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We test an equation for the probability of heavy 24 h precipitation amounts  Pr ( X  &gt;  x ) as a function of the wet-day frequency and the wet-day mean precipitation. The expression was evaluated against 9817 daily rain gauge records world-wide and was subsequently used to derive mathematical expressions for different rainfall statistics in terms of the wet-day frequency and the wet-day mean precipitation. This framework comprised expressions for probabilities, mean, variance, and return-values. We differentiated these statistics with respect to time and compared them to trends in number of rainy days and the mean rainfall intensity based on 1875 rain gauge records with more than 50 years of valid data over the period 1961–2018. The results indicate that there has been a general increase in the probability of precipitation exceeding 50 mm/day. The main cause for this increase has been a boost in the intensity of the rain, but there were also some cases where it has been due to more rainy days. In some limited regions there has also been an increase in  Pr ( X  &gt; 50 mm/day) that coincided with a decrease in the number of rainy days. We also found a general increasing trend in the variance and the 10-year return-value over 1961–2018 due to increasing wet-day frequency and wet-day mean precipitation.

A simple equation to study changes in rainfall statistics