M. Nezi, Multivariate statistical analysis of extreme rainfall and runoff in a sample of 400 river basins over USA from database MOPEX, Diploma thesis, 103 pages, Department of Water Resources and Environmental Engineering – National Technical University of Athens, Athens, October 2018.
The analysis of extreme rainfalls requires a multidimensional approach with a high level of uncertainty. The most commonly used probabilistic distribution for describing the annual maxima of daily rainfall is the Generalized Extreme Value (GEV) distribution. Based on the extreme value theory, the GEV distribution combines the three limiting-type family distribution (a) Gumbel Type I, (b) Fréchet Type II and (c) Weibull Type III. The regime of the annual maximum rainfall variable is affected by myriad of factors. In this diploma thesis we investigate the influence of soil moisture, as it is expressed by the observed accumulative daily rainfall before the extreme rainfall and streamflow scenarios occurred. This analysis is performed in 400 catchments in USA and uses the Generalized Extreme Value distribution fitted by the methods of L-moments, in an attempt to calculate the statistical parameters of the extreme annual rainfall, cumulative rainfall and extreme annual streamflow time series. In this statistical study, the temporal range of previous daily rainfall data is initially estimated in various time steps, starting from five until thirty days before the extreme observation. The analysis focuses on the correlation coefficient between the time series and which of the accumulated rainfall has the strongest statistical impact upon the maximum annual rainfall and streamflow time series. Additionally, by using the L-moment method, the study extracts the generalized extreme distribution for these time series, aiming to better understand the statistical correlation between them and their statistical behavior. We focus on the behavior of the shape parameter of the GEV distribution for detecting which of the previous extreme value distributions fits better to the specific sample of variables. It seems that our samples are better approached by the Fréchet distribution. In the end, we research the effectiveness of the catchment’s hydroclimatic and geographical characteristics upon the statistical parameters of the GEV distribution and correlation coefficient. By creating spatial probabilistic maps, we observe the vulnerability of the statistical parameters in a more spherical way.