Key theoretical and empirical results from the past two decades have established that peak discharges resulting from a single rainfall-runoff event in a nested watershed exhibit a power law, or scaling, relation to drainage area and that the parameters of the power law relation, henceforth referred to as the flood scaling exponent and intercept, change from event to event. To date, only two studies have been conducted using empirical data, both using data from the 21 km 2 Goodwin Creek Experimental Watershed that is located in Mississippi, in an effort to uncover the physical processes that control the event-to-event variability of the flood scaling parameters. Our study expands the analysis to the mesoscale Iowa River basin (A 5 32,400 km 2 ), which is located in eastern Iowa, and provides additional insights into the physical processes that control the flood scaling parameters. Using 51 rainfall-runoff events that we identified over the 12 year period since 2002, we show how the duration and depth of excess rainfall, which is the portion of rainfall that contributes to direct runoff, control the flood scaling exponent and intercept. Moreover, using a diagnostic simulation study that is guided by evidence found in empirical data, we show that the temporal structure of excess rainfall has a significant effect on the scaling structure of peak discharges. These insights will contribute toward ongoing efforts to provide a framework for flood prediction in ungauged basins.
The discovery of the Horton laws for hydrologic variables has greatly lagged behind geomorphology, which began with Robert Horton in 1945. We define the classical and the generalized Horton laws for peak flows in rainfall-runoff events, which link self-similarity in network geomorphology with river basin hydrology. Both the Horton laws are tested in the Iowa River basin in eastern Iowa that drains an area of approximately 32 400 km(2) before it joins the Mississippi River. The US Geological Survey continuously monitors the basin through 34 stream gauging stations. We select 51 rainfall-runoff events for carrying out the tests. Our findings support the existence of the classical and the generalized Horton laws for peak flows, which may be considered as a new hydrologic discovery. Three different methods are illustrated for estimating the Horton peak-flow ratio due to small sample size issues in peak flow data. We illustrate an application of the Horton laws for diagnosing parameterizations in a physical rainfall-runoff model. The ideas and developments presented here offer exciting new directions for hydrologic research and education.
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