Generalised synthesis of space-time variability in flood response: An analytical framework

We extend the method developed by Woods and Sivapalan (1999) to provide a more general analytical framework for assessing the dependence of the catchment flood response on the space–time interactions between rainfall, runoff generation and routing mechanisms. The analytical framework focuses on three characteristics of the flood hydrograph: the catchment rainfall excess rate, and the first and second temporal moments of the flood response. These characteristics are described by analytical relations, which are derived with a limited number of assumptions concerning the catchment response that comply well with many modelling approaches. The paper illustrates the development of the analytical framework and explains the conceptual meaning of the mathematical relations by taking a simple and idealised “open-book” catchment as a case study. It is shown how the components of the derived equations explicitly quantify the relative importance of processes and the space–time interactions among them during flood events. In particular, the components added to the original framework of Woods and Sivapalan (1999), which account for storm movement and hillslope routing variability in space, are demonstrated to be important and in some cases decisive in combining to bring about the flood response. The proposed analytical framework is not a predictive model but a tool to understand the magnitude of the components that contribute to runoff response, similar to the components of the St. Venant equations in fluid dynamics.