Scaling Properties of Flood Peaks

The scaling behavior of flood peak distributions is examined using a statistical model of the spatio-temporal distribution of rainfall and a hydrological model that describes the transformation of rainfall to discharge within a drainage network. Of particular interest is the empirical observation made by a number of investigators that the coefficient of variation (CV) of annual flood peaks for a region increases with drainage area up to drainage areas of approximately 100 km², and decreases with drainage area for larger drainage basins. This observation is neither consistent with simple scaling models, in which the coefficient of variation does not vary with drainage area, nor multiscaling models, in which the coefficient of variation decreases monotonically with drainage area. Model analyses illustrate that knowledge of the spatial and temporal organization of the rainfall, together with the details of the network structure of the drainage basin, is sufficient information with which to explain the observed behavior of sample CV. The interaction between the temporal variability of rainfall, relative to basin size, and the network structure is shown to be of particular importance.