Calculating credits for tree trenches and tree boxes
The credit information provided here is summary in nature. More detailed information will be provided in spring, 2014.
Credits are discussed for volume, phosphorus and total suspended solids (TSS).
Volume credit
Volume credits for tree trenches and tree boxes includes
- water that infiltrates into the underlying soil,
- water that is intercepted by the tree canopy, and
- water that is taken up and evapotranspired by trees.
Infiltration
The following volume credits apply to individual storm events.
- For a tree BMP without an underdrain, the volume credit for infiltration equals the amount of water stored between soil saturation (soil porosity) and field capacity.
- For a tree BMP with an underdrain, the volume credit for infiltration equals the amount of water stored below the underdrain between soil saturation and field capacity.
- For a tree BMP with an underdrain at the bottom, the MIDS calculator includes a volume credit equal to the soil infiltration rate times the drawdown time. The default soil is a D soil with an infiltration rate of 0.06 inches per hour. The drawdown time may be 24 or 48 hours.
Interception
Water intercepted by a tree canopy may evaporate or be slowly released such that it does not contribute to stormwater runoff. An interception credit is given by a simplified value of the interception capacity (Ic), as presented by Breuer et al. (2003) for deciduous and coniferous tree species.
- Ic coniferous = 0.087 inches (2.2 millimeters)
- Ic deciduous = 0.043 inches (1.1 millimeters)
This credit is per storm event.
Evapotranspiration
Two calculations are needed to determine the evapotranspiration (ET) credit. First is the volume of water available for ET. This equals the water stored between field capacity and the wilting point. Note this calculation is made for the entire thickness of the media regardless of whether an underdrain is present.
The second calculation is the theoretical ET. The theoretical volume of ET lost (Lindsey and Bassuk, 1991) per day is given by
\(ET = (CP) (LAI) (E_{rate}) (E_{ratio})\)
Where:
- CP is the canopy projection area (square feet);
- LAI is the Leaf Area Index;
- Erate is the evaporation rate per unit time (feet per day); and
- Eratio is the evaporation ratio.
The canopy projection area (CP) is the perceived tree canopy diameter at maturity and is given by
\(CP = Π (d/2)^2\)
where d is the diameter of the canopy as measured at the dripline (feet).
CP varies by tree species. Please refer to the Tree Species List for these values. Default values can be used in place of calculating CP. Defaults for CP are based on tree size and are
- 315 for a small tree;
- 490 for a medium sized tree; and
- 707 for a large tree.
The leaf area index (LAI) should be stratified by type into either
- deciduous tree species (LAI = 3.5 for small trees, 4.1 for medium-sized trees, and 4.7 for large trees), or
- coniferous tree species (LAI = 5.47).
These values are based on collected research for global leaf area from 1932-2000 (Scurlock, Asner and Gower, 2002).
The evaporation rate (Erate) per unit time can be calculated using a pan evaporation rate for the given area, as available at NOAA. This should be estimated as a per day value.
The evaporation ratio (Eratio) is the equivalent that accounts for the efficiency of the leaves to transpire the available soil water or, alternately, the stomatal resistance of the canopy to transpiration and water movement. This is set at 0.20, or 20 percent based on research by Lindsey and Bassuk (1991). This means that a 1 square centimeter leaf transpires only about 1/5 as much as 1 square centimeter of pan surface.
If the soil volume is less than the recommended volume, the theoretical ET must be adjusted. Since the recommended soil volume equals 2 times the canopy project area (CP), the adjustment term is given by
\(Adjustment = (S_v)/(2 CP)\)
Where Sv is the actual soil volume in cubic feet. Multiply the theoretical ET by the adjustment term to arrive at the true value for theoretical ET.
It is recommended that calculations be based over a three day period. To determine the credit, compare the volume of water available for ET to the theoretical ET over a 3 day period. The credit is the smaller of these two values.
Recommended values for porosity, field capacity and wilting point for different soils.1
Link to this table.
| Soil | Hydrologic soil group | Porosity 2 (volume/volume) | Field capacity (volume/volume) | Wilting point (volume/volume) | Porosity minus field capacity (volume/volume)3 | Field capacity minus wilting point (volume/volume)4 |
|---|---|---|---|---|---|---|
| Sand | A (GM, SW, or SP) | 0.43 | 0.17 | 0.025 to 0.09 | 0.26 | 0.11 |
| Loamy sand | A (GM, SW, or SP) | 0.44 | 0.09 | 0.04 | 0.35 | 0.05 |
| Sandy loam | A (GM, SW, or SP) | 0.45 | 0.14 | 0.05 | 0.31 | 0.09 |
| Loam | B (ML or OL) | 0.47 | 0.25 to 0.32 | 0.09 to 0.15 | 0.19 | 0.16 |
| Silt loam | B (ML or OL) | 0.50 | 0.28 | 0.11 | 0.22 | 0.17 |
| Sandy clay loam | C | 0.4 | 0.07 | |||
| Clay loam | D | 0.46 | 0.32 | 0.15 | 0.14 | 0.17 |
| Silty clay loam | D | 0.47 to 0.51 | 0.30 to 0.37 | 0.17 to 0.22 | 0.16 | 0.14 |
| Sandy clay | D | 0.43 | 0.11 | |||
| Silty clay | D | 0.47 | 0.05 | |||
| Clay | D | 0.47 | 0.32 | 0.20 | 0.15 | 0.12 |
1Sources of information include Saxton and Rawls (2006), Cornell University, USDA-NIFA, Minnesota Stormwater Manual. (See References for trees)
2Soil saturation is assumed to be equal to the porosity.
3This value may be used to represent the volume of water that will drain from a bioretention media.
4This value may be used to estimate the amount of water available for evapotranspiration
Example calculation
A parking lot is developed and will contain tree trenches containing red maple (Acer rubrum). The tree trench has 1000 cubic feet of sandy loam per tree.
Infiltration credit
The infiltration credit is given by
\((soil volume) (porosity - field capacity) = 1000 * 0.31 = 310 cubic feet\)
Evapotranspiration credit
Using the tree morphology table, red maple is a large tree with a mature canopy of 30 feet. The available storage volume is given by
\(Soil volume (field capacity - wilting point) = 1000 * 0.09 = 90 cubic feet\)
The theoretical ET volume is given by
\((CP) (LAI) (E_{rate}) (E_{ratio}) (adjustment) (3 days) = 707 * 4.7 * 0.02 * 0.2 * (1000/(2 * 707)) = 28.2 cubic feet\)
The smaller value is the theoretical ET (28.2 cubic feet), so that is the volume credit. Note that if the recommended soil volume had been used the credit would be 39.9 cubic feet.
To make this calculation we used the default value of 707 for CP and the soil volume information from the table above. The evaporation rate (Erate) of 0.24 inches per day (0.02 feet per day) was from data collected at the Southwest Research and Outreach Center in Lamberton, Minnesota.
Interception credit
The interception credit is given by
\(707 (0.043/12) = 2.5 cubic feet\)
The division by 12 converts the calculation to feet.
Total credit
The total credit is the sum of the infiltration, ET and interception credits and equals (310 + 28.2 + 2.5) or 340.7 cubic feet.
Phosphorus credits
- The phosphorus credit for water that is infiltrated is 100 percent. Volume calculations are discussed above.
- When an underdrain is present, water that does not infiltrate below the drain is captured by the underdrain. In this situation, phosphorus credits are a function of the position of the underdrain, media mix used, soil testing, and presence/absence of soil amendments. These are discussed below.
Phosphorus credit for non-volume reduction
Phosphorus credits for water entering a BMP and not infiltrating the underlying soil (i.e. going to an underdrain) are summarized in the following table. Phosphorus in soil (media) water is assumed to be 55 percent in the particulate form and 45 percent in the dissolved form.
Phosphorus credits for bioretention systems with an underdrain. This includes tree trenches and dry swales.
Link to this table
| Particulate phosphorus (PP) | Dissolved phosphorus (DP) |
|---|---|
Is Media Mix C or D being used or, if using a mix other than C or D, is the media phosphorus content 30 mg/kg or less per the Mehlich 3 (or equivalent) test1?
The assumption of 55 percent particulate phosphorus and 45 percent dissolved phosphorus is likely inaccurate for certain land uses, such as industrial, transportation, and some commercial areas. Studies indicate particulate phosphorus comprises a greater percent of total phosphorus in these land uses. It may therefore be appropriate to modify the above equation with locally derived ratios for particulate and dissolved phosphorus. For more information on fractionation of phosphorus in stormwater runoff, link here.
Example PP removal credit
|
1. Is Media Mix C or D being used or, if using a mix other than C or D, is the media phosphorus content 30 mg/kg or less per the Mehlich 3 (or equivalent) test1?
2. Does the system include approved P-sorbing soil amendments2?
The assumption of 55 percent particulate phosphorus and 45 percent dissolved phosphorus is likely inaccurate for certain land uses, such as industrial, transportation, and some commercial areas. Studies indicate particulate phosphorus comprises a greater percent of total phosphorus in these land uses. It may therefore be appropriate to modify the above equation with locally derived ratios for particulate and dissolved phosphorus. For more information on fractionation of phosphorus in stormwater runoff, link here. |
| |
|
1Other widely accepted soil P tests may be used. Note: a basic conversion of test results may be necessary
2Acceptable P sorption amendments include
- 5% by volume elemental iron filings above IWS or elevated underdrain
- minimum 5% by volume sorptive media above IWS or elevated underdrain
- minimum 5% by weight water treatment residuals (WTR) to a depth of at least 10 cm
- other P sorptive amendments with supporting third party research results showing P reduction for at least 20 year lifespan, P credit commensurate with research results
Particulate phosphorus credit
For particulate phosphorus, the following credits apply.
- If Media Mix C or D is used, the credit is 45 percent (of the particulate P).
- If a media mix other than C or D is used and the soil phosphorus as measured using the Mehlich 3 test is 30 milligrams per kilogram or less, the credit is 45 percent. Note that other soil phosphorus tests may be acceptable.
- If a media mix other than C or D is used and the soil phosphorus as measured using the Mehlich 3 test is greater than 30 milligrams per kilogram, the credit is 0 percent. Note that other soil phosphorus tests may be acceptable.
- If a media mix other than C or D is used and the soil phosphorus has not been determined, the credit is 0 percent.
Dissolved phosphorus credit
For dissolved phosphorus, the following credits apply.
- If Media Mix C or D is used, the credit, as a percent up to a maximum of 20 percent, is given by
\(Credit = 20 (S_d / 2)\)
Where Sd is the soil depth above the underdrain, in feet.
- If a media mix other than C or D is used and the soil phosphorus as measured using the Mehlich 3 test is 30 milligrams per kilogram or less, the credit, as a percent up to a maximum of 20 percent, is given by
\(Credit = 20 (S_d / 2)\)
Where Sd is the soil depth above the underdrain, in feet. Note that other soil phosphorus tests may be acceptable.
- If a media mix other than C or D is used and the soil phosphorus as measured using the Mehlich 3 test is greater than 30 milligrams per kilogram, the credit is 0 percent. Note that other soil phosphorus tests may be acceptable.
- If a media mix other than C or D is used and the soil phosphorus has not been determined, the credit is 0 percent.
Credit for P-sorbing amendments
An additional phosphorus credit of 40 percent may be received if P-sorbing amendments are used. Acceptable amendments include the following.
- 5 percent by volume elemental iron filings above IWS or elevated underdrain;
- minimum 5 percent by volume sorptive media above IWS or elevated underdrain
- minimum 5 percent by weight water treatment residuals (WTR) to a depth of at least 10 centimeters;
- other P sorptive amendments with supporting third party research results showing P reduction for at least 20 year lifespan, P credit commensurate with research results.
Example calculations
Example 1 Assume the following:
- A tree trench with an underdrain that has 1 foot of media above the underdrain
- 50 percent of annual runoff is infiltrated into the underlying soil
- 40 percent of annual runoff is captured by the underdrain
- 10 percent of annual runoff bypasses the BMP
- Media Mix A is used and soil phosphorus is 32 milligrams per kilogram
- Water Treatment Residuals, 7 percent by weight, have been mixed into the top 15 centimeters of the media.
The credits are as follows
- 100 percent credit for infiltrated runoff = 50 percent of annual runoff = 50 percent of annual phosphorus load
- For water that is captured by the underdrain
- The media is Mix A with a P content greater than 30 milligrams per kilogram, resulting in no credit for particulate or dissolved phosphorus
- A P-sorbing amendment has been added to the media and meets the requirements for a credit of 40 percent. The credit applies to the dissolved portion of phosphorus, which is 45 percent of total phosphorus. The credit is there 40 percent times 45 percent times the annual runoff volume of 40 percent, resulting in a credit of 7 percent of total annual P (0.4 * 0.45 * 0.4).
- No credit for water that bypasses the BMP
- The total credit is 57% of the annual P load.
Example 2 Assume the following:
- A tree trench with an underdrain has 1 foot of media above the underdrain
- 50 percent of annual runoff is infiltrated into the underlying soil
- 40 percent of annual runoff is captured by the underdrain
- 10 percent of annual runoff bypasses the BMP
The credits are as follows
- 100 percent credit for infiltrated runoff = 50 percent of annual runoff = 50 percent of annual phosphorus load
- For water that is captured by the underdrain
- The media is Mix C resulting in 45 percent credit for particulate phosphorus. Since particulate P is 55 percent of total P, the credit is 0.45 * 0.55 * 0.40 = 9 percent. The value of 0.4 in the equation accounts for 40 percent of the annual runoff volume.
- The media mix is C and there is 1 foot of media above the underdrain. The credit is 0.2 * 1/2 * 0.45 = 5 percent. The 1/2 adjusts for the thickness of media above the underdrain and the 0.45 accounts for 45 percent of total phosphorus being in dissolved form.
- No credit for water that bypasses the BMP
- The total credit is 64% of the annual P load (50 + 9 +5).
Total suspended solids (TSS)
- 100 percent removal for water that infiltrates
- 85 percent removal for water that is captured by an underdrain