Climate-Based Modelling
and Daylight Coefficients
John Mardaljevic
IESD, De Montfort University, Leicester, UK
5th International Radiance Scientific Workshop
13-14 September 2006
IESD, De Montfort University, Leicester, UK
Part 1: Introduction to ClimateBased Modelling
Climate-based daylight modelling is the
prediction of various radiant or luminous
quantities (e.g. irradiance, illuminance,
radiance and luminance) using sun and sky
conditions that are derived from standard
meteorological datasets (e.g. TMY2 or CIBSE
design years).
Climate-based daylight modelling does not yet
have any kind of widely-accepted formal
definition.
2
A proposal for a definition
An analysis that is founded on the totality of
contiguous meteorological data for the
evaluation period in question.
The evaluation period should be of sufficient
duration so that the analysis can be truly said
to capture or represent the prevailing
conditions for that interval, rather than be
simply a “snapshot” of specific conditions at a
particular instant, e.g. summer solstice.
A period of an entire year is needed to capture
the full range in climatic conditions.
3
The three principal modes of
climate-based evaluation
• Cumulative annual: the aggregated
luminance (or radiance) effect of all the
unique hourly sky and the sun conditions for
a full year.
• Cumulative monthly: as annual, but for
each month.
• Time-series: predict hourly (or sub-hourly)
values for a full year.
4
Why Climate-Based?
• Climate-based daylight modelling predicts
absolute measures of illumination etc. using
realistic descriptions for the sky and sun
conditions.
• The evaluation period is usually for a full
year to capture all of the naturally occurring
variation in meteorological conditions.
• Sun and (variable) sky conditions are
evaluated together.
5
Example I: The Arts Students
League (New York)
Founded in 1875, the ASL boasts an alumni
list that is a veritable Who's Who in American
art, from Winslow Homer and Georgia
O'Keeffe to Mark Rothko, Jackson Pollock and
Louise Nevelson.
6
Natural Light
The ASL artists, teachers and students, both
past and present, have all placed great value
in the daylight afforded by the skylights.
7
Scenario: A development is proposed
for the through lot immediately west
of the ASL.
Design issue: The proposed tower
has the potential to reduce the
daylighting of the two studios on the
top floor of the ASL.
8
Existing
9
Proposed
10
Traditional Methods Could Not
Address Client Concerns
• Shadow pattern study: The North facing
skylights rarely receive direct sun light.
• Overcast sky approach: The client was
aware how the character of illumination in
the ASL studios depends on the various sky
conditions, including the potential for
redirected sunlight.
Neither the shadow pattern nor the single sky
condition were considered adequate
11
Solution: Assess Daylight in
Terms of Real Illumination
Total annual illumination (TAI) is a measure
of all the visible daylight energy incident on a
surface.
The prediction of TAI is founded on standard
climate data recorded at/near the site (NYC).
The simulation accounts for overcast and
clear sky conditions, the sun and interreflection.
12
Diffuse Horizontal Irradiance
24
Hour
20
W/m2
16
500
12
400
300
8
200
4
100
0
0
1
2
3
4
5
6
7
Month
8
9
10
11
12
Direct Normal Irradiance
24
W/m2
Hour
20
1000
16
800
12
600
Climate
Data for
New York
City
TMY 94728
400
8
200
0
4
0
1
2
3
4
5
6
7
Month
8
9
10
11
12
13
Predict Total Annual
Illumination for:
(a) Existing situation.
(b) With proposed tower reflectance = 0%.
(c) With proposed tower reflectance = 50%.
Highly detailed 3D model for the area around
the ASL was used.
Reflectivity of neighbouring buildings was set
to 20%.
14
Direct sun
Direct sky
Existing
ASL_exis
klux h
50000
40000
30000
20000
10000
0
Total sun
Total sky
Total sun+sky
36946
4013
9418
29762
29907
33774
39327
Direct sun
Direct sky
Proposed
ASL_prop_r00
klux h
r0%
50000
40000
30000
20000
10000
0
Total sun
Total sky
Total sun+sky
23455
3101
7752
16537
18566
19638
26319
Direct sun
Direct sky
Proposed
ASL_prop_r50
klux h
r50%
50000
40000
30000
20000
10000
0
Total sun
Total sky
Total sun+sky
29972
6838
11517
19241
21374
26080
32893
Results
Case
TAI
Change
Existing
36,946
-
Prop. (0% refl)
23,455
-36.5%
Prop. (50% refl)
29,972
-18.9%
18
Summary
Differences in the predicted levels of total
annual illumination gave a realistic
evaluation of the daylight injury from the
proposed tower.
The mitigation effect of a reflecting* facade for
the proposed tower was quantified.
*The effect of intermediate reflectivity values can be
determined from linear interpolation of the existing
results.
19
Example II: The Hermitage
Museum St. Petersburg
Climate-based lighting simulation was used to
predict the distribution of mean illuminance
for each month, and the total annual
exposure to daylight in rooms of the General
Staff Building.
20
Method
Hourly climate data for St. Petersburg was
processed to faithfully represent local time
including summer daylight savings.
Twelve cumulative monthly climate files were
created using only the period of visiting hours
which is 10h00 to 18h00.
Separate climate files were created for the sun
and the sky components of illumination.
21
Method (cont.)
Simulations showing a hemispherical view of
the illuminance inside of the rooms were
generated for each of the 24 climate files i.e.
12 cumulative sky files and 12 cumulative
sun files.
The total annual exposure is simply the sum
of the 24 monthly sun and sky illuminance
images. The mean illuminance for each
month was the sum of the cumulative sun
and sky illuminances for that month divided
by the number of hours.
22
Results - West facing room
Front
Section
500
500
Total exposure
653 klux hrs
400
Mean Illuminance [lux]
Mean Illuminance [lux]
400
300
200
100
Direct sun
Total exposure
297 klux hrs
Diffuse light
300
200
100
0
0
J
F
M
A
M
J
J
Month
A
Mean illuminance across the year =
S
O
N
222 lux
D
J
F
M
A
M
J
J
Month
A
Mean illuminance across the year =
S
O
N
D
101 lux
23
Example III: Useful daylight
illuminance
UDI is a scheme to reduce and interpret the
voluminous data from a time-varying
illuminance calculation where the daylight
levels are predicted at an hourly (or subhourly) time-step for a full year.
Put simply, achieved UDI is defined as the
annual occurrence of illuminances across the
work plane that are within a range considered
“useful” by the occupants.
24
What’s “useful” daylight?
The range considered “useful” is based on a
survey of reports of occupant preferences and
behaviour in daylit offices with user operated
shading devices.
Daylight illuminances in the range 100 to 500
lux are considered effective either as the sole
source of illumination or in conjunction with
artificial lighting. Daylight illuminances in the
range 500 to 2000 lux are often perceived
either as desirable or at least tolerable.
25
Three (maybe four) categories
Achieved UDI is defined as the annual
occurrence of daylight illuminances that are
between 100 and 2000 lux.
Occurrences less than 100 lux is UDI fell-short.
Occurrences greater than 2000 lux is UDI
exceeded.
Perhaps divide achieved UDI into occurrence of:
(a) 100-500 lux (UDI-supplementary); and,
(b) 500-2000 lux (UDI-autonomous).
26
UDI is simple
Only three (or four) metrics are needed to
provide a compact representation of the hourlyvarying daylight illuminances for an entire year
at each of the calculation points.
The 2000 lux upper limit was based on the
reported behaviour of occupants in daylit
buildings. It was around the 2000 lux mark that
blinds were drawn and/or dissatisfaction was
noted.
Further, the occurrence of UDI exceeded (i.e.
>2000 lux) is related to the building’s propensity
for excessive solar gain and daylight glare.
27
Example application of UDI
Building with a central light-well and
standard clear double glazing.
• Basecase version is totally unshaded.
• Variant 1 has a shading overhang on the
East, South and West facades.
• Variant 2 additionally has a lantern with
shaded top over the light well.
Internal floor, wall and ceiling reflectances were set to
typical values.
28
Basecase - no shading
30 x 30m
plan
South
Variant 1
1m overhang shading on
E, S & W facades
Variant 2
Addition of lantern
with shading
29
Illuminance modelling
Hourly daylight illuminances at work plane
height across the ground floor were predicted
for the Basecase and both shading variants
using the daylight coefficient technique (900
points x ~4000 daylight hours).
London (UK) climate data was used to
generate the hourly-varying sky and sun
conditions.
The hourly simulation data were processed to
show measures of UDI.
30
5
0
30 0
30
W
25
20
40
15
15
20
10
10
5
0
05
0
05
25
60
20
25
60
20
40
15
40
15
20
10
20
10
50
10
15 15
20 20
25 25
30 30
0
5
10
0 WidthWidth
0
[m] [m]
10
15
20
25
30 30 0
05
5 Daylight
10
20
10
15
20 15
25Illuminances
30 25
Useful
[m] [m]
Shaded
facades
WidthWidth
[m] Width
30
80
30
80 14
25
60
20
25 12
60 10
20
100
5
0
05
0
05
8
40
15
40
15 6
20
10
20
10 4
2
05 0
20 15
25 20
30 25
010
515 10
5
10
15
20
25
30
0 WidthWidth
[m] Width
[m]
[m]
10
15 15
20 20
25 25
30
05
5
10
Widthfacades
[m] [m]
Width
Shaded
[%]
25
80
8
S
E
6
2
25
20
0
10
15 15
20
5
10
WidthWidth
[m] [m]
5
10
10
15 15
20 20
25
Width
Shaded
Widthfacades
[m] [m]
30
25
30
25
30
30
25
60
20
80
25
25
Depth
10 15 20
Width [m]
10
5
10 15 20
Width [m]
5
30
20
10
20
30
25
E
and Shaded Light-well
0
0
30
5
Width [m]
Work
Year%
N
100
80
40
15
60
20
10
40
20
5
10 15 20 25
Width [m]
5
10 15 20 25
Shaded
Widthfacades
[m]
2
and Variant
Shaded Light-well
30
0
30
UDI
Achieved
Exceeded
Fell-short
60
40
20
0
10
15 15
20 20
25 25
30
5
10
WidthWidth
[m] [m]
5
10 15 20 25
Widthfacades
[m]
Shaded
10
5
Shaded facades
0
Shaded
facades
0
5
10
15 20
and Shaded
Light-well
25
60
20
50
0
0
0
15
80
60
20
80
15
4
100
5
0
05
0
0
Depth
Depth
W
30
80
and Shaded
Light-well
Shaded
facades
Shaded
facades
Work100
100
and N
Shaded Light-well Year%
100
12
40
W
30
80
14
40
15
30
80
DF%
10
5
30
80
40
0
30 0
E
N
100
30
Variant
1
and Shaded
Light-well
Shaded
facades
Shaded facades
Work100
100
and N
Shaded Light-well Year%
80
60
25
30
80
5
Basecase
and Shaded
Light-well
Unshaded
Building
Shaded
facades
Shaded
facades
100 100
and DF%
Shaded
Light-well
Shaded
facades
5
0
05
0
0
Unshaded
Building
Shaded
facades
0
100 Shaded0 facades
5 facades
10 15 20
and Shaded
Light-well
Shaded
Width [m]
Work
Year [%]
Depth
[m]
30
80
10 15 20 25 30
0
Width
10 [m]
0
5
10
20
5
10 Daylight
15 15
20 Illuminances
25 25
30 30
Useful
Width
[m] [m]
5 Width
Work Year [%]
Depth [m]
25
60
20
100
[%]
30
50
0
0
0
15
Work Year [%]
10
30
80
5
Work Year [%]
Depth [m]
Work Year [%]
Depth [m]
DF [%]
15
Unshaded
Building
Useful
Daylight
Illuminances
Shaded
facades
100
100 Shaded facades
Unshaded
Building
and Shaded
Light-well
Shaded
facades
[%]
50
0
0
30 0
(c)
30
Work
Year [%]
Depth
[m]
10
0
05
10 15 20 25 30
Width [m]
5
10
20
10
15 15
20
25 25
30
Daylight
Autonomy
WidthWidth
[m] [m]
5
50
0
0
0
Work Year [%]
15
5
5
Depth [m]
25
10
20
Work Year [%]
Depth [m]
Depth DF
[m] [%]
15
30
5
Work Year [%]
Depth [m]
50
0
0
0
30
30
0
0
5
10 15 20
Width [m]
W
25
30
E
Exceeded (PE>2k)
UDI Achieved (Pudi)
31
10
Wi
Climate-based modelling of
cumulative skies in Radiance
Cumulative climate metrics (annual or
monthly) can be determined in a
straightforward manner using specially
prepared Radiance sky description files.
These contain the aggregated radiance from
all the individual sky and sun configurations.
The main technical issue that needs to be
nailed is the selection of sky model type from
the hourly integrated values in the climate
file. [CIE TC 3.37 is working on this.]
32
Prediction of time-varying
quantities using Radiance
To generate an annual time-series of hourly
(or sub-hourly) values for illuminance,
luminance etc. requires an accelerated
method such as daylight coefficients because
a “brute-force” computation would take too
long, i.e. ~4000 individual simulations for all
the daylight hours.
The issue regarding the selection of sky model
types applies also.
33
Daylight Coefficients
The daylight coefficient approach requires
that the sky be broken into many patches.
The internal illuminance at a point that
results from a patch of unit-luminance sky is
computed and cached. This is done for each
patch of sky.
It is then possible, in principle, to determine
the internal illuminance for any arbitrary sky
luminance pattern.
34
Definition
If ∆Eγα is the total illuminance produced at a
point in a room by a small element of sky at
altitude γ and azimuth α, then the daylight
coefficient is defined as:
∆Eγα
Dγα =
Lγα ∆Sγα
where Lγα is the luminance of the element of
sky and ∆Sγα is the solid angle of the patch of
sky [Tregenza 1983]. Note also that Dγα is
independent of the distribution of luminance
across the sky vault, since ∆Eγα varies in
proportion to Lγα.
35
Lγα
∆Sγα
Illuminance ∆Eγα accounts for all
the light, direct and inter-reflected,
from the sky patch at (γ,α)
∆Eγα
Figure 6-3. Daylight coefficient basics
36
The magnitude of the daylight coefficient Dγα
will depend on the physical characteristics of
the room and the external environment, e.g.
room geometry, surface reflectances, glazing
transmissivity, outside obstructions and
reflections etc.
The total illuminance E produced at the point
in the room is then calculated from:
! 2π ! π/2
Dγα Lγα cos γdγdα
E=
0
0
37
If the sky were divided into n angular zones,
then for numerical evaluation the integral is
solved using:
n
!
E=
Dp Sp Lp
p=1
This gives the illuminance as the sum of n
products of D, S and L, for each patch of sky
p. The n values of D, S and L can therefore be
treated as vectors.
38
In short...
Once a set of DCs have been determined, it is
possible to derive internal illuminances for
arbitrary sky conditions very rapidly by reusing pre-computed values - no need to do
any more simulations.
However, the the building model (geometry
and reflectances etc.) must not change. If they
do, then a new set of DCs must be computed.
39
Typical procedure
• Obtain basic climate data from a weather tape,
usually global and diffuse irradiance. Convert
the irradiance data to external horizontal
illuminances using a luminous efficacy model.
• Generate a sky luminance distribution using a
sky model.
• Derive internal illuminances from precomputed DCs.
• Determine the artificial lighting requirements
using a lighting control algorithm.
40
How can we do this with
Radiance?
First DC implementation 1997 [Mardaljevic].
Research tool for in-house use (XDAPS*).
Based on the standard Radiance release and
still in use. An end-user version called the
DLS [Cropper] appeared briefly but is no
longer supported.
End-user DC implementation called DAYSIM
released in 2000 [Reinhart]. Required
modified version of Radiance - still supported
and undergoing development.
*XDAPS = eXtensible DAylight Prediction System
41
XDAPS and DAYSIM...
...both work well in their respective ways, but
neither approach possesses the level of
generality that is a hallmark of the Radiance
‘design philosophy’.
For example, XDAPS and DAYSIM are both
geared to computing point values (e.g.
illuminances) and are not ideal for the
generation of images (e.g. a time-of-day movie
sequence).
42
The rtcontrib program
This new addition to the Radiance suite of
programs was designed to address the lack of
generality in the existing daylight coefficient
formulations.
And, in doing so, to extend the range of
application to include image generation and
the efficient modelling of varying artificial light
levels as well as varying daylight conditions.
43
Over to Greg...
44