Marine heatwaves have profoundly impacted marine ecosystems over large areas of the world oceans, calling for improved understanding of their dynamics and predictability. Here, we critically review the recent substantial advances in this active area of research, including the exploration of the three-dimensional structure and evolution of these extremes, their drivers, their connection with other extremes in the ocean and over land, future projections, and assessment of their predictability and current prediction skill. To make progress on predicting and projecting marine heatwaves and their impacts, a more complete mechanistic understanding of these extremes over the full ocean depth and at the relevant spatial and temporal scales is needed, together with models that can realistically capture the leading mechanisms at those scales. Sustained observing systems, as well as measuring platforms that can be rapidly deployed, are essential to achieve comprehensive event characterizations while also chronicling the evolving nature of these extremes and their impacts in our changing climate.

The probability distribution of daily precipitation intensities, especially the probability of extremes, impacts a wide range of applications. In most regions this distribution decays slowly with size at first, approximately as a power law with an exponent between 0 and −1, and then more sharply, for values larger than a characteristic cutoff scale. This cutoff is important because it limits the probability of extreme daily precipitation occurrences in current climate. There is a long history of representing daily precipitation using a gamma distribution—here we present theory for how daily precipitation distributions get their shape. Processes shaping daily precipitation distributions can be separated into nonprecipitating and precipitating regime effects, the former partially controlling how many times in a day it rains, and the latter set by single-storm accumulations. Using previously developed theory for precipitation accumulation distributions—which follow a sharper power-law range (exponent < −1) with a physically derived cutoff for large sizes—analytical expressions for daily precipitation distribution power-law exponent and cutoff are calculated as a function of key physical parameters. Precipitating and nonprecipitating regime processes both contribute to reducing the power-law range exponent for the daily precipitation distribution relative to the fundamental exponent set by accumulations. The daily precipitation distribution cutoff is set by the precipitating regime and scales with moisture availability, with important consequences for future distribution shifts under global warming. Similar results extend to different averaging periods, providing insight into how the precipitation intensity distribution evolves as a function of both underlying physical climate conditions and averaging time.

Daily precipitation extremes are projected to intensify with increasing moisture under global warming following the Clausius-Clapeyron (CC) relationship at about $$ 7\% /^\circ {\text{C}} $$7 % / ∘ C . However, this increase is not spatially homogeneous. Projections in individual models exhibit regions with substantially larger increases than expected from the CC scaling. Here, we leverage theory and observations of the form of the precipitation probability distribution to substantially improve intermodel agreement in the medium to high precipitation intensity regime, and to interpret projected changes in frequency in the Coupled Model Intercomparison Project Phase 6. Besides particular regions where models consistently display super-CC behavior, we find substantial occurrence of super-CC behavior within a given latitude band when the multi-model average does not require that the models agree point-wise on location within that band. About 13% of the globe and almost 25% of the tropics (30% for tropical land) display increases exceeding 2CC. Over 40% of tropical land points exceed 1.5CC. Risk-ratio analysis shows that even small increases above CC scaling can have disproportionately large effects in the frequency of the most extreme events. Risk due to regional enhancement of precipitation scale increase by dynamical effects must thus be included in vulnerability assessment even if locations are imprecise.