Why Do Precipitation Intensities Tend to Follow Gamma Distributions?

Abstract

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.

Spatial and temporal characteristics of abrupt heavy rainfall events over Southwest China during 1981–2017

“…When comparing Figure 3c,d, we can find that the long‐duration event tends to be observed with both lower mean and maximum intensity, while the short‐duration event is prone to be featured with higher mean and maximum intensity. As noted by previous studies (e.g., Martinez‐Villalobos and Neelin, 2019), this phenomenon may be related to the balance between two competing processes, that is, fluctuations in moisture convergence and moisture loss due to precipitation. That is, for a rainfall event, a higher intensity (heavy moisture loss) may break the balance and end the event, resulting in shorter duration.…”

Deep Convective Adjustment of Temperature and Moisture

“…It is worth highlighting that the adjustment process here is estimated from conditional mean precipitation, and that there will always be fluctuations away from QE, arising from both variations in large-scale dynamical transports and fluctuations in the convection itself. These variations from QE yield important qualities such as the probability distribution of precipitation accumulations, intensities, durations, and clusters (e.g., Stechmann and Neelin 2014;Neelin et al 2017;Martinez-Villalobos andNeelin 2018, 2019;Ahmed and Neelin 2019). The adjustment time scales are important to the amplitude of such fluctuations and to the resulting precipitation-related distributions.…”

Probability Models and Statistical Tests for Extreme Precipitation Based on Generalized Negative Binomial Distributions

“…Statistical analysis of real data shows that the probability distribution of the precipitation intensity can be approximated by the gamma distribution with very high accuracy. In [55], some theoretical arguments were presented to justify the gamma model for the distribution of precipitation intensities. So, the statistical approach described in Section 6 and in [2] can be also used for identification of abnormally large intensities.…”