Download Hydroclimatic extremes and the exact distribution of

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.