Determining BDE Coefficients

When designing a stormwater drainage system, one of the first questions an engineer must answer is How much rain are we designing for? The answer comes from rainfall intensity — the rate at which rain falls during a storm event of a given duration and return period. BDE coefficients are one of the most widely used ways to express that relationship in a compact, computer-friendly form.

BDE coefficients are the three parameters (B, D, and E) used in the Federal Highway Administration (FHWA) rainfall intensity equation. These coefficients are empirically derived from regional rainfall data and are typically provided for specific storm return periods, such as the 2-year, 10-year, 25-year, or 100-year storm event. When combined with the storm duration or time of concentration, the coefficients allow the software to compute the corresponding rainfall intensity.

BDE coefficients are important because rainfall intensity directly affects peak flow calculations in rational-based hydrology methods, such as the Rational, Modified Rational, and DeKalb Rational methods. The accuracy of pipe sizing, inlet capacity checks, and detention basin design depends directly on the rainfall intensity used in the calculations. Using the right BDE coefficients for the project’s region and design storm is a small step that has a big impact on the integrity of the final stormwater design.

In GeoSTORM, BDE coefficients are one of three available IDF data types for computing rainfall intensity. The other two are the IDF Data Table (used when working directly from published IDF curves) and the Polynomial Coefficient Table (used when working from polynomial-based rainfall relationships). These data types ensure compatibility with a wide range of local drainage criteria and rainfall data sources. To learn more about these data types, refer to this article in our knowledge base.

FHWA Rainfall Intensity Equation

BDE coefficients are defined by the following mathematical relationship between rainfall intensity, storm duration, and return period. The equation is typically fit to Intensity-Duration-Frequency (IDF) curves for a specific region:

Where:

I = Rainfall intensity

T_c = Storm duration or time of concentration

b, d, e = Regional coefficients

Once the BDE coefficients are defined, the software uses the rainfall intensity equation to generate the full rainfall intensity–duration relationship needed for hydrologic computations, ensuring accurate estimates of peak flow rates throughout the drainage network.

For example, the table below shows BDE coefficients published by the City of Houston, Texas. Notice how the BDE values change for each storm return period. The same equation form is used, but each return period has its own coefficient set, allowing the equation to represent different design storms such as the 2-year, 10-year, 25-year, and 100-year events.

Source: https://houstonrecovers.org/wp-content/uploads/2018/06/IDM-CH-9-Show-changes.pdf

Procedure for Computing Rainfall Intensity Using BDE Coefficients

Follow the steps below to calculate rainfall intensity using the FHWA intensity equation:

1. easeIdentifying BDE Coefficients
   Obtain BDE coefficients corresponding to the required storm event and project location from a local stormwater design manual or municipal ordinance. Each municipality may define different coefficients based on regional rainfall characteristics, so always use the values that have jurisdiction over the project site.
2. Applying FHWA Intensity Equation
   Use the following FHWA intensity equation to compute rainfall intensity based on the time of concentration and the corresponding BDE coefficients:
   
3. Computing Rainfall Intensity
   Substitute the time of concentration and BDE coefficients into the equation to compute the rainfall intensity. For example, for a 2-year storm event in the City of Houston, Texas, with the following coefficients:
   b = 75.01; d = 16.2; e = 0.8315; T_c = 20 minutesSubstitute these values into the FHWA intensity equation:
   After performing the computation, the resulting rainfall intensity for a 2-year storm event with a 20-minute time of concentration is approximately 3.80 inches per hour.

$I=\frac{75.01}{(20+16.2)^0.8315} =3.80 in/hr$

After performing the computation, the resulting rainfall intensity for a 2-year storm event with a 20-minute time of concentration is approximately 3.80 inches per hour.

Using BDE Coefficients in Rational-Based Hydrology Methods

In GeoSTORM, all rational-based hydrology methods (Rational method, Modified Rational method, and DeKalb Rational) use the following equation for computing peak flow rate:

Where:

Q = Peak flow rate

C = Runoff coefficient

I = Rainfall intensity

A = Drainage area

The difference between the rational-based hydrology methods is in how rainfall intensity (I) is determined. The following sections explain how each method uses rainfall intensity:

Rational Method

In the Rational method, rainfall intensity is computed for a storm duration equal to the watershed’s time of concentration. This intensity value is then used directly in the equation to determine the peak flow rate. Because only one duration is evaluated, this method is simple and widely used for small urban drainage areas.

Modified Rational Method

In the Modified Rational method, the user specifies the storm duration to be analyzed. The rainfall intensity is then computed for this user-defined storm duration. This intensity value is then used directly in the equation to determine the peak flow rate. This method is well-suited for detention basin design or in situations where local design criteria require evaluation of a specific storm duration.

DeKalb Rational Method

The DeKalb Rational method uses the same rainfall intensity and peak flow computation as the standard Rational Method. However, instead of providing only a peak flow, it generates a full hydrograph using a dimensionless curve developed by DeKalb County, with the peak occurring at 5 times the TOC and a total storm duration of 10 times the TOC.

To learn more about these hydrology methods, refer to this article in our knowledge base.

Defining BDE Coefficients in GeoSTORM

In GeoSTORM, the user can define BDE coefficients using the Storm Data command. Once defined, the software uses the FHWA intensity equation to compute rainfall intensity for any storm duration requested by the hydrology computation.

Follow the steps below to define BDE coefficients:

1. From the Input ribbon menu, select the Storm Data command.
   
2. The Storm Data dialog box will be displayed.
   
   Note: BDE Coefficients are available only when either the Rational Method, Modified Rational, or DeKalb Rational is selected as the Hydrology analysis engine in the Scenario Manager dialog box.
   
3. In the IDF (Intensity-Duration-Frequency) data type dropdown combo box, select the BDE Coefficients Table option.
   
4. In the Storm Frequency Data section, select the BDE Coeff Data tab. This tab provides a BDE Coefficients Data Table where the user can enter BDE coefficients for each storm event, as shown below.
   
5. After defining the BDE coefficients, the software automatically computes rainfall intensities based on the time of concentration and generates the corresponding IDF curve.
6. To view the generated IDF curve, select the IDF Precipitation Plot tab in the Storm Frequency Data section, as shown below.
   

To learn more about the Storm Data command, refer to this article in our knowledge base.

Conclusion

BDE coefficients give the user a compact, equation-based methodology to represent regional rainfall intensity for every storm return period required by a project. Once the user obtains the published BDE values for the project location, the workflow in GeoSTORM is straightforward: open the Storm Data command, select BDE Coefficients Table as the IDF data type, enter the B, D, and E values for each storm event, and let the software handle the rest. From that point on, the software automatically computes rainfall intensities for the rational-based hydrology methods, generates a complete IDF curve for review, and applies those intensities to peak flow and hydrograph calculations across the entire drainage network.

The benefit is consistency, speed, and confidence: every pipe, inlet, and detention basin in the model uses the same agency-approved rainfall data, with no manual interpolation from a printed IDF chart and fewer chances for transcription errors as the model grows. By spending a few minutes up front entering the BDE values, the user can save hours during design iteration and produce a stormwater model that is easier to defend during review.