OpenSpecEngineering

Finds the design rainfall intensity for a storm of a given duration from the coefficients of a fitted intensity–duration–frequency (IDF) curve. It also gives the rainfall depth that falls over that duration. Drainage and stormwater engineers use it to get the intensity i for the rational method and for sizing inlets, pipes, ditches and detention basins, where a city or state publishes its IDF curves as equations.

Equations

Sherman: i = a / (t_d + b)^c
Bernard: i = a·T^m / (t_d + b)^c
Depth: P = i·t_d / 60

i is the average rainfall intensity over the storm, t_d the storm duration in minutes, and T the return period in years. a, b, c and m are constants fitted to the rainfall records for one place [1][2][3]. The Sherman form fits one curve, so it has a separate set of a, b and c for each return period. The Bernard form folds the return period into the term T^m, so one set covers several return periods. P is the depth that falls in t_d; the 60 converts minutes to hours.

Units

The page has no units of its own beyond minutes for t_d. The intensity comes out in whatever units the coefficients were fitted in: mm/hr if a was fitted for mm/hr, in/hr if for in/hr. The depth is then in mm or inches. Check that the source fitted its curve with t_d in minutes; some use hours.

Limits and common mistakes

• Use coefficients only within the durations and return periods they were fitted for. Fits often go wrong below 5 minutes or beyond 24 hours.
• For the rational method, set t_d equal to the time of concentration of the catchment.
• i is an average over t_d, not the peak burst inside the storm.
• Coefficients go out of date as rainfall records grow. In the US, check them against NOAA Atlas 14 [4] for the site.

Worked example

A town publishes its IDF curves in the Bernard form, with i in mm/hr and t_d in minutes: a = 1000, m = 0.2, b = 10 and c = 0.8. A parking lot drain needs the 10-year intensity for its 30-minute time of concentration.

1. Choose IDF Equation Form Bernard.
2. Enter Coefficient a 1000, Coefficient b 10, Exponent c 0.8 and Return-Period Exponent m (Bernard) 0.2.
3. Enter Return Period (T, years) 10 and Storm Duration (td, min) 30, and press Solve. The Solution shows: Rainfall intensity i: 82.8614 (per coeff. units)
   Rainfall depth over td (i·td/60): 41.4307 (depth units)

The coefficients are in mm/hr, so the design intensity is 82.9 mm/hr and 41.4 mm falls in the 30 minutes. Check with logarithms: log₁₀ i = 3 + 0.2 − 0.8 × log₁₀ 40 = 3.2 − 1.2816 = 1.9184, so i = 82.86 mm/hr. Half an hour at that rate gives the 41.4 mm.