A fundamental probability distribution for heavy rainfall

There is currently no physical understanding of the statistics of heavy precipitation. These statistics are, however, central to diagnosing climate change and making weather risk assessments. This work derives a fundamental rainfall distribution. Interpretation of the water balance equation gives a simple expression for precipitation as the product of mass flux or advected mass, specific humidity and precipitation efficiency. Statistical theory predicts that the tail of the distribution of the product of these three random variables will have a stretched exponential form with a shape parameter of 2/3. This is verified for a global daily precipitation data set. The stretched exponential tail explains the apparent ‘heavy’ tailed behaviour of precipitation under standard assumptions used in extreme value theory. The novel implications for climate change are that the stretched exponential shape is unlikely to change, although the scale may, and precipitation efficiency is important in understanding future changes in heavy precipitation.