Analyzing the effects of excess rainfall properties on the scaling structure of peak discharges: Insights from a mesoscale river basin

Abstract

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.

Classical and generalized Horton laws for peak flows in rainfall-runoff events

“…Due primarily to the spatial and temporal variability of rainfall, defining a rainfall-runoff event for a mesoscale basin such as the Iowa River basin is not a straightforward task. Ayalew et al (2015) analyzed streamflow data from the basin for the 12-year period from 2002 to 2013. They showed that a scale invariant peak-discharge spatial organization emerges when the entire basin gets a runoff generating rainfall event at some point during a time window that is equivalent to the basin's concentration time, which is the time required for a parcel of water to travel from the most remote hillslope in the basin to the outlet.…”

“…The concentration time is about 15 days for the Iowa River basin. The criteria Ayalew et al (2015) used to define peak discharge events are briefly summarized as follows. First, they determined whether a single peaked hydrograph is observed at the outlet and noted the time when the peak discharge occurred.…”

“…Figure 2 illustrates a RF-RO event during which the entire basin received rainfall at some point during the 15-day travel time window. The interested reader may refer to Ayalew et al (2015) for a detailed discussion of RF-RO event selection and how certain properties of excess rainfall control the peak discharge scaling structure.…”

“…Our derivation uses the classical and generalized Horton laws for drainage area that are reviewed in Sec. III and a scaling relationship between peak flows and drainage area that has been observed in the Iowa River basin (Ayalew et al, 2015;Gupta et al, 2010). In Sec.…”

“…Let j ¼ 1; 2; :::; n denote a gauge and its sub-basin and i ¼ 1, 2,… denote a rainfall-runoff event. Data show that peak-discharges at the event time scale obey a scaling relationship that was first observed in the small 21 km 2 GCEW, Mississippi (Ogden and Dawdy 2003) and later in the medium-sized Iowa River basin (Ayalew et al, 2015;Gupta et al, 2010). An ordinary linear regression (OLR) model can characterize this relationship, as Furey et al (submitted) showed, lnðQ i;j Þ ¼ aðiÞ þ bðiÞlnðA j Þ þ e i;j :…”