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Abstract and Figures

The advanced Princeton Roof Model (PROM) is evaluated and then applied to quantify the heat transferred through various modular roof structures over an entire year. The goal is to identify an optimal combination of roof reflectivity and insulation thickness that will reduce energy consumption and minimize cost. Meteorological data gathered over the Northeastern United States (Princeton, NJ) is used to force PROM. Our results reveal that for new constructions or for retrofits in the region, an R8.4 (around 46 cm thick roof insulation) white roof (assumed albedo = 0.6 or greater) would significantly reduce the combined heating and cooling load attributable to the roofs. The wintertime penalty of white roofs is also shown to be insignificant compared to their summertime benefits. The findings are pertinent to many other densely populated areas with comparable climates where, despite a much higher number of heating versus cooling degree-days, white roofs are overall advantageous. A cost optimization analysis found that doubling, tripling and quadrupling the insulation thickness from the baseline case of 5.08 cm (2 in.), at an albedo of 0.45, requires 13, 17 and 19 years, respectively, to recover the additional cost incurred.
Content may be subject to copyright.
Energy
and
Buildings
102
(2015)
317–327
Contents
lists
available
at
ScienceDirect
Energy
and
Buildings
j
ourna
l
ho
me
page:
www.elsevier.com/locate/enbuild
The
joint
influence
of
albedo
and
insulation
on
roof
performance:
A
modeling
study
P.
Ramamurthy
a,b
,
T.
Sun
b,c
,
K.
Rule
d
,
E.
Bou-Zeid
b,
a
Department
of
Mechanical
Engineering,
City
College
of
New
York,
New
York,
NY
10021,
USA
b
Department
of
Civil
and
Environmental
Engineering,
Princeton
University,
Princeton,
NJ
08544,
USA
c
State
Key
Laboratory
of
Hydro-Science
and
Engineering,
Department
of
Hydraulic
Engineering,
Tsinghua
University,
Beijing
100084,
China
d
Princeton
Plasma
Physics
Laboratory,
Princeton,
NJ
08540,
USA
a
r
t
i
c
l
e
i
n
f
o
Article
history:
Received
19
December
2014
Received
in
revised
form
23
May
2015
Accepted
1
June
2015
Available
online
5
June
2015
Keywords:
Cool
roof
Roof
energy
savings
Roof
albedo
Roof
heat
flux
Roof
insulation
Princeton
Roof
Model
a
b
s
t
r
a
c
t
The
advanced
Princeton
Roof
Model
(PROM)
is
evaluated
and
then
applied
to
quantify
the
heat
transferred
through
various
modular
roof
structures
over
an
entire
year.
The
goal
is
to
identify
an
optimal
combination
of
roof
reflectivity
and
insulation
thickness
that
will
reduce
energy
consumption
and
minimize
cost.
Meteorological
data
gathered
over
the
Northeastern
United
States
(Princeton,
NJ)
is
used
to
force
PROM.
Our
results
reveal
that
for
new
constructions
or
for
retrofits
in
the
region,
an
R8.4
(around
46
cm
thick
roof
insulation)
white
roof
(assumed
albedo
=
0.6
or
greater)
would
significantly
reduce
the
combined
heating
and
cooling
load
attributable
to
the
roofs.
The
wintertime
penalty
of
white
roofs
is
also
shown
to
be
insignificant
compared
to
their
summertime
benefits.
The
findings
are
pertinent
to
many
other
densely
populated
areas
with
comparable
climates
where,
despite
a
much
higher
number
of
heating
versus
cooling
degree-days,
white
roofs
are
overall
advantageous.
A
cost
optimization
analysis
found
that
doubling,
tripling
and
quadrupling
the
insulation
thickness
from
the
baseline
case
of
5.08
cm
(2
in.),
at
an
albedo
of
0.45,
requires
13,
17
and
19
years,
respectively,
to
recover
the
additional
cost
incurred.
©
2015
Elsevier
B.V.
All
rights
reserved.
1.
Introduction
This
modeling
study
is
focused
on
understanding
the
role
played
by
roof
albedo
and
insulation
in
modulating
the
heat
transfer
through
roofs,
and
on
quantifying
the
resulting
impact
on
build-
ing
energy
consumption.
The
overall
goal
is
to
provide
guidance
on
roof
design
that
would
help
reduce
the
large
environmental
foot-
print
of
building
air
conditioning:
in
the
US,
about
20%
of
primary
energy
is
consumed
in
heating
and
cooling
of
buildings;
this
(heat-
ing
and
cooling
of
US
buildings
only)
is
equivalent
to
about
3.5%
of
the
worldwide
consumption
of
primary
energy
[1].
One
of
our
unambiguous
conclusions
from
an
associated
exper-
imental
study
[2]
was
that
white
roofs
were
highly
effective
in
reducing
the
cooling
loads
during
the
summer
months,
while
insu-
lation
thickness
(R-value)
was
the
main
determinant
of
roof
energy
efficiency
during
winter
periods.
But
the
observational
study
was
not
well
suited
for
exploring
the
optimum
(in
term
of
financial
cost)
Corresponding
author
at:
Princeton
University,
Department
of
Civil
&
Environ-
mental
Engineering,
E414,
EQuad,
Princeton,
NJ
08544,
USA.
Tel.:
+1
609
258
5429;
fax:
+1
609
258
5334.
E-mail
address:
ebouzeid@princeton.edu
(E.
Bou-Zeid).
combination
of
albedo
and
R-value
for
a
given
geographical
loca-
tion.
Our
further
investigations
detailed
in
this
article
will
use
the
Princeton
Roof
Model
(PROM),
which
is
a
component
of
the
broader
Princeton
Urban
Canopy
Model
(PUCM
[3])
and
which
can
capture
the
vertical
heterogeneity
of
complex
modern
roofing
structures,
to
address
this
fundamental
question.
The
model
will
be
applied
to
simulate
the
transfer
of
heat
in/out
of
multiple
modular
roofs
of
varying
membrane
reflectivity
and
thickness,
continuously
for
an
entire
year,
using
hydrometeorological
forcing
data
collected
in
Princeton,
NJ,
in
the
US
Northeast.
The
aim
is
to
identify
the
optimal
combination
of
albedo
and
insulation
that
would
minimize
total
cost
(material
and
operating
energy
costs)
for
roofs
in
the
region,
but
the
research
methodologies
used
here
(though
clearly
not
the
conclusions)
can
obviously
be
applied
to
any
other
site
anywhere
in
the
world.
The
observational
part
of
the
study
[2],
as
well
as
previous
research
in
the
same
region
[4],
suggest
that
the
albedo
expected
to
yield
the
highest
energy
efficiency
would
be
a
high
one,
corresponding
to
a
white
roof.
The
simulations
we
conduct
here
will
aid
in
corroborating
these
conclusions,
and
the
expan-
sion
of
the
parameter
space
(albedo
and
insulation)
will
allow
us
to
explore/identify
the
optimal
roof
design.
Research
in
the
last
two
decades
has
highlighted
the
importance
of
roofs
as
a
possible
tool
to
mitigate
urban
heat
islands
and
improve
http://dx.doi.org/10.1016/j.enbuild.2015.06.005
0378-7788/©
2015
Elsevier
B.V.
All
rights
reserved.
318
P.
Ramamurthy
et
al.
/
Energy
and
Buildings
102
(2015)
317–327
energy
sustainability
[5–7].
A
number
of
numerical
studies
have
been
conducted
to
assess
and
quantify
the
effectiveness
of
green
roofs
and
white
roofs
in
moderating
the
urban
microclimate
and
improving
energy
efficiency
of
building
structures.
Akbari
et
al.
[8]
used
DOE
2
to
simulate
energy
consumption
for
typical
buildings
at
11
Metropolitan
areas
and
quantified
the
corresponding
energy
savings.
The
DOE
2
model
has
been
extensively
used
in
the
litera-
ture
to
study
the
effectiveness
of
highly
reflective
roofs
[9].
Sailor
et
al.
[10]
further
improved
the
DOE
2
model
by
adding
a
green
roof
module.
DOE
2
is
primarily
used
as
a
numerical
engine
for
several
building
energy
simulation
programs
like
eQUEST
[11]
and
Energy-
Plus
[12].
Other
notable
models
include
the
DeST,
predominantly
used
in
China
and
Energy
Express
developed
by
CSIRO,
Australia
[11,13].
In
addition
to
the
stand-alone
building
energy
simulations
models,
urban
canopy
models
(UCM)
have
also
been
used
to
study
the
energetic
interactions
between
the
building
envelope
and
the
environment
[14].
UCMs
represent
the
street
canyon
as
an
infi-
nite
rectangular
cavity
bordered
by
two
buildings
(usually
of
equal
height
in
the
single
layer
representation;
an
infinite
regular
array
of
cubes
can
also
be
represented
with
minor
modifications
to
the
model)
[15].
These
models
are
widely
used
by
urban
climatologists
as
they
can
be
readily
coupled
to
mesoscale
climate
models.
In
this
study
we
use
the
Princeton
Roof
Model
(PROM)
to
simulate
the
energy
transfer
through
the
roof
between
the
building
interior
and
the
exterior.
PROM
is
part
of
the
broader
Princeton
Urban
Canopy
Model
and
is
explained
in
detail
in
the
succeeding
section.
2.
Methods
2.1.
Princeton
Roof
Model
A
schematic
of
PROM
is
shown
in
Fig.
1.
A
primary
advantage
in
using
PROM
is
its
ability
to
account
for
the
various
distinct
lay-
ers
in
a
roof.
Many
current
models
consider
roofs
to
be
vertically
homogenous,
and
assume
steady
state
conditions
when
solving
for
the
heat
flux
[16].
These
assumptions
might
be
acceptable
for
simple,
relatively
thin
older
roof
designs.
However,
for
the
mod-
ern
multilayer
roofs,
accounting
for
the
various
vertical
layers,
and
for
the
transient
dynamics
of
the
heat
flux
(since
the
conduction
time
scale
through
these
roofs
can
be
24
h),
becomes
impor-
tant.
In
contrast
to
these
models,
PROM
accounts
for
the
thermal
dynamics
in
individual
roofing
elements/layers
to
compute
the
heat
transferred
between
them.
PROM
is
equipped
with
a
mul-
tilayer,
spatially-analytical
and
temporally
numerical,
conductive
heat
transfer
scheme
based
on
the
Green’s
function
solution
of
the
one
dimensional
heat
equation
in
each
layer.
Individual
layers
of
the
roofing
structure
are
assigned
their
distinct
physical
and
thermal
properties.
Additionally,
this
analytical
scheme
obviates
the
need
to
spatially
discretize
the
domain,
which
reduces
numerical
errors
[17].
While
this
approach
is
comparable
to
the
relaxed
conduction
heat
transfer
equations
used
in
the
advanced
module
of
DOE2.1
[18],
PROM
can
be
applied
to
any
roofing
configuration
without
the
need
to
compute
pre-configured
roof
parameters,
as
required
in
DOE2.1.
In
addition,
the
time
steps
in
PROM
are
variable
compared
to
the
fixed
1-h
period
for
DOE2.1
(those
fixed
time
steps
are
linked
to
the
pre-configured
parameters
DOE2.1
needs).
PROM
can
also
be
used
to
model
energy
exchanges
over
vegetated
roofs.
The
imple-
mentation
and
validation
of
PROM
over
green
roofs
is
detailed
by
Sun
et
al.
[19,20];
these
references
also
provide
full
further
details
about
the
approach
used
in
PROM
for
solving
the
heat
equation.
PROM
is
one
component
of
the
broader
Princeton
Urban
Canopy
Model
(PUCM),
which
employs
the
widely-adopted
single
layer
framework
[21]
to
represent
energy
exchanges
over
an
urban
area
(though
the
other
aspects
of
PUCM
are
irrelevant
here).
This
integration
effectively
couples
the
roof
structure
to
the
shifting
meteorological
conditions
of
the
surrounding
environment.
As
such,
validations
of
PUCM
[3,15,22,23]
also
imply
that
the
con-
vective
turbulent
heat
transfer
parameterizations
of
PROM
are
reasonably
accurate;
however,
further
evaluations
are
conducted
through
this
study
to
ensure
the
model
is
able
to
capture
the
heat
transfer
dynamics
of
the
roofs
under
investigation.
In
the
succeeding
sections
of
this
article,
the
integrated,
multilayer,
spatially-analytical
scheme
implemented
in
PROM
framework
will
be
evaluated
over
different
roofing
structures.
The
model
will
then
be
used
to
simulate
energy
exchanges
over
a
suite
of
roofs
with
gradually
varying
albedo
and
roof
thickness,
forced
by
atmospheric
data
obtained
over
the
validation
site
in
Princeton,
NJ.
The
results
from
this
simulation
will
then
be
used
to
identify
the
optimal
combination
of
surface
reflectivity
and
insulation
thickness
to
minimize
heating
and
cooling
costs
over
a
whole
year.
2.2.
Model
evaluation
Before
using
PROM
to
identify
the
optimal
albedo
and
roof
thickness,
the
model
is
validated
using
the
extensive
and
unique
heat
flux
measurements
collected
at
the
Princeton
Plasma
Physics
Lab
(PPPL)
rooftops
located
in
Princeton,
New
Jersey
(40.3489
N
74.6029
W).
According
to
the
Koppen
index
[24],
the
region
Fig.
1.
Schematic
of
Princeton
Roof
Model
(PROM)–Princeton
Urban
Canopy
Model
(PUCM)
framework.
In
the
schematic
of
PROM
on
the
left,
heat
fluxes
are
denoted
with
red
arrows,
along
with
notations:
H
for
sensible
heat
flux,
LE
for
latent
heat
flux,
G
for
heat
flux
through
roof.
Figure
reproduced
from
Sun
et
al.
[19].
(For
interpretation
of
the
references
to
color
in
this
figure
legend,
the
reader
is
referred
to
the
web
version
of
this
article.)
P.
Ramamurthy
et
al.
/
Energy
and
Buildings
102
(2015)
317–327
319
Fig.
2.
Map
illustrating
the
buildings
and
roof
installation
at
the
PPPL
test
site.
The
weather
stations
(red
markers)
were
placed
in
close
proximity
to
the
heat
flux
sensors
and
thermocouples
installed
inside
the
roof
layers.
Figure
reproduced
from
Ramamurthy
et
al.
[2].
(For
interpretation
of
the
references
to
color
in
this
figure
legend,
the
reader
is
referred
to
the
web
version
of
this
article.)
experiences
a
continental
humid
climate.
Heat
flux
and
tempera-
ture
measurements
were
made
at
five
different
rooftops,
each
with
varying
albedo,
roof
thickness
and
insulation
materials.
Fig.
2
shows
the
plan
view
of
the
installation
site.
We
will
denote
the
roofs
as
ADMw-R8.4,
THYb-R3.6,
LSBb-R4.2,
LSBw-R4.2,
EGRb-R6.3,
where
the
first
three
upper
case
letters
indicate
the
building,
the
4th
lower
case
letter
indicate
whether
the
roof
is
white
(w)
or
black
(b)
and
the
two
digits
after
the
R
indicate
the
R
value
(insulation)
of
the
roof.
The
SI
unit
of
R
is
m
2
K
W
1
,
and
the
equivalent
US
unit
is
h
ft
2
F
BTU
1
.
At
each
of
the
five
roofs,
the
heat
fluxes
were
monitored
beneath
the
Ethylene
Propylene
Diene
Monomer
(EPDM)
membrane
and
at
the
bottom
of
the
final
insulation
layer,
i.e.
at
the
interface
between
the
insulation
foam
and
roof
frame.
The
complete
details
of
the
mea-
surements
and
schematics
of
the
installed
sensors
are
provided
in
Ramamurthy
et
al.
[2].
Apart
from
quantifying
the
thermal
state
of
the
roof,
the
measurements
also
included
ambient
weather
conditions.
The
incoming
and
outgoing
shortwave
radiation
were
measured
by
Davis
shortband
radiometer
(model
6450,
accuracy
±90
W
m
2
,
resolution
1
W
m
2
).
The
surface
temperature
over
different
mem-
branes
was
measured
by
ZyTemp
infrared
gun
(TN0am,
accuracy
0.6
C
for
most
of
our
measurement
range,
resolution
0.0625
C).
The
Vaisala
WXT520
was
employed
to
monitor
the
ambient
atmo-
spheric
pressure
(accuracy
±1
hPA),
relative
humidity
(accuracy
±3%),
wind
speed
(accuracy
±3%
at
10
m
s
1
),
temperature
(accu-
racy
±0.3
C),
and
precipitation
(accuracy
±5%
of
measurement).
The
weather
data
were
logged
using
a
GPRS-based
Sensorscope
mobile
weather
network
[25].
While
all
roof
structures
used
Polyisocyanurate
(PolyIso)
foam
as
the
primary
insulation
material,
over
the
LSBb-R4.2,
LSBw-R4.2
and
EGRb-R6.3
roofs,
a
gypsum
based
fiberglass
and
plywood
were
also
used
as
the
topmost
insulation
layer,
directly
beneath
the
membrane.
All
five
test
roofs
were
shielded
with
an
EPDM
mem-
brane;
however,
the
membrane
albedo
varied
between
the
rooftops
quite
considerably.
These
albedos
were
independently
measured
using
a
combination
of
downward
and
upward
facing
shortband
radiometers.
The
different
roofs
also
varied
in
age;
the
LSBw-R4.2
and
LSBb-R4.2
were
newly
installed
before
the
experiment
(in
the
summer
of
2012),
the
ADMw-R8.4
and
THYb-R3.7
were
installed
in
2005
and
2002
respectively.
The
EGRb-R6.3
roof
was
installed
in
2009.
The
measurement
accuracy
of
the
thermal
state
of
the
roof
struc-
tures
and
of
the
ambient
weather
conditions
are
adequate
for
the
analyses
conducted
here;
however,
the
largest
uncertainty
in
the
inputs
provided
to
PROM
is
in
the
imposed
thermal
properties
(thermal
conductivity
and
volumetric
heat
capacity)
of
the
mem-
branes
and
the
insulation
materials.
While
most
manufacturers
do
disclose
the
lab-tested
values,
these
numbers
vary
depending
on
the
batches
and
installation
technique;
more
importantly,
they
vary
considerably
with
aging
and
weathering
of
the
roof.
The
Poly-
Iso
foams,
whose
cell
structures
are
initially
filled
with
an
inert
gas
that
over
time
gets
replaced
by
air,
start
experiencing
an
increase
in
thermal
conductivity
[26,27].
While
these
changes
are
hard
to
esti-
mate
and
beyond
the
scope
of
this
experiment,
we
modeled
them
by
starting
with
the
common
values
used
in
the
literature
and
then
calibrating
them
over
successive
validation
runs
to
match
observa-
tions.
In
addition,
white
membranes
are
known
to
start
absorbing
more
radiation
due
to
dirt
accumulation
over
time
[28,29],
which
reduces
their
albedo.
To
capture
this
variation,
the
actual
albedo
was
measured
and
used
here.
Table
1
lists
the
thermal
conductiv-
ity
and
the
volumetric
heat
capacity
of
all
the
roofing
members
as
determined
through
this
calibration
and
used
to
parameterize
the
model.
The
calibration
might
be
biased
since
it
inherently
lumps
all
experimental
or
modeling
errors
and
determines
values
for
these
properties
that
partially
offset
these
errors,
but
the
validation
we
show
next
is
able
to
replicate
observed
fluxes
reasonably
well.
Therefore,
and
despite
the
possibility
of
some
local
error
cance-
lations,
PROM
will
be
able
to
simulate
the
heat
transfer
dynamics
in
roofs
with
sufficient
accuracy
to
allow
us
to
confidently
interpret
and
build
upon
its
output.
320
P.
Ramamurthy
et
al.
/
Energy
and
Buildings
102
(2015)
317–327
Table
1
Heat
capacity,
thermal
conductivity
and
albedo
values
used
to
validate
the
PROM
for
various
roofs.
Roof
structure
Volumetric
heat
capacity
(J
K
1
m
3
)
Thermal
conductivity
(W
m
1
K
1
)
Albedo
EGRb-R6.3
[EPDM,
Plywood,
PolyIso]
10
6
×
[1.74,
0.9,
0.04]
[0.5,
0.1,
0.035]
0.06
THYb-R3.7
[EPDM,
PolyIso]
10
6
×
[1.74,
0.07]
[0.3,
0.009]
0.1
ADMw-R8.4
[EPDM,
PolyIso] 10
6
×
[1.74,
0.16]
[0.3,
0.015]
0.35
LSBb-R4.2
[EPDM,
Densdeck,
PolyIso]
10
6
×
[1.74,
0.57,
0.1]
[0.4,
0.3,
0.02]
0.07
LSBw-R4.2
[EPDM,
Densdeck,
PolyIso]
10
6
×
[1.74,
0.57,
0.1]
[0.27,
0.3,
0.02]
0.65
09/1
5
09/1
609/1
709/
18
-100
0
100
09/1
5
09/1
6
09/1
709/1
8
-10
0
10
Model Ob
s
09/1
5
09/1
609/1
709/
18
-100
0
100
09/1
5
09/1
6
09/1
709/1
8
-20
0
20
09/1
5
09/1
609/1
709/
18
Heat Flux (W m
-2
)
-50
0
50
09/1
5
09/1
6
09/1
709/1
8
-5
0
5
09/1
5
09/1
609/1
709/
18
-50
0
50
09/1
5
09/1
6
09/1
709/1
8
-10
0
10
09/1
5
09/1
609/1
709/
18
-100
0
100
Local Tim
e
09/1
5
09/1
6
09/1
709/1
8
-20
0
20
EGRb
THYb
ADMw
LSBw
LSBb
(4a)
(3a)
(2a)
(1a)
(5a)
(1b)
(2b)
(3b)
(4b)
(5b)
Fig.
3.
Comparing
observed
heat
flux
plate
measurements
made
at
the
top
and
bottom
of
various
roofs
to
modeled
values
(30
min
averages).
The
left
column,
1a,
2a,
3a,
4a
and
5a
represent
heat
fluxes
at
the
interface
of
EPDM
membrane
and
the
insulation
layer
at
the
top
of
the
roof
structure
and
the
right
column,
1b,
2b,
3b,
4b
and
5b,
represent
the
heat
fluxes
leaving/entering
the
bottom
of
the
roof
structure.
The
model
was
validated
for
a
3-day
period
in
September
2012
(shown
in
Figs.
3
and
4).
The
forcing
data
required
to
run
the
model
was
obtained
from
the
meteorological
observations
over
PPPL
presented
above.
Fig.
3
compares
the
model
runs
indicated
by
continuous
curves
to
observed
heat
flux
plate
data
indicated
by
markers.
Overall,
given
the
heterogeneity
in
albedo,
insulation
thickness,
and
construction
materials
properties,
as
well
as
the
uncertainty
and
variability
in
the
hydrometeorological
forcing
and
15 16 17 18
0
20
40
60
21 22 23 24
0
20
40
Sep
tem
ber 201
2
Surfac
e Temperature (
º
C)
Model
Observation
a) ENG
b
b) LSBw
Fig.
4.
Comparing
observed
surface
temperature
measurements
made
at
ENGb
(a)
and
LSBw
(b)
to
PUCM
simulations.
P.
Ramamurthy
et
al.
/
Energy
and
Buildings
102
(2015)
317–327
321
Table
2
Mean
Bias
Error,
Percentage
Bias,
Root
Mean
Square
Error,
Percentage
Root
Mean
Square
Error,
and
Nash–Sutcliffe
Efficiency
for
PROM-modeled
heat
flux.
MBE
(W
m
2
) PBIAS
(%)
RMSE
(W
m
2
)
PRMSE
(%)
NSE
ADMw-R8.4
3.52
48
6.65
71.3
0.49
0.08
6.7
0.42
30.73
0.87
EGRb-R6.3
1.92
11
17.92
74.01
0.38
0.014
0.4
1.53
36.6
0.86
LSBb-R4.2
0.74
3.8
13.67
53.78
0.71
0.33 6.18 1.42 23.15 0.94
LSBw-R4.2
0.59 4.7
7.88
51.95
0.72
0.059
2.07
0.86
25.21
0.87
THYb-R3.7
1.97
15.82
11.96
67.55
0.54
1.18
21.5
2.38
37.17
0.86
The
shaded
cells
display
the
error
parameters
for
the
heat
flux
at
the
top
of
the
insulation,
underneath
the
membrane,
while
the
un-shaded
cells
represent
errors
compared
to
the
bottom
heat
flux
plate
measurements.
the
fact
that
partial
roof
shading
is
not
accounted
for
in
the
solar
radiation
inputs
which
are
taken
from
an
unshaded
measurement
site,
the
model
performs
remarkably
well
in
capturing
the
heat
entering
and
leaving
the
top
and
bottom
of
the
roof
interfaces.
The
model
is
especially
successful
in
capturing
the
bottom
heat
fluxes,
at
all
the
sites,
indicating
that
part
of
the
errors
near
the
top
are
due
to
the
hydrometeorological
variability
that
are
not
fully
captured
in
the
inputs
to
the
model.
PROM
is
also
able
to
replicate
the
diur-
nal
variation
of
fluxes
very
well.
In
fact
the
model
only
misses
the
intermittent
sharp
peaks
during
the
midday
period,
which
could
be
directly
attributed
to
the
averaged
input
forcing
data
used
to
run
the
model.
The
model
was
forced
with
30
min
averaged
dataset,
and
it
outputted
data
at
5-min
intervals,
which
were
then
averaged
over
30
min
(the
actual
time
step
of
the
model
was
5-min).
Table
2
provides
the
Root
Mean
Square
Error
(RMSE),
Mean
Bias
Error
(MBE),
and
the
corresponding
Percentage
RMSE
and
Percent-
age
Bias
(PBIAS)
between
the
observed
and
modeled
data
for
all
five
rooftops.
In
addition,
the
table
also
lists
Nash–Sutcliffe
Effi-
ciency
(NSE)
of
the
model.
The
equations
used
to
calculate
these
error
parameters
are:
MBE
=
1
N
n
!
i=1
(O
i
M
i
),
(1)
PBIAS
=
"
n
i=1
(O
i
M
i
)
"
n
i=1
O
i
,
(2)
RMSE
=
#
$
$
%
1
N
n
!
i=1
(O
i
M
i
)
2
,
(3)
PRMSE
=
RMSE
1
N
"
n
i=1
O
i
,
(4)
NSE
=
"
n
i=1
(O
i
¯
O)
2
"
n
i=1
(M
i
O
i
)
2
"
n
i=1
(O
i
¯
O)
2
.
(5)
In
the
above
set
of
equations,
O
i
and
M
i
respectively
represent
the
observed
and
modeled
values;
¯
O is
the
mean
of
the
observed
values;
and
N
is
the
number
of
samples.
The
average
PBIAS
for
the
top
heat
flux,
underneath
the
mem-
brane
is
17%,
compared
to
7%
for
the
bottom
heat
flux.
The
corresponding
NSE
index,
which
indicates
the
strength
of
the
model
to
predict
observed
values,
improves
from
a
modest
0.56
for
the
modeled
top
to
0.88
for
bottom
heat
fluxes.
As
explained
above,
the
higher
error
values
at
the
top
of
the
roof,
underneath
the
mem-
brane,
are
potentially
due
to
the
low
sampling
rate
of
the
forcing
data.
However,
the
errors
observed
at
the
bottom
of
the
roof
are
on
the
order
of
the
accuracy
of
the
measurements
of
the
heat
flux
plates.
In
addition,
bias
errors,
which
are
much
lower
than
RMS
errors
here,
are
more
representative
of
the
model’s
performance
when
time-averaged
or
time-integrated
heat
fluxes
are
considered,
which
will
be
the
case
for
this
study
where
we
focus
on
yearly
heating
and
cooling
loads.
In
addition
to
heat
flux
validations
at
the
top
and
the
bottom
of
the
roof
layer,
Fig.
4
compares
the
external
roof
surface
tem-
perature
simulated
by
the
model
to
its
observed
values.
Similar
to
heat
fluxes,
the
model
performs
well
in
simulating
the
diurnal
variation
of
roof
temperatures.
In
particular,
the
model
captures
the
peak
temperature
values
during
the
midday
period
and
the
nightly
lows
well.
The
anomalies
are
a
result
of
minor
differences
in
accurately
defining
the
thermal
properties
of
the
membrane
and
shading
caused
by
buildings
adjacent
to
the
roof.
The
MBE,
RSMSE
and
NSE
values
for
ENGb
and
LSBw
are
[0.62
K,
3.26
K
and
0.96]
and
[3.73
K,
7.30
K
and
0.83],
respectively.
These
comparisons
demon-
strate
that
PROM
is
a
robust
and
reliable
tool
for
modeling
heat
fluxes
through
the
roofs
for
the
purposes
of
this
study.
3.
Model
setup
The
primary
objective
of
this
study
is
to
provide
guidance
on
the
optimal
combination
of
roof
insulation
thickness
and
roof
sur-
face
albedo
in
terms
of
costs
incurred;
minimizing
the
cost
is
also
expected
to
yield
significant
energy
savings
but
this
has
to
be
con-
firmed
through
the
analyses.
To
that
end,
a
modular
conventional
roof
structure
consisting
of
three
layers,
an
EPDM
membrane
at
the
top,
PolyIso
foam
insulation
in
the
middle,
and
a
concrete
deck
at
the
bottom,
was
simulated.
Based
on
the
calibrated
values
in
Table
1,
EPDM,
PolyIso
and
the
concrete
deck
were
assigned
ther-
mal
conductivities
of
0.3,
0.023
and
1.16
W
K
1
m
1
,
respectively,
while
their
volumetric
heat
capacities
were
set
to
1.74,
0.07
and
0.4
MJ
K
1
m
3
,
respectively.
For
different
simulations,
the
albedo
of
the
rooftops
was
varied
from
0.05
to
0.75,
in
steps
of
0.15,
and
the
insulation
foam
thickness
was
varied
from
0
to
23.876
cm
(0.0025,
3.5763,
5.6083,
9.2659,
14.1427,
19.0195,
23.876).
In
terms
of
R-
value,
this
is
equivalent
to
varying
the
roof
insulation
from
R0.17
to
R10.5
(the
US
equivalent
is
from
R1
to
R60
(R1,
R10,
R15,
R24,
R36,
R48
and
R60)).
The
thermal
properties
of
all
the
materials
were
fixed
and
remained
unchanged
between
simulations.
Other
model
parameters
are
listed
in
Table
3.
Input
meteorological
data
for
the
model
were
obtained
from
an
eddy
covariance
flux
tower
located
on
the
campus
of
Princeton
University,
Princeton,
NJ,
which
is
about
4
km
from
the
experimen-
tal
roofs.
The
incoming
longwave
and
shortwave
radiation
were
observed
using
a
HuskeFlux
4-component
radiometer,
NR01
(accu-
racy:
±10%
for
daily
totals).
A
Campbell
Scientific
CSAT3
sonic
Table
3
Physical
and
aerodynamic
properties
used
in
PROM.
Properties
Values
Thermal
roughness
length
for
roof
surface
0.001
m
Momentum
roughness
length
for
roof
surface
0.01
m
Roof
surface
albedo
[0.05,
0.15,
0.30,
0.45,
0.60,
0.75]
Roof
surface
emissivity
[0.92]
Roof
volumetric
heat
capacity
[EPDM,
PolyIso,
Deck]
[1.74,
0.07,
0.42]
×
10
6
J
K
1
m
3
Roof
thermal
conductivity
[EPDM,
PolyIso,
Deck]
[0.3,
0.023,
1.16]
W
K
1
m
1
Roof
thickness
[EPDM,
Deck]
[0.0028,
0.254]
m
PolyIso
variable
thickness
[0.0025,
3.5763,
5.6083,
9.2659,
14.1427,
19.0195,
23.876]
cm
Internal
constant
building
temperature
23
C
322
P.
Ramamurthy
et
al.
/
Energy
and
Buildings
102
(2015)
317–327
Fig.
5.
Boxplot
showing
monthly
variation
in
ambient
temperatures
for
the
one
year
run,
recorded
at
Princeton,
NJ.
The
top
edge
of
the
box
represents
the
75th
percentile
and
the
bottom
edge
represents
the
25th
percentile.
The
top
and
bottom
whiskers
represent
the
95th
and
the
5th
percentile.
The
horizontal
black
line
shows
the
median
and
the
circle
indicates
the
mean.
The
plus
symbols
represent
data
points
that
are
removed
from
the
mean
by
more
than
±
one-and-a-half
times
the
interquartile
range.
anemometer
was
used
to
measure
the
wind
speed
(accuracy
(offset
error):
less
than
±0.08
m
s
1
for
the
horizontal
wind
components
and
less
than
±0.04
m
s
1
for
the
vertical
wind
component)
and
a
Vaisala
HMP45C
was
used
to
observe
air
temperature
and
spe-
cific
humidity
(accuracy
for
RH:
±3%
and
for
temperature
±0.5
C).
A
LICOR
7500
(accuracy:
±1.5%)
was
used
to
measure
atmospheric
pressure.
The
simulations
were
forced
using
data
gathered
between
May
1st,
2010
and
30th
April
2011.
The
averaged
monthly
varia-
tion
in
temperature
for
the
12-month
period
is
shown
in
Fig.
5.
While
May
through
September
represented
the
warmer
period
or
the
cooling
period,
November
through
March
was
the
heating
period
during
the
colder
months.
The
average
temperatures
during
the
summer
months
(June–August)
were
around
30
C,
daily
peaks
close
to
38
C
were
not
uncommon.
January
was
the
coldest
month
with
average
daily
temperatures
close
to
0
C.
Overall,
the
cooling
and
heating
degree
days
for
this
one
year
period
were
1397
and
5086,
respectively.
4.
One
year
run
Multiple
runs
over
the
same
one-year
period
were
completed
with
the
data
gathered
from
Princeton
and
for
the
various
com-
binations
of
albedo
and
roof
thicknesses
discussed
above.
Fig.
6
shows
the
variation
of
the
heat
transfer
through
the
roof
for
var-
ious
albedo
values
for
warmer
(May–September,
heat
gain)
and
colder
(October–March,
heat
loss)
months;
April
is
omitted
since
it
is
a
mild
month
with
relatively
low
gains
or
losses.
The
x-axis
rep-
resents
the
insulation
thickness
in
cm
(the
equivalent
R-values
are
shown
just
inside
the
axis
box),
and
the
y-axis
represents
the
aver-
age
heat
lost/gained
per
unit
area
per
day.
In
the
figure,
the
heat
lost
through
the
roof
structures
is
taken
as
negative
and
shown
on
the
negative
axis,
while
the
heat
gained
during
the
warmer
months
is
positive.
The
average
heat
entering/leaving
the
roof
structure
per
unit
area
per
day
J
0
(J
m
2
day
1
)
was
calculated
following:
J
0
=
1
N
d
&
t
2
t
1
Qdt,
(6)
where
Q
indicates
the
heat
flux
between
the
roof
deck
and
the
inte-
rior
of
the
building
(W
m
2
);
N
d
represents
the
total
number
of
days;
and
t
1
and
t
2
are
the
start
and
end
time
periods
(s).
Analyzing
the
summer
months,
it
is
clear
that
for
very
low
insu-
lation
thickness,
the
differences
between
various
albedo
values
are
quite
significant.
When
insulation
thickness
is
less
than
4
cm,
a
roof
with
an
˛
=
0.05
gains
718
kJ
m
2
day
1
compared
to
a
highly
reflective
roof
(˛
=
0.75),
which
only
gains
212
kJ
m
2
day
1
.
While
the
heat
gained
is
reduced
as
insulation
thickness
increases,
even
for
a
moderately
insulated
R6.3
roof,
the
heat
gains
from
the
low-
est
albedo
roof
are
nearly
four
times
higher
than
from
the
highest
albedo
roof:
the
highly
reflective
R6.3
roof
gains
54
kJ
m
2
day
1
compared
to
a
black
(˛
=
0.05)
roof
that
admits
190
kJ
m
2
day
1
.
When
the
insulation
thickness
exceeds
18
cm,
the
heat
gained
for
all
albedo
values
remains
almost
constant,
indicating
that
addi-
tional
insulation
is
not
needed.
The
family
of
curves
shows
that,
for
warmer
months,
albedo
plays
a
dominant
role
in
reducing
the
energy
gained
through
the
roofs.
In
fact,
increasing
the
albedo
of
a
very
low
insulation
roof
(<R10)
from
˛
=
0.05
to
˛
=
0.75
is
roughly
equivalent
to
adding
14
cm
of
insulation
thickness
(see
more
on
this
concept
of
expressing
the
increase
in
albedo
as
an
equivalent
increase
in
R-value
in
Gaffin
et
al.
[4]).
In
stark
contrast,
during
the
colder
months,
the
differences
in
albedo
values
do
not
affect
the
heat
loss
in
a
significant
manner.
For
a
roof
with
less
than
4
cm
of
insulation
(lesser
than
R10),
the
difference
in
heat
lost
between
˛
=
0.05
and
˛
=
0.75
is
roughly
125
kJ
m
2
day
1
,
and
for
a
roof
with
insulation
thickness
higher
than
24
cm
the
difference
is
reduced
to
50
kJ
m
2
day
1
.
However,
insulation
thickness
plays
a
dominant
role
in
controlling
the
heat
loss
through
the
roof
structures.
A
roof
with
˛
=
0.30
loses
nearly
600
kJ
m
2
day
1
at
R10
compared
to
175
kJ
m
2
day
1
at
R6.3.
Sim-
ilar
to
warmer
months,
this
difference
is
significantly
reduced
for
insulation
thickness
greater
than
18
cm
(R8.4).
As
we
also
point
out
in
the
associated
experimental
study
[2],
this
discrepancy
between
summer
time
benefits
and
winter
time
penalties
of
cool
roofs,
despite
the
fact
that
the
Northeastern
US
has
about
5
times
more
heating
degree
days
than
cooling
degree
days,
is
related
to
the
neg-
ligible
impact
of
albedo
during
peak
heating
periods
(which
occur
during
nighttime
and
in
the
winter
when
the
insolation
periods
are
short),
as
opposed
to
its
prominent
role
during
peak
cooling
periods
(occurring
in
the
afternoon
and
in
the
summer
when
the
insolation
periods
are
long).
The
model
results
suggest
that
for
newer
constructions,
a
high
albedo
(˛
>
0.7,
although
this
value
might
be
difficult
to
maintain
for
roofs
as
they
age
in
practice)
R8.4
roof
is
a
practical
solution
for
P.
Ramamurthy
et
al.
/
Energy
and
Buildings
102
(2015)
317–327
323
Fig.
6.
Thermal
energy
(J
0
)
gained/lost
as
a
function
of
insulation
thickness
from
the
one-year
simulations
using
PROM.
The
curves
represent
different
albedos
˛.
Warmer
months
include
May
to
September,
while
the
colder
months
extend
from
October
to
March.
significantly
reducing
energy
losses/gains
during
winter
and
sum-
mer
months
at
the
NYC
Metropolitan
region.
Beyond
an
R8.4
roof
insulation,
the
reductions
in
energy
consumption
become
incre-
mental.
Another
point
to
underline
is
that
since
it
is
difficult
to
maintain
high
reflectivity
over
an
extended
period
of
time,
a
thick
insulation
layer
would
reduce
the
need
to
constantly
maintain
high
membrane
reflectivity.
Rain,
dust
and
air
pollution
are
known
to
reduce
the
solar
reflectance
of
white
roofs
[29];
the
decline
in
solar
reflectance,
particularly
in
the
first
year
of
operation,
could
be
con-
siderable.
Bretz
et
al.
[28]
found
that
some
white
roofs
lost
nearly
70%
of
their
reflectivity
within
a
year,
resulting
in
an
estimated
20%
reduction
in
energy
savings
for
succeeding
years
compared
to
the
savings
in
the
first
year.
The
staining
causing
albedo
reduction,
while
not
permanent,
would
require
considerable
effort
to
remove
and
regain
the
original
reflectivity.
Bretz
et
al.
[28]
tested
40
sam-
ples
of
weathered
and
unweathered
roofs
obtained
from
various
regions
in
US
and
Canada
and
suggested
periodic
power
washing
to
maintain
the
membrane
reflectivity.
At
the
PPPL
site,
over
the
ADMw-R8.4
roof,
an
area
of
1
m
×
1
m
was
cleaned
thoroughly
and
the
subsequent
change
in
albedo
was
observed.
Fig.
7
depicts
the
daily
variation
in
the
albedo
measured
during
peak
solar
radiation
from
May
1,
2012
to
October
1,
2012.
In
the
five-month
period,
the
roof
albedo
dropped
dramatically
from
0.65,
post
cleaning,
to
0.35.
In
fact,
during
a
15-day
period,
beginning
June
2012,
the
albedo
suddenly
dropped
by
more
than
25%
before
stabilizing
at
around
0.35
after
the
beginning
of
August
2012.
White
roofs,
on
the
other
hand
could
be
advantageously
used
to
moderate
the
urban
microclimate.
Urban
areas,
in
general
expe-
rience
higher
temperatures
compared
to
the
surrounding
rural
environment
though
what
is
now
a
very
well
documented
anthro-
pogenic
climate
modification
known
as
the
urban
heat
island
(UHI)
effect
[30,31].
Apart
from
increased
anthropogenic
heat
releases,
the
thermal
and
radiative
properties
of
the
built
environment
sus-
tain
this
higher
energy
state
[32].
This
phenomenon
has
a
direct
impact
on
human
health
[33],
as
it
abets
and
augments
the
impact
of
heat
waves
in
urban
areas
and
also
increases
cooling
loads
on
air
conditioning
systems
[34]
by
raising
the
ambient
air
temperature.
White/cool
roofs
can
be
effectively
used
to
reduce
the
impact
of
UHI
by
reflecting
most
of
the
incoming
shortwave
radiation
back
into
the
atmosphere.
This
will
remain
a
significant
advantage
of
such
roofs
even
if
higher
insulation
reduces
the
direct
impact
of
albedo
on
heat
transfer
in/out
of
the
building.
To
illustrate
this
microclimatic
influence
of
white
roofs,
Fig.
8
shows
the
influence
of
albedo
and
roof
insulation
on
the
simulated
05/01
06/01
07/01
08/01
09/01
10/01
0.25
0.3
0.35
0.4
0.45
0.5
0.55
0.6
0.65
0.7
2012
Albedo
Fig.
7.
Variation
in
peak
time
albedo
over
the
reflective
ADMw-R8.4
roof
at
the
PPPL
test
site
in
Princeton,
NJ,
after
cleaning.
324
P.
Ramamurthy
et
al.
/
Energy
and
Buildings
102
(2015)
317–327
Fig.
8.
Modeled
sensible
heat
flux
released
during
warmer
months
(May
to
September)
as
a
function
of
insulation
thickness
from
the
one-year
simulations
using
PROM.
The
curves
represent
different
albedos
˛.
convective
sensible
heat
flux
from
the
roof
to
the
atmosphere
for
the
warmer
months.
Unlike
the
ground/roof
flux
seen
in
Fig.
6,
sen-
sible
heat
flux
is
entirely
dependent
on
albedo.
Insulation
thickness
does
not
play
a
role
in
determining
the
magnitude
of
sensible
heat
and
the
figure
clearly
shows
that
as
insulation
thickness
increases,
the
sensible
heat
remains
almost
constant
for
all
albedos.
Impor-
tantly,
as
albedo
values
increase,
sensible
heat
flux
falls
down
rapidly.
The
magnitude
of
sensible
heat