ANALYSES OF HYDROLOGICAL DATA BY USING FAT-TAIL DISTRIBUTION AND FRACTAL THEORY

Abstract

 We tried to model hydrological data by using fat-tail distribution and fractal theory. First, we confirmed that annual maximum 1-hour precipitation is not fractal but white noises by spectrum analysys. We can generate the data by random numbers whose distribution is GEV or the Gumbel distribution. Lévy distribution’s tail is too fat. Secondly, we tried to model time series data of water quality by using fractal model like fBm or fLm. We found that not only Lévy distribution but also GEV and the Gumbel distribution are appropriate for distribution by which random numbers are generated when the spectral synthesis method is applied as fraclatl-generationg method.