Storm water management is critical to preserving the urban water environment.  A storm water drainage system consists of conveyance and storage facilities, with detention and retention basins being the major storage facilities designed to control storm water quantity and quality.  Such storage facilities need to be placed at strategic locations to effectively attenuate peak flood flows, so all feasible combinations of basin locations, storage volumes, and allowable release rates must be evaluated to optimize costs and benefits.  Decision making relies on numerical simulations performed for the entire watershed with and without the proposed drainage facilities. 

This article presents a study in which the Federal Aviation Administration approach to determining runoff volume was revised to extend its application from on-line to off-line storm water detention basin designs.  A detention basin is on-line if the inflow channel directly flows through it, and off-line if storm water is diverted into the basin from the channel when the inflow exceeds the channel capacity.  In general, off-line detention basins are more economical than on-line basins.  The revised method is a very useful when dealing with flood control in small urban catchments up to 150 acres.

The volumetric method has been recommended for small detention basin designs.  For the design event, the average rainfall intensity for a specified duration can be depicted as:

P_e - C₁ / (C₂ + T_d)^C2                                                                        (1)

Where:
                I = rainfall intensity in inch/hr
                T_d= rainfall duration in minutes
                C₁, C₂, and C₃ are local empirical constants.

Eq. 1 has been used widely to model the decay nature of the rainfall intensity-duration-frequency (IDF) relationship.  The revised FAA procedure presented in this article can work with either a continuous IDF formula or table.  Using the Rational method, the detention storage volume can be directly calculated as the difference between the inflow and outflow volumes.  A storm water detention basin is always designed with the entire watershed tributary to the basin. Therefore, in this study, the design rainfall duration is set to be longer than the time of concentration of the watershed.

For simplicity, the inflow hydrograph to the basin is approximated by a trapezoidal shape (Figure 1).  The inflow hydrograph has a linear rising limb over the time of concentration of the tributary watershed, and the peaking portion of the inflow hydrograph is a plateau from the time of concentration, Tc, to the end of the rainfall event at Td.  Runoff water is diverted into the off-line basin at a preset flow rate, Qb.  The detention volume is the area of bcde. Referring to Figure 1, the outflow volume (area abefg) can be calculated as:

S₀ = Q_a (T_d + T_c - 2T_b) / 2 + Q_b(T_d + T_c - T_b)                                               (2)

Where:
                S₀ = outflow volume
                T_c = time of concentration of the tributary watershed
                T_d = rainfall duration
                T_b= time to begin the diversion.

Using a linear approach, the peak inflow occurs at Tc, and the time to start flow diversion can be approximated by:

T_b = (Q_b / Q_p) T_c                                                                              (3)

Where:
                Q_p= peak inflow determined by the Rational method for the selected T_d as:

Q_p = œ CIA                                                                                      (4)

Where:
                œ = unit conversion factor equal to 1 for acre and feet or 1/360 for hectare and mm
                C = runoff coefficient
                A = watershed area.

For mathematical convenience, the outflow volume, So, is expressed by the average release over the rainfall duration, Td, as:

S₀ = mQ_aT_d                                                                                       (5)

Equating Eq. 2 to Eq. 5 yields the value of m to be:

m = (1/2) [1 + (T_c - 2T_b) / T_d] + (Q_b / Q_a) [1 - (T_c - T_b) / T_d]           for T_d >T_c                      (6)

For an on-line detention basin, Q_b = 0 and T_b = 0.  As a result, Eq. 6 is reduced to

m = (1/2) (1 + T_c / T_d)               for T_d >T_c                                                     (7)

Eq. 7 agrees with previous studies (Aron and Kibler in 1990 and Guo in 1999).  According to the Rational method, the inflow volume or area abcdefg in Figure 1, to the basin is equal to:

  Q_s = œ CIA T_d = Q_p T_a                                                                    (8)

in which Si = inflow volume.  Aided by Eq. 5 and Eq. 8, the detention volume, Sd (area bcde in Figure 1) for the selected Td is:

                       S_d = S_i - S_o = (Q_p - mQ_a)T_d                                                              (9)

The basic concept used in the volumetric method is to find the maximum volume difference by Eq. 9 in terms of rainfall duration.  The method begins with Td = Tc, and then uses an increment of 5 minutes or 10 minutes for storm duration tocompute the detention volume until the maximum storage volume is identified.  The design storage volume, Ss, for the basin is determined by:

                        S_s = max S_d = max (S_i -S_o )                                                            (10)

The aforementioned maximization procedure identifies the design storm and the maximal detention volume.

Design Example for Off-line Basin

The example catchment is located next to a roadside ditch that carries the storm water generated from a tributary area of 25 ha (62 acres):

• The runoff coefficient for the tributary area is 0.68.
• The time of concentration of the catchment is 20 minutes.
• The total allowable storm water release from the watershed is set to be 62 cfs.

The drainage system illustrated in Figure 2 is designed to pass no more than 15 cfs into the roadside ditch.  A flow diversion device is installed to transfer excess storm water into the detention basin.  The maximum release from the detention basin for this case is 47 cfs, which is the difference between the total allowable release of 62 and the on-line release of 15 cfs.  Denver's rainfall intensity curve for the 100-year event is prescribed with:

• C₁ = 74.1
• C₂ = 10.0
• C₃ = 0.786

The task is to determine the off-line detention storage volume.  As indicated in Eq. 10, the detention volume can be maximized by a test over a range of storm duration.  For example, try T_d = 50 minutes.  The calculations are summarized as follows:

(1) Inflow volume

I = 74.1 / (10 + 50) ^0.786 = 2.97   inch/hr

Q_p = CIA = 0.68 * 2.97 * 62 = 125.2  cfs                               

Si = œ CIA T_d = 1 * 0.68 * 2.97 * 62 * 50 = 8.68          acre-ft

(2) Outflow volume

T_b = (Q_b/Q_p) T_c = (15/125.2) * 20 = 2.40    minutes

m = (1/2) [1 + (20 - 2 * 2.4) / 50] + (15/47) [1 + (20 - 2.4) / 50] = 1

S_o = mQ_aT_d = 1.1 * 47 * 50 * 60 / 43560 = 3.51  acre-ft

(3) Storm water detention volume, Sd, for the 50-minute rain storm is:

S_d = 8.68 - 3.15 = 5.18   acre-ft

Repeating this process for the range of rainfall durations from 40 to 80 minutes, Table 1 summarizes the variation of detention storage volumes.  The maximum storage volume is identified to be 5.22 acre-ft with storm duration of 60.0 minutes.

Conclusion

Over the years, the FAA method has been used with the assumption that the peak outflow could be estimated by the gravity flow through the outfall pipe, i.e., Manning's equation.  As a result, the flow-full capacity was then used to determine the outflow volume, i.e., m=1.0.  Recognizing that the value of m must reflect the on-line and off-line operations, the current approach using the FAA method underestimated the required storm water storage volume.

The design procedure documented in this article has been included in the Urban Storm Water Design Criteria Manual (2001) and recommended by Urban Drainage and Flood Control District (UDFCD) for storm water designs in the Denver metropolitan area.  The computer model, UD-Detention, can be downloaded with many other EXCEL spreadsheets from UDFCD's Web site, www.UDFCD.com.