• Comprehensive and extended review on probabilistic methods for hydroclimatic extremes. • Synthesis of methods used in analyses of extremes in precipitation, streamflow and temperature. • Over 20 probability distribution estimation methods in 25 comparative studies reviewed. • Identification of most promising contemporary probabilistic methods. Here we review methods used for probabilistic analysis of extreme events in Hydroclimatology. We focus on streamflow, precipitation, and temperature extremes at regional and global scales. The review has four thematic sections: (1) probability distributions used to describe hydroclimatic extremes, (2) comparative studies of parameter estimation methods, (3) non-stationarity approaches, and (4) model selection tools. Synthesis of the literature shows that: (1) recent studies, in general, agree that precipitation and streamflow extremes should be described by heavy-tailed distributions, (2) the Method of Moments (MOM) is typically the first choice in estimating distribution parameters but it is outperformed by methods such as L-Moments (LM), Maximum Likelihood (ML), Least Squares (LS), and Bayesian Markov Chain Monte Carlo (BMCMC), (3) there are less popular parameter estimation techniques such as the Maximum Product of Spacings (MPS), the Elemental Percentile (EP), and the Minimum Density Power Divergence Estimator (MDPDE) that have shown competitive performance in fitting extreme value distributions, and (4) non-stationary analyses of extreme events are gaining popularity; the ML is the typically used method, yet literature suggests that the Generalized Maximum Likelihood (GML) and the Weighted Least Squares (WLS) may be better alternatives. The review offers a synthesis of past and contemporary methods used in the analysis of hydroclimatic extremes, aiming to highlight their strengths and weaknesses. Finally, the comparative studies summary helps the reader identify the most suitable modeling framework for their analyses, based on the extreme hydroclimatic variables, sample sizes, locations, and evaluation metrics reviewed.

Extreme temperature is a major threat to urban populations; thus, it is crucial to understand future changes to plan adaptation and mitigation strategies. We assess historical and CMIP6 projected trends of minimum and maximum temperatures for the 18 most populated Canadian cities. Temperatures increase (on average 0.3°C/decade) in all cities during the historical period (1979–2014), with Prairie cities exhibiting lower rates (0.06°C/decade). Toronto (0.5°C/decade) and Montreal (0.7°C/decade) show high increasing trends in the observation period. Higher-elevation cities, among those with the same population, show slower increasing temperature rates compared to the coastal ones. Projections for cities in the Prairies show 12% more summer days compared to the other regions. The number of heat waves (HWs) increases for all cities, in both the historical and future periods; yet alarming increases are projected for Vancouver, Victoria, and Halifax from no HWs in the historical period to approximately 4 HWs/year on average, towards the end of 2100 for the SSP5–8.5. The cold waves reduce considerably for all cities in the historical period at a rate of 2 CWs/decade on average and are projected to further reduce by 50% compared to the observed period. • CMIP6 simulations for extreme temperature estimation of the largest Canadian cities. • Prairies' cities exhibit a lower rate of temperature increase compared to the cities in Great lakes in observation period. • Cities in Prairies are projected to have 12% more summer days than the rest of the cities. • The number of heat waves increases significantly, especially for Vancouver, Victoria, and Halifax. • Cold waves are expected to decrease by 50% in future.

• Eight rainfall models are compared as input for a simplified continuous hydrologic model. • The comparison is performed by investigating the simulated runoff properties. • Results suggest that all rainfall models lead to realistic runoff time series. • Four models will be further optimized to be adapted for data-scarce applications. Continuous hydrologic modelling is a natural evolution of the event-based design approach in modern hydrology. It improves the rainfall-runoff transformation and provides the practitioner with more effective hydrological output information for risk assessment. However, this approach is still not widely adopted, mainly because the choice of the most appropriate rainfall simulation model (which is the core of continuous frameworks) for the specific aim of risk analysis has not been sufficiently investigated. In this paper, we test eight rainfall models by evaluating the performances of the simulated rainfall time series when used as input for a simplified continuous rainfall-runoff model, the COSMO4SUB, which is particularly designed for small and ungauged basins. The comparison confirms the capability of all models to provide realistic flood events and allows identifying the models to be further improved and tailored for data-scarce hydrological risk applications. The suggested framework is transferable to any catchment while different hydrologic and rainfall models can be used.

• A first comprehensive and systematic review on the research of extreme precipitation in China. • Variation and regional characteristics of extreme precipitation under non-stationary conditions due to climate change and human activities. • Supports and basis for engineering application and further research on extreme precipitation and flood in China. Recent years have witnessed global massive property losses and casualties caused by extreme precipitation and its subsequent natural disasters, including floods and landslides. China is one of the countries deeply affected by these casualties. If the statistical characteristics and laws of extreme precipitation could be clearly grasped, then the negative impacts triggered by it may be minimized. China is a vast country and diverse in climate and terrain, hence different regions may be suitable for different analyses and research methods. Therefore, it is necessary to clarify the research progress, methods and current status of extreme precipitation across the country. This paper attempts to provide a comprehensive review of techniques and methods used in extreme precipitation research and engineering practice and their applications. The literature is reviewed focusing on seven aspects: (1) annual maxima method (AM), (2) peaks over threshold method (POT), (3) probable maximum precipitation (PMP), (4) non-stationary analysis of precipitation extremes, (5) intensity-duration-frequency curves (IDF), (6) uncertainty in extreme precipitation frequency analysis, and (7) spatial variability of extreme precipitation. Research on extreme precipitation in China is generally based or centered on the above seven aspects. The current study aims to provide ideas for further research on extreme precipitation frequency analysis and its response to climate change and human activities.

Globally, extreme temperatures have severe impacts on the economy, human health, food and water security, and ecosystems. Mortality rates have been increased due to heatwaves in several regions. Specifically, megacities have high impacts with the increasing temperature and ever-expanding urban areas; it is important to understand extreme temperature changes in terms of duration, magnitude, and frequency for future risk management and disaster mitigation. Here we framed a novel Semi-Parametric quantile mapping method to bias-correct the CMIP6 minimum and maximum temperature projections for 199 megacities worldwide. The changes in maximum and minimum temperature are quantified in terms of climate indices (ETCCDI and HDWI) for the four Shared Socioeconomic Pathways (SSP1-2.6, SSP2-4.5, SSP3-7.0, and SSP5-8.5). Cities in northern Asia and northern North America (Kazan, Samara, Heihe, Montréal, Edmonton, and Moscow) are warming at a higher rate compared to the other regions. There is an increasing and decreasing trend for the warm and cold extremes respectively. Heatwaves increase exponentially in the future with the increase in warming, that is, from SSP1-2.6 to SSP5-8.5. Among the CMIP6 models, a huge variability is observed, and this further increases as the warming increases. All climate indices have steep slopes for the far future (2066–2100) compared to the near future (2031–2065). Yet the variability among CMIP6 models in near future is high compared to the far future for cold indices.

The Köppen-Geiger (KG) climate classification has been widely used to determine the climate at global and regional scales using precipitation and temperature data. KG maps are typically developed using a single product; however, uncertainties in KG climate types resulting from different precipitation and temperature datasets have not been explored in detail. Here, we assess seven global datasets to show uncertainties in KG classification from 1980 to 2017. Using a pairwise comparison at global and zonal scales, we quantify the similarity among the seven KG maps. Gauge- and reanalysis-based KG maps have a notable difference. Spatially, the highest and lowest similarity is observed for the North and South Temperate zones, respectively. Notably, 17% of grids among the seven maps show variations even in the major KG climate types, while 35% of grids are described by more than one KG climate subtype. Strong uncertainty is observed in south Asia, central and south Africa, western America, and northeastern Australia. We created two KG master maps (0.5° resolution) by merging the climate maps directly and by combining the precipitation and temperature data from the seven datasets. These master maps are more robust than the individual ones showing coherent spatial patterns. This study reveals the large uncertainty in climate classification and offers two robust KG maps that may help to better evaluate historical climate and quantify future climate shifts.

Abstract Extremes are rare and unexpected. This limits observations and constrains our knowledge on their predictability and behavior. Graphical tools are among the many methods developed to study extremes. A major weakness is that they rely on visual-inspection inferences which are subjective and make applications to large datasets time-consuming and impractical. Here, we advance a graphical method, the so-called Mean Excess Function (MEF), into an algorithmic procedure. MEF investigates the mean value of a variable over threshold, and thus, focuses on extremes. We formulate precise and easy-to-apply statistical tests, based on the MEF, to assess if observed data can be described by exponential or heavier tails. As a real-world example, we apply our method in 21,348 daily precipitation records from all over the globe. Results show that the exponential-tail hypothesis is rejected in 75.8% of the records indicating that heavy-tail distributions (alternative hypothesis) can better describe rainfall extremes. The spatial variation of the tail heaviness reveals that heavy tails prevail in regions of Australia and Eurasia, with a “hot spot” found in central Russia and Kazakhstan. We deem this study offers a new diagnostic tool in assessing the behavior of extremes, easy to apply in large databases, and for any variable of interest. Our results on precipitation extremes reinforce past findings and further highlight that exponential tails should be used with caution.