Testing some simple formulas for estimating the probability of heavy 24-hr precipitation and sub-daily return values

Estimates, based on a simple formula that approximates the probability of heavy 24-hr rainfall, give surprisingly high correlations with the observed number of days with more than 20 mm precipitation from rain gauge data around the world. A background for this formula is presented, which includes a series of past projects EU-SPECS, KlimaDigital, CORDEX FPS southeast Africa, and EU-SPRINGS. Although the initial analysis focussed on Norway, subsequent work has shown that this simple formula provides a reasonable description of the frequencies of heavy rainfall recorded by rain gauge data from all around the world where data has been available. Furthermore, a comparison with intensity-duration-frequency (IDF) analysis in Norway suggests that there is a fractal dependency between temporal scales that may be utilised in a simple IDF formula, and one question is whether this framework works elsewhere as it is related to the said formula for 24-hr precipitation. Even if such simple models are not sufficiently accurate for estimating design values, they may nevertheless be useful for benchmarking because they are easy to apply and require very little computational resources. The IDF framework has been tested on results from convection permitting regional climate model simulations to assess whether the fractal scaling varies in space. It may also provide a framework for downscaling future heavy precipitation statistics, both in terms of dynamical as well as empirical-statistical downscaling. A demonstration of both the formula for heavy 24-hr precipitation as well as for IDFs are incorporated in a test app for monitoring precipitation https://ocdp.met.no.