Rainfall Intensity from an IDF Power-Law Curve
Rainfall Intensity from an IDF Power-Law Curve
Stormwater systems are sized using a design rainfall intensity that depends on both storm duration and how rare (return period) the storm is. Rather than reading a chart every time, agencies fit their local IDF curves to a power-law formula I = a/(t+b)^c that can be evaluated directly for any duration.Because I decreases as duration t increases (a longer storm has a lower peak intensity), a stormwater designer must select the right duration — usually the time of concentration of the drainage area — before plugging it into this formula, or the resulting design intensity will be wrong for the site.
The design intensity is I = a/(t + b)^c, an empirical power-law fit to the local IDF curve. where a, b and c are curve-fitting constants for the return period and location, and t is the storm duration.
Inputs
a_idf := 900 mm/hr=2.5e-04 m/s
t_dur := 30=30
b_idf := 10=10
c_idf := 0.75=0.75
Plugging the storm duration into the fitted power-law curve gives the design rainfall intensity for that duration and return period.
I_rain := a_idf/(t_dur + b_idf)^c_idf=1.57e-05 m/s
Results
A 30-minute design intensity on the order of 55–60 mm/hr is a reasonable, fairly intense design storm value for many temperate regions. Because intensity falls off with duration raised to a fractional power, doubling the storm duration does not halve the intensity — it drops more slowly, which is why time of concentration must be estimated carefully rather than rounded up casually.
Assumptions & limitations
- Curve constants (a, b, c) are location- and return-period-specific.
- Duration t must equal the drainage area’s time of concentration for a proper design storm.
- Point rainfall only; areal reduction for large watersheds not applied.