can be approximated within the radius of convergence to any predetermined accuracy by a truncated Volterra series [Volterra, 1959]: