Intensity-duration-frequency curve


An intensity-duration-frequency curve is a mathematical function that relates the rainfall intensity with its duration and frequency of occurrence. These curves are commonly used in hydrology for flood forecasting and civil engineering for urban drainage design. However, the IDF curves are also analysed in hydrometeorology because of the interest in the time concentration or time-structure of the rainfall.

Mathematical approaches

The IDF curves can take different mathematical expressions, theoretical or empirically fitted to observed rainfall data. For each duration, the empirical cumulative distribution function, and a determined frequency or return period is set. Therefore, the empirical IDF curve is given by the union of the points of equal frequency of occurrence and different duration and intensity Likewise, a theoretical or semi-empirical IDF curve is one whose mathematical expression is physically justified, but presents parameters that must be estimated by empirical fits.

Empirical approaches

There is a large number of empirical approaches that relate the intensity, the duration and the return period, from fits to power laws such as:
In hydrometeorology, the simple power law is used according to Monjo as a measure of the time-structure of the rainfall:
where is defined as an intensity of reference for a fixed time, i.e., and is a non-dimensional parameter known as n-index. In a rainfall event, the equivalent to the IDF curve is called Maximum Averaged Intensity curve.

Theoretical approaches

To get an IDF curves from a probability distribution, it is necessary to mathematically isolate the precipitation, which is directly related to the average intensity and the duration, by the equation, and since the return period is defined as the inverse of, the function is found as the inverse of, according to: