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Hydroclimatic extremes and the exact distribution of maximum annual daily precipitation Carlo De Michele The daily amount of precipitation is the variable, historically most sampled, and investigated in the hydrologic Literature. It has been considered as the reference variable to quantify the input to the hydrologic cycle. Its maximum annual value is used to represent high values, or extremes. In hydrology, this variable has a key role in the design of several hydraulic structures through the determination of the quantile with a fixed level of probability, or return period. The calculation of the quantile of maximum annual daily precipitation requires the statistical analysis of data sample, and the determination of the probability distribution. In Literature, the asymptotic model, i.e. the Generalized Extreme Value (GEV) distribution, has been adopted as the principal candidate to describe the behavior of maximum annual daily precipitation. Even if, this distribution represents the best pragmatic choice, it is useful only within the range of data, providing inaccuracies when it is adopted to calculate the quantile for high return periods. Here, 1) it is derived the exact distribution of maximum annual daily precipitation, as alternative to the asymptotic distribution, 2) it is tested its capability of representing data extensively, with respect of a global database GHCN (including over 75000 stations in 180 countries and territories), 3) it is compared the performance of the exact distribution against the asymptotic model GEV.