A potential rule of thumb for hourly rainfall?

Future global warming will be accompanied by more intense rainfall and flash floods due to increased evaporation, as a consequence of higher surface temperatures which also lead to a higher turn-around rate for the global hydrological cycle. In other words, we will see changing rainfall patterns. And if the global area of rainfall also shrinks, then a higher regional concentration of the rainfall is bound to lead to more intense downpours (the global rainfall indicator is discussed here). 

Even with successful mitigation and cut in CO2-emissions, there will be a need for climate change adaptation (e.g. keeping the global warming below 2°C according to the Paris accord). We must be better prepared for more water in inconvenient forms and critical infrastructure may need to be upgraded to withstand it.

Engineers typically make use of so-called intensity-duration-frequency (IDF) estimates to design buildings, bridges or roads that are dimensioned to weather these conditions. Farmers need to know how to manage their fields to avoid erosion and loss of crops. Hence, IDF curves are useful for climate adaptation.

The IDF curves traditionally need sub-daily rainfall measurements (e.g. rainfall recorded every hour) which are not so common everywhere. The standard commonplace rain gauge data, however, record the rainfall accumulated over 24-hr segments (Figure 1).

a potential rule of thumb for hourly rainfall

Figure 1. Location of 24-hr rain gauge measurements from the global historical climate network (GHCN). 

The question is whether it is possible to make use of 24-hr rain gauge data to say something about IDF statistics, even if it doesn’t involve measurements accumulated over intervals of minutes to hours.

There have been some attempts to estimate IDF curves based on 24-hr data that recently were accompanied by a new “rule of thumb” that gives approximate results (Benestad et al., 2021):

x_\tau(L) = \alpha \mu \left(L/24\right)^\zeta \ln(f_w \tau).

In this expression(illustrated in Figure 2), x_\tau(L) is the return level for rainfall accumulated over time duration L (units in hours), \alpha is a statistical correction factor (accounting for the fact that rainfall is not really exponentially distributed), \mu is the wet-day mean precipitation (here a threshold of 1 mm/day was used to distinguish ‘wet’ and ‘dry’ days), \zeta describes the dependency between different temporal scales, f_w is the wet-day frequency, and \tau is return interval. 

a potential rule of thumb for hourly rainfall 9

Figure 2 IDF- curve estimated for a location in Norway. 

The question is whether this formula can quantify sub-daily rainfall statistics outside Norway, so it should be tested for other parts of the world to see if it provides useful information on a more general basis.

It should be fairly straight-forward to calibrate \zeta against already established IDF curves for sites with sub-daily rain measurement (see Benestad et al., (2021) for more details). This timescale dependency is expected to depend on relative occurrences of convective storms, cyclones, atmospheric rivers, weather fronts, and orographic rainfall (rainfall triggered by moist air blowing over hills and mountains forcing air ascent).

An advantage of this “rule of thumb” formula is its simplicity. It needs the two key rain fall parameters wet-day mean precipitation \mu and frequency f_w, and if the correction factor \alpha and the timescale cross-dependency \zeta have similar values across regions, then it may provide a quick first guess of the IDF curves for sites where hourly rainfall measurements are absent.


  1. R.E. Benestad, J. Lutz, A.V. Dyrrdal, J.E. Haugen, K.M. Parding, and A. Dobler, “Testing a simple formula for calculating approximate intensity-duration-frequency curves”, Environmental Research Letters, vol. 16, pp. 044009, 2021. http://dx.doi.org/10.1088/1748-9326/abd4ab

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