Introduction of time variance to linear conceptual catchment models

Abstract

Most linear conceptual models relating rainfall and runoff are time invariant and are based on two simple components, the linear channel and the linear reservoir. Time variant versions of these two components are defined, and expressions are obtained for their impulse responses. The convolution integral is used both to study different combinations of the two basic time variant components and to obtain the response of any time variant linear system to a given input. The theoretical background of more advanced models is discussed and it is suggested that time variance may be introduced into any linear model founded on these two conceptual components.