Flood Scaling And Network Geometry - Exploring The Role Of The Width Function
Anderson, Scott 1 ; Pitlick, John 2
1 University of Colorado at Boulder, Geography
2 University of Colorado at Boulder, Geography
Flooding and flood processes play an integral role in the geomorphological and ecological systems of landscapes, and can have large impacts on human developments. Changing climate has rendered many of the conventional methods of flood analysis, based on statistical analysis of historical records, less viable, and has prompted an increased interest in the specific processes involved in flood generation. With this motivation, flood scaling has become a point of interest. Floods have been shown to scale with basin area according to a power law, with a scaling exponents ranging between ~0.4-1 (Gupta and Dawdy, 1995). The specific scaling exponent varies from basin to basin as well as from event to event, and is presumably the integration of the precipitation event, geology, vegetation, network geometry, and antecedent conditions. The width function has been proposed as a means of exploring the impact of network geometry on flood scaling. The width function is defined as the number of stream links a given distance from the basin outlet. If one assumes spatially uniform precipitation and uniform time spent on hillslopes, the width function would define the flood hydrograph. While these assumptions are clearly not generally valid, it explains the interest in the metric.
This study looks at four medium sized basins (1,000-10,000 sq. mi.) ranging the climatic scale of snowfall-dominated to mixed precipitation to rainfall-dominated regimes. For each basin, annual flood series were pulled for all USGS gages with at least three years of record. For each gage, flood size for 11 return intervals ranging from 1.01 to 200 years was calculated using the methodology set out in USGS bulletin 17b. These gage locations were used to defined sub-basins, and the width function of each sub-basin was derived in ArcGIS. Power law relationships were fit for floods of various return intervals as well as the peak of the width function. Initial results show that all floods and the width function peaks are well approximated by power laws (R2 ~0.8-0.9), with scaling exponents falling with in the expected 0.4-1 range. In one snow-melt dominated basin, there is a fairly consistent relationship between the peak of the width function and flood size, such that plotting the two against each other after normalizing both the mean of the population yields a 1:1 relationship. However, this feature is not readily apparent in other basins. A full analysis of results awaits.
Gupta, V. K., and D. Dawdy (1995), Physical interpretations of regional variations in the scaling exponents of flood quantiles, Hydrol. Processes, 9(3–4), 347–361, doi:10.1002/hyp.3360090309.