Rainfall-runoff modelling using a spatially distributed electrical circuit analogue

Abstract

The assessment and prevention of floods require appropriate forecasting and knowledge of the related hydrological processes. Due to the similar form of the governing equations, flood hydrograph shows a clear analytical and mathematical analogy with electrical circuits. In this paper, a spatially distributed hydrological model is developed which is analogue to a network of electrical resistance–capacitance with five circuits for describing the hydrological processes leading to floods. The spatially distributed hydrological model simulates rainfall, potential evapotranspiration, canopy interception, surface storage and soil storage. The parameters for analogical modelling were derived from translation of the physical catchment characteristics. A two-parameter Weibull equation aggregates the response functions of each pixel and calculates the hydrograph of the catchment. We applied the model to the ‘Open-Book’ or ‘tilted V-catchment’ theoretical benchmark problem, as well as to four hourly flood events and simulation of daily discharges. For the last two cases, data were used from the mountainous catchment of upper Tarqui in the Andes of Ecuador. Comparison of single versus multiple circuit designs for the benchmark problem indicates that the multiple circuit analogy provides a result similar to other hydrological models. The results further illustrate the usefulness of the methodology for flood modelling and how it can simplify the simulation for ungauged basins of temporal and spatial variations of influencing hydrological processes.