Calculating credits for tree trenches and tree boxes

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Recommended pollutant removal efficiencies, in percent, for tree trench/tree box BMPs. Sources. NOTE: removal efficiencies are 100 percent for water that is infiltrated. TSS=total suspended solids; TP=total phosphorus; PP=particulate phosphorus; DP=dissolved phosphorus; TN=total nitrogen
TSS	TP	PP	DP	TN	Metals	Bacteria	Hydrocarbons
85	link to table	link to table	link to table	50	35	95	80

Credit refers to the quantity of stormwater or pollutant reduction achieved either by an individual BMP or cumulatively with multiple BMPs. Stormwater credits are a tool for local stormwater authorities who are interested in

• providing incentives to site developers to encourage the preservation of natural areas and the reduction of the volume of stormwater runoff being conveyed to a best management practice (BMP);
• complying with permit requirements, including antidegradation (see [1]; [2]);
• meeting the MIDS performance goal; or
• meeting or complying with water quality objectives, including Total Maximum Daily Load (TMDL) Wasteload Allocations (WLAs).

This page provides a discussion of how tree trench/tree box practices can achieve stormwater credits. Tree systems with and without underdrains are both discussed, with separate sections for each type of system as appropriate.

Overview

Tree trenches and tree boxes are specialized bioretention practices. They are therefore terrestrial-based (up-land as opposed to wetland) water quality and water quantity control process. Tree systems consist of an engineered soil layer designed to treat stormwater runoff via filtration through plant and soil media, evapotranspiration from trees, or through infiltration into underlying soil. Pretreatment is REQUIRED for all bioretention facilities, including tree-based systems, to settle particulates before entering the BMP. Tree practices may be built with or without an underdrain. Other common components may include a stone aggregate layer to allow for increased retention storage and an impermeable liner on the bottom or sides of the facility if located near buildings, subgrade utilities, or in karst formations.

Pollutant removal mechanisms

Like other bioretention practices, tree trenches and tree boxes have high nutrient and pollutant removal efficiencies (Mid-America Regional Council and American Public Works Association Manual of Best Management Practice BMPs for Stormwater Quality, 2012). Tree practices provide pollutant removal and volume reduction through filtration, evaporation, infiltration, transpiration, biological and microbiological uptake, and soil adsorption; the extent of these benefits is highly dependent on site specific conditions and design. In addition to phosphorus and total suspended solids (TSS), which are discussed in greater detail below, tree practices treat a wide variety of other pollutants.

Removal of phosphorus is dependent on the engineered media. Media mixes with high organic matter content typically leach phosphorus and can therefore contribute to water quality degradation. The Manual provides a detailed discussion of media mixes, including information on phosphorus retention.

Location in the treatment train

Stormwater treatment trains are multiple Best Management Practice (BMPs) that work together to minimize the volume of stormwater runoff, remove pollutants, and reduce the rate of stormwater runoff being discharged to Minnesota wetlands, lakes and streams. Under the Treatment Train approach, stormwater management begins with simple methods that prevent pollution from accumulating on the land surface, followed by methods that minimize the volume of runoff generated, and is completed by BMPs that reduce the pollutant concentration and/or volume of stormwater runoff. Tree trenches and tree boxes can be incorporated anywhere in the stormwater treatment train but are most often located in upland areas of the treatment train. The strategic distribution of tree BMPs help control runoff close to the source where it is generated.

Methodology for calculating credits

This section describes the basic concepts and equations used to calculate credits for volume, Total Suspended Solids (TSS) and Total Phosphorus (TP). Specific methods for calculating credits are discussed later in this article.

Tree practices generate credits for volume, Total Suspended Solids (TSS) and Total Phosphorus (TP). Practices with underdrains do not substantially reduce the volume of runoff but may qualify for a partial volume credit as a result of evapotranspiration, infiltration occurring through the sidewalls above the underdrain, and infiltration below the underdrain piping. Tree practices are effective at reducing concentrations of other pollutants including nitrogen, metals, bacteria, and hydrocarbons. This article does not provide information on calculating credits for pollutants other than TSS and TP, but references are provided that may be useful for calculating credits for other pollutants.

Assumptions and approach

In developing the credit calculations, it is assumed the tree practice is properly designed, constructed, and maintained in accordance with the Minnesota Stormwater Manual. If any of these assumptions is not valid, the BMP may not qualify for credits or credits should be reduced based on reduced ability of the BMP to achieve volume or pollutant reductions. For guidance on design, construction, and maintenance, see the appropriate article within the tree section of the Manual.

In the following discussion, the water quality volume (V_WQ) is delivered instantaneously to the BMP. The V_WQ is stored within the filter media. The V_WQ can vary depending on the stormwater management objective(s). For construction stormwater, V_WQ is 1 inch off new impervious surface. For MIDS, V_WQ is 1.1 inches.

Volume credit calculations - no underdrain

Volume credits are calculated based on the capacity of the BMP and its ability to permanently remove stormwater runoff via infiltration into the underlying soil, evapotranspiration (ET) from trees, and interception of rainfall by the tree canopy. The total volume credit, V in cubic feet, is given by

\( V = V_{inf}\ + V_{ET}\ + V_I \)

where

V_inf is the volume of captured water that is infiltrated, in cubic feet;

V_ET is the volume of captured water that is lost to evapotranspiration, in cubic feet; and

V_I is the volume of precipitation intercepted by the tree canopy, in cubic feet.

Interception credit

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 (I_c), as presented by Breuer et al. (2003) for deciduous and coniferous tree species.

• I_{c coniferous} = 0.087 inches (2.2 millimeters)
• I_{c deciduous} = 0.043 inches (1.1 millimeters)

This credit is per storm event.

Infiltration and ET credits

Schematic showing the terms used for calculating volume credits for a tree trench/tree box with no underdrain.

The infiltration and ET credits are assumed to be instantaneous values entirely based on the capacity of the BMP to capture, store, and transmit water in any storm event. Because the volume is calculated as an instantaneous volume, the water quality volume (V_WQ) is assumed to be instantly stored in the bioretention media. The volume of water between saturation and field capacity is assumed to infiltrate through the bottom of the BMP. The volume credit (V_infb) for infiltration through the bottom of the BMP into the underlying soil, in cubic feet, is given by

\( V_{inf_b} = (n-FC)\ D_M\ (A_M + A_B)\ / 2 \)

where

n is the porosity of the media in cubic feet per cubic foot;

FC is the field capacity of the media in cubic feet per cubic foot;

A_M is the area at the surface of the media, in square feet;

A_B is the area at the bottom of the media, in square feet; and

D_M is the media depth within the BMP, in feet.

ET is calculated as the volume of water between field capacity and the permanent wilting point. 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.

The second calculation is the theoretical ET. The theoretical volume of ET lost (Lindsey and Bassuk, 1991) per day per tree is given by

\(ET = (CP) (LAI) (E_{rate}) (E_{ratio})*3\)

Where:

CP is the canopy projection area (square feet);

LAI is the Leaf Area Index;

E_rate is the evaporation rate per unit time (feet per day);

E_ratio is the evaporation ratio; and

3 accounts for the number of days over which ET occurs (the average number of days between rain events in Minnesota).

Caution: The theoretical ET must be adjusted if the actual soil volume is less than the recommended volume. See the adjustment calculation below.

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 (E_rate) 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 (E_ratio) 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 S_v 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

The annual volume captured and infiltrated by the BMP can be determined with appropriate modeling tools, including the MIDS calculator. Example values are shown below for a scenario using the MIDS calculator. For example, a permeable pavement system designed to capture 1 inch of runoff from impervious surfaces will capture 89 percent of annual runoff from a site with B (SM) soils.

Annual volume, expressed as a percent of annual runoff, treated by a BMP as a function of soil and Water Quality Volume. See footnote¹ for how these were determined.
Link to this table

Soil	Water quality volume (VWQ) (inches)
	0.5	0.75	1.00	1.25	1.50
A (GW)	84	92	96	98	99
A (SP)	75	86	92	95	97
B (SM)	68	81	89	93	95
B (MH)	65	78	86	91	94
C	63	76	85	90	93

¹Values were determined using the MIDS calculator. BMPs were sized to exactly meet the water quality volume for a 2 acre site with 1 acre of impervious, 1 acre of forested land, and annual rainfall of 31.9 inches.

Volume credit calculations - underdrain

If an underdrain is present, the volume credits for ET and canopy interception remain the same as shown above. Volume credits for infiltration are available only if the BMP permanently removes a portion of the stormwater runoff via infiltration through sidewalls or beneath the underdrain piping. The ET and infiltration credits are assumed to be instantaneous values based on the design capacity of the BMP for a specific storm event. Instantaneous volume reduction, also termed event based volume reduction, can be converted to annual volume reduction percentages using the MIDS calculator or other appropriate modeling tools.

The main design variables impacting the infiltration volume credit includes whether the underdrain is elevated above the native soils and if an impermeable liner on the sides or bottom of the basin is used. Other design variables include media top surface area, underdrain location, basin bottom area, total depth of media, soil water holding capacity and media porosity, and infiltration rate of underlying soils. The infiltration volume credit (V_inf), in cubic feet, is given by

\( V_{inf} = V_{inf_b}\ + V_{inf_s}\ + V_U \)

where:

V_infb = volume of infiltration through the bottom of the basin (cubic feet);

V_infs = volume of infiltration through the sides of the basin (cubic feet); and

V_U = volume of water stored beneath the underdrain that will infiltrate into the underlying soil (cubic feet).

Volume credits for infiltration through the bottom of the basin (V_infb) are accounted for only if the bottom of the basin is not lined. As long as water continues to draw down, some infiltration will occur through the bottom of the BMP. However, it is assumed that when an underdrain is included in the installation, the majority of water will be filtered through the media and exit through the underdrain. Because of this, the drawdown time is likely to be short. Volume credit for infiltration through the bottom of the basin is given by

\( V_{inf_B} = A_B\ DDT\ I_R/12 \)

where

I_R = design infiltration rate of underlying soil (inches per hour);

A_B = surface area at the bottom of the basin (square feet); and

DDT = drawdown time for ponded water (hours).

The drawdown time is typically a maximum of 48 hours, which is designed to be protective of plants grown in the media. The Construction Stormwater permit requires drawdown within 48 hours and recommends 24 hours when discharges are to a trout stream. With a properly functioning underdrain, the drawdown time is likely to be considerably less than 48 hours.

Volume credit for infiltration through the sides of the basin is accounted for only if the sides of the basin are not lined with an impermeable liner. Volume credit for infiltration through the sides of the basin is given by

\( V_{inf_s} = (A_M - A_U)\ DDT\ I_R/12 \)

where

A_M = the area at the media surface (square feet); and

A_U = the surface area at the underdrain (square feet).

This equation assumes water will infiltrate through the entire sideslope area during the period when water is being drawn down. This is not the case, however, since the water level will decline in the BMP. The MIDS calculator assumes a linear drop in water level and thus divides the right hand term in the above equation by 2.

Volume credit for media storage capacity below the underdrain (V_U) is accounted for only if the underdrain is elevated above the native soils. Volume credit for media storage capacity below the underdrain is given by

\( V_U = (n-FC)\ D_U\ (A_U + A_B)/2 \)

where

A_B = surface area at the bottom of the media (square feet);

n = media porosity (cubic feet per cubic foot);

FC is the field capacity of the soil, in cubic feet per cubic foot; and

D_U = the depth of media below the underdrain (feet).

This is an instantaneous volume. This will somewhat overestimate actual storage when the majority of water is being captured by the underdrains. This equation assumes water between the soil porosity and field capacity will infiltrate into the underlying soil.

The volume of water passing through underdrains can be determined by subtracting the volume loss (V) from the volume of water instantaneously captured by the BMP. No volume reduction credit is given for filtered stormwater that exits through the underdrain, but the volume of filtered water can be used in the calculation of pollutant removal credits through filtration.

The volume reduction credit (V) can be converted to an annual volume if desired. This conversion can be generated using the MIDS calculator or other appropriate modeling techniques. The MIDS calculator obtains the percentage annual volume reduction through performance curves developed from multiple modeling scenarios using the volume reduction capacity for biofiltration, the infiltration rate of the underlying soils, and the contributing watershed size and imperviousness.

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. Note that the following calculations are on a per tree basis. Total volume credit for the BMP will equal the per tree value times the number of trees, assuming all trees are of the same relative size (large in this case).

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

\((CP) (LAI) (E_{rate}) (E_{ratio}) (adjustment) (3 days) = 707 * 4.7 * 0.02 * 0.2 * (1000/(2 * 707)) * 3 = 28.2 cubic feet\)

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 (E_rate) 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.

Total suspended solids credit calculations

TSS reduction credits correspond with volume reduction through infiltration/ET and filtration of water captured by the tree BMP and are given by

\( M_{TSS} = M_{TSS_{i+ET}} + M_{TSS_f} \)

where

M_TSS = TSS removal (pounds);

M_TSSi+ET = TSS removal from infiltrated and evapotranspired water (pounds); and

M_TSSf = TSS removal from filtered water (pounds).

Pollutant removal for infiltrated and evapotranspired water is assumed to be 100 percent. The event-based mass of pollutant removed through infiltration and ET, in pounds, is given by

• underdrain - \( M_{TSS_{i+ET}} = 0.0000624\ (V_{inf_b} + V_{inf_s} + V_U + V_{ET})\ EMC_{TSS} \)
• no underdrain - \( M_{TSS_{i+ET}} = 0.0000624\ V_{WQ}\ EMC_{TSS} \)

where

EMC_TSS is the event mean TSS concentration in runoff water entering the BMP (milligrams per liter).

The EMC_TSS entering the BMP is a function of the contributing land use and treatment by upstream tributary BMPs. For more information on EMC values for TSS, link here. If there is no underdrain, the the water quality volume (V_WQ)) is used in this calculation.

Removal for the filtered portion is less than 100 percent. The event-based mass of pollutant removed through filtration, in pounds, is given by

\( M_{TSS_f} = 0.0000624\ (V_{total} - (V_{inf_b} + V_{inf_s} + V_U))\ EMC_{TSS}\ R_{TSS} \)

where

V_total is the total volume of water captured by the BMP (cubic feet); and

R_TSS is the TSS pollutant removal percentage for filtered runoff.

The Stormwater Manual provides a recommended value for R_TSS of 0.85 (85 percent removal) for filtered water, while the MIDS calculator provides a value of 0.65 (65 percent). Alternate justified percentages for TSS removal can be used if proven to be applicable to the BMP design.

The above calculations may be applied on an event or annual basis and are given by

\( M_{TSS_f} = 2.72\ F\ V_{annual}\ EMC_{TSS}\ R_{TSS} \)

where

F is the fraction of annual volume filtered through the BMP; and

V_annual is the annual volume treated by the BMP, in acre-feet.

Phosphorus credit calculations

Total phosphorus (TP) reduction credits correspond with volume reduction through infiltration/ET and filtration of water captured by the tree BMP and are given by

\( M_{TP} = M_{TP_{i+ET}} + M_{TP_f} \)

where

M_TP = TP removal (pounds);

M_TPi+ET = TP removal from infiltrated water (pounds); and

M_{TP_f} = TP removal from filtered water (pounds).

Pollutant removal for infiltrated water is assumed to be 100 percent. The mass of pollutant removed through infiltration, in pounds, is given by

• underdrain - \( M_{TP_{i+ET}} = 0.0000624\ (V_{inf_b} + V_{inf_s} + V_U + V_{ET})\ EMC_{TP} \)
• no underdrain - \( M_{TP_{i+ET}} = 0.0000624\ V_{WQ})\ EMC_{TP} \)

where

EMC_TP is the event mean TP concentration in runoff water entering the BMP (milligrams per liter).

The EMC_TP entering the BMP is a function of the contributing land use and treatment by upstream tributary BMPs.

The filtration credit for TP in bioretention with underdrains assumes removal rates based on the soil media mix used and the presence or absence of amendments. Soil mixes with more than 30 mg/kg phosphorus (P) content are likely to leach phosphorus and do not qualify for a water quality credit. If the soil phosphorus concentration is less than 30 mg/kg, the mass of phosphorus removed through filtration, in pounds, is given by

\( M_{TP_f} = 0.0000624\ (V_{total} - (V_{inf_b} + V_{inf_s} + V_U + V_{ET}))\ EMC_{TP}\ R_{TP} \)

Information: Soil mixes C and D are assumed to contain less than 30 mg/kg of phosphorus and therefore do not require testing

Again, assuming the phosphorus content in the media is less than 30 milligrams per kilogram, the removal efficiency (R_TP) provided in the Stormwater Manual is a function of the fraction of phosphorus that is in particulate or dissolved form, the depth of the media, and the presence or absence of soil amendments. For the purpose of calculating credits it can be assumed that TP in storm water runoff consists of 55 percent particulate phosphorus (PP) and 45 percent dissolved phosphorus (DP). The removal efficiency for particulate phosphorus is 80 percent. The removal efficiency for dissolved phosphorus is 20 percent if the media depth is 2 feet or greater. The efficiency decreases by 1 percent for each 0.1 foot decrease in media thickness below 2 feet. If a soil amendment is added to the BMP design, an additional 40 percent credit is applied to dissolved phosphorus. Thus, the overall removal efficiency, (R_TP), expressed as a percent removal of total phosphorus, is given by

\( R_{TP} = (0.8 * 0.55) + (0.45 * ((0.2 * (D_{MU_{max=2}})/2) + 0.40_{if amendment is used})) * 100 \)

where

the first term on the right side of the equation represents the removal of particulate phosphorus;

the second term on the right side of the equation represents the removal of dissolved phosphorus; and

D_MUmax=2 = the media depth above the underdrain, up to a maximum of 2 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? If yes, particulate credit = 100% of the particulate fraction (assumed to be 55% of total P) If no or unknown, particulate credit = 0% 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 Particulate fraction (55% of TP) * removal rate for that fraction (80% for bioretention and tree trench and 68% for swale main channel) = 0.55 * 0.80 = 0.44 or 44% for bioretention and tree trench (with underdrain) and 0.55 * 0.68 or 36% for swale main channel (with underdrain) If particulate is 75% of TP, removal = 0.75 * 0.80 or 60% for bioretention and tree trench (with underdrain) and 0.75 * 0.68 or 51% for dry swale	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? If yes, credit as a % (up to a maximum of 20%) = 20 * (depth of media above underdrain, in feet/2) If no or unknown, credit = 0% 2. Does the system include approved P-sorbing soil amendments2? If yes, additional 40% credit Example DP removal credit DP removal if dissolved credit is 20% = Dissolved fraction (45%) * removal rate for that fraction (20%) = 0.09 or 9 percent Adjust DP removal if depth is less than 2 feet. Example depth = 1 foot then DP removal = 0.45 * 10% * 1/2 = 0.045 Adjust DP removal if dissolved credit is higher due to use of P-sorbing soil amendments Adjust if the fraction (percentage) of DP is different than 45% 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.
TP removal = PP removal + DP removal

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 80 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 80 percent of the particulate phosphorus. 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 S_d 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 S_d 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.

Total phosphorus credit

The credit for total phosphorus equals the particulate credit plus the dissolved credit.

Example calculations

Example 1 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
• 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 therefore 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 percent 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
• Media Mix C is used

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 80 percent credit for particulate phosphorus. Since particulate P is 55 percent of total P, the credit is 0.80 * 0.55 * 0.40 = 18 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 phosphorus credit is 73 percent of the annual P load (50 + 18 +5).

Related pages

• Trees
  • Overview for trees
  • Types of tree BMPs
  • Plant lists for trees
  • Street sweeping for trees
  • References for trees
  • Supporting material for trees

• Calculating credits
  • Calculating credits for bioretention
  • Calculating credits for infiltration basin
  • Calculating credits for permeable pavement
  • Calculating credits for green roofs
  • Calculating credits for sand filter
  • Calculating credits for stormwater ponds
  • Calculating credits for stormwater wetlands
  • Calculating credits for iron enhanced sand filter
  • Calculating credits for swale
  • Calculating credits for tree trenches and tree boxes

The following pages address incorporation of trees into stormwater management under paved surfaces

• Design guidelines for tree quality and planting - tree trenches and tree boxes
• Design guidelines for soil characteristics - tree trenches and tree boxes
• Construction guidelines for tree trenches and tree boxes
• Protection of existing trees on construction sites
• Operation and maintenance of tree trenches and tree boxes
• Assessing the performance of tree trenches and tree boxes
• Calculating credits for tree trenches and tree boxes
• Case studies for tree trenches and tree boxes
• Soil amendments to enhance phosphorus sorption
• Fact sheet for tree trenches and tree boxes
• Requirements, recommendations and information for using trees as a BMP in the MIDS calculator
• Requirements, recommendations and information for using trees with an underdrain as a BMP in the MIDS calculator