Dissecting the effect of rainfall variability on the statistical structure of peak flows

This study examines the role of rainfall variability on the spatial scaling structure of peak flows using the Whitewater River basin in Kansas as an illustration. Specifically, we investigate the effect of rainfall on the scatter, the scale break and the power law (peak flows vs. upstream areas) regression exponent. We illustrate why considering individual hydrographs at the outlet of a basin can lead to misleading interpretations of the effects of rainfall variability. We begin with the simple scenario of a basin receiving spatially uniform rainfall of varying intensities and durations and subsequently investigate the role of storm advection velocity, storm variability characterized by variance, spatial correlation and intermittency. Finally, we use a realistic space–time rainfall field obtained from a popular rainfall model that combines the aforementioned features. For each of these scenarios, we employ a recent formulation of flow velocity for a network of channels, assume idealized conditions of runoff generation and flow dynamics and calculate peak flow scaling exponents, which are then compared to the scaling exponent of the width function maxima. Our results show that the peak flow scaling exponent is always larger than the width function scaling exponent. The simulation scenarios are used to identify the smaller scale basins, whose response is dominated by the rainfall variability and the larger scale basins, which are driven by rainfall volume, river network aggregation and flow dynamics. The rainfall variability has a greater impact on peak flows at smaller scales. The effect of rainfall variability is reduced for larger scale basins as the river network aggregates and smoothes out the storm variability. The results obtained from simple scenarios are used to make rigorous interpretations of the peak flow scaling structure that is obtained from rainfall generated with the space–time rainfall model and realistic rainfall fields derived from NEXRAD radar data.