# Describing rainfall using intensity-duration-frequency

The three main factors that describe a rain event, and the relation between them, are depicted in this article.

Not every rainfall event is the same, so when we are designing urban drainage systems we need to consider different types of rainfall. There are three main factors that describe a rain event.

## Duration

The duration of a rainfall event is simply the amount of time from the start to the end of a rainfall event. If there are shorter breaks without rain during the event, these are also included in the duration.

## Intensity

Intensity is how much rain falls at any given moment. As discussed in the previous activity when we talked about hydrographs, we usually express rainfall volume as a depth (in mm); the rainfall rate or intensity is measured as depth per time, e.g. in mm/hr or l/s, ha. Recall that a rainfall rate or intensity of e.g., 36 mm/hr does not have to mean we actually had 36 mm/hr: if this intensity was observed during e.g., a 5 minute interval (1/12th of an hour), the actual rainfall volume in that 5 minute interval is 36 / 12 = 3 mm.

As you know from your own experience, rainfall intensity will almost always vary throughout an event. It is important to distinguish when we are talking about the intensity at a given time during the rain (which can be changing constantly) or the average intensity of the event. Later on in this article we will talk mainly about the average intensity of design rainfall events.

## Frequency (return interval)

It is quite rare to see very heavy rain, while small, non-intense rainfall events occur frequently. When we talk about the frequency of a rainfall event, we mean how often we will (over a longer time) expect to see a rain that is this at least this intense, e.g. how often will a rain occur with an intensity of 100 mm/hr. If we look at 100 years of rainfall observations, a once-per-5-year rain would occur 20 times in that 100-year record. That means that the probability for this event to occur during any given year is 20%.

Instead of talking about frequencies we often talk about return intervals. For a rain with a once-per-5-year frequency (i.e. 20% probability during any given year), the average return interval is 5 years. We also call this simply “a 5-year rain”. Frequency and return interval are each other’s inverse: a frequency of 1/5 years means the same as return interval of 5 years. Similarly, a return interval of 100 years means the same as a frequency of 1/100 years.

This does not mean that we will always see such an event in any given 5-year period: a specific 5-year period may be a little drier than normal, without any such event; or it may be wetter, and we might get 2 or more of such events.

We can calculate the probability of an event with a given return interval occurring in a certain time interval as in the following example:

• A 5-year event has a 1/5 chance (= 20%) of occurring in any given year.
• This means it has a 4/5 chance (= 80%) of not occurring in any given year.
• The chance of such an event not occurring for 10 consecutive years is (4/5)^10 ≈ 11%
• This means there is an 89% chance that we will see at least one such event in the next 10 years.

We can calculate these probabilities for different return intervals of the rainfall event and for different times into the future:

Probability of seeing such an event in a … year period
Return interval [years] 1 10 100
1 100% 100% 100%
5 20% 89% 100%
10 10% 65% 100%
100 1% 10% 63%
1000 0% 1% 10%

As you can see in the table, a 100 year event sounds quite rate, but the odds of seeing such an event in the next 100 years are quite high! Since urban drainage systems will usually be in place for several decades or even longer, we cannot neglect these rare events entirely.

We also must keep in mind that, just because we saw a rare event yesterday, that does not affect the chance of seeing it again soon. If there was a 10-year rain last month, that does not mean there cannot be another one next week or next year!

## Relation between Frequency, duration and rain intensity: IDF-curves

From your experience, you have probably observed that:

• Duration: Shorter rains can be more intense than longer rains: a) If it starts raining heavily, you might delay going out, or, when already out, run for cover to stay dry. You expect the rain to end relatively soon, so you expect to wait a few minutes. b) If it is raining only lightly, you will behave differently. You know that you may have to wait a long time before the rain stops. Since it is more likely this will take a long time, you might still go out to do your walk or shopping rather than wait (probably) a long time for the rain to stop. You will neither run under a roof for cover since you know that you have to stay there the whole day.
• Frequency: Light rainfall events are relatively common, while heavy (long and/or intense) events are rarer.
a) When you observe a light rain you may think “Oh, it rains again” but you will not be surprised or concerned. This may e.g. be a rain with a return interval of a few days or months.
b) When you observe a very intense rain but without flood risks, you may think “It rains really a lot today”, you may watch the rain since it happens rarely, but you are not concerned since the water is safely discharged. This may be a 5- or 10-year rain.
c) In contrast, when you observe a 30- or even 100-year rain, you will see a lot of water flowing on the street, you may observe flooding of basements or ground floors, you may be concerned, and you will not go out. These rains involve a clear risk and you know that they will be covered in the news.

While you likely have observed situation a and b more or less commonly, you may never or maximum one or two times have observed situation c.

From experience to statistical rain data:

These two relationships are also visible when statistically examining historical rainfall data. Based on historical data from a rain gauge, we can summarize the relationship between intensity, duration, and frequency in a so-called IDF curve as shown in the demo in the next step. From this curve we can, for a specific frequency (or return interval) and a specific duration, look up the maximum average intensity that we can expect for such an event. In the demo, you can test different values to see that:

• Larger return intervals give higher rainfall intensities.
• Shorter events result in higher intensity, longer events in lower intensity.

It is important to note that these IDF curves only give an average rainfall intensity over the rain event. They do not describe any change in duration over time. Note also the total rainfall volume, i.e. the duration multiplied by the (average) intensity. Longer events have a lower intensity, but a larger total rainfall volume.

This last point has implications for designing drainage systems: for short events the critical factor will more often be the rate of rainfall (or runoff) and, thus, the peak flow, which affects e.g. how large pipes have to be to transport water. Longer events are important for the total volume of rainfall (or runoff), which is important when designing facilities that store stormwater.