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Copy and Paste This Permanent Link:http://www.stormh2o.com/september-2008/retention-volume-modeling.aspx

Additional Article Content

• Figure One
• Figure Three
• Figure Two
• Figure Four
• Figure Five
• Table One
• References

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Natural watersheds retain and dissipate most rainwater. This water is retained on the surfaces of vegetation and in ground depressions, such as puddles, wetlands, and marshes. Natural processes such as transpiration by plants, infiltration into the soil, and evaporation dissipate this water. A natural watershed’s retention and dissipation capacity is sufficient to prevent any runoff from occurring during most rainfalls. Occasionally, when there is a heavy rainfall, a small amount of the rainwater becomes surface runoff that enters nearby creeks, rivers, and lakes.

The natural processes that retain and dissipate the rainwater are diminished when land is developed, whether for agriculture or for urban use. Land development removes vegetative cover, fills in low areas, compacts the soil, and creates impervious areas. The result is increased water runoff flowing more frequently across the land and discharging into the watershed’s rivers, streams, and lakes. This increased runoff causes downstream flooding, accelerated soil loss from erosion, unstable stream banks, and pollution of water resources.

Problems in Mitigating Increased Runoff
Detention basins temporarily hold collected runoff and slowly release the water. They are constructed in an attempt to mitigate the downstream flooding problems by limiting the peak discharge rate of the runoff. However, they do not reduce the volume of runoff discharged into the nearby creeks, rivers, and lakes. Consequently, the runoff volume discharged remains greater than when the land was in its natural condition. Therefore, detention basins fail to match the natural runoff pattern that occurred prior to the land being developed. Streambank erosion, stream channel instability, and occasionally even downstream flooding continue to be problems.

Retention basins hold a certain volume of water. There are two types of retention basins: water-quality basins and water-volume basins. Water-quality retention basins remove pollutants collected by the runoff. These basins allow the runoff to pass through after holding it long enough to give natural processes time to remove a percentage of the pollutants. They do not reduce the volume of runoff discharged. Water-volume basins capture and dissipate the runoff, thereby reducing the volume and frequency of discharges from a site. A discharge of runoff occurs only when the runoff volume exceeds the basin’s maximum retention volume. However, the actual volume available for retaining the runoff from the next rainfall depends upon the dissipation of the water held from the previous rainfall. Therefore, a key factor in determining the effectiveness of a water-volume basin is the dissipation rate.

Two commonly used methods for estimating the maximum retention volume for a water-volume retention basin are the “90% Rule” and the “Two-Year-Difference Rule.” The 90% Rule requires the capture of 90% of the runoff coming from a developed site. The Two-Year-Difference Rule requires that the maximum retention volume should be equal to the difference between the two-year runoff from the developed site and the two-year runoff from the site in a natural undeveloped condition. Neither rule addresses the necessary dissipation rate relative to the storage volume. Therefore, it is uncertain that the maximum retention volume derived by these rules will adequately address the adverse effects caused by the increased runoff coming from developed land.

An Alternative Method for Determining Retention Volume and Dissipation
An alternative to these methods is to use a simulation model. This model is set up on a Microsoft Excel spreadsheet and uses local historical precipitation data. The runoff volume for each day of the simulation is estimated using the TR-55 runoff equations (USDA 1986). The retained water volume for each day is calculated by taking the difference between the precipitation volume and the runoff volume, then subtracting the daily dissipation volume. This retained water volume is added to the precipitation of the next day, which is valid because the effect of the retained water on the next day’s runoff volume has the same effect as if it were part of the precipitation for the next day. Adding the previous day’s retained water to the precipitation provides the continuity needed for determining the appropriate combination of retention and dissipation to replicate the natural runoff.

The model performs two simulations. One simulation applies to runoff coming from land in a natural condition, and the other applies to runoff from developed land that has a retention basin. The first simulation establishes the performance benchmark for comparison. The simulation generates a data set containing daily precipitation verses runoff volume. This data set is displayed as points on a chart similar to the chart found in the TR-55 manual (USDA 1986), which forms what is called the runoff pattern. The second simulation applies to runoff coming from developed land with retention. It estimates the runoff discharged from a retention basin of a given size and dissipation rate. The runoff pattern generated from the retention simulation is compared to the pattern generated from the natural simulation.

Simulating the runoff discharged from a developed site with retention involves two runoff calculations. The first calculation uses the TR-55 runoff equation 2–2 (USDA 1986) to calculate the runoff entering the basin from the developed site (Q_site). The second calculation uses the alternate TR-55 runoff equation 2–1 (USDA 1986) and substitutes the site runoff volume for the precipitation volume in order to estimate the runoff discharged from the retention basin (Q_out).

The simplified version of the TR-55 runoff equation is used in the first calculation because it estimates the runoff coming directly from the surface area. The second calculation uses the alternate runoff equation because it contains two variables needed in simulating the retention and dissipation of rainwater held in the retention basin. The variable S is the “potential maximum retention after runoff begins” (USDA 1986) and represents the maximum available retention volume for the basin. The variable Ia, called the initial abstraction, “is all losses before runoff begins. It includes water retained in surface depression, water intercepted by vegetation, evaporation, and infiltration” (USDA 1986). This initial abstraction variable represents the daily dissipation volume. This depends on the time (called the recovery time) it takes to empty the basin. It is equal to the maximum retention volume divided by the recovery time. For example, if a retention basin has a volume of 3 inches and the recovery time is six days, then the daily dissipation volume is 0.5 inch. The simplified version of the TR-55 runoff equation (equation 2–3) assumes a recovery time of five days based on its empirical equation (equation 2–2) that relates the initial abstraction I_a to the maximum retention S. However, when simulating the retention basin, the recovery time and related initial abstract is not assumed to be five days. Rather, the recovery time is a variable that is estimated based on the sum of all the available means for dissipating the retained water (i.e., infiltration beds, irrigation, reuse). The retained water is calculated by subtracting both the basin’s discharge volume (Q_out) and the dissipation volume from the runoff entering the basin from the developed site (Q_site). Adding the retained water from the previous day to the runoff volume for the developed site (Q_site) before calculating the basin’s discharge volume maintains the continuity between each day in the simulation.

One of the principal reasons for retaining runoff coming from developed land is to stop accelerated streambank erosion. When runoff volume coming from land in a natural condition exceeds the volume coming from a two-year rainfall, the streambanks become unstable and erosion occurs. Therefore, the model calculates the theoretical runoff volume generated from a two-year rainfall. It then counts the number of times the simulated runoff exceeds this theoretical two-year runoff volume for both the natural simulation and the developed simulation. These two counts are compared with an objective that the number of days exceeding the two-year runoff be the same for both the developed conditions and the natural conditions. Therefore, using Excel’s “Goal Seek” function, the model varies the retention volume until the number of days exceeding the two-year runoff volume equals the number of days for the natural simulation.

Simulating the Grand Rapids Area Runoff
A runoff simulation was performed for the Grand Rapids, MI, area. It is presented here to illustrate the application and results obtained from this method. This simulation utilized 37 years of daily precipitation collected at the weather station located at the Gerald R. Ford International Airport in Grand Rapids. The rainfall frequency information needed for calculating the two-year runoff volume came from the Rainfall Frequency Atlas of the Midwest (Huff and Angel 1992). The model assumes silty soils belonging to hydrologic group C with a ground cover of woods in good condition for the natural conditions. Referring to TR-55 Table 2–2a (USDA 1986), the CN value of 70 represents the natural conditions. The variables used in the runoff equation for the natural condition are as follows:

• The maximum retention volume (S) equals 4.3 inches using TR-55 equation 2–4.
• The initial abstraction (I_a), equals 0.86 inch using TR-55 Equation 2–2.

The daily precipitation-runoff results generated from the runoff simulation from land in a natural condition are shown in Figure 1. The light green line represents the theoretical runoff from land with a curve number of 70. The green dots represent the runoff estimated by the model. Figure 2 displays the results generated from the land in a fully developed condition with a curve number of 98. For comparison, these results, displayed as small blue dots, are overlaid onto the Figure 1 chart for the natural conditions.

Comparing Retention Volumes
Estimates of the maximum retention volumes for different development intensities (i.e., CN = 98, 95, 90, and 85) were made using the simulation model, the 90% Rule, and the Two-Year-Difference Rule. The resulting volumes are tabulated in Table 1. Note that the volumes of the two rules do not change with regard to the various recovery-time scenarios. This is because these rules do not include any kind of dissipation rate. These results are also displayed on a Chart (Figure 3) to graphically illustrate the difference between the retention volumes derived by the model and the two rules.

A Simulation of Runoff Volumes From Detention
A third simulation model was set up to compare detention basin runoff volumes with previous model runoff volumes for natural conditions and from developed conditions having retention. The discharge rates used for this simulation were selected based upon rates commonly intended to provide downstream bank protection. The developed site’s runoff that enters the detention basin is first estimated using the TR-55 runoff equation, which is the same as for the retention basin modeling. However, the discharge volume from the detention basin is the lesser of either the volume held in the basin or the maximum daily discharge volume. The maximum daily discharge volume is 1.19 inches per day when the basin’s discharge rate is limited to 0.05 cubic feet per second (cfs) per acre, or 0.39 inch per day when the basin’s discharge rate is limited to 0.02 cfs/acre. The 0.05-cfs/acre-discharge rate represents the standard requirement currently in practice of the Grand Rapids area for protecting downstream banks. The 0.02 cfs/acre-discharge rate is what would be required to limit the daily runoff volume to the two-year runoff volume. This simulation also assumed that the detention basins have sufficient capacity to detain all runoff volumes without an overflow. The results of the two detention scenarios are shown in Figures 4 and 5 as yellow dots overlaid onto the runoff chart previously created for the natural condition and the developed condition with retention.

These charts clearly illustrate how ineffective detention basins are at preventing downstream bank erosion. Even if the discharge were restricted to the two-year runoff volume, the number of days when the discharge equals that volume is much greater than under the natural conditions. This increased frequency of two-year discharge volumes does not give the damaged vegetation along the edge of the bank sufficient time to rejuvenate, and bank erosion would still result. The purpose of detention is primarily for peak flow attenuation to mitigate downstream flooding. Therefore, stormwater detention basins should not be considered an effective best management practice in preventing downstream bank erosion.

Conclusion
This simulation model is a better design tool for estimating retention volumes, because it considers the combination of both retention volume and dissipation rate or recovery time. The model is relatively easy to set up using an Excel spreadsheet. It applies local historical precipitation data to the TR-55 method for estimating runoff volumes. The model helps in gaining a better understanding of the functional relationship between runoff retention volumes and dissipation rates. Once the model is set up, an easy-to-use spreadsheet template can be created for use throughout the local area. This template can form the basis for guiding the design of many of the low-impact development management practices, such as infiltration systems, runoff capture and reuse systems, and rain gardens. In addition, various design scenarios can be simulated for comparison with the natural runoff pattern. Therefore, the simulation model should be preferred over the rule-based methods in achieving the watershed goal of matching pre-settlement runoff characteristics.

This model provides the key runoff control parameters of retention volume and dissipation rate to effectively replicate the runoff coming from land in a natural condition. Therefore, other site-development design parameters such as detention volume and peak discharge rate, water-quality volumes, and first flush volumes are not necessary for properly managing a site’s runoff. Thus, designers can better direct their efforts toward creating more cost-effective means for cleaning, infiltrating, and reusing the captured runoff.