Design Storm Hyetograph

Design Storm Hyetograph Generator

Time-Series Rainfall Distribution

1. Distribution Method
Generation Method	SCS / NRCS 24-Hour Alternating Block (IDF)
Time Step ($\Delta t$)	1 Minute (0.017 hr) 5 Minutes (0.08 hr) 10 Minutes (0.17 hr) 15 Minutes (0.25 hr) 30 Minutes (0.50 hr) 60 Minutes (1.00 hr)

2. SCS Storm Parameters
Rainfall Type	Type I (Pacific Maritime) Type IA (PNW Coastal) Type II (Most of US) Type III (Gulf/Atlantic)
Total 24-Hr Depth ($P$)		mm

2. IDF Equation Parameters
Uses the generalized Intensity-Duration formula: $I = \frac{a}{(t_d + b)^c}$
Total Storm Duration		Hours
Target Total Depth (Optional - scales IDF)		mm
Coefficient ($a$)
Time Constant ($b$)		Min
Exponent ($c$)

Total Depth 0.0 mm

Total Duration 0.0 hr

Peak Intensity 0.0 mm/hr

Time to Peak Hr 0.0

Design Storm Hyetograph (Intensity & Depth)

Rainfall Mass Curve (Cumulative Depth)

Time-Series Tabular Data

Time (Hours)	Cumulative Fraction	Cumulative Depth (mm)	Incremental Depth (mm)	Intensity (mm/hr)

Guidance on IDF Coefficients (a, b, c)

IDF parameters are highly specific to local climate, geography, and the target Return Period. There are no universal default values. However, here are typical ranges and how to find them:

Parameter	Typical Range	Description & Behavior
Coefficient ($a$)	500 - 5000+ (Metric) 20 - 200 (Imperial)	The primary scaling factor. It increases significantly for higher Return Periods (e.g., $a$ for a 100-yr storm is much larger than for a 2-yr storm).
Time Constant ($b$)	5.0 - 30.0 mins	A time offset that flattens the curve at very short durations to prevent intensity from approaching infinity at $t=0$.
Exponent ($c$)	0.60 - 1.00	Dictates how rapidly the storm intensity decays over time. Values closer to 1.0 mean intensity drops off very sharply.

How to determine your exact local values:

• Local Manuals: Consult your local Department of Transportation (DOT) Drainage Manual or regional meteorological agency. They usually publish these exact $a, b, c$ tables for various return periods.
• Curve Fitting (Excel Solver): If you only have raw data points (Duration vs. Intensity) from a source like NOAA Atlas 14, use Excel's Solver tool to minimize the sum of squared errors between your local data and the formula $I = a / (t_d+b)^c$.

Theoretical Background

1. SCS/NRCS 24-Hour Rainfall Distributions The Natural Resources Conservation Service (NRCS) developed synthetic rainfall distributions to model extreme 24-hour storms across the United States. They represent the temporal distribution of rainfall depth.

• Type I & IA: Pacific maritime climates with wet winters and dry summers. Least intense peak.
• Type II: Represents most of the US. Highly intense, sudden peak exactly at hour 12.
• Type III: Gulf of Mexico and Atlantic coastal areas. High intensity, driven by tropical storms.

The incremental depth at any time step is calculated by interpolating the standard dimensionless mass curve fractions ($P_t / P_{24}$) and multiplying by the total 24-hour depth.

2. Alternating Block Method (from IDF) Used to construct a synthetic design storm directly from a localized Intensity-Duration-Frequency (IDF) curve.

• Divide the total storm duration ($T_d$) into equal time steps ($\Delta t$).
• Calculate the average intensity for durations $t = \Delta t, 2\Delta t, 3\Delta t \dots$ using the generalized IDF equation: $I = \frac{a}{(t + b)^c}$
• Calculate total cumulative depth for each duration: $D(t) = I \cdot t$
• Find the incremental depth added in each time step: $\Delta D_n = D_n - D_{n-1}$
• Scaling (Optional): If a Target Total Depth is provided, the entire sequence is proportionately scaled so the final cumulative depth exactly matches the target, while preserving the IDF curve's temporal shape.
• Alternating Sort: Place the largest increment in the center of the storm. Place the second largest to the right, third largest to the left, fourth to the right, and so on. This creates a perfectly balanced, centrally-peaking storm profile.

References & Sources

• Chow, V. T., Maidment, D. R., & Mays, L. W. (1988). Applied Hydrology. McGraw-Hill. (Comprehensive methodology for the Alternating Block Method and design storm construction). [Source]
• USDA Natural Resources Conservation Service (NRCS). (1986). Urban Hydrology for Small Watersheds (TR-55). Conservation Engineering Division. (Source for the standard Type I, IA, II, and III dimensionless rainfall distribution curves). [Download TR-55 PDF]
• Keifer, C. E., & Chu, H. H. (1957). Synthetic Storm Pattern for Drainage Design. Journal of the Hydraulics Division, ASCE. (Early formulations of synthetic hyetographs from IDF data). [View on ASCE]

Version 1.0

CivilSheets by Sothearith Seak