Precipitation Accumulations, Intensities and Durations*

Precipitation accumulations (the integrated precipitation amount over the course of an event) exhibit large fluctuations, yielding distributions with a long power law regime, followed by a sharp decrease at a characteristic large-event cutoff scale. This cutoff scale limits the largest events experienced in a particular region. First-passage processes for fluctuations of moisture relative to a temperature-dependent threshold for onset of precipitation yield quantitative prototypes for this behavior including expressions for the cutoff in terms of the interplay between moisture loss by precipitation and moisture convergence fluctuations. The behavior of accumulations under coarse graining (e.g., daily precipitation) is important as these quantities are routinely used for characterization and assessment, for example of climate change effects. Earlier work has sometimes fit Gamma distributions to daily intensities, with no physical explanation. In this work we show that daily intensity distributions can be explained through these stochastic prototypes, with the traditional Gamma distributions as approximations. These results help to understand relations in US accumulations from hourly observations and daily rainfall.