Temporal scales of rainfall–runoff processes and spatial scaling of flood peaks: space–time connection through catchment water balance

Abstract

This paper investigates the scaling behaviour of annual flood peaks, exhibited through what is taken to be a power law relationship between mean annual flood and catchment size, E[ Q p]= cA θ . We also study the dependence on catchment size of the coefficient of variation of annual flood peaks, CV[ Q p]. We attempt to interpret these relationships in terms of the interactions between the land surface and the atmosphere – in particular, the effects of temporal variability of rainfall (within-storm patterns, multiple storms and seasonality) and runoff processes (overland flow, subsurface flow and channel flow). The spatial scaling of flood peaks, as expressed by the coefficients c, θ and CV, has been analysed based on, initially, simulated runoff fields produced by a simple linear rainfall–runoff model for hypothetical catchments, and later by a more realistic, distributed model for an actual catchment in the semi-arid, south-west of Western Australia. It is found that the main controls on c and θ are runoff processes, soil depth and mean annual rainfall, with additional controls on c including temporal rainfall variability, the underlying water balance, and the spatial variability of rainfall. Runoff generation at catchment scales can be specified as being fast or slow according to a relative catchment travel time. The scaling exponent θ is high and almost constant with A for slow catchments, where deep soils combined with low annual rainfall leads to domination by subsurface flow. Conversely, θ is lower in fast catchments, where shallow soils combined with high annual rainfall leads to dominance by surface runoff processes with relatively short travel times. The interaction between within-storm patterns and fast runoff processes is the important control on c, clearly shown in small catchments, while multiple storms and seasonality are crucial in large catchments. The presence of multiple runoff processes with a broad spectrum of time scales leads to an increase of CV[ Q p], as does the introduction of spatial variability of rainfall.