The applicability of power-law frequency statistics to floods

Many natural hazards satisfy power-law (fractal) frequency-size statistics to a good approximation for medium and large events. Examples include earthquakes, volcanic eruptions, asteroid impacts, landslides, and forest fires. A major question is whether this is also true for floods. A number of authors have argued in favor of the applicability of power-law statistics to floods. We discuss these arguments and consider a number of examples, using both instrumental records and paleoflood studies. In our analyses we consider both annual and partial-duration flood series. We argue that use of annual floods for statistical considerations strongly biases the flood-frequency estimates, as in some years, the annual flood will be much smaller than a number of ‘statistically independent’ floods (partial-duration floods) in other years. We examine six USGS hydrologic stations with drainage areas from 41 to 95,300 km2, representing very different climatic regions and hydrologic conditions, and with periods of records ranging from 74 to 110 water years. Excellent power-law fits to each partial-duration series are found taking Q∼Tα, with Q the discharge associated with the recurrence interval T, and the power-law exponent α ranging from 0.27 to 0.90. We also consider paleoflood estimates for Axehandle Alcove on the Colorado River and Bonza Alcove on the Paria River, and find that that power-law extrapolations based on instrumental partial-duration series for stations in each of these two areas is within a half order of magnitude when compared to their respective paleoflood estimates. Finally, we consider an alternative approach to extreme streamflows that has been proposed, examining the cumulative probability distribution of instrumental daily mean streamflows. We show that this distribution is in good agreement with the power-law correlation found using the partial-duration series.