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 (P_maxp%). 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 P_maxp% 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.

The aim of this study was to detect trends in maximum annual daily precipitation in the Upper Vistula Basin. We analyzed data from 51 weather stations between 1971 and 2014. Then we used the Mann–Kendall test to detect monotonical trends of the precipitation for three significance levels: 1, 5, and 10%. Our analysis of weather conditions helped us describe the mechanism behind the formation of maximum annual daily precipitation. To analyze precipitation seasonality, we also used Colwell indices. Our study identified a significant trend of the highest daily precipitation for the assumed significance levels (0.01, 0.05, 0.1) for 22% of the investigated weather stations at different elevations. The significant trends found were positive and an increase in precipitation is expected. From 1971 to 2014, the maximum daily total precipitation most often occurred in the summer half-year, i.e., from May until September. These months included a total of 88% of days with the highest daily precipitation. The predictability index for the highest total precipitation within the area was high and exceeded 5%. It was markedly affected by the coefficient of constancy (C) and to a lesser degree by the seasonality index (M). Our analysis demonstrated a convergence of the Colwell indices and frequency of cyclonic situation and, therefore, confirmed their usability in the analysis of precipitation seasonality.

The paper addresses the frequency, amount and geographic coverage of anomalously heavy precipitation in southern Poland in relation to atmospheric circulation at the monthly and seasonal scales between 1881 and 2010. The Carpathian Mountains and their foreland were selected for the study as an area known for its high precipitation totals and frequent precipitation-triggered natural disasters, such as floods and landslides. Records from 18 stations were used to identify anomalously heavy precipitation (AHP) defined for the purposes of the study, as the top quartile (Q _{75 %}) plus 1.5 times the interquartile gap (H) of the precipitation total (P ≥ Q _{75 %} + 1.5H). The study found that most cases of AHP were recorded at one single station each. This suggests that, in addition, to the influence of circulation, local factors also play a major role in the formation of particularly heavy precipitation. The greatest absolute anomalously high precipitation totals were recorded in two disparate parts of the study area: (i) its western part exposed to wet air masses from over the Atlantic Ocean brought in by the dominant western circulation in the temperate zone and (ii) elevated parts of its south-eastern part. Two months with AHP (AHP months) occurred over the entire area (18 stations) in May 1940 and 2010. The latter case had both the greatest absolute totals (over 500 mm) and relative totals defined as their ratio to the long-term average (500 %), and it triggered a catastrophic flood in the Upper Vistula basin.