Effects of Excess Rainfall on the Temporal Variability of Observed Peak-Discharge Power Laws

Department of Environmental Engineering, University of Colorado at Boulder, Boulder, Colorado, United States
Advances in Water Resources (Impact Factor: 3.42). 11/2005; 28(11):1240-1253. DOI: 10.1016/j.advwatres.2005.03.014


Few studies have been conducted to determine the empirical relationship between peak discharge and spatial scale within a single river basin. Only one study has determined this empirical relationship during single rainfall–runoff events. The study was conducted on the Goodwin Creek Experimental Watershed (GCEW) in Mississippi and shows that during single events peak discharge Q(A) and drainage area A are correlated as Q(A) = αAθ and that α and θ change between events. These observations are the first of their kind and to understand them from a physical standpoint we examined streamflow and rainfall data from 148 events in the basin.A time series of excess rainfall was estimated for each event in GCEW by assuming that a threshold infiltration rate partitions rainfall into infiltration and runoff. We evaluated this threshold iteratively using conservation of mass as a criterion and found that threshold values are consistent physically with independent measurements of near-surface soil moisture. We then estimated the excess rainfall duration for each event and placed events into groups of different durations. For many groups, data show that α is linearly related to excess rainfall depth and that the event-to-event variability in Q(A) is controlled mainly by variability in α through changes in . The exponent θ appears to be independent of for all groups, but mean values of θ tend to increase as the duration increases from group to group. This later result provides the first observational support for past theoretical results, all of which have been obtained under idealized conditions. Moreover, this result provides an avenue for predicting peak discharges at multiple spatial scales in the basin.

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Available from: Vijay K. Gupta, Aug 25, 2014
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    • "Although Gupta et al . [ 2010 ] showed that the historical flood event of June 2008 that devastated the Iowa River basin in Eastern Iowa ( A % 32 , 400 km 2 ) obeys scaling invariance with drainage area , no study , to the best of our knowledge , has demonstrated whether or not the findings from the 21 km 2 GCEW [ Furey and Gupta , 2005 , 2007 ] hold true in larger watersheds . Apart from demon - strating the existence of scale - invariant peak discharges in a mesoscale river basin at the rainfall - runoff event scale , such a study would help establish the physical connection between the flood scaling parame - ters and rainfall and catchment physical properties that vary from event to event . "
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    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 km2 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=32,400 km2), 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 towards ongoing efforts to provide a framework for flood prediction in ungauged basins (PUB). This article is protected by copyright. All rights reserved.
    Full-text · Article · May 2015 · Water Resources Research
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    • "Although these and other theoretical studies (e.g., [13] [15] [16] [22]) significantly enhanced our understanding, more must be done to definitively link the flood-scaling exponent h and intercept a to basin physical processes that can be either measured or estimated. Furey and Gupta [23] analyzed 148 individual rainfall–runoff events from the 21 km 2 GCEW and showed that both the floodscaling exponent h and the intercept a are dependent on rainfall duration. The latter observation was shown to be a direct consequence of the inverse relationship between rainfall intensity and duration. "
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    ABSTRACT: We have conducted extensive hydrologic simulation experiments in order to investigate how the flood scaling parameters in the power-law relationship Q(A)=αAθQ(A)=αAθ, between peak-discharges resulting from a single rainfall-runoff event Q(A)Q(A) and upstream area AA, change as a function of rainfall, runoff coefficient (CrCr) that we use as a proxy for catchment antecedent moisture state, hillslope overland flow velocity (vhvh), and channel flow velocity (vcvc), all of which are variable in space. We use a physically-based distributed numerical framework that is based on an accurate representation of the drainage network and apply it to the Cedar River basin (A=16,861km2A=16,861km2), which is located in Eastern Iowa, USA. Our work is motivated by seminal empirical studies that show that the flood scaling parameters αα and θθ change from event to event. Uncovering the underlying physical mechanism behind the event-to-event variability of αα and θθ in terms of catchment physical processes and rainfall properties would significantly improve our ability to predict peak-discharge in ungauged basins (PUB). The simulation results demonstrate how both αα and θθ are systematically controlled by the interplay among rainfall duration TT, spatially averaged rainfall intensity E[I]E[I], as well as E[Cr]E[Cr], E[vh]E[vh], and vcvc. Specifically, we found that the value of θθ generally decreases with increasing values of E[I]E[I], E[Cr]E[Cr], and E[vh]E[vh], whereas its value generally increases with increasing TT. Moreover, while αα is primarily controlled by E[I]E[I], it increases with increasing E[Cr]E[Cr] and E[vh]E[vh]. These results highlight the fact that the flood scaling parameters are able to be estimated from the aforementioned catchment rainfall and physical variables, which can be measured either directly or indirectly.
    Full-text · Article · Sep 2014 · Advances in Water Resources
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    • "Peak discharge is a helpful criterion for characterizing flood magnitude and its dependence on watershed area is widely accepted, as the body of literature can attest. One example is the relationship between discharge and catchment area both for single-event peak flow and mean annual peak flow ((Furey and Gupta, 2005; Gupta et al., 1996; Marchi et al., 2010) among others). We consider specific peak discharge, i.e. maximal peak discharge normalized by catchment area (Fig. 7). "
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    ABSTRACT: We propose an extended study of recent flood-triggering storms and resulting hydrological responses for catchments in the Pyrenean foothills up to the Aude region. For hydrometeorological sciences, it appears relevant to characterize flash floods and the storm that triggered them over various temporal and spatial scales. There are very few studies of extreme storm-caused floods in the literature covering the Mediterranean and highlighting, for example, the quickness and seasonality of this natural phenomenon. The present analysis is based on statistics that clarify the dependence between the spatial and temporal distributions of rainfall at catchment scale, catchment morphology and runoff response. Given the specific space and time scales of rainfall cell development, we show that the combined use of radar and a rain gauge network appears pertinent. Rainfall depth and intensity are found to be lower for catchments in the Pyrenean foothills than for the nearby Corbières or Montagne Noire regions. We highlight various hydrological behaviours and show that an increase in initial soil saturation tends to foster quicker catchment flood response times, of around 3 to 10 h. The hydrometeorological data set characterized in this paper constitutes a wealth of information to constrain a physics-based distributed model for regionalization purposes in the case of flash floods. Moreover, the use of diagnostic indices for rainfall distribution over catchment drainage networks highlights a unimodal trend in spatial temporal storm distributions for the entire flood dataset. Finally, it appears that floods in mountainous Pyrenean catchments are generally triggered by rainfall near the catchment outlet, where the topography is lower.
    Full-text · Article · Feb 2014 · Atmospheric Research
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