NRCS Unit Hydrograph Shape Factors

In a previous article you learned about How NRCS Hydrographs Are Made. This article takes the discussion to a deeper level and explains the affect the Unit Hydrograph has on the final runoff hydrograph. It also describes how you can easily modify the Unit Hydrograph’s Shape Factor (a.k.a. Peaking Factor) to match your local drainage ordinance, if it requires a modified Unit Hydrograph.

For example, the states of Michigan, Florida and Delaware and nearby regions (Delmarva), each employ non-standard Unit Hydrograph Shape Factors. These can be easily be replicated in Hydrology Studio without having to use other software, spreadsheets, etc., with just a single data entry… the Shape Factor.

What’s a Unit Hydrograph?

A unit hydrograph is itself a hydrograph. But it is one resulting from 1 inch of rainfall excess on a watershed over a given time interval, for example, 1 minute. It is not the final runoff hydrograph but reflects the watershed’s unique characteristics. Think of the unit hydrograph like a person’s DNA. Once a unit hydrograph of a particular watershed is known, any design storm can be applied to it for computing the final runoff hydrograph.

If all unit hydrographs (UH) conform to a constant shape, that is, a constant amount of volume under its rising limb, then both the time and discharge ordinates can be normalized to produce a dimensionless UH. The flows can be expressed as ratios of the UH peak Q and the timeline values can be measured as ratios of the time-to-peak (Tp). So once we know the peak Q of this unit hydrograph, we can display it with some real numbers.

The standard curvilinear and equivalent triangular UH. Same Qp, Tp, volume.

The peak discharge for the Unit Hydrograph is computed as:

Where:

Qp = peak outflow, cfs (cms)
484 = Shape Factor (Peaking Factor) (0.208 metric)
A = catchment area, sq. miles (sq kilometers)
Q = total excess precipitation, 1 inch (1 mm)
Tp = time to peak (hrs)

The Time to Peak, Tp, and the Time Base, Tb, are what determines the characteristics of the Unit Hydrograph. These values are computed as follows:

Where:

Tp = time to peak (hrs)
Tc = time of concentration (hrs)
D = time interval (hrs)

Where Did 484 Shape Factor Originate?

The SCS (now the NRCS) examined a large number of actual watersheds nationwide and developed a standard dimensionless UH which has 37.5 percent of the volume under the rising limb. After deriving an equation for Qp to be in cfs, Tp in hours, A in square miles, Q in inches, there had to be a constant to take care of all these conversions… 484.

They also learned that the inflection point on the descending limb occurred at approximately 1.7 times Tp. And became the basis for the shape of the original curvilinear unit hydrograph. An example of the equivalent triangular UH is shown below on an actual watershed.

NRCS Unit Hydrograph
Standard NRCS UH where 37.5 percent of its volume is under the rising limb.

It’s Not a “One Size Fits All”

Over the years, use of the 484-based SCS dimensionless hydrograph consistently overestimated discharges in flat, swampy areas. In others it underestimates, for example mountainous regions. This underestimate / overestimate ranges from 23 to 45 percent from the standard UH-484 edition. Depending on the project location and geography, the standard UH may need to be modified.

This is easily done by changing the Shape Factor. Where it overestimates, the Shape Factor should be decreased, and increased in areas where it underestimates the peak discharge. The Shape Factor basically scales the UH up or down, while still maintaining the 1-inch of volume under the entire hydrograph.

Here’s an example: In the state of Michigan a study was done to evaluate whether the shape of the standard NRCS Dimensionless UH is applicable to Michigan streams.

Turns out it wasn’t.

The study analyzed 24 gaged streams and 74 different flood events. The results demonstrate that the recorded floods are best reproduced if the UH has just 28.5 percent of its volume under the rising limb instead of the standard 37.5.

In an effort to provide guidance to the engineering community, they devised a set of UH ordinates that produce a UH that fits their 28.5 rising limb rule, and aptly named it the MDEQ SCS Method. These ordinates are 0.0, 0.5, 1.0, 0.8, 0.6, 0.4, 0.2 and 0; and Tc <= 60 minutes. Unless you’re intimately familiar with how unit hydrographs are constructed, you may be inclined to plug those ordinates into WinTR-something and let it produce the hydrographs.

The good news is that Hydrology Studio generates its unit hydrographs on the fly. There’s no need to specify ordinates of a custom unit hydrograph.

The good news is that Hydrology Studio generates its unit hydrographs on the fly. There’s no need to specify ordinates of a custom UH. Just enter the appropriate Shape Factor in the program’s Settings and you’re good to go.

You can easily determine the Shape Factor by dividing the desired percentage rising limb volume by the standard UH of 37.5 and multiplying by 484. So in Michigan’s case, 28.5/37.5 x 484 = 368.

Below is the MDEQ SCS Method UH for a typical drainage area produced by Hydrology Studio by simply using a Shape Factor of 368.

Michigan MDEQ SCS Method example
Specify a Shape Factor of 368 to mimic the MDEQ SCS Method

The chart confirms the Peak Factor of 368 precisely re-shapes the Michigan UH so that only 28.5 percent of the volume is under the rising limb, and the remaining volume on the descending side. It also proves the UH adheres to the MDEQ ordinates while maintaining the required total volume from 1-inch of precipitation.

Below is an overlay of the Standard and the MDEQ SCS unit hydrographs for a 10-acre drainage area. It should be noted that while one can modify the Peak Factor, the volume under the UH must remain at 1-inch over the drainage area. Hydrology Studio maintains this volume for you.

SCS Unit Hydrograph Peak Factors
Different Peak Factors, different peak discharges, same volume.

Below are final runoff hydrographs of the same drainage area using a 6-hour design storm, overlaid. Notice they both peak at the same time but have different peak discharges and volumes.

NRCS Unit Hydrograph Shape Factors
Final runoff hydrographs comparing the different Peak Factors.

Use this same procedure for any other unit hydrograph recipe. For example, the Delmarva Unit Hydrograph, DUH, requires 22 percent of its volume under the rising limb. The Peak Factor can be computed using the ratio of (22/37.5) x 484 = 284.

One More Thing…

We often times read or hear about drainage authorities requiring the use of unique Shape Factors for both pre and post development runoff modeling. Results of studies performed by the New Jersey Department of Agriculture (NJDA) indicate that the degree of urbanization has limited influence on the overall distribution of flow, and hence the Shape Factor.

NJDA study results appear to be consistent with NRCS, whose guidance does not support changing unit hydrographs between pre and post-development runoff estimation. NRCS sensitivity studies show no one characteristic of a watershed by itself has a strong correlation to the unit hydrograph Shape (peak rate) Factor.

Bottom line… avoid mixing and matching Shape Factors in the same pre- and post-development project.

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