# Where do IDF curves come from?

This article explains how the intensity-duration-frequency (IDF) curves are derived as well as some examples of IDF data from different countries.

In the previous step we explored intensity-duration-frequency curves. In this step we will have a look at how these are obtained, as well as some examples of IDF data from different countries.

## Estimating IDF curves

IDF curves are based on historical precipitation data. First, we divide the continuous rainfall data into separate rainfall events. Usually, we require that there is a minimum dry time between two separate events, e.g. 2 hours. A dry time between rainy periods of e.g. 1 hour is then considered part of the rainfall event. Very small events (e.g. < 0.2 mm) are usually discarded. The definitions of a rainfall event in the paragraph above (minimum dry time, minimum volume) are somewhat arbitrary, and different values can be used.

Based on these rainfall events, different statistical methods can be used to summarize their occurrence in the form of IDF curves. For example, to study the intensities we can expect for 30-minute events, we can first find (within each event) the 30-minute window with the highest average rainfall intensity. We can then calculate the corresponding return intervals. For example, taking the 3 largest events, we may see that they have 30-minute intensities of 60 mm/hr or more. If we used a 20-year record, this means that the frequency of a 30-minute event with an intensity of 60 mm/hr will be: 3 events / 20 years = 0.15 events / year, or a return interval of 6.7 years. This procedure can then be repeated for the 4, 5, … largest events; and for different duration windows (e.g. 5, 10, 15, … minutes) to obtain a collection of points where each point has an intensity, duration and frequency.

We could plot these points on the IDF graph directly, but usually a simple formula is developed that provides an estimate of these points. As you saw in the demo, having a continuous curve (instead of just points) makes it easy to calculate expected intensities for any combination of duration and return interval.

## Limitations of IDF curves

Since IDF curves are based on historical rainfall data, there are some things to keep in mind:

• They apply to the location where the rainfall data is from. Historical rainfall data varies a lot across the globe, and so do IDF curves. What may be a rare event in northern Europe may be a relatively common event in a tropical region with more thunderstorms or regions of e.g. India affected by monsoon rains.
• The length of the rainfall series used affects the quality of the resulting IDF curves. If we have 100 years of data, we get very reliable estimates of 1-month rains, since there will be many such events in the data. But there may only be 1 or 2 100-year events in this dataset (or even none at all!). And the chance of having a 1000-year event in a 100-year record is only 10%. So the uncertainty in the estimates from IDF curves can be considerable, especially for longer return intervals which are derived from extrapolation of the recorded rain data.

## Example 1: Sweden

In Sweden, the most used IDF curve is a single equation which is applied to the entire country(1):

Where I is the intensity (in mm/hr), R the return interval (in months), and D the duration (in minutes). This equation is considered valid for return intervals up to 10 years and durations up to 24 hours.

In the interactive exercise where you explored IDF-curves, the curves shown were calculated using the equation above.

## Example 2: Germany

Germany’s national meteorological service, the Deutscher Wetterdienst, provides more detailed rainfall data. All of Germany has been divided into a grid with a size of 8.2×8.2 km, and for each grid different rainfall values are available. The provided data covers durations from 5 minutes to 3 days, and return intervals from 1 year to 100 years. In the image below we see the rainfall volume for 2 and 6 hour long rains with a 20-year return interval. There is considerable variation across the country, with the southern parts close to the Alps seeing heavier rainfall than the rest of the country.

An interesting note about this data is that the uncertainties associated with these rainfall estimates are quantified. For return intervals of 1 to 5 years the uncertainty is ±10%, for 5-50 years it is ±15%, and for 50-100 years it is ±20%.

## Example 3: United Kingdom

In the UK, the main source of IDF data is the Flood Estimation Handbook (FEH) that was last updated in 2013. Like the German data, this also recognizes that expected rainfalls vary across the country. A special feature is that rainfall estimates can either be obtained for a specific point, or for a specific catchment. The idea is that, for larger catchments, it is unlikely that the entire catchment will experience a similarly extreme rainfall during a single rainfall event, and so the most intense catchment average rainfall that needs to be accounted for is smaller than the highest point rainfall, given the same duration and return interval.

Note that the data from the FEH is usually given as a depth-duration-frequency rather than a intensity-duration-frequency. However, for a given duration and intensity we can simply calculate the corresponding depth and vice versa. Unfortunately, this data is not available freely.