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TOOL-018 / STORMWATERReleased calculator

IDF Curve Interpolator

Interpolate rainfall intensity between the durations and return periods in the table you supply.

Method & assumptionsWorked exampleFAQ
Interpolation only. Values outside the first and last tabulated duration or return period are not estimated.
01

Local IDF table

Enter intensity at each duration and return period, then the duration and return period you need.

Intensity units
Return periods
Duration 1
Duration 2
Query inside the table

Switching units converts the stored intensity and rounds only the text in the field. Duration and return period stay in minutes and years. A blank field stays blank. The previous result is cleared when an input changes or an entry is rejected.

02

Interpolated intensity

Enter a table and interpolate.

Ready for interpolation

Review the local table, then interpolate inside its durations and return periods.

ln I on ln d and ln T
03 / METHOD & LIMITS

Log-log interpolation inside a local IDF table

Supply the intensities. The calculator reads between tabulated durations and return periods and stops at the edge of the table.

ln I(d, T) = (1−u)(1−v) ln I11 + u(1−v) ln I21 + (1−u)v ln I12 + uv ln I22u = ln(d / d1) / ln(d2 / d1) · v = ln(T / T1) / ln(T2 / T1) · depth P = i × t

US intensity uses the released design-storm inch, 0.0254 m, which is 25.4 mm/h per in/h. Duration stays in minutes and return period stays in years when you switch units. The field text is rounded for display. The stored intensity keeps full precision.

Input guidance

Duration · d
Enter at least two durations in minutes, in increasing order. The same unit is used for SI and US.
Return period · T
Enter at least two return periods in years, in increasing order.
Intensity · I
Enter a positive intensity in every cell. Millimetres per hour in SI, inches per hour in US. A blank cell is required and is not zero.

Applicability and limitations

FHWA HEC-22, 4th edition (FHWA-HIF-24-006, February 2024), Section 4.1.1, says an IDF curve relates duration and frequency to intensity, and that you read it by finding the duration, moving to the return period, and reading intensity. Section 4.2.2.2 says the Rational Method uses those curves and names NOAA and NRCS as sources of regional curves. NOAA Atlas 14 Volume 2 Version 3.0 (Bonnin et al., 2006) defines an IDF curve as a log-log plot of intensity against duration. A numbered interpolation equation in either document is UNVERIFIED. Volume 2 Section 4.8 is spatial interpolation between stations and is not used. The 2022 HDSC assessment says Atlas 14 production curves are cubic-spline smoothed (NA14 assessment, Section 1.1). This calculator does not apply that spline.

Model bounds: interpolation only, no extrapolation. The table is yours. Do not paste a depth table into the intensity cells. Return-period log-log weights are the project method, and that equation number is UNVERIFIED. Depth is P = i × t from the design-storm helper, not another interpolation. Time of concentration, peak runoff, and code compliance are outside this result.

Method reference

Formula FORMULA-TOOL018-IDF-LOGLOG-INTERPOLATION-001, with depth from FORMULA-TOOL002-DESIGN-STORM-DEPTH-001. Sources SRC-IDF-CURVE-HEC22-TOOL018-001, SRC-NOAA-ATLAS14-IDF-TOOL018-001, and SRC-PROJECT-METHOD-TOOL018-001, each version 1.0.0.

FAQ

Frequently asked questions

What interpolation does this calculator use?

It interpolates rainfall intensity with bilinear log-log weights. For a duration between d1 and d2, u = ln(d / d1) / ln(d2 / d1). For a return period between T1 and T2, v = ln(T / T1) / ln(T2 / T1). ln of the intensity is the same weighted combination of the four bracketing cells. A query that lands on a tabulated duration and return period returns that cell exactly. FHWA HEC-22, 4th edition, FHWA-HIF-24-006, February 2024, Section 4.1.1, tells you to read an IDF curve by duration and return period, https://www.fhwa.dot.gov/engineering/hydraulics/pubs/hif24006.pdf. NOAA Atlas 14 Volume 2 Version 3.0 defines an IDF curve as a log-log plot of intensity against duration, https://www.weather.gov/media/owp/oh/hdsc/docs/Atlas14_Volume2.pdf. A numbered HEC-22 or NOAA equation for this algebra is UNVERIFIED.

Does it extrapolate beyond my table?

No. The target duration and return period must lie on or between the first and last tabulated values. A shorter, longer, rarer, or more frequent query is rejected, and any previous result is cleared.

Do I enter a NOAA Atlas 14 depth table?

No. Enter intensity. NOAA Precipitation Frequency Data Server tables are often precipitation depth. Convert depth to intensity with I = P / t before you enter the cell. Log-log interpolation of intensity is not the same number as interpolating depth and then dividing by duration. This calculator does not download Atlas 14.

Which units can I enter?

Duration is minutes and return period is years in both SI and US. SI intensity is millimetres per hour. US intensity is inches per hour, converted with the Rational Method inch of 0.0254 m, which is 25.4 mm/h per in/h. The stored value keeps full precision. Only the text in the field is rounded. Canonical depth is millimetres, from P = i × t. In US mode the result, the depth, and the four corner intensities are labelled in/h and in, with the millimetre values beside them.

What happens if a cell is blank?

A blank or whitespace-only duration, return period, intensity, or query is required. It is not treated as zero. A zero or negative intensity is also rejected. The previous result is cleared.

Why is the return period also on a log scale?

The authorized model uses the same log-log weights on both axes of the table you supply. HEC-22 Section 4.1.1 says to select the return-period curve. It does not give the algebra between curves. NOAA Atlas 14 Volume 2 Section 4.8 is spatial interpolation between stations, not this table. The 2022 Atlas 14 assessment says production curves are smoothed with cubic splines. This calculator does not use that spline. The return-period equation number is UNVERIFIED.

How is rainfall depth calculated?

Depth uses the released design-storm helper: P = i × t, with i in millimetres per hour and t in minutes. It is the product of the interpolated intensity and the query duration. It is not a second interpolation.

Does this prove code compliance or size a drain?

No. You supply the table, the duration, and the return period. The result does not choose a design storm, calculate time of concentration, compute peak runoff, or establish a permit or code determination.

CONTINUE YOUR WORKFLOW

Use the intensity you already have

One supplied intensityRainfall depth

P = i × t when the intensity is already known and no table interpolation is required.

Peak flowRational Method

Q = C × i × A uses an intensity you supply. This page does not calculate it.

Duration contextTime of concentration

A design duration is often related to time of concentration. This page does not estimate it.

Related

Continue from this result

ReleasedDesign-storm depth

P = i × t for one supplied intensity

ReleasedRational Method peak runoff

Uses an intensity you already have

ReleasedTime of concentration

A duration often starts from time of concentration

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