Linking space–time variability of river runoff and rainfall fields: a dynamic approach

Statistical self-similarity in the spatial and temporal variability of rainfall, river networks, and runoff processes has been observed in many empirical studies. To theoretically investigate the relationships between the various time and space scales of variability in rainfall and runoff process we propose a simplified, yet physically based model of a catchment–rainfall interaction. The channel network is presented as a random binary tree, having topological and hydraulic geometry properties typically observed in real river networks. The continuous rainfall model consists of individual storms separated by dry periods. Each given storm is disaggregated in space and time using the random cascade model. The flow routing is modelled by the network of topologically connected nonlinear reservoirs, each representing a link in the channel network. Running the model for many years of synthetic rainfall time series and a continuous water balance model we generate an output, in the form of continuous time series of water discharge in all links in the channel network. The main subject of study is the annual peak flow as a function of catchment area and various characteristics of rainfall. The model enables us to identify different physical processes responsible for the empirically observed scaling properties of peak flows.