An intensity-duration-frequency curve (IDF curve) is a mathematical function that relates the intensity of an event (e.g. rainfall) 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,[2][3] but it is also possible to define IDF curves for drought events.
[4][5] Additionally, applications of IDF curves to risk-based design are emerging outside of hydrometeorology, for example some authors developed IDF curves for food supply chain inflow shocks to US cities.
[6] The IDF curves can take different mathematical expressions, theoretical or empirically fitted to observed event data.
For each duration (e.g. 5, 10, 60, 120, 180 ... minutes), the empirical cumulative distribution function (ECDF), 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[7] 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.
There is a large number of empirical approaches that relate the intensity (I), the duration (t) and the return period (p), from fits to power laws such as: In hydrometeorology, the simple power law (taking
is defined as an intensity of reference for a fixed time
[2][3] In a rainfall event, the equivalent to the IDF curve is called Maximum Averaged Intensity (MAI) curve.
it is necessary to mathematically isolate the total amount or depth of the event