Hourly precipitation extremes are crucial in hydrological design. Their frequency and magnitude is encapsulated in the probability distribution tail. Traditional extreme-analysis methods rely on theorems, like the Pickands-Balkema-de Haan, indicating specific type of tails assuming asymptotic convergence—a questionable assumption for real-world samples. Moreover, popular stochastic models for hourly precipitation presume light-tailed distributions to facilitate their mathematical formulation. In practice, limited information on hourly precipitation extremes makes identifying and quantifying their tail highly uncertain, especially on a station-by-station basis. Yet no comprehensive regional analysis of tails has been undertaken to quantify a climatology of tails for diagnostic and prognostic purposes. Here we undertake such an analysis for the conterminous United States. We introduce a novel Bayesian-adjustment approach to assess the best model between power-type and stretched-exponential tails showing that the latter performs better. We present climatology of the tail and quantify its heaviness in over 4,000 hourly precipitation records across the United States and present three main conclusions. First, we show that hourly precipitation tails are heavier than those commonly used with important implications including underestimation of extremes. Second, we provide spatial maps of the tail behavior which reveal some strikingly coherent spatial patterns that can be used for inference in the absence of local observations. Third, we find a nonlinear increase in the tail heaviness with elevation and we formulate parametric functions to describe this law. These results can improve the accuracy of frequency analysis, probabilistic prediction, rainfall-runoff modeling, and downscaling of historical observations and climate model projections.

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.

Hydroclimatic variables such as precipitation and temperature are often measured or simulated by climate models at coarser spatiotemporal scales than those needed for operational purposes. This has motivated more than half a century of research in developing disaggregation methods that break down coarse-scale time series into finer scales, with two primary objectives: (a) reproducing the statistical properties of the fine-scale process and (b) preserving the original coarse-scale data. Existing methods either preserve a limited number of statistical moments at the fine scale, which is often insufficient and can lead to an unrepresentative approximation of the actual marginal distribution, or are based on a limited number of a priori distributional assumptions, for example, lognormal. Additionally, they are not able to account for potential nonstationarity in the underlying fine-scale process. Here we introduce a novel disaggregation method, named Disaggregation Preserving Marginals and Correlations (DiPMaC), that is able to disaggregate a coarse-scale time series to any finer scale, while reproducing the probability distribution and the linear correlation structure of the fine-scale process. DiPMaC is also generalized for arbitrary nonstationary scenarios to reproduce time varying marginals. Additionally, we introduce a computationally efficient algorithm, based on Bernoulli trials, to optimize the disaggregation procedure and guarantee preservation of the coarse-scale values. We focus on temporal disaggregation and demonstrate the method by disaggregating monthly precipitation to hourly, and time series with trends (e.g., climate model projections), while we show its potential to disaggregate based on general nonstationary scenarios. The example applications demonstrate the performance and robustness of DiPMaC.

As droughts have widespread social and ecological impacts, it is critical to develop long-term adaptation and mitigation strategies to reduce drought vulnerability. Climate models are important in quantifying drought changes. Here, we assess the ability of 285 CMIP6 historical simulations, from 17 models, to reproduce drought duration and severity in three observational data sets using the Standardized Precipitation Index (SPI). We used summary statistics beyond the mean and standard deviation, and devised a novel probabilistic framework, based on the Hellinger distance, to quantify the difference between observed and simulated drought characteristics. Results show that many simulations have less than ±10% error in reproducing the observed drought summary statistics. The hypothesis that simulations and observations are described by the same distribution cannot be rejected for more than 80% of the grids based on our H distance framework. No single model stood out as demonstrating consistently better performance over large regions of the globe. The variance in drought statistics among the simulations is higher in the tropics compared to other latitudinal zones. Though the models capture the characteristics of dry spells well, there is considerable bias in low precipitation values. Good model performance in terms of SPI does not imply good performance in simulating low precipitation. Our study emphasizes the need to probabilistically evaluate climate model simulations in order to both pinpoint model weaknesses and identify a subset of best-performing models that are useful for impact assessments.