Calculating credits for tree trenches and tree boxes

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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

File:Tree trench schematic with interception.png

Schematic illustrating the three types of volume credits for a tree BMP. Click on the image for a more detailed discussion.

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

• 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 between soil saturation and field capacity and stored below the underdrain.
• 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 (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.

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;

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

E_ratio is the evaporation ratio.

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

\(Adjustment = (actual soil volume)/(2 CP)\)

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.

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 (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

<math>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 credit and equals (310 + 28.2 + 2.5) or 340.7 cubic feet.