Fractal theory and the estimation of extreme floods

Abstract

It was in the context of floods that Hurst introduced the concept of the rescaled range. This was subsequently extended by Mandelbrot and his colleagues to concepts of fractional Gaussian noises and fractional Brownian walks. These studies introduced the controversial possibility that the extremes of floods and droughts could be fractal. An extensive study of flood gauge records at 1200 stations in the United States indicates a good correlation with fractal statistics. It is convenient to introduce the parameter F which is the ratio of the 10 yr flood to the 1-yr flood; for fractal statistics F is also the ratio of the 100 year flood to the 10 yr flood and the ratio of the 1000 yr flood to the 100 yr flood. It is found that the parameter F has strong regional variations associated with climate. -from Author