LID PLANTER BOX MODELING
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1 LID PLANTER BOX MODELING Clear Creek Solutions, Inc., 2010 Low Impact Development (LID) planter boxes are small, urban stormwater mitigation facilities. They are rain gardens in a box. WWHM4 provides the user with three types of planter boxes: Flow-Through Planter Box In-Ground Planter Box In-Ground Planter Box without Infiltration with Infiltration These are all part of WWHM4 s LID Toolbox. The flow-through planter box is a raised box that collects roof runoff and then filters and discharges the runoff through an underdrain. The in-ground planter box without infiltration is, as the name implies, in the ground and typically collects road and other impervious area runoff. Once the runoff enters the inground planter box it is handled the same as in the flow-through planter box. The in-ground planter box with infiltration looks the same as the in-ground planter box without infiltration, but of course the big difference is the opportunity for some of the runoff to infiltrate into the native soil under the in-ground planter box. Both the flow-through planter box and the in-ground planter box without infiltration elements in WWHM4 have an automatic sizing option. (The in-ground planter box with infiltration element does not.) For this discussion we will select a flow-through planter box and size it with the automatic sizing option. Before we start I should note that all of the WWHM4 planter box elements use the same internal algorithms as the WWHM4 bio swale/rain garden element. As described in the rain garden documentation, WWHM4 uses the modified Green Ampt equation to compute the surface infiltration into the amended soil. The water then moves through the top amended soil layer at the computed rate, determined by Darcy s and Van Genuchten s equations. As the soil approaches field capacity (i.e., gravity head is greater 1
2 than matric head), the model determines when water will begin to infiltrate into the second amended soil layer (lower layer). This occurs when the matric head is less than the gravity head in the first layer (top layer). More details and associated equations can be found in the attached appendix. Like rain gardens, planter boxes perform two functions: (1) they provide water quality treatment of stormwater runoff and (2) they reduce total runoff volume. The effectiveness of a planter box in reducing stormwater runoff depends on the size of the planter box compared to the contributing drainage area and whether or not there is infiltration to the native soil. For the purposes of this example we will model a project with a flow-through planter (and no native soil infiltration). So let s get started. We will model a 1-acre building in Berkeley, California. The first thing that we will do is to locate our project on the project map. Berkeley is located in Alameda County, California. We click on the map to select the project location. Based on our project location WWHM4 selects the appropriate precipitation record and precipitation multiplication factor. We then have the option to fill in the Site Information boxes. 2
3 For the Pre-Project scenario we select a standard land use basin. We have to decide the appropriate pre-project land use for the project site. Because this project is located in Alameda County and has to meet the county s regulations, we select C/D soil, Grass vegetation, and Flat land slope (0-5%). The project site is 1 acre. POC 1 represents the pre-project runoff. For the Mitigated scenario we will use the standard basin element to represent the planned commercial development and the flow-through planter box element to represent the flow-through planter box. The planned commercial development site is limited to 1 acre. A portion of this site has to be reserved for the flow-through planter box; the remainder will be roof. Mitigation will be the flow-through planter box. Initially we will reserve 10% of the total planned commercial development site for the planter box. The means the roof area will be 0.9 acres and the planter box 0.1 acres. 3
4 First we add the land use basin element, rename it Commercial Bldg and assign 0.9 acres of Roof land use. 4
5 To see all of the WWHM4 LID Toolbox elements we click on the LID Toolbox bar and then select the flow-through planter box element (top row, third from the left). We name it FT Planter Box. We connect the land use basin (roof area) to FT Planter Box and connect the box s outlet to POC 1. Now we can size the planter box. 5
6 We have a limited area for the planter box (the planter box area plus roof area cannot exceed 1 acre). We have initially assumed that the roof area will be 0.9 acres. We are going to size the planter box area to get the smallest area possible while still meeting Alameda County s hydromod flow duration requirements. But we have to let WWHM4 know what is the maximum planter box area allowed for this development. For this example it is 0.1 acres. Therefore we put that area in the Maximum Planter Box Area (ac) box. We may have to change it later, but this is our initial value. We are now ready to click Size Planter Box. WWHM4 will then select an underdrain diameter, orifice diameter, planter length, planter width, freeboard, soil layer depths and soil types, and riser height and diameter prior to iterating to match the pre-project flow durations. We could have done all of this manually, but I think that I will let WWHM4 take the first shot at a solution. If I don t like the results I can always go back and change any of the input and try again. Well, take a break while WWHM4 runs through its sizing iterations. I will meet you back here after I go for a run around the block. 6
7 In the middle of the iteration process we get a warning message: Planter area exceeds maximum allowed area. Please adjust landuse to allow for a larger planter box. That means the discharge out of the planter box exceeds the pre-project flow durations. Because we are constricted to a total area of 1 acre we need to make the roof area smaller to make the planter box area larger. We will change the roof area from 0.90 acres to 0.85 acres and the planter box area from 0.10 acres to 0.15 acres and then try again. 7
8 We get the same warning message. We will increase the planter box area to 0.16 acres and reduce the roof area to 0.84 acres. 8
9 Finally, we get the message that we have been waiting for: Planter Box has been sized. The planter box dimensions are feet by feet. This equals 5756 square feet or acres. We set the maximum area to 0.16 acres, so we now have some extra area to work with. We can try increasing the roof area, keeping in mind that a small increase in roof area produces a lot of runoff and the need for a larger planter box. We also have the option of increasing the soil layer depths, riser height, and/or freeboard to store more water in the planter box prior to release. Or we can increase the planter box dimensions to equal the entire 0.16 acres. But before we make any changes to the planter box design let s first look at the flow duration results. 9
10 We go to the Analysis screen and click on POC 1 to plot flow durations. All of the duration values pass. Our flow through planter box is good to go. To equal the 0.16 acres we set aside for the planter box we can now increase the length and width from feet to feet. This increases the actual planter box area to equal 0.16 acres. You might be of the mind to try increasing the roof area. Remember that the current roof area is 0.84 acres. When we tried a roof area of 0.85 acres we didn t have enough corresponding planter box area to meet flow duration requirements. We can probably try to fine tune the roof area a bit (increasing it to a maximum allowed area between 0.84 and 0.85). I will let you take on that task if you want to explore further. Personally, I am good with what we got. 10
11 I manually change the planter length and width values from to feet. Then I click on the Run Scenario button to manually run the model with this new input. 11
12 These new final results show that 91.7% of the total runoff flows through the soil and out of the planter box via the underdrain. The remaining 8.3% of the runoff discharged by overtopping the riser. Alameda County has a water quality treatment requirement that a minimum of 80% of the total runoff volume be filtered (in this case, through the soil). This design meets that requirement. Now if you want to size the planter box manually you need to determine the values for the following input: 12
13 Underdrain diameter (feet): this is the perforated pipe at the bottom of the planter box that collects and discharges the water traveling down through the soil. The underdrain diameter should be larger than the orifice diameter, otherwise the underdrain diameter size is not a critical factor in the size of the planter box; 6 inches (0.5 ft) is a typical underdrain diameter. Orifice diameter (inches): this is the outlet control on the downstream end of the underdrain pipe. The orifice controls the release rate for the flow through the planter box unless the soil is controlling (see below for more details). The orifice diameter should be set to produce a discharge that is equal to the discharge value at the lower end of the flow duration range. For Alameda County this is 10% of Q2. You can find this discharge value by going to Analysis and clicking on POC 1 (assuming you have already run the model to generate runoff). 13
14 In our example 10% of Q2 equals cfs. 14
15 We can then click on the down arrow next to Show Planter Table to look at the stagestorage-discharge tables for the planter box. 15
16 The discharge column (4th column in the top table and the 5th column in the bottom table) shows the flow through the orifice. If you are sizing the orifice diameter you will want to put in a diameter value that will produce a discharge approximately equal to the discharge at lower end of the flow duration range at the common stage (in this case, 3 feet). Our value ( cfs) is actually larger than 10% of Q2 ( cfs). This example shows that this initial orifice diameter rule is not a hard, fast rule, and the initial orifice diameter size may be exceeded when the soil properties influence the discharge. 16
17 Freeboard (feet): this is the maximum allowed water depth above the top of the riser. If, during the simulation run, the water in the planter box ponds on the surface to a depth greater than the riser height plus the freeboard then the simulation will stop and an error message saying that there is insufficient storage will be posted on the screen. If that happens then increase the freeboard to create more surface storage or the riser diameter to increase surface discharge and prevent the ponding to go so high on the surface. 17
18 The planter box material layers input consists of specifying two soil layers and their associated depth of soil. Typically, planter boxes are designed with a layer of moderately well draining soil on top and a layer of gravel on the bottom. The top soil layer provides a growth medium for plants and filtration for the stormwater entering the planter box. The bottom gravel layer provides storage for stormwater prior to discharge via the underdrain pipe. The user has the option to specify either a soil in Soil Group A (NRCS classification system), B, C, or D. WWHM4 has soil parameter values for each soil group. These parameters include wilting point, minimum and maximum hydraulic conductivity, and Van Genuchten number. For the purposes of stormwater control and water quality treatment an A soil probably drains too fast and C and D soils drain very slowly. Therefore, a Soil Group B soil is a good compromise. If you do pick a C or D soil you may encounter a situation where the soil is controlling the planter box discharge instead of the underdrain orifice. That is not necessarily bad, but it is important to recognize that fact when manually sizing the planter box so that you don t waste time playing around with the orifice diameter when it doesn t make any difference to the final result. 18
19 The soil depth for each layer can be set by the user. Because a flow-through planter box is raised above the ground you don t want to have too large of a soil depth; otherwise the box is going to look like a square column rising above the pavement. Too small of a soil depth and it will be difficult to both grow plants and store water in the box. Typical soil layer depths are in the range of 1 to 2 feet. The planter box outlet structure data is for the riser. The job of the riser is to discharge excessive flow when there is ponding on the surface of the planter box. Flow via the riser should happen only in extreme events to prevent overtopping of the planter box. Riser height above planter surface (feet): this is the maximum ponding depth before there is discharge through the riser. Riser diameter (inches): this is the diameter of the riser (kind of obvious) and controls the rate of discharge through the riser. 19
20 SUMMARY: 1. Locate project site on map. 2. Input Predeveloped and Mitigated land use information for each basin in the project site. Connect the Predeveloped basin to the POC Add the planter box element to the Mitigated scenario. 4. Input the planter box element maximum area. 5. Remove the planter box area from the land use basin element total area. 6. Connect the planter box element to POC Size planter box automatically using Size Planter Box option. 8. Check flow duration results on Analysis screen. Make planter box changes if necessary. 9. Add additional mitigation facilities, if needed. 10. Finished. 20
21 APPENDIX: LID PLANTER BOX MODELING WATER MOVEMENT THROUGH THE SOIL COLUMN Water movement through the soil column is dependent on soil layer characteristics and saturation rates for different discharge conditions. Consider a simple two-layered bioretention facility designed with two soil layers with different characteristics. As water enters the facility at the top, it infiltrates into the soil based on the modified Green Ampt equation (Equation 1). The water then moves through the top soil layer at the computed rate, determined by Darcy s and Van Genuchten s equations. As the soil approaches field capacity (i.e., gravity head is greater than matric head), we can determine when water will begin to infiltrate into the second layer (lower layer) of the soil column. This occurs when the matric head is less than the gravity head in the first layer (top layer). Since the two layers have different soil characteristics, water will move through the two layers at different rates. Once both layers have achieved field capacity then the layer that first becomes saturated is determined by which layer is more restrictive. This is determined by using Darcy s equation to compute flux for each layer at the current level of saturation. The layer with the more restrictive flux is the layer that becomes saturated for that time step. The next time step the same comparison is made. The rate and location of water discharging from the soil layer is determined by the discharge conditions selected by the user. There are four possible combinations of discharge conditions: 1. There is no discharge from the subsurface layers (except for evapotranspiration). This means that there is no underdrain and there is no infiltration into the native soil. Which this discharge condition is unlikely, we still need to be able to model it. 2. There is an underdrain, but no native infiltration. Discharge from the underdrain is computed based on head conditions for the underdrain. The underdrain is configured to have an orifice. (It is possible for the orifice to be the same diameter as the underdrain.) With a maximum of three soil layers determining head conditions for the orifice is complicated. Each modeled layer must overcome matric head before flow through the underdrain can begin. Once matric head is overcome by gravity head for all of the layers then the underdrain begins to flow. The flow rate is determined based on the ability of the water to move through the soil layers and by the discharge from the orifice, whichever is smaller. Head conditions are determined by computing the saturation level of the lowest soil layer first. Once the lowest soil layer is saturated and flow begins then the gravity head is considered to be at the saturation level of the lowest soil layer. Once the lowest soil layer is saturated completely then the head will include the gravity head from the next soil layer above 21
22 until gravity head from all soil layers is included. Gravity head from ponding on the surface is included in the orifice calculations only if all of the intervening soil layers are saturated. 3. There is native infiltration but no underdrain. Discharge (infiltration) into the native soil is computed based a user entered infiltration rate in units of inches per hour. Specific head conditions are not used in determining infiltration into the native soil. Any impact due to head on the infiltration rate is considered to be part of the determination of the native soil infiltration rate. Because it is possible to have a maximum of three soil layers, each modeled layer must overcome matric head before infiltration to the native soil can begin. Once matric head is overcome by gravity head for all modeled layers then infiltration begins at a maximum rate determined either by the ability of the water to move through the soil layers or by the ability of the water to infiltrate into the native soil, whichever is limiting. 4. There is both an underdrain and native infiltration. Underdrain flow and native infiltration are computed as discussed above. However, there is one other limitation to consider. In the case where the flow through the soil layer is less than the sum of the discharge through the underdrain and the native infiltration then the flow through the soil layer becomes the limiting flow and must be divided between the native infiltration and the underdrain. This division is done based on the relative discharge rates of each. Note that wetted surface area can be included in the discharge calculations by adding the infiltration through the wetted surface area to the lower soil layer and the upper surface layer individually. This is done by computing the portion of the wetted surface area that is part of the upper surface layer and computing the infiltration independently from the portion of the wetted surface area that is part of the lower soil layers. Water Movement Equations There are several equations used to determine water movement from the surface of the bioretention facility, through the soil layers, and into an underdrain or native infiltration. The water movement process can be divided into three different zones: 1) Surface ponding and infiltration into the top soil layer (soil layer 1) 2) Percolation through the subsurface layers 3) Underdrain flow and native infiltration 22
23 Surface ponding and infiltration into the top subsurface layer The modified Green Ampt equation (Equation 1) controls the infiltration rate into the top soil layer: ( )(d ) f K 1 F (Equation 1; Ref: Rossman, 2009) f = soil surface infiltration rate (cm/hr) soil porosity of top soil layer soil moisture content of top soil layer suction head at the wetting front (cm) F= soil moisture content of the top soil layer (cm) d= surface ponding depth (cm) K= hydraulic conductivity based on saturation of top soil layer (cm/hr) K (relative hydraulic conductivity) can be computed using the following Van Genuchten approximation equation: (Equation 2; Ref: Blum et al, 2001) A few issues arise when dealing with multiple subsurface soil layers. The K value used in Equation 1 must be computed from the top soil layer. Infiltration into the upper soil layer must not exceed the lesser of the maximum percolation rates for each of the soil layers. Finally, the rate of percolation of the top layer may be reduced because the layer or layers beneath the top layer cannot accept the percolation flux because of existing saturation levels. 23
24 Percolation through the subsurface layers Water storage and movement through the three subsurface layers will be computed using Darcy s equation as shown below: q K h z (Equation 3) Where: q = Darcy flux (cm/hr) K = hydraulic conductivity of the porous medium (cm/hr) h = total hydraulic head (cm) z = elevation (cm) The total head, h, is the sum of the matric head,, and the gravity head, z: h z. (Equation 4) Substituting for h yields: q K d ( z ). dz (Equation 5) Hydraulic conductivity and matric head vary with soil moisture content. These values can be computed by solving the Van Genuchten s equation (Equation 6) for both values. Note that 0 when the soil is saturated. (Equation 6; Ref: Blum et al, 2001) Effective saturation (SE) can be computed using the following Van Genuchten equation: 24
25 (Equation 7; Ref: Blum et al, 2001) Ignoring z (elevation head) results in h = hm (matric head). EVAPOTRANSPIRATION FROM THE SOIL COLUMN Evapotranspiration is an important component of the bioretention facility s hydrologic processes. Evapotranspiration removes water from bioretention surface ponding and the soil column during non-storm periods. The routine will satisfy potential evapotranspiration (PET) demands in the same sequence as implemented in HSPF: 1. Water available from vegetation interception storage 2. Water available from surface ponding 3. Water available from the bioretention soil layers (top layer first) Water will be removed from vegetation interception storage and surface ponding and the bioretention soil layers (starting at the top layer) down to the rooting depth at the potential rate. Water is taken from the soil layers below the rooting depth based on a percentage factor to be determined. Without this factor there will be no way to remove water from below the rooting depth once it becomes completely saturated. 25
26 REFERENCES Blum, V.S., S. Israel, and S.P. Larson Adapting MODFLOW to Simulate Water Movement in the Unsaturated Zone. MODFLOW 2001 and Other Modeling Odysseys, International Groundwater Modeling Center (IGWMC), Colorado School of Mines, Golden, Colorado, September 11-14, In MODFLOW 2001 and Other Modeling Odysseys, Proceedings. pp Rossman, L.A Modeling Low Impact Development Alternatives with SWMM. Presented at CHI International Stormwater and Urban Water Systems Conference, Toronto, Ontario, Canada, February 20,
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