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A scale-invariant approach to flood-frequency analysis

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Abstract

In order to study historical flood-frequency records we plot the log of the number of floods on a river per unit time in which the peak discharge exceeds a specified value against the log of that value. For ten benchmark stations we find good correlations with scale-invariant (fractal) statistics. We suggest that the underlying physical processes associated with the generation of floods are sufficiently scale invariant over time scales from one to one hundred years that they provide a rational basis for the application of scale-invariant statistics. Our results fall within the range of flood-frequency estimates made by other statistical techniques. We propose that the ratio of the ten-year peak discharge to the one-year peak discharge β is a quantitative measure of flood potential. With scale invariance β is also the ratio of the one-hundred year flood to the ten-year flood. We find that the values of β for ten stations on rivers throughout the country range from 2.04 to 8.11 and find strong regional variations that can be correlated in terms of climate. Our results are consistent with the observed fractal statistics in sedimentary sections. We have also carried out R/S analyses for the ten stations and have obtained values of the Hurst exponent. We find that the Hurst exponent cannot be used for flood-frequency forecasting.

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Authors and Affiliations

  1. Dept. of Geological Sciences, Cornell University, 14853, Ithaca, NY

    D. L. Turcotte & L. Greene

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  1. D. L. Turcotte
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  2. L. Greene
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Turcotte, D.L., Greene, L. A scale-invariant approach to flood-frequency analysis. Stochastic Hydrol Hydraul 7, 33–40 (1993). https://doi.org/10.1007/BF01581565

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