Purple-Roof's Green Roof Modeler

Welcome to Purple-Roof's Green Roof Modeler (v0.1.0, beta).

Select a location (currently limited to the United States), then click "Let's model”. Then the Modeler will compare the performance of forty (40) common green roof profiles, using historical weather for the selected location. For more information, check click "How To Use the Modeler" above.

Modeling Parameters:

How The Model Works

The diagram below illustrates the primary functions within the modeler. The modeler constructs a series of continuous flow vegetative and hydrologic models, using a daily timestep. Generally there are six functions, as outlined below.

  1. Determine antecedent conditions (final conditions of the preceding increment).
  2. Use precipitation from weather data as water inputs. Use roof geometry to estimate efficiency of rainfall capture.
  3. Calculate water balance based on the antecedent moisture content, water received, and profile parameters. This determine runoff versus retention.
  4. Calculate plant stress based on plant-available water.
  5. Calculate evaporation, which takes into account water remaining after water balance, and which considers the updated stress level.
  6. Save the increment as a final snapshot (antecedent conditions for next increment). Repeat.

About the Modeler

Purple-Roof's Green Roof Modeler is a joint effort between Green Roof Specialty Products (the creators of Purple-Roof) and Green Roof Diagnostics (GRD). GRD selects equations, determines parameters, and is generally responsible for ensuring accuracy, applicability, and objectivity of the Green Roof Modeler. Purple-Roof wraps delivers the Modeler to the public in a graphic user interface.


We are developing this project together to build upon our collective strengths and shared interests. GRD seeks to improve performance standards and for practicioners, such as civil engineers, to utilize improved green roof performance standards. Purple-Roof wants to help architects and engineers use higher performing green roof assemblies on more of their projects.

We are actively developing this project and will continually release new versions. Each version will include full documentation of calculations, per below.

Model Equations

The following sections cover each of the steps above in greater detail. Please note that these are equations for version 0.1.0. This page will be updated with current equations for each version of the Modeler.

Version 0.1.0 utilizes a series of static, emperical equations in a continuous flow pattern.

1. Initial Antecedent Conditions

As antecedent conditions are not known before the first increment, the assumed antecedent condition is 0% plant stress and profile water retention of 20% of its ASTM maximum water storage capacity. These are reasonable assumptions that neither benefit nor penalize any particular assembly.

Regardless of the accuracy of this initial assumption, the effects of this initial assumption are minimal, as they have no bearing on the model after the first rain event.

2a. Roof Geometry

The Modeler assumes a uniform roof slope of 2 percent. Version 0.1.0 currently does not accept user input for these variables, though input will be allowed in later versions.

Note: slope is currently not considered in any equations other than water inputs. Future versions will utilize slope as a variable affecting the water balance equation.

2b. Water Inputs (Precipitation)

Version 0.1.0 utilizes weather data from a specific US location for a specific historical year. Weather data is obtained from Aeris Weather, though different sources may be used in the future. Aeris aggregates weather data from a variety of pubic and private sources.

Note: later versions may consider other water input sources, such as cisterns or contributing drainage areas.

Rainfall that is observed falling from the sky onto the ground is not necessarily the same volume of rainfall that lands onto a rooftop, due to wind, roof slope, and orientation of roof slope. Observed rainfall is adjusted per the following equation.

Win = Robs * Ω * ϑ ((X × π) / 180 ) * ( 1 + arain * X )

Win = rainfall (mm day-1) adjusted to roof slope and orientation

Robs = the observed rainfall (mm day-1);

Ω (Omega) = surface area (m2) of the roof

arain = dimensionless program parameter; The value of arain depends on the orientation of the roof and local wind and rainfall characteristics since roofs oriented to a dominant wind direction receive more rainfall than flat roofs or those oriented towards another direction

X = slope of the roof (degrees).

Note that version 0.1.0 currently sets the value of arain to a constant value of 1, as local wind and rainfall characteristics are not currently available.


Eline Vanuytrecht."Runoff and vegetation stress of green roofs under different climate change scenarios".Landscape And Urban PlanningVolume 122, Februrary 2014.Equation #1

Find it at: Elsevier

3a. Profile Parameters

Differences between green roof profiles account for some of the more significant differences in performance between green roof applications. Green Roof Diagnostics and others are currently researching these conditions. Green Roof Diagnostics is parameterizing values to be used in modeling.

Version 0.1.0 currently utilizes the following parameters:

0.35ASTM E-2399 maximum retention value of green roof soil / green roof media, i.e. 35% per volume (35% volumetric water capacity)
0.93ASTM E-2399 maximum retention value of mineral wool in green roofs, i.e. 93% per volume (93% volumetric water capacity)
0.75Efficiency factor without detention layer: actual retention is assumed to peak at 75% of ASTM values
1.05Efficiency factor detention layer: actual retention is assumed to peak at 105% of ASTM values
Mixed SedumPlant palette assumed to be mixed sedum
0.56Crop coefficient of evapotranspiration
12LStress threshold of available water. I.e. the selected plants are assumed to begin to exhibit stress when available water drops below 12 liters per square meter of soil surface area. For a 100mm (4-inch) thick green roof profile, this equates to 12% volumetric water capacity, or approximately 1/3 of total maximum water-holding capacity of a soil-only green roof.

The crop coefficient of 0.56 for Sedums is an estimated average for mixed Sedum, utilizing multiple publications that document a range of crop coefficients for a single species of Sedum. The ASTM values listed are based on values commonly observed within the industry, and documented by multiple ASTM tests. The remaining parameters are derived from soon-to-be-published research performed by Green Roof Diagnostics, based on research from 2016-2019.

3b. Water Balance Equation and Runoff

Currently the Green Roof Modeler is using a very simple water balance equation. Conceptually a water balance equation assumes that the green roof is a "reservoir" that receives water (with 100% efficiency) until it reaches capacity, and after reaching capacity, runoff begins and occurs instantaneously.

We chose this simple equation for version 0.1.0, but future versions will more accurately predict efficiency and detention.

Wro = Win − (WSmax − WSact)

Wro = amount of water lost by runoff (l day-1) if Win exceeds the actual storage capacity of the roof

Win = rainfall (mm day-1) adjusted to roof slope and orientation (output of formula 1)

WSmax = maximum amount of water retained on the roof (l day-1). WSmax depends on the roof type and surface area.

WSact = actual amount of water retained on the roof (l day-1). WSact depends on incoming rainfall and outgoing green roof evapotranspiration and is updated on a daily basis. WSact varies between zero when the roof is completely dry and WSmax when the roof is saturated with rainfall.


Eline Vanuytrecht."Runoff and vegetation stress of green roofs under different climate change scenarios".Landscape And Urban PlanningVolume 122, Februrary 2014.Equation #2

Find it at: Elsevier

4. Stress

Plant stress is an important factor to consider when designing and selecting a green roof. We think it is important to include plant stress in any modeling efforts. Zero plant stress might not be an attainable goal, but plant stress should be minimized and/or reduced to a few manageable occurrences per year.

The primary contributor to plant stress is lack of available water, and the equation below only considers lack of available water as a factor causing stress. Later versions may consider other, minor, factors.

S = 100 * (1 - (WSact / (p * WSmax) ) )

S = stress level

p is the threshold for vegetation water stress

WSmax = maximum amount of water retained on the roof. Result of water balance equation.

WSact = actual amount of water retained on the roof. Result of water balance equation.


Eline Vanuytrecht."Runoff and vegetation stress of green roofs under different climate change scenarios".Landscape And Urban PlanningVolume 122, Februrary 2014.Equation #4

Find it at: Elsevier

5. Evapotranspiration (ET)

Evapotranspiration is the combined loss of water via evaporation and transpiration, i.e. all water that is lost from the green roof in the form of water vapor.

The definition of retained water is water that is absorbed by the green roof and which only leaves the roof through evaporative processes. Therefore evapotranspiration is the single most important process in the continued function of a retention-oriented green roof.

The Modeler uses the global standard FAO Penman-Monteith evapotranspiration equation. Specifically, FAO Penman-Monteith estimates evapotranspiration for a reference crop of grass. This value is then multiplied by a stress factor and a crop coefficient factor (see above for both) to determine evapotranspiration on a given date.

ETo =

0.408Δ (Rn - G) + γ


T + 273

U2 (es - ea)

Δ + γ (1 + 0.34U2)

ET = ETo * Ks * Kc


ETo = reference evapotranspiration [mm day-1],

Rn = net radiation at the crop surface [MJ m-2 day-1],

G = soil heat flux density [MJ m-2 day-1],

T = mean daily air temperature at 2 m height [°C],

u2 = wind speed at 2 m height [m s-1],

es = saturation vapour pressure [kPa],

ea = actual vapour pressure [kPa],

es - ea = saturation vapour pressure deficit [kPa],

Δ = slope vapour pressure curve [kPa °C-1],

γ = psychrometric constant [kPa °C-1].

Ks = water stress coefficient

Kc = crop coefficient

Unavailable climatic data is estimated using the FAO guidelines for missing climatic data, using formulae from the PyETo Python library.


Food and Agriculture Organization (FAO) of the United Nations."Chapter 2 - FAO Penman-Monteith equation".Crop evapotranspiration - Guidelines for computing crop water requirements - FAO Irrigation and drainage paper 56Rome, 1998.

Find it at: FAO

6. Final Conditions

The state of the green roof after evapotranspiration occurs is saved as an "increment" or a final snapshot of that day. The next day is then modeled, using the prior day's conditions as antecedent. E.g. when the model completes May 15, that data is saved, and the final water retained within the green roof and the final plant stress on May 15 becomes the antecedent conditions used by the Modeler to begin May 16.

This process is repeated for each day of the weather series. Currently version 0.1.0 is generating 365-day models, per calendar year.