Role of rainfall variability in the statistical structure of peak flows

This thesis examines the role of rainfall variability and uncertainties on the spatial scaling structure of peak flows using the Whitewater River basin in Kansas, and Iowa River basin in Iowa as illustrations. We illustrate why considering individual hydrographs at the outlet of a basin can lead to misleading interpretations of the effects of rainfall variability. The variability of rainfall is characterized in terms of storm intensity, duration, advection velocity, zero-rain intermittency, variance and spatial correlation structure. We begin with the simple scenario of a basin receiving spatially uniform rainfall of varying intensities and durations, and advection velocities. We then use a realistic space-time rainfall field obtained from a popular rainfall model that can reproduce desired storm variability and spatial structure. We employ a recent formulation of flow velocity for a network of channels and calculate peak flow scaling exponents, which are then compared to the scaling exponent of the channel network width function maxima. The study then investigates the role of hillslope characteristics on the peak flow scaling structure. The basin response at the smaller scales is driven by the rainfall intensities (and spatial variability), while the larger scale response is dominated by the rainfall volume as the river network aggregates the variability at the smaller scales. The results obtained from simulation scenarios can be used to make rigorous interpretations of the peak flow scaling structure obtained from actual space-time model, and actual radar-rainfall events measured by the NEXRAD weather radar network.

An ensemble of probable rainfall fields conditioned on the given radar-rainfall field is then generated using a radar-rainfall error model and probable rainfall generator. The statistical structure of ensemble fields is then compared with that of given radar-rainfall field to quantify the impact of radar-rainfall errors on 1) spatial characterization of the rainfall events and 2) scaling structure of the peak flows. The effect of radar-rainfall errors is to introduce spurious correlations in the radar-rainfall fields, particularly at the smaller scales. However, preliminary results indicated that the radar-rainfall errors do not significantly affect the peak flow scaling exponents.