March-April 2006

Simplifying the Design of Urban Stormwater Detention Systems

Computer-based modeling makes designs faster and easier.

With development occurring at a rapid rate in many parts of the United States and across the globe, stormwater experts are grappling with ways to deal with increased runoff and water-quality problems. More than half the rain that falls on some developed areas may become runoff, and during intense storms, the runoff in these areas can lead to flash flooding. Use of detention ponds has become a best management practice in urbanizing areas to deal with both water-quantity and -quality issues. But designing detention ponds can be a time-consuming and complex science that doesn’t always keep pace with development.

A first-of-its-kind computer-based model for designing smaller catchments will help stormwater experts deal with rapid development. The model, dubbed SUDS (Simplified Urban Detention System), cuts detention pond design time to just minutes. Piloted with success in Greenville County, SC, SUDS allows users with watershed data to design detention ponds that limit the post-development peak discharge rate to pre-development peak discharge for up to six storms. The user inputs the data and selects the options, and SUDS outputs recommendations. The model was created in Visual Basic by civil engineering and design firm Woolpert Inc. in collaboration with Greenville County.

A simplified urban detention design procedure is desirable for a number of reasons: Fewer data are required. The SUDS design procedure also eliminates the trial and error inherent in other procedures, reducing design time. The model offers more uniformity in design, which makes the review process simpler, less time-consuming, and more consistent across reviewers. Designs are “right sized” in most cases and conservative in the remainder. So, if a developer is willing to accept a design that may be conservative, he or she can reduce engineering design costs.

Greenville County proved to be an ideal place to develop a pilot project for the SUDS model. The region is the fastest growing in the state and needs detention design to keep pace with development. The steps used in the Greenville County version of SUDS are similar to those that could be applied to any location; the model can be customized to work in just about any part of the world.

From Greenville County’s perspective, stormwater experts and developers wanted a simple model targeted to urbanizing areas—a model that would provide accurate, consistent numbers for detention design. The county found that SUDS accomplishes this goal.

Simplified Design

The model was created mainly for design of smaller detention ponds—a 1-acre pond in a 100-acre watershed, for example, as opposed to a 10-acre pond in a 1,000-acre watershed. Developers started with the premise that design of smaller ponds should not require the complex trial-and-error approaches to pond sizing typical of models with extensive inputs.

Additionally, many of these existing methods are based on Technical Release 55 (TR-55), a simplified procedure used to calculate runoff volume, peak rate of discharge, hydrographs, and storage volumes for detention ponds. TR-55 was developed by the US Department of Agriculture Soil Conservation Service (now the Natural Resources Conservation Service). Peak discharge estimates in TR-55 are based on data generated with unit hydrograph procedures that use a constant peak rate factor of 484 on the unit hydrograph peak discharge equation for all land uses, a value corresponding to areas that are mostly impervious (Meadows 2000). The result is that prediction of pre-disturbed discharges is overpredicted, which, in turn, causes an underestimation of the storage needed for detention.

As a result of these issues, designers sought a process for smaller urban catchments that considers the impact of land use on the shape of the hydrograph.

The SUDS model was developed on the premise that hydrologic computational procedures can be greatly simplified by developing

1. a replacement for the TR-55 peak discharge calculator that accepts variable peak rate factors based on land use;
2. a procedure for sizing reservoirs that predicts the required storage volume based solely on the ratio of pre-developed peak over post-developed peak discharge and runoff volume;
3. a program that automatically sizes outlet structures for reservoirs sized under the procedure described above (2) such that the post-disturbed peak discharge from the pond matches the pre-disturbed peaks for up to six design storms (i.e., water-quality volume, two-year storm, 10-year storm, 100-year storm);
4. a user-friendly graphic interface to input required hydrologic parameters and constraints on pond sizes; and
5. an updatable user database and regulatory database that has all the acceptable sizes of outlets, regulatory constraints, and any other constraints that may be placed on the particular design.

The SUDS model estimates runoff based on watershed area, land use, time of concentration, travel time, and imperviousness. Based on user input constraints and reservoir shape, the model determines dimensions of reservoir and outlet characteristics, including reservoir surface area, depth, size of outlet, stage-of-emergency spillway, and relevant inflow and outflow discharges.

Subsequent computations determine storage and outlet sizes for various storms—such as two-, 10-, and 50-year storms (or other storms as required by regulatory authority)—given user-selected pond geometry and corresponding constraints such as outside dimensions, depths, and length/width ratio. In addition, the model sizes the reservoir for water-quality volume, permanent pool volume, and a forebay if desired. The output is in a data file as well as in Windows tabular output. Graphic output is under development.

Briefly, here is how SUDS works:

1. The designer inputs the pre- and post-development watershed characteristics and constraints on pond size and shape.
2. The designer selects an outlet type.
   The model then considers a range of detention pond options using user-defined acceptable sizes and shapes of outlets that have already been entered in the user database. Within seconds, SUDS outputs recommended designs that fit within the range of the regulatory and designer-input characteristics and constraints.
3. The designer selects the desired design option.
   SUDS then produces a final design.

Model Details, Greenville County
First, inputs were calibrated to Greenville County hydrologic and soil conditions. Then, the following steps were followed:

Step 1. Subdivide Watershed Into Subwatersheds
The model can accept up to eight subwatersheds. This action allows the model to differentiate between smaller developed areas that are dramatically different hydrologically from larger undisturbed areas and not “mask out” their impacts, as would be the case with lumped-parameter models. An example of the importance of subdividing the watershed is that if the watershed is primarily undisturbed with about 20% of its area in development, discharge considering the disturbed area alone is much greater than that computed using a lumped-parameter approach based on area weighted parameters, particularly in the range of 2 to 7 inches of precipitation, as is typical of Greenville County.

Step 2. Determine Hydrologic Parameters for Each Subwatershed
These parameters are area, NRCS curve number (CN), time of concentration, travel time, peak rate factor (PRF), and time to peak. The model is set up to simplify computations of time of concentration and travel time. For each of these two, the user interface generates an input page for each subwatershed. The flow path for both time of concentration and travel time can be subdivided into up to eight sections each. For each section, the user inputs flow characteristics necessary to compute travel time. Overland flow and channel flow can be handled with capability to calculate flow in unlined and lined channels as well as circular conduits. Drop-down menus allow the user to choose among standard conditions and user-defined options. Travel time and time of concentration are calculated by summing the incremental flow times in all segments. Drop-down menus also allow the user to select standard land-use classes for CN and PRF values or exercise a user-defined option for each.

Step 3. Calculate Runoff Volume
Runoff volume, Q (in), is calculated in SUDS from CN and rainfall, P (in), using the NRCS equation:

where S (in) is the so-called maximum potential abstraction given by:

where CN is the NRCS curve number that defines the impact of cover and soil characteristics.

Step 4. Calculate Peak Discharge From Each Subwatershed
Peak discharge for each subwatershed is calculated in SUDS using a specially calibrated equation based on time of concentration, initial abstraction (dependent on curve number and rainfall), and PRF. An example computational procedure that considers the impact of PRF on peak discharge was given by Meadows (1991). As part of the SUDS model development, a modification of TR-55 was developed. The TR-55 equation for peak runoff has the same form as TR-55, or:

where q_u(cfs/in-mi²) is the so-called unit peak discharge, Q (in) is runoff volume, and A (mi²) is subwatershed area. A predictor for the unit peak discharge, taking into account PRF and initial abstraction, I_a (in), was developed by regression techniques on a large dataset of runoff and peak discharge values for varying values of I_a, PRF, and P values. In the development, a gamma function unit hydrograph (Haan, Barfield, and Hayes 1994) was used whose shape depends on PRF, time of concentration, T_c (hr) and initial abstraction, I_a (in), and precipitation, P (in), or:

where C₁, I₁, I₂, T₁, T₂ are constants that depend on PRF, or:

The root mean square error in peak discharge estimate using Equations 3 through 5 runoff was determined for each of a dataset of more than 350 points generated with a version of SEDIMOT III using a gamma function unit hydrograph whose shape is determined by the peak rate factor. The results are shown in Table 1.

Modifications are being made to add the user option to generate a runoff hydrograph from a rainfall excess hyetograph using the gamma function unit hydrograph with user choice of peak rate factor.

Step 5. Route Subwatershed Peak Discharge to the Watershed Outlet Where It Becomes q_p,d
This requires a functional relationship between the two peaks. Using a large dataset described above, flow was routed down channels with different flow times and the following relationship developed:
:

where K is a coefficient given by:

where T_t (hr) is the travel time from the subwatershed outlet to the pond inlet. The accuracy of prediction of the sixth equation was determined by applying it to the same dataset used on Equation 4. The RMS errors in prediction of the ratio in the sixth equation were calculated and are given in Table 2.

Modifications are being made to add the user option to route the subwatershed hydrograph to the reservoir site using the Muskinghum-Cunge procedure.

Step 6. Predict Cumulative Peak Discharge at Detention Pond Inlet
Because peak discharges from routed subwatershed flows will not occur at the same time, it is necessary to make adjustments to each peak to predict total peak discharge. To make the determination, it was not necessary to sum all points on the hydrographs but simply those corresponding to times of peak for the routed subwatershed flows. As shown in Figure 1, total watershed peak discharge should fall under the peak of one of the subwatersheds. Therefore, the hydrograph function can predict routed discharge for each subwatershed at time-to-peak of all subwatersheds, with the sums taken at routed time-to-peak for each subwatershed. The model then would select the maximum value.

Step 7. Determine Required Storage Volume for Each Storm
If the inflow and outflow hydrographs are assumed to be triangular, then the ratio of storage volume to runoff volume is given by a linear function of the ratio of pre-disturbed peak to post-disturbed peak. However, the hydrographs are not triangles, and an alternative was necessary. Using the large dataset previously discussed, a predictor was developed, which is a polynomial function of the ratio of pre-disturbed and post-disturbed peak discharges, shown graphically in Figure 2.

Step 8. Determine the Water-Quality Volume (WQV) and/or Permanent Pool Volume
Water-quality volume, V_WQV (ac-ft), is typically defined as the volume of runoff based on a defined first flush of runoff. This would be:

(Note: Q_WQV (in) is not a volume but a depth; multiply it by the area to get the volume):

where Q_WQV (in) is the required first flush runoff to be stored (typically 0.5 to 1.0 in), AWQV (ac) is the area from which the runoff must be stored. This is usually defined as the total watershed area or the impervious area of the watershed, depending on regulatory authority requirements. A low-water drainage outlet is typically required to slowly drain the WQV, with a size such that the WQV will drain within a defined time limit. The WQV can be stored in the reservoir or diverted to a parallel reservoir.

An additional permanent pool can be included below the WQV but is typically not drained during the storm. This volume remains in the pond between storms and prevents resuspension of stored sediment at the beginning of storm flow before water is ponded. Additionally, it has a resident time equal to the time between storms, which allows a sizeable portion of sediment and particulate nutrients to settle out of the stored water. This settling decreases the concentration of sediment and nutrients in storm flow. The permanent pool volume can be defined as a fraction of a design storm or as a defined runoff volume from a defined area of the watershed, similar to the ninth equation.

Step 9. Determine Reservoir Shape, Surface Area, and Stage for Each Storm
The user must specify whether or not the model determines stage-area relationships or the user inputs stage-area data. If the user inputs stage-area data, then the model interpolates, using a cubic spline function between input areas, to determine the maximum stage for each storm. The depth of flow in the emergence spillway is added to this, along with a required freeboard, and the total depth of the reservoir is determined.

If the user selects the option to let the model determine stage-area information, then the shape of the reservoir and constraints become the user inputs. Shapes can be rectangular with vertical sides, trapezoidal with vertical sides, or trapezoidal with sloping sides. A constraint of the model requires the reservoir to be symmetrical about its longitudinal centerline. A maximum and minimum length, width, and depth must also be specified. In addition, for trapezoidal shapes, a ratio of upstream width to downstream width and the sideslopes must be specified. With these reservoir inputs and the required storage volume for each storm, the model selects all the dimensions of the reservoir.

If a WQV is specified, then the model selects the surface area and depth required for the WQV. If a permanent pool is specified, then the user must input maximum and minimum depths and widths of the aquatic vegetation bench. With this information, the model determines the dimensions of the permanent pool. If a forebay is specified, the reservoir is sized to accommodate the volume of a berm as well as the expected volume of sediment to be stored in addition to the runoff.

Step 10. Determine Preliminary Emergency Spillway Size
The model determines a preliminary emergency spillway size based on user constraints on width, soil resistance to erosion, and the type of crest (i.e., vegetated, bare, or lined). The size is based on application of a broad-crested spillway equation to predict peak discharge, q_p (cfs), or:

where C is the weir coefficient, VP (ft/sec) is the velocity peak discharge, L (ft) is the length of the weir (dimension perpendicular to the flow path) and H (ft) is the total flow depth through the weir, and Vlimit (ft/sec) is a limiting velocity based on type of soil, vegetation, and/or lining. Values for Vlimit are defined using a drop-down menu.

Based on these characteristics, a spillway width and maximum depth is calculated by SUDS. This can later be refined once the size of the principal spillway is determined.

Step 11. Determine Size of Principal Spillway
SUDS allows the use of drop inlet spillway or weir outlets. The following discussion focuses on drop inlets. The user selects the type of drop inlet and associated orifices for each design storm. The barrel is always assumed to be circular in shape. Options for the drop inlet include:

• Rectangular riser with rectangular orifices
• Rectangular riser with circular orifices
• Circular riser with circular orifices

Before sizing the spillways, SUDS has already determined the elevation of peak storage for each design storm. Sizing of the principal spillway consists of determining the size of the drop inlet spillway barrel, the dimensions and locations of orifices on the riser for each design storm, and final dimensions for the emergency spillway.

Sizing the barrel. Using the elevation of the peak water surface during a given design storm, the model iterates through the size options in the user-defined database and selects the size that will transmit each design storm when the head in the riser, H (ft), is equal to the difference in the maximum water level for that storm and elevation of the invert of the intersection of the barrel with the riser. The equation used for calculating discharge through the pipe is:

where d (ft) is the pipe diameter, Kb is the bend head loss coefficient, L (ft) is the length of the pipe, and H (ft) is the head in the riser above the invert of the intersection of the riser and the barrel, So (ft/ft) is the slope of the barrel, and n is the Manning’s roughness for the barrel. For the initial calculations, H is assumed to be the maximum height of water for the given storm. The model selects the maximum size calculated over all storms and then uses the 11th equation to determine the head in the riser, H_R, for each storm, which will be used in calculating flow through the side orifices.

Sizing side orifices. After sizing the barrel, SUDS then sizes the design storm orifices, which are located on the side of the riser. Sizing consists of calculating the number of orifices of a given size for each storm and then calculating a vertical offset for a selected group of the orifices to allow the post construction peak to be less than or equal to the target peak discharge (less than or equal to the pre-disturbed peak discharge). In selecting the orifices, SUDS uses the user-defined database on allowable options. Since the size selected will not be the exact size needed to match the target peak discharge, SUDS selects an offset distance for some of the orifices to exactly match the target peak discharge. Flow in the orifice is based on head above the orifice center, which will be the distance from the center of the orifice to the crest of the second set of orifices, or H₁. Using the orifice equation, flow will be defined as:

where n1 is the number of orifices in row 1, C₁, above the orifice crest, is the orifice coefficient, A₁ (ft2) is the area of one orifice, H₁ (ft) is the impounded head for that storm, and d₁ (ft) is the diameter of one orifice. Thus:

Inputting the user-defined options for orifice diameters available for the riser, the 12th equation can be solved for n₁ and d₁ using a trial-and-error technique to determine the size that gives the closest discharge to Q₁, but is slightly larger than Q₁.

Adjustments to match needed discharge.
After selecting the size and number of orifices, a fraction of the orifices will be moved to a higher elevation to exactly match the target peak discharge for that design storm. This is necessary because outflow is a function of head as well as orifice area (see Equation 12); therefore, adjustments must be made in the height of a portion of the orifices to bring the value of Q₁ as close as possible to the target peak discharge. Referring to Figure 3, let n1u be the number of orifices whose crest elevations are not adjusted and n1a be the number of orifices whose crests elevations are moved up a distance , then:

The value of §₁ is adjusted until the predicted Q_1c matches the value of Q₁, or is slightly larger. The maximum value for is 0.75 times the distance to the next row of orifices. The model selects the combination of n_1a and §₁ that meets these constraints.

These calculations are performed with an iterative routine that uses a recursive algorithm that searches for the best solution that minimizes the time to drain for the reservoir without exceeding the pre-disturbed peak flows for each of the design storms. There are two options for orifice location for the maximum detention storm: vertical on the side of the riser or horizontal on top of the riser. In addition, orifices are sized to exactly match the pre-disturbed peak flow for the maximum detention storm. If a water-quality volume orifice is specified by the user, then the model sizes the orifice to drain the water-quality volume within a defined minimum and maximum time.

Step 12. Display the Output and Allow User Changes
Given the shape selected by the user and constraints such as length-to-width ratio, etc., the model selects the final dimensions and elevations of outlets as described above and prints a summary of reservoir and outlet characteristics along with relevant inflow and outflow discharges.

It should be mentioned that the number of possible designs that will work is endless. The model uses an objective function for optimization of the design that minimizes the time required to draw down the detention storage.

How the Model Will Be Used
SUDS will be used not only by Greenville County stormwater experts but also by private developers. Indeed, the goal is for all private developers in the county to use the model when designing smaller catchments, thereby establishing consistency in detention design and evaluation throughout the region. Private developers’ engineers will be able to access SUDS.

Recent work on the model includes creating options for low-impact development designs.

Although the model has been calibrated to Greenville County hydrologic and soil conditions, its flexibility allows it to be reconfigured for use in just about any part of the world.