[1] Theoretically, if the distribution of daily rainfall is known or justifiably assumed, then one could argue, based on extreme value theory, that the distribution of the annual maxima of daily rainfall would resemble one of the three limiting types: (a) type I, known as Gumbel; (b) type II, known as Fr echet; and (c) type III, known as reversed Weibull. Yet, the parent distribution usually is not known and often only records of annual maxima are available. Thus, the question that naturally arises is which one of the three types better describes the annual maxima of daily rainfall. The question is of great importance as the naive adoption of a particular type may lead to serious underestimation or overestimation of the return period assigned to specific rainfall amounts. To answer this question, we analyze the annual maximum daily rainfall of 15,137 records from all over the world, with lengths varying from 40 to 163 years. We fit the generalized extreme value (GEV) distribution, which comprises the three limiting types as special cases for specific values of its shape parameter, and analyze the fitting results focusing on the behavior of the shape parameter. The analysis reveals that (a) the record length strongly affects the estimate of the GEV shape parameter and long records are needed for reliable estimates; (b) when the effect of the record length is corrected, the shape parameter varies in a narrow range; (c) the geographical location of the globe may affect the value of the shape parameter; and (d) the winner of this battle is the Fr echet law.

Climate extremes threaten human health, economic stability, and the well-being of natural and built environments (e.g., 2003 European heat wave). As the world continues to warm, climate hazards are expected to increase in frequency and intensity. The impacts of extreme events will also be more severe due to the increased exposure (growing population and development) and vulnerability (aging infrastructure) of human settlements. Climate models attribute part of the projected increases in the intensity and frequency of natural disasters to anthropogenic emissions and changes in land use and land cover. Here, we review the impacts, historical and projected changes,and theoretical research gaps of key extreme events (heat waves, droughts, wildfires, precipitation, and flooding). We also highlight the need to improve our understanding of the dependence between individual and interrelated climate extremes because anthropogenic-induced warming increases the risk of not only individual climate extremes but also compound (co-occurring) and cascading hazards. ▪  Climate hazards are expected to increase in frequency and intensity in a warming world. ▪  Anthropogenic-induced warming increases the risk of compound and cascading hazards. ▪  We need to improve our understanding of causes and drivers of compound and cascading hazards.

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Abstract. The upper part of a probability distribution, usually known as the tail, governs both the magnitude and the frequency of extreme events. The tail behaviour of all probability distributions may be, loosely speaking, categorized into two families: heavy-tailed and light-tailed distributions, with the latter generating "milder" and less frequent extremes compared to the former. This emphasizes how important for hydrological design it is to assess the tail behaviour correctly. Traditionally, the wet-day daily rainfall has been described by light-tailed distributions like the Gamma distribution, although heavier-tailed distributions have also been proposed and used, e.g., the Lognormal, the Pareto, the Kappa, and other distributions. Here we investigate the distribution tails for daily rainfall by comparing the upper part of empirical distributions of thousands of records with four common theoretical tails: those of the Pareto, Lognormal, Weibull and Gamma distributions. Specifically, we use 15 029 daily rainfall records from around the world with record lengths from 50 to 172 yr. The analysis shows that heavier-tailed distributions are in better agreement with the observed rainfall extremes than the more often used lighter tailed distributions. This result has clear implications on extreme event modelling and engineering design.

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An operational framework for flood risk assessment in ungauged urban areas is developed within the implementation of the EU Floods Directive in Greece, and demonstrated for Volos metropolitan area, central Greece, which is frequently affected by intense storms causing fluvial flash floods. A scenario-based approach is applied, accounting for uncertainties of key modeling aspects. This comprises extreme rainfall analysis, resulting in spatially-distributed Intensity-Duration-Frequency (IDF) relationships and their confidence intervals, and flood simulations, through the SCS-CN method and the unit hydrograph theory, producing design hydrographs at the sub-watershed scale, for several soil moisture conditions. The propagation of flood hydrographs and the mapping of inundated areas are employed by the HEC-RAS 2D model, with flexible mesh size, by representing the resistance caused by buildings through the local elevation rise method. For all hydrographs, upper and lower estimates on water depths, flow velocities and inundation areas are estimated, for varying roughness coefficient values. The methodology is validated against the flood event of the 9th October 2006, using observed flood inundation data. Our analyses indicate that although typical engineering practices for ungauged basins are subject to major uncertainties, the hydrological experience may counterbalance the missing information, thus ensuring quite realistic outcomes.

Trends in short‐lived high‐temperature extremes record a different dimension of change than the extensively studied annual and seasonal mean daily temperatures. They also have important socioeconomic, environmental, and human health implications. Here, we present analysis of the highest temperature of the year for approximately 9000 stations globally, focusing on quantifying spatially explicit exceedance probabilities during the recent 50‐ and 30‐year periods. A global increase of 0.19°C per decade during the past 50 years (through 2015) accelerated to 0.25°C per decade during the last 30 years, a faster increase than in the mean annual temperature. Strong positive 30‐year trends are detected in large regions of Eurasia and Australia with rates higher than 0.60°C per decade. In cities with more than 5 million inhabitants, where most heat‐related fatalities occur, the average change is 0.33°C per decade, while some east Asia cities, Paris, Moscow, and Houston have experienced changes higher than 0.60°C per decade.