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Rational Method

Using the Rational Method


Although HydroCAD is used primarily with the SCS/NRCS runoff methodology, it can also generate runoff hydrographs based on the Rational method.  However, since Rational method was developed primarily for predicting peak flows, its use is not advised for volume-sensitive routing calculations.

The Rational method predicts the peak runoff according to the formula: Q=CiA, where C is a runoff coefficient, i is the rainfall intensity, and A is the subcatchment area. This formula is applicable to US or metric evaluation, as long as consistent units are employed. (In traditional US usage, the intensity and area are given in inches-per-hour and acres, respectively. Converting the units leaves a factor of approximately 1.01, which is usually omitted in manual calculations, but must be included to match the HydroCAD results.)

Click for complete self-training materialsIn order to generate a complete runoff hydrograph, it is assumed that the runoff begins at the start of the storm and increases linearly to the peak value. The peak runoff is sustained until the event duration has elapsed, and then decreases linearly to zero.

The rate at which the hydrograph rises and falls is based on the Tc and a rise/fall factor. For "standard" Rational method, the rise and fall factors are both one. That is, the rise and fall occur over the exact interval Tc. Variations of the Rational method (often called the Modified Rational method), may use different rise and fall factors, which can be set directly on the Settings|Calculation screen.

When using the Rational method, the correct intensity and duration must be specified. If an IDF file is defined, the intensity is automatically calculated for each duration. An IDF file also allows use of the duration analysis report, which simplifies the process of determining the critical duration at each node.

Since a hydrograph produced by the Rational method does not reflect the total runoff or the intensity variations of a real storm, it is not recommended for the design and analysis of detention ponds. It is strongly advised that the SCS-UH or SBUH methods be used when pond routing calculations will be performed.

Frequently Asked Questions

Why is the HydroCAD peak less that when using Q=CiA?

The rainfall duration must be greater than or equal to the Tc times the rise factor (normally 1), otherwise the runoff won't have time to rise to the maximum value.  You may also need to use a smaller time step (dt) in order to have sufficient resolution to capture the momentary peak.

Why is there a flat top on the hydrograph?

The flat top occurs when the duration is greater then the Tc times the rise factor.  The runoff will remain constant until the end of the rainfall duration has elapsed.  (See illustration above.)

When I change the duration, why are all the subcatchments recalculated?

Since the rainfall is assumed to be uniform across the entire site, the same duration and intensity must be applied to all subcatchments.  It makes no sense to combine hydrograph for different events, since they can't occur at the same time.  This illustrates the inherent complexity of using the Rational for all but the simplest of watersheds.

What happens when I combine several subcatchments?

A trapezoidal hydrograph is generated for each subcatchment, and the hydrographs are summed together.  All subcatchments will use the same intensity and duration, as described above.  However, the Tc is a physical characteristic of each subcatchment, so the Tc values are unchanged.  If the duration is less than a certain Tc, that subcatchment will not have time to attain it's theoretical maximum, and will produce a triangular hydrograph with a reduced peak.  If the duration exceeds the Tc, the peak is reduced due to the lower rainfall intensity associated with the longer duration, resulting in a flat-topped hydrograph.  The time-to-peak will also vary, depending on the Tc for each subcatchment.

Note: Summing the peak flows produced by different durations would be incorrect.  This approach violates the assumption of uniform rainfall across the site.  When combining flows from several areas, all subcatchments must be subject to the same rainfall conditions.

Click for complete self-training materialsHow do I determine the rainfall intensity?

Although you can enter the intensity manually on the Settings|Calculation screen, its more convenient to have HydroCAD lookup the value from an appropriate IDF curve.

What duration should I use?

Although some localities may dictate the use of a specific rainfall duration, proper use of rational method requires that the critical duration be used for each point in the watershed.

How do I determine the critical duration?

For a single subcatchment, the critical duration is equal to the Tc, but for complex watersheds the critical duration is harder to determine, and often requires a trial-and-error approach.  HydroCAD-7 (and later) simplifies this process with an automatic critical duration analysis.  This report analyzes a large number of duration/intensity combinations (based on the specified IDF curve) to determine the duration that causes the highest peak flow at a given point in the watershed.  (For a pond or reach, the critical duration is the value that results in the highest water surface elevation.)

To view the critical duration report, open a report window at the desired node and select the Duration tab.  (If the Duration tab is missing, you probably haven't provided an IDF file on the Settings|Calculation screen.)  To generate the report, click the Update button.

For a single subcatchment, the critical duration will be equal to the Tc.  But as you move downstream, the critical duration will increase, especially for a pond, which takes longer to fill to it's maximum elevation and discharge.  For full details, click the Help button on the report screen.

Why are the Rational and SCS runoff values different?

The Rational and SCS methods use different equations and can generally be expected to produce different results. Even if the results are similar under certain conditions, the non-linear nature of the SCS runoff equation means that the results will deviate as the rainfall depth or C/CN values are changed.

For Further Reading

The following article by Paul Schiariti, P.E. provides further insights into the Rational Method, including comparisons to the SCS method, and a discussion of the critical duration (see page 7).  Our thanks to the New Jersey Conservation District Employees Association for posting this document.

Basic Hydrology - TR-55 vs. Modified Rational Method

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