IDF Rainfall Intensity (Three-Parameter)

Four formulas on this site take a rainfall intensity as an input and none of them will tell you where to get one. The rational method wants $i$, Kirpich exists purely to tell you which duration to read $i$ at, the curve number wants a depth that is an intensity in disguise, and the soil-loss equation hides storm energy inside its R factor. Every one of them says "read it off an IDF curve" and stops. This is that curve. Intensity-duration-frequency analysis takes a rain gauge record, extracts the worst rainfall of each duration in each year, fits a frequency distribution to those annual maxima, and plots the result as a family of curves — one per return period. The three-parameter form $i = a/(t+b)^c$ is the algebra that gets drawn through those points, and with a = 1000, b = 10 minutes and c = 0.75, a 30-minute storm gives $1000/40^{0.75} = 62.9$ mm/h. The word frequency in the name is doing real work, incidentally. Each curve in the family belongs to one return period, and so do the three constants that draw it — reading a 2-year set of constants at a 100-year duration produces a number that means nothing at all.

Now the part that catches people, and it catches them badly. The constants are not physics. They are regression output, and the units of the fit are baked into their numeric values. An $a$ fitted for millimetres an hour against minutes is nonsense for inches an hour against hours: the two differ by 25.4 in one direction and by $60^c$ in the other, and nothing in the number itself warns you. They are equally not transferable between places, which is exactly why every jurisdiction publishes its own table rather than citing someone else's. This page pins one convention — mm/h against minutes, which nearly every SI publication uses — and converts whatever duration unit you type before applying it. The intensity and the duration are handled as real quantities with real units. Only $a$ and $c$ carry the convention, and both say so on their labels.

Three habits keep this honest. Read the curve at the time of concentration, not at a round number of minutes, because the whole justification of the rational method is that the storm lasts exactly as long as the catchment takes to respond. Respect the fitted band: IDF studies run from about 5 minutes to 24 hours, and a power law evaluated at 90 seconds is arithmetic rather than data — the solver will say so. And check the date on your table. IDF analysis assumes the rainfall record is statistically stationary, and where an authority has reissued its curves the old ones are simply superseded, not merely conservative or merely cautious. There is no number this page could hardcode that would be right for your site, so the answer is always the same: use your own authority's current publication, and note which edition you used on the drawing.