Thresholds in Deterministic Models of the Rainfall-Runoff Process

Abstract

Thresholds are encountered when a deterministic approach is adopted to hydrological problems. The general definition of a threshold—the point at which a stimulus begins to produce a response–is applicable to these problems. In the catchment process some thresholds, such as the time for initiation of runoff, are immediately obvious and can be simply measured. The chapter aims to indicate where thresholds usually occur in catchment processes, to demonstrate how thresholds are typically built into conceptual models, and to outline the parameter estimation problems raised by their presence. Usually, a few variables and thresholds are considered in stochastic models which are relatively simple in their structure. In contrast, conceptual hydrological models tend to be more complex and represent a variety of processes and several thresholds. The conceptual models of particular hydrological interest are mathematical representations of catchment response to precipitation based on understandings of the operative physical processes.