Energy Convers. Mgmt Vol. 37, No. 12, pp. 1703-1711, 1996
Copyright © 1996 Elsevier Science Ltd
Printed in Great Britain. All fights reserved
PII: S0196-8904(96)00021-0
0196-8904/96 $15.00+ 0.00
Pergamon
LUMINOUS EFFICACY OF DAYLIGHT UNDER
DIFFERENT SKY CONDITIONS
JOSEPH C. LAM and DANNY H. W. LI
Department of Building and Construction, City University of Hong Kong, Tat Chee Avenue, Kowloon,
Hong Kong
(Received 9 June 1995)
Abstraet--Daylighting is recognised as an important and useful strategy in terms of energy-efficient
building design in hot climates. However, daylighting is always accompanied by unwanted solar heat gain,
particularly during the cooling season. To achieve and evaluate daylighting design, solar radiation and
outdoor illuminance data are needed. In 1991, a measuring station was installed at the City University
of Hong Kong to measure global and diffuse solar radiation and outdoor illuminance. The measured data
are analysed, and empirical models to determine luminous efficacy under different sky conditions are
developed and presented. Implications for energy efficiency in building designs are discussed. Copyright
© 1996 Elsevier Science Ltd
Global
Direct
Diffuse
Efficacy
Irradiance
Illuminance
Energy
NOMENCLATURE
C =
Eb¢ =
E~ =
E~ =
Ib¢ =
ldc =
I~ =
K=
Kb~ =
Kac =
Ksc =
Kdo =
Kso =
Kap =
Ksv =
Kt =
ct =
Cloud cover
Direct (beam) outdoor illuminance for clear sky (lm/m:)
Diffuse outdoor illuminance for clear sky (lm/m 2)
Global outdoor illuminance for clear sky (lm/m 2)
Direct (beam) solar irradiance for clear sky (W/m 2)
Diffuse solar irradiance for clear sky (W/m:)
Global solar irradiance for clear sky (W/m 2)
Diffuse fraction (ratio of diffuse to global solar radiation)
Direct (beam) luminous efficacy for clear sky (lm/W)
Diffuse luminous efficacy for clear sky (lm/W)
Global luminous efficacy for clear sky (lm/W)
Diffuse luminous efficacy for overcast sky (lm/W)
Global luminous efficacy for overcast sky (lm/W)
Diffuse luminous efficacy for partly cloudy sky (lm/W)
Global luminous efficacy for partly cloudy sky (lm/W)
Clearness index (ratio of global to extraterrestrial solar radiation)
Solar altitude
INTRODUCTION
It has been shown that daylighting design with lighting control can achieve significant energy
savings in office buildings, up to 40% of electric lighting usage [1, 2]. Daylighting is particularly
attractive in hot climates since it reduces electricity use, not only for artificial lighting but also for
air-conditioning, due to less heat dissipation from electric light fittings [3]. A recent study in Hong
Kong has revealed that very few buildings in Hong Kong have incorporated daylighting schemes,
and daylighting has been identified as one of the key areas in an energy-efficient design strategy [4].
The objective of daylighting design is to maximize the utilization of available outdoor
illuminance without imposing excessive cooling load and causing glare. In subtropical Hong Kong
the solar heat gain is a major component of building cooling load, accounting for nearly half of the
total building envelope load for both residential and office buildings [5, 6]. To evaluate the
daylighting design, we need to know the incident solar irradiation data and the corresponding
outdoor daylight illuminance, so that the trade-off between solar heat gain and daylighting benefits
can be properly assessed. This paper presents work on solar radiation and daylight illuminance
measurements and analysis.
1703
1704
LAM and LI: DAYLIGHTUNDER DIFFERENT SKY CONDITIONS
LOCAL CLIMATE
Hong Kong is situated along the southern coast of China within the subtropical region and
experiences distinct seasonal changes in weather due to its location on the southern edge of the
continent of Asia, facing a vast expanse of ocean. Winter months are between December and
February. The mean temperature is around 15-18°C with monsoon winds from the North and
Northeast. Spring is from March till early May and is usually cloudy with periods of light rain.
The summer season spans from May to September with monsoon winds from the South and
Southeast with an average temperature of 27-29°C. It is hot and humid with occasional showers
and thunderstorms. At times, the typhoon strikes Hong Kong and brings heavy rain and strong
winds. Autumn is short and normally runs from October to November. Sunny bright skies
dominate autumn with dry conditions and a mean temperature of 25°C.
THE MEASURING STATION
Hourly data of solar radiation and outdoor illuminance on the horizontal plane have been
measured since 1991. The measuring station is located on the roof of the City University of
Hong Kong, free of obstruction. Two pyranometers (CM 11) manufactured by Kipp and Zonen,
Netherlands, are used to measure the solar radiation. The diffuse radiation pyranometer is fitted
with a shadow-ring (CM121) to shade the thermopile from the direct sun. The two pyranometers
are connected to an integrator (CM12) which calculates the radiation over selected periods. A
Pascal program has been written to capture the data from the integrator and store the data on a
microcomputer. Details of the solar radiation measurement can be found in Ref. [7].
For outdoor illuminance measurement, silicon photovoltaic cells with cosine and colour
correction, measuring outdoor illuminance level up to around 150 klx, are used. Measured data
are converted into digital signals by an analog/digital converter, captured and stored in a microcomputer. All measurements are referred to true solar time. This facilitates computations which
involve solar altitude and extraterrestrial radiation on a unit horizontal surface and comparison
of data for different locations.
DATA ANALYSIS
Kittler et al. [8] suggested a number of formulae as well as graphical methods for the evaluation
and presentation of solar radiation and outdoor illumination data. For building energy analysis,
many researchers use the luminous efficacy to correlate solar irradiance and daylight iUuminance
[9-11]. In the calculation of daylight availability and lighting energy use in buildings, the luminous
efficacy enables daylight data to be generated from the more widely measured solar radiation data
for places where measured outdoor iUuminance data are not available.
In this study, three-years (1991-1993) of measured hourly data were sorted into three categories
according to the clearness index Kt: clear, partly cloudy and overcast sky conditions as follows:
(a) clear sky (Kt > 0.65)
(b) partly cloudy sky (0.3 < Kt ~<0.65)
(c) overcast sky (0 < Kt ~<0.3)
where Kt = global solar radiation/extraterrestrial solar radiation.
Clear sky
Monthly-average-hourly direct illuminance and solar radiation data were used to determine the
direct luminous efficacy K~, which is defined as the ratio ofilluminance to solar irradiance. Figure 1
shows the variation of average K~ with respect to solar altitude ~t. It can be seen that K~ has a
strong correlation with ~t. Regression analysis has been carried out and K~ can be expressed in
terms of • as follows:
K~ = 59.15 + 1.12~ - 0.0061u 2 (lm/W)
(R=0.91,
R 2=0.82
and
RMSE=4.21m/W)
(1)
LAM and LI: DAYLIGHT UNDER DIFFERENT SKY CONDITIONS
1705
140
120
u
V
E
100
n
[]
[]
o
o
¢:
80
. m
u)
o¢-
60
E
40
o
a
20--
0
0
I
10
I
20
I
30
I
40
t
60
I
50
I
70
I
80
90
Solar altitude a,
Fig. 1. Direct luminous efficacyfor clear sky against solar altitude.
where R, R 2 and RMSE are the correlation coefficient, coefficient of determination and root-meansquare error, respectively. An R 2 of 0.82 indicates that 82% of the variation in direct luminous
efficacy can be explained by changes in solar altitude. Figure 1 also indicates that Kb~ increases with
~t. Similar findings have been reported by Littlefair [10, 11] for the U.K. and other locations.
Diffuse efficacy was calculated as the ratio of diffuse illuminance to its corresponding diffuse
radiation. The diffuse efficacy under clear sky Kd¢ has an average value of 130.6 lm/W with a
standard deviation of 10.9. Figure 2 plots Ka¢ against ~. It can be seen that the data are very
scattered and no clear pattern or relationship can be observed. Generally, K~c is much higher than
Kb¢ particularly at low solar altitude.
Figure 3 shows the plot of global efficacy Kgc against ct. Through regression analysis, K~ can be
expressed as:
Kgc = 78.51 + 1.1 let - 0.0094~t 2 (3)(lm/W)
(R=0.80,
R2=0.64
and
(2)
RMSE=3.01m/W)
The correlation between global efficacy and ~t is not so strong as that between direct efficacy and ct
as R 2 is only 0.64. This is due to the influence of the diffuse component on the global efficacy.
Global radiation has direct and diffuse components, and K~ can be regarded as a combination of
direct luminous efficacy K~ and diffuse luminous efficacy Kd~ and can be written as:
K, = E ~ = E ~ + Eo~=K~I~ + Ko~Io~
I~
I~
Ig~
= Kb~(1 -- K) + KacK
(3)
1706
LAM and LI: D A Y L I G H T U N D E R DIFFERENT SKY CONDITIONS
160
iO
•
150
I
E
140
0
m
~
•
>,
°
0
¢l
¢..)
=
u
130
II
•
B
i
•
B
•
i1
a
•
B
°~
¢:
0
q)
U
(/)
0
r-
0
•
120
•
U
U
II
E
i
q)
o3
C3
1 1 0 --
1 O0 --
90
0
I
10
I
20
I
30
I
40
I
50
f
60
I
70
I
80
90
Solar altitude oc
Fig. 2. Diffuse luminous efficacy for clear sky against solar altitude.
where E~, E,~ and Eb¢ are the global, diffuse and direct illuminance; Ig¢, I,~ and I~¢ the corresponding
solar irradiance; and Kg¢, Kd¢ and K~ their respective luminous efficacies. The diffuse fraction K is
the ratio of diffuse to global radiation. For clear sky, Kb¢ dominates, as K is very small. T h u s , / ~
increases with =, but more gradually than Kb¢.
Overcast sky
Overcast sky means no direct solar component is measured. Global efficacy K~ is very close to
diffuse efficacy Kdo under overcast sky conditions, ranging from 82 to 142.5 lm/W. Similarly to
diffuse efficacy under clear sky, Kao does not correlate well with =. Average luminous efficacy under
overcast sky is 116.2 lm/W with a standard deviation of 13.5, which is close to the 115 lm/W
reported for the U.K. [11]. Luminous efficacy under an overcast sky is generally less t h a n / ~ . This
may be due to the interreflections between the clouds near the horizon and the buildings
surrounding the measuring station.
Partly cloudy sky
Global luminous efficacy Kgp plotted against solar altitude is shown in Fig. 4. The scatter of data
points, especially at low solar altitude, can be observed. This is due to different cloud conditions
for a given value of clearness index Kt. Partly cloudy sky can be treated as a combination of clear
and overcast skies: the direct component in the clear sky and the diffuse component scattered
in both the clear and cloudy parts of the sky. Thus, the direct luminous efficacy can simply be
determined from equation (1), and the diffuse luminous efficacy under partly cloudy sky conditions
can be considered as a linear combination of the diffuse efficacy under clear and overcast sky
conditions with cloud cover C as an indicator of the actual sky condition. Hence:
Kdp = (1 -- C ) K ~ + CKdo.
(4)
LAM and LI: DAYLIGHT UNDER DIFFERENT SKY CONDITIONS
1707
120
•
•0
, . .
•
°
1 O0
80
t~
O
°m
t~
60--
O
¢..m
E
_.=
40-
t~
.Q
O
C.9
20--
0
I
10
0
1
20
t
30
I
40
L
50
I
60
I
70
t
80
90
S o l a r a l t i t u d e ~.
Fig. 3. Global luminous efficacy for clear sky against solar altitude.
160
m
a
B|
.i
El
140
D
%
!1
|
i:
,
"[: [
120
in
Da
1 O0
i"
.!!
•m
•
i!
I
R
8O
:I
•
I
o
(.9
• D
60
_=
[]
°"
Q
I
40
0
K
I
I
I
I
I
I
I
10
20
30
40
50
60
70
80
Solar altitude cL
Fig. 4. Global luminous efficacy for partly cloudy sky against solar altitude.
ECM
37/12--B
90
1708
L A M and LI: D A Y L I G H T U N D E R D I F F E R E N T S K Y C O N D I T I O N S
For subtropical Hong Kong, average measured K~ and Kdo have been found to be 130.6 and
116.2 Ira/W, respectively. Substituting these values into equation (4) gives:
Kdp =
130.6
-- 14.4C
(lm/W)
(5)
As shown in equation (3), the global luminous efficacy can be obtained from the direct and diffuse
efficacies with the diffuse fraction K as an indicator of the relative importance of the direct and
diffuse components under a particular sky condition. Therefore, from equations (1), (3) and (5),
the global luminous efficacy is given by
K~ = K(130.6-14.4C) -t- (1 - K)(59.15 -4- 1.12~t - 0.0061a 2) (lm/W).
(6)
Equations (1), (5) and (6) were used to predict, respectively, the direct, diffuse and global
efficacies under partly cloudy sky conditions. The predicted efficacies were compared with the
measured data for 1993. The root-mean-square errors are 17.7, 10.5 and 9.5 lm/W for the direct,
diffuse and global efficacies, respectively; representing 19, 8.2 and 8.5% of the mean measured
values.
AVERAGE
SKY
CONDITIONS
Average efficacy under all sky conditions for different times of the day and different seasons will
be useful to architects and building engineers. This will give designers an indication of the prevailing
relationship between daylight illuminance and solar irradiance. Tables 1 and 2 show the average
values of global and diffuse luminous effieacies on a horizontal plane, respectively. Each value is
the ratio of the measured average illuminance for that hour to the corresponding average radiation.
Knowing the average radiation data, the corresponding average illuminance level can be readily
determined by using these luminous efficacies.
The yearly average global luminous efficacy is 110.1 lm/W with a standard deviation of 14.3, and
the yearly average diffuse luminous efficacy is 120.5 lm/W with a standard deviation of 16.4. Diffuse
Table 1. Average global luminous efficacy (lm/W)
Month
Jan.
Feb.
Mar.
Apr.
May
Jan.
Jul.
Aug.
Sep.
Oct.
Nov.
Dec.
6
7
8
9
10
---95
94
100
I00
95
83
----
78
82
92
117
123
109
121
119
II0
84
86
76
87
103
ll2
111
124
ll5
126
125
118
I00
94
95
98
118
ll9
108
127
117
125
126
121
106
102
108
103
124
113
ll6
125
126
129
129
123
109
107
104
True solar time
11
12
13
106
122
118
113
126
125
128
132
124
113
107
114
107
127
105
104
125
126
127
132
126
114
I09
Ill
106
136
103
104
114
131
128
133
122
114
108
109
14
15
16
17
18
104
131
101
106
125
124
130
133
123
114
108
107
101
133
100
125
128
123
131
132
123
108
104
103
88
116
91
102
ll9
121
130
132
118
I01
95
90
80
85
84
100
113
115
124
124
I12
83
80
74
---107
98
105
I18
106
94
----
Table 2. Average diffuse luminous efficacy (Ira/W)
True solar time
Month
Jan.
Feb.
Mar.
Apr.
May
Jun.
Jul.
Aug.
Sep.
Oct.
Nov.
Dec.
6
7
8
9
10
I1
12
13
14
15
16
17
18
---90
99
99
102
106
110
----
70
73
93
133
123
117
132
131
134
75
77
89
114
I14
114
131
129
120
133
133
132
105
106
102
131
121
121
125
135
128
133
134
129
116
119
112
134
130
130
138
131
129
132
134
130
123
118
126
139
132
132
135
134
130
131
132
130
120
121
130
135
135
135
128
134
131
130
131
130
118
124
127
140
132
132
126
136
135
130
129
127
115
128
128
139
126
126
127
125
135
134
128
128
113
126
124
133
120
120
129
125
132
136
129
127
103
122
117
119
121
121
120
123
130
135
131
130
ll0
117
101
75
84
85
120
108
124
132
130
130
78
75
70
---88
99
102
125
127
130
----
LAM and LI: DAYLIGHT UNDER DIFFERENT SKY CONDITIONS
1709
100
80
v
(D
t-,'.
(D
60
o
r~
Q)
._>
40
E
0
20
0 I
0
I
10
I
20
I
30
I
40
I
50
I
60
I
70
I
80
I
90
I
100
I~"~'--~
110
120
Global illuminance (klx)
Fig. 5. Cumulative frequency distribution for measured outdoor global luminance.
luminous efficacy is generally higher than global luminous efficacy, indicating that the diffuse
component in daylighting design is more energy-efficient. Data at low altitude (i.e. near sunrise and
sunset) are the major contributors to the standard deviation. Global luminous efficacies from May
to September are higher than those of the same hour in other months, mainly due to high direct
luminous efficacy at high solar altitude in the summer.
LIGHTING
DESIGN
AND
ENERGY
IMPLICATIONS
The main application of luminous efficacy data is to enable illuminance data to be generated
from measured solar irradiance. For daylighting design and calculations, a cumulative frequency
distribution of outdoor illuminance can indicate the percentage of the working year in which a
given illuminance is exceeded. The cumulative frequency distribution has been calculated for the
measured outdoor global illuminance and is shown in Fig. 5. The data are based on typical office
hours from 08:00 to 17:00 in Hong Kong. Assuming a 500 Ix indoor design illuminance for office
space and a daylight factor of 2%, the required outdoor illuminance should be 25,000 Ix. From
Fig. 5, it can be seen that just over 50% of the time in a year, the outdoor illuminance would be
above 25,000 Ix. In other words, just over 50% of the time, daylighting alone would be adequate
to achieve the 500 Ix indoor design lighting level for offices with a 2% daylight factor design. This
has significant implications for energy efficiency in office building in Hong Kong, where electric
lighting accounts for 20-30% of the total electricity use and is a major component in total cooling
load [12].
Figure 6 shows the cumulative frequency distribution of the global luminous efficacy. The
cumulative percentage drops rapidly from about 100 to 130 lm/W, indicating that, for most times
of the year, the global luminous efficacy lies between these two values. In terms of energy efficiency,
1710
LAM and LI: DAYLIGHTUNDER DIFFERENT SKY CONDITIONS
100
80
-
Q)
t~
t~
c-
60-
O
0}
L--
Q.
G)
.>
40
-
E
0
20 -
0
50
I
60
I
70
I
80
90
100
110
120
130
140
150
160
Global luminous efficacy (Im/W)
Fig. 6. Cumulative frequencydistribution for global luminous efficacy.
this is much better than the 16-40 lm/W for incandescent and 50-80 lm/W for fluorescent lamps
commonly installed at homes and in office buildings [13], because less heat is introduced to achieve
the same lighting level and less cooling will be required. This is particularly beneficial to places with
subtropical climates like Hong Kong, where air-conditioning during the hot summer months
accounts for 40-60% of the total electricity consumption in buildings [12].
CONCLUSIONS
Three-year measured outdoor illuminance and solar irradiance data have been gathered and
analysed. It has been found that the direct luminous efficacy increases with solar altitude ~. The
diffuse efficacy under clear sky has an average value of 130.6 lm/W and has no clear correlation
with ~. The global luminous efficacy under clear sky conditions increases with ~, though more
gradually than the direct luminous efficacy. The overcast sky luminous efficacy/~ has an average
value of 116.2 lm/W. For partly cloudy conditions, it is believed that the global luminous efficacy
K~ can be estimated from its corresponding diffuse fraction, cloud cover and ~. Yearly average
global and diffuse luminous effcacies under average sky conditions are l l0.1 and 120.5 lm/W,
respectively. In subtropical Hong Kong, just over 50% of the time, daylighting alone will be
adequate for office space with a 2% daylight factor design. About 80% of the year, the global
luminous effcacy lies between 100 and 130 lm/W, which is much higher than the luminous efficacy
of most electric lighting schemes. This has great implications for energy efficiency in building
designs. More work is needed to assess the likely energy savings and other environmental issues,
such as glare and lighting controls.
Acknowledgement--Danny H. W. Li is supported by a City Universityof Hong Kong Studentship.
LAM and LI: DAYLIGHT UNDER DIFFERENT SKY CONDITIONS
1711
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Kuala Lumpur, ASHRAE, 200 (1989).
4. C. J. Goodsall, Identifying Appropriate Energy Conservation Strategies for Buildings in Hang Kong. City University of
Hong Kong (1994).
5. J. C. Lain, Architectural Science Review 36, 157 (1993).
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1I. P. J. Littlefair, Lighting Research and Technology 20, 177 (1988).
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13. W. M. C. Lain, Sunlighting as Formgiverfor Architecture. Van Nostrand Reinhold Company, New York (1986).