# Bioretention: Sizing and modeling

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This article describes recommended design approaches when available space for the practice is constrained.

Before beginning the sizing calculations certain parameters must be known or estimated. See Bioretention: Sizing for parameter descriptions and conceptual diagram illustrating key components of bioretention practices. Note that some of these parameters are limited:

1. The maximum total depth will be limited by construction practices i.e. not usually > 2 m.
2. The maximum total depth may be limited by the conditions underground e.g. the groundwater or underlying geology/infrastructure.
3. The minimum total depth will be limited by the need to support vegetation (e.g not less than 0.6 m to support deep rooting perennials and shrubs).
4. Bioretention has a maximum recommended catchment impervious area to practice permeable (footprint) area ratio, R (or I/P ratio) of 20.

## Size a bioretention cell receiving flows directly to the storage reservoir for a constrained depth

If there is a constraint to the depth (dT) of the practice, calculate the required storage reservoir footprint area (Ar), as: ${\displaystyle A_{r}={\frac {i\times D\times A_{i}}{(d_{r}\times n')+(f'\times D)}}}$

Where:

• Ar = Area of the infiltration practice storage reservoir (m2)
• Ai = Catchment impervious area (m2)
• D = Duration of design storm (h)
• i = Intensity of design storm (mm/h)
• n' = Effective porosity of the fill material in the storage reservoir of the practice
• dr = Storage reservoir depth, based on depth available between the elevation of the invert of the underdrain perforated pipe and one (1) metre above the seasonally high water table or top of bedrock (m) or other value determined to be suitable through groundwater mounding analysis.

If R is greater than 20, consider decreasing catchment impervious area (Ai) by draining less area to the practice.

## Size a bioretention cell where drainage area and practice area are fixed

If the land area is limited, determine the I/P ratio, which is the ratio of catchment impervious area (Ai) to practice pervious footprint area (Ap):

${\displaystyle R={\frac {A_{i}}{A_{p}}}}$

Where:

• R = Ratio of catchment impervious area to practice pervious footprint area, also referred to as I/P ratio
• Ap = Practice pervious footprint area in m2
• Ai = Catchment impervious area in m2

Then calculate the required storage reservoir depth (dr), as: ${\displaystyle d_{r}={\frac {D\left[(R\times i)-f'\right]}{n'}}}$

Where:

• D = Duration of design storm (h)
• i = Intensity of design storm (m/h)
• n' = Effective porosity of the storage reservoir fill material

These equations assume that infiltration occurs primarily through the base of the facility.

This spreadsheet tool has been set up to perform all of the infiltration practice sizing calculations shown above.

## Calculate drawdown time

Two footprint areas of 9 m2.
Perimeter = 12 m (left) Perimeter = 20 m (right)

In some situations, it may be possible to reduce the size of the bioretention required, by accounting for rapid drainage. Typically, this is only worth exploring over sandy soils with rapid infiltration. Note that narrow, linear bioretention features drain faster than round or blocky footprint geometries.

• Begin the drainage time calculation by dividing the storage reservoir area of the practice (Ar) by the perimeter (x).
• Use the following equation to estimate the time (t) to fully drain the facility:
${\displaystyle t={\frac {nA_{r}}{f'x}}ln\left[{\frac {\left(d_{r}+{\frac {A_{r}}{x}}\right)}{\left({\frac {A_{r}}{x}}\right)}}\right]}$

Where:

• n is the porosity of the storage reservoir fill material
• Ar is the storage reservoir footprint area (m2),
• f' is the design infiltration rate of the native soil (mm/h),
• x is the perimeter of the practice (m), and
• dr is the depth of the storage reservoir (m).

This 3 dimensional equation makes use of the hydraulic radius (Ar/x), where x is the perimeter (m) of the facility.
Maximizing the perimeter of the facility directs designers towards longer, linear shapes such as bioswales.