Flood frequency analysis (FFA) entails the estimation of the upper tail of a probability density function (PDF) of annual peak flows obtained from either the annual maximum series or partial duration series. In hydrological practice, the properties of various methods of upper quantiles estimation are identified with the case of known population distribution function. In reality, the assumed hypothetical model differs from the true one and one cannot assess the magnitude of error caused by model misspecification in respect to any estimated statistics. The opinion about the accuracy of the methods of upper quantiles estimation formed from the case of known population distribution function is upheld. The above-mentioned issue is the subject of the paper. The accuracy of large quantile assessments obtained from the four estimation methods is compared to two-parameter log-normal and log-Gumbel distributions and their three-parameter counterparts, i.e., three-parameter log-normal and GEV distributions. The cases of true and false hypothetical models are considered. The accuracy of flood quantile estimates depends on the sample size, the distribution type (both true and hypothetical), and strongly depends on the estimation method. In particular, the maximum likelihood method loses its advantageous properties in case of model misspecification.

The classical approach to flood frequency analysis (FFA) may result in significant jumps in the estimates of upper quantiles along with the lengthening series of measurements. Our proposal is a multi-model approach, also called the aggregation technique, which has turned out to be an effective method for the modeling of maximum flows, in large part eliminating the disadvantages of traditional methods. In this article, we present a probability mixture model relying on the aggregation the probabilities of non-exceedance of a constant flow value from the candidate distributions; and we compare it with the previously presented model of quantile mixture, which consists in aggregating the quantiles of the same order from individual models. Here, we defined an asymptotic standard error of design quantiles for both statistical models in two versions: without the bias of quantiles from candidate distributions with respect to aggregated quantiles and with taking it into account. The simulation experiment indicates that the latter version is more accurate and allows for reducing the quantile bias with respect to the unknown population quantile. For the case study, the 0.99 quantiles are determined for both variants of aggregation along with the assessment of its accuracy. The differences between the two proposed aggregation methods are discussed.

Many distributions have been used in flood frequency analysis (FFA) for fitting the flood extremes data. However, as shown in the paper, the scatter of Polish data plotted on the moment ratio diagram shows that there is still room for a new model. In the paper, we study the usefulness of the generalized exponential (GE) distribution in flood frequency analysis for Polish Rivers. We investigate the fit of GE distribution to the Polish data of the maximum flows in comparison with the inverse Gaussian (IG) distribution, which in our previous studies showed the best fitting among several models commonly used in FFA. Since the use of a discrimination procedure without the knowledge of its performance for the considered probability density functions may lead to erroneous conclusions, we compare the probability of correct selection for the GE and IG distributions along with the analysis of the asymptotic model error in respect to the upper quantile values. As an application, both GE and IG distributions are alternatively assumed for describing the annual peak flows for several gauging stations of Polish Rivers. To find the best fitting model, four discrimination procedures are used. In turn, they are based on the maximized logarithm of the likelihood function (K procedure), on the density function of the scale transformation maximal invariant (QK procedure), on the Kolmogorov-Smirnov statistics (KS procedure) and the fourth procedure based on the differences between the ML estimate of 1% quantile and its value assessed by the method of moments and linear moments, in sequence (R procedure). Due to the uncertainty of choosing the best model, the method of aggregation is applied to estimate of the maximum flow quantiles.

The ice phenomena are an inherent component of rivers in temperate, continental, and polar climate zones. Evident progress in global warming leads to a decrease in snow cover on land and ice phenomena in water bodies, disrupting the stability of the hydrological cycle and aquatic ecosystems. Although common observations indicate the disappearance of ice phenomena in rivers over recent decades, detailed quantitative research is lacking in many regions, especially in the temperate zone. In this paper, ice phenomena were analyzed on the rivers of southern Poland, located in the upland and mountain areas of the country, as no such studies have been conducted so far. The temporal changes in the annual number of days with ice (NDI) phenomena were studied in locations where ice phenomena were observed every year for at least 30 years between 1951 and 2021. Using straightforward but commonly accepted procedures, such as the Mann-Kendall test, statistically significant decreasing trends in the annual NDI were revealed for the majority of gauging stations. The Theil-Sen (TS) slope mean values were -1.66 (ranging from -3.72 to -0.56), -1.41 (from -3.22 to -0.29), and -1.33 (from -2.85 to -0.29) for the datasets representing the periods 1992–2020, 1987–2020, and 1982–2020, respectively. The results for the annual NDI were additionally presented within the context of meteorological characteristics such as annual and winter (Nov-Apr) air temperature, precipitation, and water temperature. Correlation and regression analyses revealed that the main factor triggering the decrease in NDI is the increase in the average winter air temperature. An increase in temperature by 1°C results in a decrease in NDI by up to twenty days. If these negative trends continue, ice phenomena may disappear completely from southern Polish rivers within few decades.

The Upper Vistula Basin is a flood-prone region in the summer season (May–October) due to intensive rainfall. From the point of view of water management, it is particularly important to assess the variability in this main factor of flood risk, as well as to establish the depth–duration–frequency (DDF) relationship for maximum precipitation, this having not yet been derived for the region. The analysis of a 68-year (1951–2018) data series of summer maximum precipitation collected by 11 meteorological stations showed the series’ stationarity, which supports the conclusion that there is no increase in the risk of rainfall floods due to the intensification of extreme precipitation. A new approach is proposed for the determination of the DDF relationship, where the best-fitted distribution for each station is selected from among the set of candidate distributions, instead of adopting one fixed distribution for all stations. This approach increases the accuracy of the DDF relationships for individual stations as compared to the commonly used approach. In particular, the traditionally used Gumbel distribution turns out to be not well fitted to the investigated data series, and the advantage of the recently popular GEV distribution is not significant.