Symbol used for the tree trench system/box (w/o underdrain) BMP in the MIDS calculator. Note the symbol shows multiple trees since tree trench systems contain multiple trees.

For a tree trench system/box without an underdrain, stormwater runoff captured by the BMP is infiltrated into the underlying soil between rain events or lost through evapotranspiration. A small portion of precipitation is also intercepted by trees in the BMP. All pollutants in the captured and intercepted water are credited as being reduced. Pollutants in the stormwater that bypasses the BMP are not reduced. The user should be aware of the difference between a tree trench system and a tree box.

• Tree trench system is a BMP that includes multiple trees. This BMP is commonly used in areas where pavement overlies the trench system. Runoff from the impermeable surface or through a permeable pavement surface is delivered underground to the underlying media in which the trees are planted. This Manual includes case studies and a discussion of types of tree BMPs.
• Tree box (also called soil box) typically includes a single tree. They are typically proprietary products or are included in bioretention BMPs. If a tree is included in a bioretention BMP, we recommend using the bioretention BMP in the MIDS calculator instead of this BMP.

## Changes to Version 4 of the MIDS Calculator

Information: Changes have been made to Version of the MIDS Calculator
• Added the following question: Total media and soil depth available for tree rooting. This was done to allow trees to extend roots below the engineered media layer. This increases the potential soil volume available to trees, thus potentially allowing more trees to be incorporated into the design.

## MIDS calculator user inputs for tree trench system/box

Screen shot of the Watershed tab for tree trench system/box BMP in the MIDS calculator. In this example, 1 acre of Forest/open space, 1 acre of managed Turf, and 1 acre of Impervious Cover drain to the BMP. The BMP is being routed to a constructed stormwater pond.
Screen shot of the BMP Parameters tab for tree trench system/box BMP in the MIDS calculator.
Screen shot of the BMP Summary tab for tree trench system/box BMP in the MIDS calculator.

For Tree trench system/box (w/o underdrain) BMPs, the user must input the following parameters to calculate the volume and pollutant load reductions associated with the BMP.

• Watershed tab:
• BMP Name: this cell is auto-filled but can be changed by the user.
• Routing/downstream BMP: if this BMP is part of a treatment train and water is being routed from this BMP to another BMP, the user selects the name of the BMP to which water is being routed from the dropdown box. All water must be routed to a single downstream BMP. Note that the user must include the BMP receiving the routed water in the Schematic or the BMP will not appear in the dropdown box.
• BMP Watershed Area: BMP watershed areas are the areas draining directly to the BMP. Values can be added for four soil types (Hydrologic Soil Groups (HSG) A, B, C, D) and for three Land Cover types (Forest/Open Space, Managed Turf, and Impervious Cover). The surface area of the BMP should be included as a managed turf land cover under the hydrologic soils group of the native soils located under the BMP. Units are in acres.
• BMP Parameters tab:
• Media surface area (AM): This is the surface area at the surface of the media. For a tree trench system this is the cumulative area for all similar trees in the system. Similar trees are trees of the same type (deciduous or coniferous) and size (large, medium, or small tree). See Plant lists for trees for more information. Units are in square feet.
• Bottom surface area (AB): This is the surface area at the bottom of the media within the BMP. It represents the area where the engineered media changes to native soils. For a tree trench system this is the cumulative area for all similar trees in the system. Similar trees are trees of the same type (deciduous or coniferous) and size (large, medium, or small tree). See Plant lists for trees for more information. Units are in square feet.
• Media depth (DM): This is the depth of the engineered media between the media surface and the native soils. Units are in feet.
• Total media and soil depth available for tree rooting: This is the depth of engineered media and the underlying soil into which tree roots can extend.
• Media field capacity minus wilting point (FC - WP): This is the amount of water between field capacity and the permanent wilting point stored in the media. This is water often considered to be available for uptake by plants. If multiple types of media are used in the BMP, this value should be a weighted average of the soil water storage values of the media. Values for field capacity and wilting point based on soil type can be found here. Units are in cubic feet of water per cubic feet of media. The recommended range for this value is 0.05 to 0.17.
• Media porosity minus field capacity (n - FC): This is the amount of water stored in the media between media porosity (soil saturation) and field capacity that is thus available for infiltration into the underlying soils. If multiple types of media are used in the BMP, this value should be a weighted average of the soil water storage values of the media. Values for porosity and field capacity based on soil type can be found here. Units are in cubic feet of pore space per cubic feet of media. The recommended range for this value is 0.15 to 0.35.
• Tree type (most common): The user selects the type of tree planted in the tree trench/box from a drop down menu. The user can select a tree type of deciduous or coniferous. If both deciduous and coniferous trees are planted at the site, they should be treated as separate Tree trench system/tree box BMPs.
• Tree size (average for all trees): The user selects the size of tree planted in the tree trench/box system. The user can select small, medium or large. Tree size for different tree types are listed in the tree species list. If multiple tree sizes are planted at the site, they should be treated as separate Tree trench system/tree box BMPs.
• Number of trees: The user enters the total number of trees planted in the tree trench/tree box system.
• Underlying soil - Hydrologic Soil Group: The user selects the most restrictive soil (lowest hydraulic conductivity) within 5 feet below the soil/media interface in the tree trench/box. There are 14 soil options that fall into 4 different Hydrologic Soil Groups (Hydrologic Soil Group (HSG) A, B, C, or D) for the user. These correspond with soils and infiltration rates contained in this Manual. Once a soil type is selected, the corresponding infiltration rate will populate in the Infiltration rate of underlying soils field. The user may also select User Defined. This selection will activate the User Defined Infiltration Rate cell allowing the user to enter a different value from the values in the predefined selection list. The maximum allowable infiltration rate is 1.63 inches per hour.
• Required drawdown time: This is the time in which the stormwater captured by the BMP must drain into the underlying soil/media. The user must select from predefined values of 48 or 24 hours. The MPCA Construction Stormwater General Permit requires drawdown within 48 hours, but 24 hours is Highly Recommended when discharges are to a trout stream. The calculator uses the Infiltration rate of underlying soils and the Media depth (DM) times porosity to check if the BMP is meeting the drawdown time requirement. The user will encounter an error and be required to enter a new Media depth (DM) if the stormwater stored in the BMP cannot drawdown in the required time.
• BMP Summary tab: The BMP Summary tab summarizes the volume and pollutant reductions provided by the specific BMP. It details the performance goal volume reductions and annual average volume, dissolved P, particulate P, and TSS load reductions. Included in the summary are the total volume and pollutant loads received by the BMP from its direct watershed, from upstream BMPs, and a combined value of the two. Also included in the summary are the volume and pollutant load reductions provided by the BMP, along with the volume and pollutant loads that exit the BMP through the outflow. This outflow load and volume is what is routed to the downstream BMP, if one is defined in the Watershed tab. Finally, percent reductions are provided for the percent of the performance goal achieved, percent annual runoff volume retained, total percent annual particulate phosphorus reduction, total percent annual dissolved phosphorus reduction, total percent annual TP reduction, and total percent annual TSS reduction.

## Model input requirements and recommendations

If the following requirements for inputs into the MIDS calculator are not met, then an error message will inform the user to change the input to meet the requirement.

• The Bottom surface area must be equal to or smaller than the Media surface area.
• The Number of trees must be 1 or more.
• The infiltration rates of the underlying soils cannot exceed 1.63 inches per hour.
• The basin must meet the user-specifed drawdown time requirement. The drawdown time requirement is checked by comparing the user defined drawdown time with the calculated drawdown time (DDTcalc), given by

$$DDT_{calc} = D_M/(n - FC) / (I_R/12)$$

where
DM is the media depth (ft);
n - FC is media porosity minus field capacity (ft3/ft3); and
IR is the infiltration rate of the native soils (in/hr).
If DDTcalc is greater than the user-specified required drawdown time then the user will be prompted to enter a new media depth or infiltration rate of the underlying soils.

## Methodology

### Required treatment volume

Required treatment volume, or the volume of stormwater runoff delivered to the BMP, equals the performance goal (1.1 inches or user-specified performance goal) times the impervious area draining to the BMP plus any water routed to the BMP from an upstream BMP. This stormwater is delivered to the BMP instantaneously.

### Volume reduction

The Volume reduction capacity of BMP [V] is calculated using BMP inputs provided by the user. For this BMP, the Volume reduction capacity [V] is equal to the sum of the Volume reduction stored in soil media (infiltration), the Volume reduction of BMP from ET (VET), and the Volume reduction of BMP from interception (VI).

The total instantaneous Volume reduction capacity of BMP [V] due to these three mechanisms is calculated using BMP design inputs provided by the user. This Volume reduction capacity of BMP [V] is then compared to the Required treatment volume in order to determine the Volume of retention provided by BMP, which is the instantaneous volume credit that can be claimed for that BMP.

#### Volume reduction stored in soil media (infiltration)

Stormwater runoff will flow into the media of the tree trench and fill the pores of the soil, eventually reaching water saturation. Water will then drain from the soils through infiltration into the underlying soils until the water content in the media reaches field capacity. The volume of water stored in the media between saturation and field capacity is the capture volume of the BMP. The capture volume (V) is given by

$$V = (A_M + A_B)/2) * (n - FC) * D_M$$

where

AM is the media surface area (ft2);
AB is the surface area at the bottom of the basin (ft2);
n - FC is the media porosity minus field capacity (ft3/ft3); and
DM is the media depth (ft).

The stored water must drain within the specified drawdown time. The underlying soil controls the infiltration rate. The user must input the soil with the most restrictive hydraulic conductivity in the 5 feet directly below the BMP media.

#### Volume reduction of BMP from interception (VI)

The second mechanism contributing to the Volume reduction capacity of BMP is interception. Water intercepted by a tree canopy may evaporate or be slowly released such that it does not contribute to stormwater runoff. The interception capacity (IC) is determined based on data for deciduous and coniferous tree species (IC = 0.40 inched for coniferous trees and 0.14 inches for deciduous trees)[1]. These values intercept approximately 30% and 57% of annual rainfall over the canopy area. This credit is per storm event. To determine the interception volume of an individual tree, the Ic is multiplied by the canopy projection area (CP), which is the perceived tree canopy diameter at maturity. Although CP varies by tree species and size, for the MIDS calculator CP is determined solely based on the size of the tree (CP = 315 square feet for a small tree, 490 square feet for a medium sized tree, and 707 square feet for a large tree). The volume of water lost through interception (VI) in cubic feet is given by

$$V_I = I_C/12 * CP * N$$

where

IC = the interception capacity for an individual tree (in);
CP is the canopy projection area for an individual tree (ft2); and
N is the total number of trees planted in the tree trench.

#### Volume reduction of BMP from ET (VET)

The final mechanism contributing to the Volume reduction capacity of BMP is evapotranspiration (ET) of a portion of the water stored in the media between field capacity and wilting point. The volume of water lost through evapotranspiration (VET) is assumed to be the smaller of two calculated values, potential ET and measured ET.

##### Potential ET (ETpot)

Potential ET (ETpot) is equal to the amount of water stored in the media between field capacity and the wilting point, and is given by

$$ET_{pot} = D_M * (A_M + A_B)/2 * (FC - WP)$$

where
DM is the total media depth (ft);
AM is the surface area of the media (ft2);
AB is the surface area at the bottom of the basin (ft2); and
(FC – WP) is the difference between field capacity and wilting point (ft3/ft3).
##### Measured ET (ETmea)

Measured ET (ETmea) is the amount of water lost to ET as measured using available data. For this BMP in the MIDS Calculator, ETmea is calculated based on the leaf area index (LAI); canopy projection (CP); an average pan evaporation rate; an adjustment to the pan evaporation rate that accounts for leaf and stomata effects; the average time between rain events in MN; the soil volume available for tree rooting (Sv); and the number of trees in the BMP. Measured ET is given by

$$ET_{mea} = N * CP * LAI * E_{rate} * E_{ratio} * 3 days * (adjustment)$$

where
N is the number of trees in the BMP;
CP is the canopy projection area (ft2);
LAI is the leaf area index;
Erate is the pan evaporation rate for a given area (set at 0.02 ft/day);
Eratio is an adjustment that accounts for leaf and stomata effects relative to evaporation from a pan surface (set at 0.20, or 20 percent);
Three days is the typical time period between precipitation events in Minnesota based on analysis of rainfall data.

The "adjustment" factor is a multiplier that accounts for BMP conditions where the soil volume that is less than the recommended volume. Since the recommended soil volume equals 2 times the canopy projection area (CP), the adjustment term is the lesser between 1 and the following term

$$(adjustment) = S_v / (2*CP)$$

where
Sv is the actual soil volume available for each individual tree (ft3), and is given by

$$S_v = (0.5*(A_M + A_B) * D_M) / N$$

where
DM is the total media depth (ft);
AM is the surface area of the media (ft2);
AB is the surface area at the bottom of the basin (ft2); and
N is the number of trees planted in the tree trench/box.

The LAI is stratified by tree type and tree size. For coniferous trees, the LAI = 5.47. For deciduous trees, the LAI = 3.5 for small trees; 4.1 for medium sized trees; and 4.7 for large trees. These values are based on collected research for global leaf area from 1932-2000 (Scurlock, Asner and Gower, 2002). The pan evaporation rate is set at 0.02 ft/day, which is based on evaporation data collected at the University of Minnesota Southwest Experiment Station at Lamberton, Minnesota. The Eratio term accounts for the reduced efficiency of the leaves to transpire the available soil water or, alternately, the stomatal resistance of the canopy to transpiration and water movement, relative to evaporation from a pan surface. 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 a 1 square centimeter pan surface.

#### Comparison of volume reduction capacity with volume performance goal

The MIDS calculator compares the Volume reduction capacity of BMP [V] with the Required treatment volume, and the lesser of the two values is used to populate the Volume of retention provided by BMP. This comparison between potential and actual treatment volumes ensures that the BMP does not claim more credit than is due based on the actual amount of water routed to it. The Volume of retention provided by BMP is the actual volume credit the BMP receives toward the instantaneous performance goal. For example, if the BMP is oversized the user will only receive volume credit for the Required treatment volume routed to the BMP.

Annual volume retention is assessed by converting the instantaneous Volume reduction capacity of BMP [V] to an annual volume reduction percentage. This is accomplished through the use of performance curves developed from a range of modeling scenarios. These performance curves use the Volume reduction capacity of BMP [V], the infiltration rate of the underlying soils, the percent imperviousness of the contributing watershed area, and the size of the contributing watershed to calculate the Percent annual runoff volume retained and annual Retention volume provided by BMP.

Recommended values for porosity, field capacity and wilting point for different soils.1

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

### Pollutant Reduction

Schematic illustrating how pollutant reductions (TSS, dissolved and particulate P) are calculated for the tree trench system-tree box BMP in the MIDS calculator.

Pollutant load reductions are calculated on an annual basis. Therefore, the first step in calculating annual pollutant load reductions is converting Volume reduction capacity of BMP, which is an instantaneous volume reduction, to an annual volume reduction percentage. This is accomplished through the use of performance curves (add link to addendum) developed from multiple modeling scenarios. The performance curves use Volume reduction capacity of BMP [V], the infiltration rate of the underlying soils, the contributing watershed percent impervious area, and the size of the contributing watershed to calculate a percent annual volume reduction. While oversizing a BMP above Required treatment volume will not provide additional credit towards the performance goal volume, it may provide additional pollutant reduction.

All pollutants associated with the reduced volume of water are captured for a 100 percent removal. Water that bypasses the BMP through the overflow is not treated for a 0 percent removal. A schematic of the removal rates can be seen to the right.

NOTE: The user can modify event mean concentrations (EMCs) on the Site Information tab in the calculator. Default concentrations are 54.5 milligrams per liter for total suspended solids (TSS) and 0.3 milligrams per liter for total phosphorus (particulate plus dissolved). The calculator will notify the user if the default is changed. Changing the default EMC will result in changes to the total pounds of pollutant reduced.

## Routing

A tree trench/tree box BMP can be routed to any other BMP, except for a green roof and a swale side slope or any BMP that would cause water to be rerouted back to the tree trench/tree box BMP. All BMPs can be routed to a tree trench/tree box BMP except for a swale side slope BMP.

## Assumptions for tree trench system/box

The following general assumptions apply in calculating the credit for a tree trench/box. If these assumptions are not followed the volume and pollutant reduction credits cannot be applied.

• The tree trench system has been properly designed, constructed and will be properly maintained.
• Stormwater runoff entering the tree trench/box has undergone pretreatment.
• Stormwater captured by the BMP enters the BMP media instantaneously. This will slightly underestimate actual infiltration since some water will infiltrate through the basin bottom and sidewalls during a rain event, thus creating more volume for storage in the BMP.
• Evapotranspiration is independent of plant type, plant density and weather conditions.

## Example application in the MIDS calculator

Schematic showing the site layout for a tree trench system with no underdrain. The site consists of 2.2 acres, of which 1.4 acre is an impervious parking lot and 0.8 acre is turf. Note the turf area includes the area of the BMP. The entire site is on HSG B soils.
Schematic showing the dimensions of the tree trench system. The surface area of the system is 5600 square feet and the bottom surface area is 3230 square feet. The media depth is 4 feet.

This example was completed using Version2 of the Calculator.

A tree trench system is to be constructed in a watershed that contains a 1.4 acre parking lot surrounded by 0.8 acres of pervious area (turf area and the tree trench BMP area). All of the runoff from the watershed will be treated by the tree trench system. The soils across the area have a unified soils classification of SM (HSG type B soil). The surface area of the tree trench basin is 5600 square feet at the media surface. The area at the media-soil interface is 3320 square feet. The total media depth will be 4 feet. Following the MPCA Construction Stormwater General Permit requirement, the water in the media of the tree trench needs to drawdown in a 48 hour time period. The media will be Media Mix D, which is a loamy sand composition resulting in a difference between the media wilting point and field capacity of 0.05 cubic feet per cubic foot and a difference between the media porosity and field capacity of 0.35 cubic feet per cubic foot. The tree trench will be planted with 10 medium sized deciduous trees. The following steps detail how this system would be set up in the MIDS calculator.

Step 1: Determine the watershed characteristics of your entire site. For this example we have a 2.2 acre site with 1.4 acres of impervious area and 0.8 acres of pervious area in type B soils. The pervious area includes the turf area and the area of the tree trench basin.

Step 2: Fill in the site specific information into the “Site Information” tab. This includes entering a Zip Code (55414 for this example) and the watershed information from Step 1. The Managed turf area includes the turf area and the area of the tree trench basin. Zip code and impervious area must be filled in or an error message will be generated. Other fields on this screen are optional.

Step 3: Go to the Schematic tab and drag and drop the “Tree trench system/Box (w/o underdrain)” icon into the “Schematic Window”

MIDS calculator screen shot for Results tab for tree trench with no underdrain.
MIDS calculator screen shot for Results tab for tree trench with no underdrain.

Step 4: Open the BMP properties for the tree trench by right clicking on the “Tree trench system/Box (w/o underdrain)” icon and selecting “Edit BMP properties”, or by double clicking on the “Tree trench system/Box (w/o underdrain)” icon.

Step 5: Click on the “Minnesota Stormwater Manual Wiki” link or the “Help” button to review input parameter specifications and calculation specific to the “Tree trench system/Box (w/o underdrain)” BMP.

Step 6: Determine the watershed characteristics for the tree trench. For this example the entire site is draining to the tree trench. The watershed parameters therefore include a 2.2 acre site with 1.4 acres of impervious area and 0.8 acres of pervious turf area in type B soils. There is no routing for this BMP. Fill in the BMP specific watershed information (1.4 acres on impervious cover and 0.8 acres of Managed turf in B soils).

Step 7: Enter in the BMP design parameters into the “BMP parameters” tab. Tree trench systems requires the following entries.

• Surface area at media surface which is 5600 square feet
• Bottom surface area (area at media-soil interface) which is 3230 square feet
• Media depth which is 4 feet
• Media field capacity minus wilting point which is 0.05 cubic feet per cubic foot
• Media porosity minus field capacity which is 0.35 cubic feet per cubic foot
• Tree type is Deciduous
• Tree Size is Medium
• Number of Trees is 10
• Underlying soil – Hydrologic Soil Group which is SM (HSG B; 0.45 in/hr) from the dropdown box
• Required drawdown time (hrs) which is 48 from the dropdown box

Step 8: Click on “BMP Summary” tab to view results for this BMP.

Step 9: Click on the “OK” button to exit the BMP properties screen.

Step 10: Click on “Results” tab to see overall results for the site.

## Requirements

Measurement of depth from the bottom of the infiltration BMP to the seasonally high water table or bedrock. Note that there must be a minimum of 2 feet separation when soils beneath the BMP are ripped, with a total separation distance of 3 feet or more. Infiltration BMPs include any BMP that allows water to infiltrate into the underlying soil.
Warning: The following are requirements of the Minnesota Construction Stormwater General Permit
• 3 foot separation from the bottom of the tree system to the seasonal high water table
• Use the most restrictive infiltration rate within 5 feet of the bottom of the BMP
• For measured infiltration rates, apply a safety factor of 2
• Pretreatment

## Recommendations

Caution: The following are recommendations for inputs into the MIDS calculator
• Drawdown time of 24 hours when the discharge is to trout streams
• Field tested infiltration rates rather than table values

## Information

Information: The following information may be useful in determining inputs for the MIDS calculator