Probabilistic model of maximum precipitation depths for Krakow (southern Poland, 1886-2002)

This study was designed to empirically determine what relationships existed between three characteristics of precipitation: maximum depth, duration, and probability of exceedance. Annual maximum series for intervals of between one and 120 h were identified using the 1886-2002 pluviographic record from Krakow. The Gumbel distribution was selected from a group of four of the most popular theoretical maximum value distributions and identified as the optimum solution. Its parameters were determined. Confidence intervals for quantiles were obtained using the bootstrap method. Formulae were derived for the relationships between the Gumbel distribution parameters, i.e., the alpha location and beta scale, depending on precipitation duration. These take the form of a polynomial of the second degree. The model developed was subjected to a two-step validation with a positive result.