The process of propagation from meteorological to hydrological drought is studied using the Vistula basin in Poland (193,960 km²) as a case study. The study aims to set a background for the analysis of processes influencing drought propagation in the basin, including the availability of data on hydro-meteorological factors, groundwater, and major human activities that might influence the water cycle in the region. A recent history of drought events in the basin is derived based on a statistical analysis of flow measured at nine gauging stations located along the river, starting from upstream downwards in the 1951–2018 period. The study is enhanced by the analysis of the temporal and spatial variability of a number of drought indices. As a result, the factors affecting temporal and spatial variability of drought—with particular emphasis on the interaction between the variability induced by natural processes and human interaction—are identified. The drought dynamics is studied by analysis of the relationships between meteorological and hydrological drought indices. The results indicate that the Vistula River basin has been influenced in its upstream part mainly by the mining industry, and the middle and downstream parts are additionally affected by industry and agriculture.

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.

If the maximum annual peak flow series are a mixture of summer and winter flows, a seasonal approach to flood frequency analysis is necessary. While considering seasonal maxima as mutually independent events, the annual maxima distribution is defined as the product of seasonal distributions. However, if the independency assumption does not hold, a bivariate approach with dependent margins should be applied, i.e. the copula approach. The impact of dependency on design quantiles is investigated here in the context of the Fréchet-Hoeffding inequality defining copula bounds and the definition of dependency. The results of the two approaches are compared using six catchments in the San River basin, where in four cases the dependency of seasonal maxima has been identified as positive significant and no strong dominance of any one season is observed. The product model leads to higher estimates of design quantiles than do models where the dependency is taken into account and, therefore, is safe.

The flow regime in the River Vistula is influenced by climatic and geographical factors and human intervention. In this study, we focus on an analysis of flow and precipitation variability over time and space following the course of the River Vistula. Multi-purpose statistical analyses of a number of runoff and precipitation characteristics were performed to present a general overview of the temporal and spatial changes. Since the important feature of the hydrological regime of Polish rivers is the seasonality of runoff associated with the occurrence of cold (winter) and warm (summer) seasons within a hydrological year, a seasonal approach is applied to describe specific seasonal features that can be masked when using annual data. In general, the results confirm popular impressions about changes in winter season runoff characteristics, i.e., significantly decreasing daily maxima, increasing daily minima and a decrease in concentration, and so a bigger uniformity of winter daily flows. An interesting behaviour of minimum flows in the summer has been revealed, which is contrary to social perceptions and the alarming changes taking place in the other parts of the world. Additionally, precipitation indexes related to the formation of droughts show no trends, e.g., the mean value of the maximum dry spell length.

A classical approach to flood frequency modeling is based on the choice of the probability distribution to best describe the analyzed series of annual or seasonal maximum flows. In the paper, we discuss the two main problems, the uncertainty and instability of the upper quantile estimates, which serve as the design values. Ways to mitigate the above-mentioned problems are proposed and illustrated by seasonal maximum flows at the Proszówki gauging station on the Raba River. The inverse Gaussian and generalized exponential distributions, which are not commonly used for flood frequency modeling, were found to be suitable for Polish data of seasonal peak flows. At the same time, the heavy tailed distributions, which are currently recommended for extreme hydrological phenomena modeling, were found to be inappropriate. Applying the classical approach of selecting the best fitted model to the peak flows data, significant shifts in the upper quantile estimates were often observed when a new observation was added to the data series. The method of aggregation, proposed by the authors, mitigates this problem. Elimination of distributions that are poorly fitted to the data series increases the stability of the upper quantile estimates over time.

The Flood Frequency Analysis (FFA) concentrates on probability distribution of peak flows of flood hydrographs. However, examination of floods that haunted and devastated the large parts of Poland lead us to revision of the views on the assessment of flood risk of Polish rivers. It turned out that flooding is caused not only by the overflow of the levee crest but also due to the prolonged exposure to high water on levees structure causing dangerous leaks and breaches that threaten their total destruction. This is because the levees are weakened by long-lasting water pressure and as a matter of fact their damage usually occurs after the culmination has passed the affected location. The probability of inundation is the total of probabilities of exceeding embankment crest by flood peak and the probability of washout of levees. Therefore, in addition to the maximum flow one should also consider the duration of high waters in a river channel. In the paper the new two-component model of flood dynamics: "Duration of high waters–Discharge Threshold–Probability of non-exceedance" (DqF), with the methodology of its parameter estimation was proposed as a completion to the classical FFA methods. Such a model can estimate the duration of stages (flows) of an assumed magnitude with a given probability of exceedance. The model combined with the technical evaluation of the probability of levee breaches due to the duration (d) of flow above alarm stage gives the annual probability of inundation caused by the embankment breaking. The results of theoretical investigation were illustrated by a practical example of the model implementation to the series of daily flow of the Vistula River at Szczucin. Regardless of promising results, the method of risk assessment due to prolonged exposure of levees to high water is still in its infancy despite its great cognitive potential and practical importance. Therefore, we would like to point out the need for and usefulness of the DqF model as complementary to the analysis of the flood peak flows, as in classical FFA. The presented two-component model combined with the routine flood frequency model constitutes a new direction in FFA for embanked rivers