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.

Precipitation accumulations, integrated over precipitation events in hourly data, are examined from 1979 to 2013 over the contiguous United States during the warm season (May–October). As expected from theory, accumulation distributions have a characteristic shape, with an approximate power law decrease with event size followed by an exponential drop at a characteristic cutoff scale sL for each location. This cutoff is a predictor of the highest accumulation percentiles and of a similarly defined daily precipitation cutoff PL. Comparing 1997–2013 and 1979–1995 periods, there are significant regional increases in sL in several regions. This yields distribution changes that are weighted disproportionately toward extreme accumulations. In the Northeast, for example, risk ratio (conditioned on occurrence) for accumulations larger than 109 mm increases by a factor of 2–4 (5th–95th). These changes in risk ratio as a function of size, and connection to underlying theory, have counterparts in the observed daily precipitation trends.

Precipitation sustains life and supports human activities, making its prediction one of the most societally relevant challenges in weather and climate modeling. Limitations in modeling precipitation underscore the need for diagnostics and metrics to evaluate precipitation in simulations and predictions. While routine use of basic metrics is important for documenting model skill, more sophisticated diagnostics and metrics aimed at connecting model biases to their sources and revealing precipitation characteristics relevant to how model precipitation is used are critical for improving models and their uses. This paper illustrates examples of exploratory diagnostics and metrics including: (1) spatiotemporal characteristics such as diurnal variability, probability of extremes, duration of dry spells, spectral characteristics, and spatiotemporal coherence of precipitation; (2) process-oriented metrics based on the rainfall-moisture coupling and temperature-water vapor environments of precipitation; and (3) phenomena-based metrics focusing on precipitation associated with weather phenomena including low pressure systems, mesoscale convective systems, frontal systems, and atmospheric rivers. Together, these diagnostics and metrics delineate the multifaceted and multiscale nature of precipitation, its relations with the environments, and its generation mechanisms. The metrics are applied to historical simulations from the Coupled Model Intercomparison Project Phase 5 and Phase 6. Models exhibit diverse skill as measured by the suite of metrics, with very few models consistently ranked as top or bottom performers compared to other models in multiple metrics. Analysis of model skill across metrics and models suggests possible relationships among subsets of metrics, motivating the need for more systematic analysis to understand model biases for informing model development.

Purpose of Review: Review our current understanding of how precipitation is related to its thermodynamic environment, i.e., the water vapor and temperature in the surroundings, and implications for changes in extremes in a warmer climate. Recent Findings: Multiple research threads have i) sought empirical relationships that govern onset of strong convective precipitation, or that might identify how precipitation extremes scale with changes in temperature; ii) examined how such extremes change with water vapor in global and regional climate models under warming scenarios; iii) identified fundamental processes that set the characteristic shapes of precipitation distributions. Summary: While water vapor increases tend to be governed by the Clausius-Clapeyron relationship to temperature, precipitation extreme changes are more complex and can increase more rapidly, particularly in the tropics. Progress may be aided by bringing separate research threads together and by casting theory in terms of a full explanation of the precipitation probability distribution.