Peak Flow Estimation

Introduction

This article discusses three common methods used for estimating stormflows in drainage design - the Rational Method (RM), the Modified Rational Method and the TR55 peak flow method. The methods are briefly introduced along with the limitations of their use Recommendations for the use of these methods are also provided

The Rational Method

The Rational method is a simple and widely used approach for estimating peak runoff rates from small catchments Three inputs are required: the runoff coefficient, the rainfall intensity, and the drainage area. The method is generally the first choice when conducting preliminary drainage device designs The rational method is based on the following equation:

Q = CiA where:

Q is the peak runoff rate in cubic feet per second (cfs)

C is the runoff coefficient, a dimensionless factor for the portion of rainfall that turns into runoff

I is the rainfall intensity in inches per hour

A is the drainage area in acres

The runoff coefficient is a function of the type of land use, soil type, topography, and other factors that impact runoff Typical values for the runoff coefficient range from 0.1 for pervious areas, such as grassed areas, to 0.9 for impervious areas – hard standings, roadways, parking lots and roofs

The rainfall intensity is obtained from intensity-duration-frequency (IDF) curves for the area determined from local or regional rainfall data

Limitations of the Rational Method include:

The assumption that the runoff coefficient, rainfall intensity, and drainage area are constant over time, which is generally not the case for complex watersheds

No hydrograph production or runoff timing, which are important for the design of flood control/attenuation systems.

The Modified Rational Method

The Modified Rational method is a variation of the Rational Method that considers the time of concentration of the catchment in its calculation. By including a correction factor for the time of concentration, the method provides more accurate estimates of peak flow rates It is a more complex method than the Rational Methods requiring additional inputs as a correction factor and the time of concentration

The modified rational method uses the following equation:

Q = CIA/(t + T) where:

Q is the peak runoff rate in cubic feet per second (cfs)

C is the runoff coefficient, a dimensionless factor for the portion of rainfall that turns into runoff

I is the rainfall intensity in inches per hour

A is the drainage area in acres t is the time of concentration in minutes

T is the time of concentration correction factor

The time of concentration correction factor is a function of the shape and size of the catchment; it accounts for the lag time between peak runoff rate and the peak rainfall intensity. It is a more accurate method than the original rational method, especially when considering larger catchments or catchments with longer times of concentration.

The Modified Rational Method has its limitations:

It assumes the rainfall intensity and runoff coefficient are constant over time, which is generally not the case for larger more complex watersheds

The method does not provide information on the full hydrograph or runoff time, which are key for flood control/attenuation design

TR55 Peak Flow Method

The TR-55 method is a hydrologic model developed by the United States Department of Agriculture’s (USDA) National Resources Conservation Service (NRCS) for estimating runoff volume, peak flow, and hydrographs from small watersheds. The method is based on the Soil Conservation Service (SCS) Curve Number (CN) method – the SCS Method; this method utilises a dimensionless curve number to characterize the combined effects of soil, land use, and management practices on the runoff process The TR-55 method is more complex than the Rational and Modified Rational methods. It requires additional inputs such as the curve number, antecedent moisture condition, and initial abstraction.

However, it provides additional information on the runoff process, including the full hydrograph and the timing of the runoff making it a preferred method for the design of flood control/attenuation systems The TR55 method is more suitable for assessing complex watersheds as it accounts for runoff coefficient variability and variable rainfall intensity over time

The key steps in the TR-55 method include:

1. Determination of the average CN for the watershed based on the land use and soil type

2. Determination of rainfall depth and duration for the design storm based on the probability of occurrence and rainfall data/IDF curves

3 Calculation of rainfall excess using the SCS dimensionless unit hydrograph method. This method assumes that the runoff is generated uniformly throughout the watershed and that the runoff rate is proportional to the rainfall excess

4. Estimation of runoff volume using the CN method, which converts the rainfall excess to the runoff volume based on the CN and the initial abstraction

5 Estimation of peak flow rate utilising the runoff volume, the drainage area, and the time of concentration.

The TR55 method also has limitations:

It assumes that the runoff is generated uniformly throughout the watershed and that the runoff rate is proportional to the rainfall excess

The method requires more input data and may be more time-consuming and difficult to use than the Rational and Modified Rational methods

Discussion

The Rational Method (RM) is typically used for sizing drainage inlets and pipes, and ditch networks for small catchments up to 25 acres or so; some municipal drainage departments in the United States of America permit its use on catchments up to 200 acres in area. A common rule of thumb is the use of the RM for catchment areas less than 50 acres and the use of the TR55 peak flow method for catchments greater than 200 acres. The TR55 method should be used for hydrograph production and for flood routing to ponds/reservoirs A primary benefit of the TR55 method is its ability to model the response of a drainage system to prolonged rainfall events

The RM considers a storm of a short critical duration to determine peak flows and as such is typically not used for (or recommended for) storage calculations as would be required for sizing or evaluating attenuation ponds The Modified Rational Method (MRM) can be used for sizing detention and retention facilities. For this method a series of trapezoidal shaped hydrographs are created for different storm durations; the greatest difference in volume between the pre and post hydrographs becomes the critical hydrograph for the subject storm.

With respect to rainfall/runoff coefficients, the coefficients for the RM - developed mostly for the design of culverts and ditches – tend to be conservative and when projected to large areas, where longer storms are more appropriate, tend to produce peak flows that are excessive.

Research[1] comparing the results of the RM and MRM with the SCS method revealed the following:

RM/MRM peak flow rates are close to those of the SCS for larger drainage areas

Runoff volumes are significantly different (RM/MRM being 3 to 4 times less).

Detention basin/dry pond volume will be significantly smaller when flood routing is done by the MRM hydrograph method

Conclusion

In conclusion, each method for estimating runoff has its own benefits and disadvantages The Rational method is simple and easy to use but has limitations in accuracy. The Modified Rational method is an improvement over the Rational Method by accounting for the time of concentration but still has limitations with hydrograph production. The TR-55 method is the most sophisticated one however it is a more difficult model to utilize - especially if calculations are to be done manually The method of choice will depend on the size of the watershed, and whether hydrograph production and flood routing calculations are required

References

[1] Paul Schiatriti – Mercer County Soil Conservation District – Basic Hydrology – TR55 vs MRM