Risk management has reduced vulnerability to floods and droughts globally^1,2, yet their impacts are still increasing³. An improved understanding of the causes of changing impacts is therefore needed, but has been hampered by a lack of empirical data^4,5. On the basis of a global dataset of 45 pairs of events that occurred within the same area, we show that risk management generally reduces the impacts of floods and droughts but faces difficulties in reducing the impacts of unprecedented events of a magnitude not previously experienced. If the second event was much more hazardous than the first, its impact was almost always higher. This is because management was not designed to deal with such extreme events: for example, they exceeded the design levels of levees and reservoirs. In two success stories, the impact of the second, more hazardous, event was lower, as a result of improved risk management governance and high investment in integrated management. The observed difficulty of managing unprecedented events is alarming, given that more extreme hydrological events are projected owing to climate change³.

The combined analysis of precipitation and water scarcity was done with the use of the Standardized Precipitation Index (SPI) and the Standardized Runoff Index (SRI), developed as a monthly, two-variable SPI-SRI indicator to identify different classes of hydrometeorological conditions. Stochastic analysis of a long-term time series (1966–2005) of monthly SPI-SRI indicator values was performed using a first-order Markov chain model. This provided characteristics of regional features of drought formation, evolution and persistence, as well as tools for statistical long-term drought hazard prediction. The study was carried out on two subbasins of the Odra River (Poland) of different orography and land use: the mountainous Nysa Kłodzka basin and the lowland, agricultural Prosna basin. Classification obtained with the SPI-SRI indicator was compared with the output from the NIZOWKA model that provided identification of hydrological drought events including drought duration and deficit volume. Severe and long-duration droughts corresponded to SPI-SRI Class 3 (dry meteorological and dry hydrological), while severe but short-term droughts (lasting less than 30 days) corresponded to SPI-SRI Class 4 (wet meteorological and dry hydrological). The results confirm that, in Poland, meteorologically dry conditions often shift to hydrologically dry conditions within the same month, droughts rarely last longer than 2 months and two separate drought events can be observed within the same year.

Flooding in East-Central Europe in May and June 2010 also affected the Odra River Basin. Unlike a typical summer flood scenario, in 2010 intensive precipitation was observed as early as May. Also, the location of the most intensive rainfall shifted to the catchments of the right bank tributaries...

As determining the probability of the exceedance of maximum precipitation over a specified duration is critical to hydrotechnical design, particularly in the context of climate change, a model was developed to perform a frequency analysis of maximum precipitation of a specified duration. The PMAXΤP model (Precipitation MAXimum Time (duration) Probability) harbors a pair of computational modules fulfilling different roles: (i) statistical analysis of precipitation series, and (ii) estimation of maximum precipitation for a specified duration and its probability of exceedance. The input data consist of homogeneous 30-element series of precipitation values for 16 different durations: 5, 10, 15, 30, 45, 60, 90, 120, 180, 360, 720, 1080, 1440, 2160, 2880, and 4320 min, obtained through Annual Maximum Precipitation (AMP) and Peaks-Over-Threshold (POT) approaches. The statistical analysis of the precipitation series includes: (i) detecting outliers using the Grubbs-Beck test; (ii) checking for the random variable’s independence using the Wald-Wolfowitz test and the Anderson serial correlation coefficient test; (iii) checking the random variable’s stationarity using nonparametric tests, e.g., the Kruskal-Wallis test and Spearman rank correlation coefficient test for trends of mean and variance; (iv) identifying the trend of the random variables using correlation and regression analysis, including an evaluation of the form of the trend function; and (v) checking for the internal correlation of the random variables using the Anderson autocorrelation coefficient test. To estimate maximum precipitations of a specified duration and with a specified probability of exceedance, three-parameter theoretical probability distributions were used: a shifted gamma distribution (Pearson type III), a log-normal distribution, a Weibull distribution (Fisher-Tippett type III), a log-gamma distribution, as well as a two-parameter Gumbel distribution. The best distribution was selected by: (i) maximum likelihood estimation of parameters; (ii) tests of the hypothesis of goodness of fit of the theoretical probability distribution function with the empirical distribution using Pearson’s χ² test; (iii) selection of the best-fitting function within each type according to the criterion of minimum Kolmogorov distance; (iv) selection of the most credible probability distribution function from the set of various types of best-fitting functions according to the Akaike information criterion; and (v) verification of the most credible function using single-dimensional tests of goodness of fit: the Kolmogorov-Smirnov test, the Anderson-Darling test, the Liao-Shimokawa test, and Kuiper’s test. The PMAXTP model was tested on data from two meteorological stations in northern Poland (Chojnice and Bialystok) drawn from a digital database of high-resolution precipitation records for the period of 1986 to 2015, available for 100 stations in Poland (i.e., the Polish Atlas of Rainfall Intensities (PANDa)). Values of maximum precipitation with a specified probability of exceedance obtained from the PMAXTP model were compared with values obtained from the probabilistic Bogdanowicz-Stachý model. The comparative analysis was based on the standard error of fit, graphs of the density function for the probability of exceedance, and estimated quantile errors. The errors of fit were lower for the PMAXTP compared to the Bogdanowicz-Stachý model. For both stations, the smallest errors were obtained for the quantiles determined on the basis of maximum precipitation POT using PMAXTP.