Estimating Maximum Daily Precipitation in the Upper Vistula Basin, Poland

final version published on line: https://www.mdpi.com/2073-4433/10/2/43

Abstract: The aim of this study was to determine the best probability distributions for calculating the
maximum annual daily precipitation with the specific probability of exceedance (Pmaxp%). The novelty
of this study lies in using the peak-weighted root mean square error (PWRMSE), the root mean
square error (RMSE), and the coefficient of determination (R2) for assessing the fit of empirical and
theoretical distributions. The input data included maximum daily precipitation records collected in
the years 1971–2014 at 51 rainfall stations from the Upper Vistula Basin, Southern Poland. The value
of Pmaxp% was determined based on the following probability distributions of random variables:
Pearson’s type III (PIII), Weibull’s (W), log-normal, generalized extreme value (GEV), and Gumbel’s
(G). Our outcomes showed a lack of significant trends in the observation series of the investigated
random variables for a majority of the rainfall stations in the Upper Vistula Basin. We found that
the peak-weighted root mean square error (PWRMSE) method, a commonly used metric for quality
assessment of rainfall-runoff models, is useful for identifying the statistical distributions of the best
fit. In fact, our findings demonstrated the consistency of this approach with the RMSE goodness-of-fit
metrics. We also identified the GEV distribution as recommended for calculating the maximum daily
precipitation with the specific probability of exceedance in the catchments of the Upper Vistula Basin.