Potential distribution of extreme rainfall in the Basque Country

The Potential Distribution model can describe at once the probability distribution and temporal distribution of rainfall. It also allows the incorporation of the dependence of the probability with the number of independent stations. This paper analyzes the probability distribution and temporal distribution of extreme rainfall in the Autonomous Community of the Basque Country using daily data from 43 stations, with an average of 31 active stations between 1961 and 2000. It was found that this model provided a good adjustment (NMAE = 1.4%) for rainfall over 115 mm in 24 h, and is consistent with other analyses of extremes. Finally, the article proposes a mathematical relationship to estimate the maximum expected rainfall for a return period equal to or more than 10 years, with a duration longer than 1 minute, and for a given set of independent stations. This relationship depends on two exponents, one for the return period (m = 0.23 ± 0.02) and another for the duration (n = 0.63 ± 0.06). In addition, it also depends on a scale factor, which takes values between Po = 42 ± 2 mm to the south of the region and Po = 71 ± 5 mm to the north, with an average value for the Basque Country equal to 58 ± 2 mm.