NREL is a national laboratory of the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

Estimating Heat and Mass Transfer Processes in 

Green Roof Systems: 

Current Modeling Capabilities and Limitations

Paulo César Tabares-Velasco, Ph.D.

Postdoctoral Researcher

National Renewable Energy Laboratory

ASHRAE Energy Modeling Conference

April 4, 2011

Work done at:

Building Science Group 

Architectural Engineering Dept.

Pennsylvania State University

NREL/PR-5500-51149
 NATIONAL RENEWABLE ENERGY LABORATORY 2 

1. Introduction

2. Heat and Mass Transfer

3. Current Capabilities and 

 Limitations

4. Inputs

5. Conclusions

Outline
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Roofs receive an important amount 

of solar radiation during summer

– 50% more in summer months than 

south walls at 40oN latitude (Duffie and 

Beckman 1991)

Green roofs are becoming a popular 

sustainable technology

– Growth of 30%–50% during the last 5 

years

– 703 green roofs nationwide

– ~102 acres (greenroofsplants.com)

Roofs
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Green Roofs

Green roofs are “specialized roofing systems that support 

vegetation growth on rooftops”

Consist of several layers: 

1. Vegetation

2. Substrate (porous media)

3. Drainage/filter membrane
 NATIONAL RENEWABLE ENERGY LABORATORY 5 

Green Roof Benefits

1. Reduce energy demand on space conditioning 

2. Extend life of roofing membrane

3. Reduce the urban heat island effect in cities

4. Reduce storm water runoff

5. Improve air quality

6. Improve roof aesthetics
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Green Roof Drawbacks

1. Cost ($10-24/ft2) 

2. Hard for retrofit

3. More complicated design

4. Water leaks?

5. Structural load
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1. Introduction

2. Heat and Mass Transfer

3. Current Capabilities and 

 Limitations

4. Inputs

5. Conclusions

Outline
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Thermal Benefits of Green Roofs

Not a conventional insulation material

Modulate heat flux through the roof by:

– Shading

– Insulation

– Thermal mass

– Evapotranspiration (ET, QET) 

Combined effect:

– Plants and substrate

Require energy and mass balance
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Traditional Roof Green Roof

=−−− 0 N sensible ET QQQR substrate

Where,

 RN = net radiation

 Qsensible = sensible heat flux due to convection

 QET 

 = latent heat flux due to convection

 Qsubstrate/roof = conductive heat flux through roof

=−− 0 N sensible QQR roof

Energy Balance
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Substrate 

wetness

“Wet” 0.68 0.23 0.09

“Dry” 0.29 0.57 0.14

10

N

ET

R

Q

N

roof GR

R

Q ,

N

sensible

R

Q

N ET sensible ++= QQQR roof ,GR

Tabares –Velasco & Srebric. 2011

Accurate energy balance required mass balance and vice versa

Energy Balance
 NATIONAL RENEWABLE ENERGY LABORATORY

0

0.1

0.2

0.3

0.4

350 700 1050 1400 1750 2100

Reflectivity

Wavelength (nm)

Spectral Reflectivity of Green Roof Sample

Dry Leaves Wet leaves

11

 Absorbed short-wave irradiance

 Thermal radiative heat transfer between: 

 Plants and sky

 Plants and top substrate

PAR

Visible

(IQR LAI) ( TTTQ LAI) n solar solar soil leaf solar IR sky soil leaf soil leaf IR

= τρρ ,,,, + τεε ,,,,,,

Net Radiation N ET sensible ++= QQQR substrate
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N ET sensible ++= QQQR substrate

12

Constant

Bowen Ratio 

Vapor Pressure Differential

Plant’s stomata resistance, rs 

Soil/Substrate resistance , rs

( )

β β

ThQ Q sensible convection

ET

∆

==

ETfactor

solar reflectance = solar reflectanc ×Qe

( )( ) so air

as

p

ET ee

rr

C

Q − +=

γ

ρ

fwaterfsolarf VPD f temp)()()()( LAI

r

s

r l=

Plants transpiration is controlled by stomatal resistance: adjustable 

pores in the leaf that allow the gas transport into leaf/enviroment

Evapotranspiration
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N ET sensible ++= QQQR substrate

13

 Thermal conductivity depends on substrate type and water 

content

 Previous soil models overestimate thermal conductivity of 

green roof substrate

Conduction

0

0.2

0.4

0.6

0.8

1

0.000.050.100.150.200.250.300.350.400.450.500.55

k (W/ m K)

Substrate Water Content (m3/m3)

Substrate Thermal Conductivity

Soil Model 1 Soil Model 2 Soil Model 3

Data Mulch Model GR 1 Model GR 2
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1. Introduction

2. Heat and Mass Transfer

3. Current Capabilities and 

 Limitations

4. Inputs

5. Conclusions

Outline
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Field Experimentation: 

– Temperature Reduction (Hoeschele and Schmidth 1977) 

– Heat Flux Reduction (Liu and Baskaran 2003) 

– R-value (Minke et al. 1982, Wong et al. 2003) 

– Evapotranspiration (Schmidt 2003, Berghage et al. 2007) 

 

Wind Tunnel/Lab:

– R-value (Bell and Spolek 2009, Tabares-Velasco and Srebric 2009)

– Cooling effect (Onmura et al. 2001) 

– Soil evaporation (Yamanaka et al. 1997)

– Soil properties (Sailor et al 2008)

Full Laboratory Experimentation: 

– (Tabares-Velasco 2009, Tabares-Velasco and Srebric 2011)

 

Latent Heat Fluxes through a Green Roof for Early Summer 

Condition

0

50

100

150

200

250

300

350

400

0 4 8 12 16 20 24

Time (h)

W/m2

0

16

32

48

63

79

95

111

127

Btu/h ft2

Day 1 Day 2 Day 3 Day 4

D 1 D 2 D 3 D 4

Berghage et al. 2007

Studies
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Theoretical Models: 

– Early models (Saiz Alcazar 2005, Hilten 2005, Wong et al 2003)

– Latest models (Gaffin et al. 2005, Sailor 2008, Tabares-Velasco and Srebric 2009)

Software: 

– Using early models: DOE 2

– Using latest models : ESP-r, EnergyPlus, MIT Design 

Advisor

– Web-based: Green Roof Energy Calculator

Software and Models
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1. Experimental data for validation

2. Complete model validation

3. Constant properties for roof substrate

4. Mass balance

5. Drainage layer performance data

6. Experimental data for winter conditions

1. Snow melting

2. Plant dormancy 

7. Inter-comparison model performance for winter and summer

Gaps and Limitations: Previous 

Studies
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1. Experimental data for validation

2. Complete model validation

3. Constant properties for roof substrate

4. ~Mass balance

Penn State Center for Green Roof Research

Gaps and Limitations Addressed at 

PennState
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Developed and validated a heat and mass transfer green 

roof model

• Designed and built a new apparatus “cold plate”

• Obtained dynamic and quasi-steady state data

• Verified and validated green roof model

o Detailed laboratory experiments 

o Surface temperature

o Evapotranspiration

o Conduction

o Net radiation...

o Outdoor validation

Previous Work at PennState 
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20 Box

Green Roof Sample

Lamps

Environmental Chamber

Supply Air Return Air

Platform 

Cold Plate

 Inspired by ASTM C177 “hot plate” and C1363 “hot 

box” 

 Requires an environmental chamber

 Measures simultaneously heat and mass transfer 

phenomena 

“Cold Plate” Apparatus
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“Cold Plate” Apparatus
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Heat Flux through Green Roof Substrate

0

10

20

30

40

50

60

0 4 8 12 16 20 24 28 32 36 40 44

Experiment Number

Heat Flux (W/m2

)

Data Calculated

Soil

UVA

Soil

 Day Base Humidity Solar Wind Temp Base II

UVA 

Plants

Model Validation: Conduction
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1. Introduction

2. Heat and Mass Transfer

3. Current Capabilities and 

 Limitations

4. Inputs

5. Conclusions

Outline
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• LAI: 0-5 (typically 1–3) 

• Stomatal resistance:

– Succulent plants: 450–1000 s/m

– Desert plants: 225–1125 s/m (Jones 

1992)

– Lab experiments for 

Sedums/Delosperma 500–700 s/m 

(Tabares-Velasco and Srebric 2011) 

– EnergyPlus limit is 300 s/m!!!

• Plant coverage: 0%–100% (upper 

limit about 80%)

• Irrigation: extensive roofs typically 

not irrigated

Model Inputs

24
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• Substrate thermal conductivity:

– ~0.2 W/mK (dry)

– ~ 0.4-0.6 W/mK (wet)

• Bowen ratio: ~0.2

• Green roof R-value (under laboratory 

conditions): 4.3–4.8 ft2hF/Btu (but don’t 

use it!)

Model Inputs (continued)

25
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1. Introduction

2. Heat and Mass Transfer

3. Current Capabilities and 

 Limitations

4. Inputs

5. Conclusions

Outline
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• Current green roof models are more sophisticated 

and complete than 10 years ago

• Accurate green roof modeling requires energy and 

mass balance

• All models should to be (fully) validated before 

implementation in building energy simulations 

software

• DON’T try this at HOME! 

• Validated green roof model is coming soon!

Conclusions

27
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Thank you!
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• Dr. Jelena Srebric, Pennsylvania State 

University

• Dr. Robert Berghage, Pennsylvania State 

University

• Consejo Nacional de Ciencia y Tecnología 

(CONACYT)

• ASHRAE

• NSF (check it out!) 

www.nsf.gov/news/special_reports/greenre

volution/index.jsp

Acknowledgments