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Sky luminance data validation: Comparison of seven models with four data banks
Solar Energy, Vol. 52, No. 4, pp. 337-346, 1994 Copyright © 1994 Elsevier Science Ltd Printed in the USA. All rights reserved 0038-092X/94 $6.00 + .00
Pergamon 0038-092X(94)E0001-F
SKY LUMINANCE DATA VALIDATION: COMPARISON OF SEVEN MODELS WITH FOUR DATA BANKS PIERRE INEICHEN,** BENOTT MOLINEAUX,* and RICHARDPEREZ* * t • University of Geneva, GAP, 1231 Conches, Switzerland • *ASRC, State University of New York, Albany, NY, U.S.A. Abstract--In order to insure the comparability of the data acquired within the International Daylight Measurement Program, we made a preliminary investigationon the behavior of four daylight data banks when compared with the predictions of seven sky luminance distribution models. We present, in this study, the results of these comparisons, focusingon the performance of the models depending on the site of measurements, the position of the point source of light within the sky, and the weather conditions. We obtain on the whole very similar results, independently of the instrument and the site of measurement, even with limited data banks that cannot be taken as representative of the various climates.
l. INTRODUCTION
In the field of interior design, a good knowledge of the energy and daylight availability is essential for an efficient use of these renewable resources. Solar radiation is measured in many stations throughout the world; this is not the case for daylight. In order to provide for this lack of data, the "Commission Internationale de rEclairage" (CIE) has organized an International Daylight Measurement Program (IDMP) with the objective of collecting worldwide data on daylight availability. In January 1993, IDMP regrouped 15 "research class stations"[21] around the world: 5 in Europe, 5 in Japan, 2 in the U.S., 2 in Asia, and 1 in Australia. We operate one such a station in Geneva, Switzerland, where we measure irradiance (global, diffuse, and beam), illuminance (global, diffuse, beam, and vertical) and luminance (zenith, sky). The development and evaluation of luminous efficacy and sky luminance distribution models require measured values that are severely tested and validated. To achieve this goal, Molineaux and Ineichen [14 ] developed an effective automatic quality control procedure. In this article, we are concerned with the performance of sky luminance models and with the quality of the data used for their evaluation. We present a preliminary investigation on the behavior of daylight data banks from four different countries when compared to the predictions of seven models. The results give a good idea of the quality and comparability of the daylight measurements being collected within IDMP, in view of a large-scale exchange of data.
each data bank, we give, in Table 1, the location of the station, the number of days involved in this study, the time step of the acquisition, the measured parameters, and the type and manufacturer of the sensors. The measurements are independent (different manufacturers, different calibration of sensors, different methods of measurement, etc.) and cover a period of approximately 10 days with clear, intermediate, and overcast conditions. For Geneva, we chose a 9-day period in August 1992.
Data from Japan The station is located in Koto-Ku, at Takenaka Corporation, Technical Research Laboratories. All the Japanese instruments are manufactured by EKO in Japan. The data bank includes 8 days of data, from May 12 to May 21, 1992. The measurements are taken every 30 min and are instantaneous values. The scan duration is 2 min 35 s; irradiances and illuminances are measured at the beginning of the scan [ 5 ]. Data from the U.S. The data set was taken at Battelle Institute, Berkeley in 1985 and 1986 by J. Michalsky et al. [13] and reactualized by R. Perez et al. [16] at ASRC (Albany). The sky scanner is a homemade instrument by Kleckner et al. [ 8 ]; one scan consists of 186 points of measurement. Only the beam illuminance was simultaneously recorded during the data acquisition. The other illuminance and irradiance components are integrals or modeled values. We used 11 days of data from September 16 to September 31, 1985. Data from Great Britain The city of Garston is located 30 km northwest of London; the station is at the BRE (Building Research Establishment) and under the responsibility of P. Littlefair. As in Geneva, their sky scanner is manufactured by PRC Krochmann (During the analysis of BRE's
2. DESCRIPTIONOF THE SITES We obtained a limited set of data from three other laboratories in Japan, the U.S., and Great Britain. For * ISES members. 337
338
P. INEICHEN, B. MOLINEAUX, and R. PEREZ
Table 1. Data banks; location of the station, number of days involved in this study, time step of the acquisition, measured parameters, and type and manufacturer of the sensors Country
Japan
U.S.A.
Great Britain
Switzerland
City Institute Latitude Longitude Altitude Sky scanner No. pts. per scan No. days/no, scans Time step Dvh Bvn Gvh Bn Gh, Dh Diffuse Vertical irradiances Vertical illuminances
Koto-Ku Takenaka Corp. 35.7°N 139.8°E 22 m EKO 145 8/203 30' EKO ML-010S EKO ML-010SD EKO ML-010S EKO MS-52 EKO MS-801 Shadow band 5/50 NESW NESW
Berkeley LBL 37.9°N 122.2°W 396 m MASP (Battelle) 186 11/423 15' Scan integral Sun luminance Dvh + Bvn sin(hs) Luminous efficacy Luminous efficacy Scan integral ---
Garston BRE 51.7°N 0.4°W 80 m PRC Krochmann 145 9/257 15' LMT LiCor + NIP tube LMT NIP CM11 Shadow band 5/50 NESW NESW
Geneva University 46.2°N 6.1 °E 400 m PRC Krochmann 145 9/376 15' LiCor LiCor + NIP tube PRC 910GV NIP CMI 1 Rotating disk -NESW
data, Littlefair [11] noted the same problems as we had with our scanner described by Ineichen and Molineaux [14]). The diffuse components are measured with a 50 m m x 508 m m shadow band and are corrected using skies with nonuniform luminance distribution, including the CIE overcast and clear skies [ 11 ]. We have 9 days of data from August 20, 1991 to January 15, 1992.
Data from Geneva To use a comparable set of data, we extracted from our data bank a 9-day data set from August 22, 1992 to September 1, 1992. Our instrument is a PRC sky scanner and we are recording instantaneous values every 15 min. The duration of the scan is 30 s and we are measuring the illuminance and irradiance components during the first 15 s of the scan. Our sensors are calibrated outdoors side by side against a LiCor and a CM10 substandard, which are calibrated, respectively, at the Institut de M~trologie (Berne, Switzerland) and at the World Radiation Centre (WRC, Davos, Switzerland). 3. INTERCOMPARISON OF THE DATA
The first step of our analysis was to test the coherence of the data. We compared the horizontal diffuse illuminance, Dvh, with the integral of the luminances over the hemisphere. For the integral, we took into account all luminance measurements for which the distance to the sun was greater than 6 ° (respectively, 144 and 185 measurements / scan). Considering that illuminances are easier to measure, and illuminance sensors easier to calibrate, we made the hypothesis that the value of Dvh was correct if the three basic illuminances (direct, global, and diffuse) were coherent with each other. As we noted some disparity between Dvh and the scan integral, we normalized the integral of the scan to the corresponding diffuse horizontal illuminance.
4. DESCRIPTION OF THE SKY LUMINANCE DISTRIBUTION MODELS
All the models used in this study (except the Perez model) are summarized in a publication from Perez et al. [ 17 ], Table 2 gives the input data, the governing parameters, etc., for each model.
Brunger model The model is a three-component continuous model and was originally developed for modeling the sky radiance; it is a superposition of three distinct terms, isotropic, circumsolar, and horizontal brightening factor. The weighting parameters are Dh/Gh and the clearness index Kt [2]. Matsuzawa model This model is a combination of the three CIE standard skies: clear, intermediate, and overcast. The governing parameter is an illuminance "cloud ratio" defined as Dvh/Gvh [12]. A S R C - C I E model Perez et al. [17] modified Matsuzawa's model to take into account the high turbid intermediate skies. The interpolating parameters are Perez' epsilon and delta (clearness and brightness) coefficients. We reference here two versions of the model [ 15, ! 7 ] ; the best results are obtained with the most recent version, which was used in this study. Perez model Five coefficients describe the quality and the quantity of the luminance of the sky dome. Each of the coefficients has a specific physical effect and depends on epsilon and delta: (a) darkening or brightening of the horizon region; (b) luminance gradient near the horizon; (c) relative intensity of the circumsolar region; (d) width of the circumsolar region; and (e) the relative backscattered light [ 18 ].
Sky luminance data validation
339
Table 2. Sky luminance distribution models: Summary of the input data, governing parameters, and number of coefficients Model
Input
Geometry
Brunger Matsuzawa
Gh, Dh, Dvh Gvh, Dvh
Z, lo Z
ASRC-CIE
Gh, Bn
Z, Io
Perez Perraudeau Kittler Harrison
Gh, Bn Gh, Dh Bvn, albedo Opaque cloud cover (Gh, Dh)*
Z, Io Z Z, Ivo, Ma Z
Weighting parameter
Coefficients matrix
K, Kt Kv CIE skies Epsilon, delta CIE skies Epsilon, delta Nebulosity index Ilium. turbidity Op. cloud cover (normalized K)*
4X(9X9)=324
5 × (8 × 4) = 160 5 × 8 = 40
* When op. cloud cover not available. Kt = clearness index; K = Dh/Gh; Kv = Dvh/Gvh.
Perraudeau model The formulation of the model is a product of three functions, depending respectively on the angular distance to the sun (zeta), the height of the considered point, and the sun height. The five discrete sky conditions are parameterized with a nebulosity index, which is a normalized cloud ratio[20 ]. Harrison model The Harrison model needs an opaque cloud cover [ 3 ] to combine two basic luminance distributions: clear and cloudy sky. We used a normalized D h /G h coefficient as opaque cloud cover. Kittler model Based on the light diffusion theory, the Kittler [ 9 ] model is a complex formula that calculates the absolute or relative sky luminance pattern. The governing parameter is the atmospheric illuminance turbidity. 5. COMPARING THE MODELS The performance of each model is evaluated with the mean bias difference: M B D = 1 . ~ (computed valuei - measured valuei)
gion becomes negligible) we normalize the calculated values with an average luminance (and not an integrated illuminance). • Absolute comparison: for these comparisons, we use luminance values expressed in cd. m -2 and normalized by Dvh. The result will be a nonzero MBD, depending on the ability of the model to describe the climate. In Table 3 we give the number of occurrences in the data banks involved in this study for each model parameter, for the sun height and Linke turbidity coefficient. All sky performance We first analyzed the behavior of the models with the available parameters. Fig. 1 represents the behavior of the models with 12 geometrical and meteorological parameters. Each figure represents the difference between computed and measured values ( C - M ) expressed in cd. m -~ versus the considered parameter. The abscissa is divided into bins; for each of them we represent the M B D (point) surrounded by _+1 standard deviation (SD) (line):
SD =
•
[(C-
M)i - ( C - - M ) ]
i=1
and the root mean square difference: RMS N
=
• ~ (computed v a l u e i - m e a s u r e d valuei) 2 i=1
both expressed in relative values (%). We used two methods to compare the performances of the models described above: • Relative comparison: in this case, the sum or the average of the evaluated sky luminance points is normalized by a corresponding measured value. The mean bias difference ( M B D ) will always be zero. Considering the points near the horizon are as important as the points near the zenith (if one considers a vertical surface, the luminance from the zenith re-
All the calculated values are normalized by the mean luminance (relative comparison ); we did not take into account the points near the horizon (6 ° of elevation for Koto-Ku, Garston, and Geneva; 10 ° for Berkeley) because of the nonuniformity of the horizon. One can point out that, although the different models do not have the same overall performance, the dependence patterns are very similar and show that the bias becomes greater near the sun (cf. pt. azimuth, zeta, Lvm dependence graphs). All of these models were developed for values of zeta (angular distance between the considered point and the sun) greater than about 12 ° to 15 °. It should also be noted that some of the error may be attributed to the instruments' nonzero field of view; because of the steep luminance gradient near the sun, and because of the possible stray light, the instrument will have a tendency to overestimate for points close to the sun's position.
No. o f occurrences
Linke turbidity
Sky conditions
No. o f o c c u r r e n c e s
Sun height
Sun g e o m e t r y
No. o f occurrences
In
Perraudeau
No. o f occurrences
Kv
Matsuzawa
No. o f occurrences
Epsilon
No. o f occurrences ASRC-CIE
K
No. o f occurrences
Kt
No. of occurrences Brunger
Epsilon
Perez
0.1
1.065
1.4
0.3
15 °
2
1.75 --~ 2.25
296
6° ~
357
0 --~ 0.05
214
0 ~
717
1~
610
0.9 --~ 1
133
0 ~
645
1~
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3
0.9
0.2
0.2
2.25 ~ 4
218 2.75
15 ° --~ 25 °
268
0.05 ~
281
0.3 --~ 0.65
237
1.4 ~
53
0.8 ~
216
0.1 ~
39
1.065 --~ 1.23
Bin 2
0.3
1.5
764
6
26
2.75 ~
181
25 ° ~
155
3.25
35 °
0.2 --~ 0.7
0.65
250
3 ~
37
0.7 --~ 0.8
172
0.2 ~
55
1.23 ~
Bin 3
1.95
55
13
3.25 ~
202
35 ° ~
151
0.7 ~
6
44
0.6 ~
142
3.75
45 °
0.9
0.7
0.3 --~ 0.4
81
1.5 ~
Bin 4
328 55 °
0.6
0.5
7
3.75 --~ 4.25
287
45 ° ~
0.9
46
0.5 ~
95
0.4 ~
107
1.95 --~ 2.8
Bin 5
4.25 ~ 3
33
55 ° ~
75
0.4 ~
115
0.5 ~
168
2.8 ~
4.75
65 °
0.5
0.6
4.5
Bin 6
75 °
0.4
0.7
6.2
0
4.75 --~ 5.25
42
65 ° ~
102
0.3 ~
152
0.6 ~
117
4.5 ~
Bin 7
T a b l e 3. N u m b e r o f o c c u r r e n c e s o f different sky c o n d i t i o n s for the m o d e l p a r a m e t e r s , sun height, a n d L i n k e turbidity coetficient
159
0.1--~0.2
41
0.8---~0.9
Bin 9
F o r epsilon > 6
133
0.2---~0.3
193
0.7--~0.8
47
6 . 2 --~
Bin 8
Sky luminance data validation Harrison
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Fig. 1. Performance of seven models versus different parameters for all the stations. The luminance values are normalized by the mean luminance. The pt. azimuth is the angular distance between the azimuth of the point and the azimuth of the sun.
Considering the overall performances, two models give slightly better results: the Perez and Brunger models. We chose these two models for further analysis. The detailed results obtained with the Perez model and data from all four sites are represented in Fig. 2. On the scatter-plot, one has the calculated values (Lvc) versus the corresponding measured values (Lvm). The diagonal line is representative of an ideal model. In order to underline the importance of the region near the sun, where the M B D and R M S become significant, we added histograms representing the number of considered points.
Performance in four regions of the sky Using the M B D and SD indicators, we analyzed the behavior of the models for four different regions in the sky vault:
• the zenith region--all the points higher than 60 ° above the horizon (pt. height > 60 °, ~ 2 0 % of the points); • the "south" region--the region in the direction of the sun (pt. azimuth < 45 ° and pt. height < 60 °, ~ 2 0 % of the points); • the " n o r t h " region--the region opposite to the sun region (pt. azimuth > 135 ° and pt. height < 60 °, ~ 2 0 % of the points); and • the "east-west" region--the region on the left-hand side and the right-hand side of the sun (45 ° < pt. azimuth < 135 ° and pt. height < 60 °, ~ 4 0 % of the points). For all these cases, we normalize the integrated value of the scan to the diffuse illuminance (Dvh); we neither consider points within 15 ° of the sun, nor the points near the horizon.
342
P. INEICHEN, B. MOLINEAUX, and R. PEREZ
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Fig. 2. Performance of the Perez model versus different parameters, for all the hemisphere and the four stations; the calculated luminance values are normalized by Dvh: (A) as in Fig. l; (B) relative number of points for each of the 33 bins; (C) distribution of the MBD around the ideal model (MBD = 0), and each histogram is a compilation of three of the above bins; and (D) overall histogram of the distribution of the MBD.
1f!
tad
All stations (1259 scans)
G e n e v a (376 scans)
G a r s t o n (257 scans)
Berkeley (423 scans)
K o t o - K u (203 scans)
Station
2%
0%
--
--
5475
5039
--
5421
5381
--
5967
5475
2%
- 1%
--
2704
5848
--
2957
5967
3%
4%
--
5088
3184
--
5448
2957
0%
0%
--
7189
5493
--
7820
5448
5%
-2%
6991
MBD
7820
Lvm
37%
43%
46%
46%
40%
44%
46%
46%
42%
43%
45%
46%
36%
41%
42%
42%
27%
40%
44%
48%
RMS
Perez
--
--
-1%
-1%
--
--
-2%
-3%
--
--
4%
1%
--
--
0%
-3%
--
--
-4%
2%
MBD
39%
44%
46%
48%
42%
45%
47%
48%
43%
46%
48%
54%
39%
45%
46%
48%
27%
37%
41%
45%
RMS
Brunger
--
--
-1%
1%
--
--
-2%
1%
--
--
2%
1%
--
--
0%
0%
--
--
-3%
3%
MBD
39%
47%
49%
51%
42%
48%
49%
52%
47%
52%
54%
54%
38%
44%
45%
45%
29%
45%
49%
53%
RMS
ASRC-C1E
--
--
-1%
0%
--
--
-2%
1%
--
--
2%
-1%
--
--
-1%
-3%
--
--
-3%
3%
MBD
42%
53%
55%
57%
43%
51%
53%
56%
52%
60%
62%
67%
43%
51%
52%
51%
31%
49%
53%
57%
RMS
Matsuzawa
--
--
0%
2%
--
--
-2%
1%
--
--
4%
5%
--
--
1%
0%
--
--
-3%
5%
MBD
43%
55%
55%
57%
45%
51%
51%
52%
58%
74%
74%
79%
42%
60%
59%
59%
33%
40%
44%
48%
RMS
Harrison
--
--
2%
8%
--
--
1%
8%
--
--
7%
11%
--
--
2%
4%
--
--
0%
14%
MBD
46%
50%
53%
60%
45%
51%
56%
63%
41%
42%
47%
53%
43%
48%
48%
52%
38%
46%
51%
65%
RMS
Perraudeau
--
--
-1%
0%
--
--
-2%
1%
--
--
4%
5%
--
--
-1%
-3%
--
--
-2%
2%
MBD
45%
55%
57%
57%
46%
53%
56%
58%
45%
48%
51%
51%
46%
54%
55%
53%
37%
53%
56%
58%
RMS
Kittler
Dvh Dvh Lvm Lvm
Dvh Dvh Lvm Lvm
>6 °
>6 ° > 15 °
Without
>6 °
>6 ° Without
Without
With
> 15 °
>6 ° Without
>6 ° Without
>6 °
>15 °
>6 °
>6 °
Without
With
Without
Without
Lvm Lyre
With Without
Dvh
Dvh
>6 ° > 15 °
Without
>6 ° Without
Lvm Lyre
>6 ° Without
With Dvh
Dvh
>6 ° > 15 °
Without Without
>6 °
Without
>6 °
With
Zeta
Dvh Lyre Lvm
Horizon Dvh
Norm.
T a b l e 4. M e a n bias difference ( M B D ) a n d root m e a n s q u a r e difference ( R M S ) b e t w e e n m o d e l a n d m e a s u r e m e n t s for t h e f o u r stations a n d t h e s e v e n m o d e l s , for different n o r m a l i z a t i o n s , a n d c u t t i n g v a l u e for zeta with a n d w i t h o u t t h e h o r i z o n p o i n t s
344
P. INEICHEN,
B. MOLINEAUX,
T h e results are presented in Table 4. O n e can see, in this table, t h a t even if some o f the models have a bias o f approximately zero for the complete sky, this is not the case if we test different regions o f the sky separately. T h e two previously selected models give the best description o f the sky vault for all the considered regions. Note that, as we previously observed, the SD rem a i n s high for all models. This is u n d e r s t a n d a b l e because of the effect of "one-of-a-kind" cloud patterns that c a n n o t be deterministically modeled. However, techniques are being developed to incorporate this " c l o u d noise" into a realistic model [1, 19].
Table 4 shows the results obtained w h e n applying the seven models to the four limited data sets, for four different conditions: • T h e scans are normalized by Dvh and evaluated over Berkeley
R.
PEREZ
the whole hemisphere. This represents the overall performance o f the model. • The scans are normalized by Dvh, but without taking into account the first series o f points above the horizon, in order to eliminate the effect of a nonideal horizon (in Geneva, we have a 6 ° high m o u n t a i n in the southeast direction). • T h e scans are normalized by the m e a n value of Lvm ( M B D is zero), without the horizon. This is the intrinsic performance of the model. • T h e same as above, but with cutting the points that are within 15 ° from the sun. This shows the circumsolar region influence o n the model. Fig. 3 is a graphical representation of the site dependence of Brunger's model. T h e graphs representing the dependence with the relative azimuth o f the considered point (pt. a z i m u t h ) show a significant degradation o f the M B D a n d the SD for the station of G a r s t o n a n d G e n e v a near the sun position (0 ° on the graphs). Concerning the data from Geneva, we k n o w that the in-
6. SITE DEPENDENCE OF THE MODELS
Koto-Ku
and
Garston
Geneva
All stations ~un h e g h l ]
C-~
+"10+[+"'""""t""+" 20+ .i~
k:.Wmq,
6~
"I"+''++~] BO+
.,~ -.~m.0 t.+~
........ "II
20 ~ .~+ 60 + BO+ . . . . .
.......
l~+ll+Hlli+ .... ........"'ll II++II,IHI+...... "+' .
~0+ ~
60+ ~0 ~
:o, '' k:~m:q
p+: heigt~l C: m
',,
I pl:++
++ I +"++
20"'to+60+El~"
pJ: h'+ghl t[ C: ~
U t,,
.... .
2O+ 40+ 6OI
]
EI~
•.~,I~HHHIH+,....
I+++++l i++ +-i _,ao,. ' o,. ' ,m,,
C: ~
20".a~"60~B(P
20 + 40+ 60+ 80+
~tt"t~t~t~ ....... +~mH~t~ •
+,m0 .........
+r .... -H ........ It°..... I¢d~10~ 4 C-M
I
"~+I'~ ] ++ll+++l+++i+illm
" 1 ~': + ~ '
t 1
+, ......... +,++,,+
20o.IO+6PP~,
•
20o40,,6~B0
pt J J+ l , l , ,
~.+ 1
:+¢*,,o. ,m. m.
,,
.... '*1+It~' .......
.,;.'
',~II+, 1.............. "I~ +'+.................. "~' ................. "I ~i++...... +°I+...... ......... IF.... -r + ;++I+ + r-+ I..... -1 ,:u "' '-,m,,''o. ,;,c.. " -m,, o,, 9o. "''..~o.' ~ + " -,m,, ~ ,m., +i +]i + z..... +...... z.+1 +. ,z:+il
Ic
TM
.+,+~ ............. +~ , ................. llt~ ............... 1,,+ ............. i~,~1~,1~, ~,i~;~ 3o, ~ ; ~ , ~ ~ ~i~,';~ Lvm
+10 4
C-M
Lvm
C-M
Lvm
0
. 10 '1 Ic=Vmz +10 4 o
.10 .I
[calm21
10"
i011cd/n'~l
I0 +
I0 + Icdlm21
I0"
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Icdh~l
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I¢ cli-'.21
i...... ",'+'+'+'14'~+'+'ql'"""++'+'+"++++'+"++ ""IIHIlHIHIII~I +II I+I'++IIIEHHI~I,,+H'I 300o
leO/m21
30~0
{cd,vn,?.)
3000
~
Icalm21
[cd/m2]
.':il.+--..+.+.,+,+.<`'+.<:.~,~+,+, +, , ,d1;+,+m-l "+.... +.'+I~...+;"""+"+'?."Q1F++_++:°] _ _
,=.0:o+,+o~,,+o.2o.., .,:,~ ++0.2 o., ..~;:.... o....
~
I
~
o.2
",0. I-+++H,, + ........ , ,;,If +Ira+,++++,+ :3 +,, ......+ ++llttHHl + H.l, ......, ['+'++I+IiHII'iII ~ .-I
of+ ~li++ ,,+~h1++ +o++,+~+,+++ +, +O~(X)
Iksxl 10000
~
I+uxl leO00
~00
pax] I0~(0
1}~00
IWax]
,o+ +0ml,+i,i. ,,,++,+,++,,i~t,ll+, Ifl~+tf~ ++I +~ +1I °' +~1+" ~l+,It~ +ll °",,.+++,~+++,+l,+,++0 +
KcUm~
O.2 O.4 O.6 O.8 1.0
°F ~
0.2 0.+ O,60,B
+t°~
1.0
0.2 0.41 0,6 0.8 1.o
+1t++
•l
o.4
o6
,HIHOI~-.• + +.-
~hti++~ +. +,+1 ~+;++,++~]
k:~,,,+l
I~d/m~l 10000
[+;+ -]
0.2 O.4 0.6 O.8 1.0
+t~....
I(X)O0 C-M
40000
Iluml
{>~'~+h
~P,HffHIIHIJIIII++IIII 0.2 O.4 0 . 6 0 . g
] F+
1,0
.,o .~.,,+m+lll<.I.......... ,',,I++~,~++.,IH .ll,tHli~lii~lHi~l~• • II+I+H~i+II+++II+IEIII+I • ImmH+lllHl~ll+ O . 2 0 A 0.6 0.8 1.O
0.2 O++40.60.B I+0
0.2 0.4 0.6 O.B 1.0
0.2 0.4 0.60.B 1.8
0.2 0,4 O 6 0 . a
,(+I .0
Fig. 3. Performance of the Brunger model versus different parameters, for the four stations; the luminance values are normalized by the mean luminance.
Sky luminance data validation
345
Table 5. Histograms of the models' performances for different sky regions. The first bar represents the overall performance, the other bars represent the four sky regions' performances (zenith, south, north, and east-west) 100% 80% 60%
]
40%
20% 0% -20% -40% -60%
Perez Sky region All sky Zenith South North East-west
NbPt.
Lvrn MBD
153'655 5039 30'966 28'214 30'659 63'816
5025 8302 3572 4309
SD
1% 37% 0% -2% 5% 3%
Brunger MBD
SD
0% 39%
37% 3% 38% -3% 33% 2% 31% 0%
ASRC-CIE
Matsuzawa
MBD
MBD
SD
2% 39%
38% 4% 40% -1% 36% -3% 33% 4%
SD
2% 43%
38% 8% 40% -9% 34% 7% 33% 7%
Harrison MBD
SD
-3% 44%
Perraudeau MBD
SD
3% 47%
Kittler MBD
SD
2% 46%
43% -1% 43% -13% 42% 9% 46% 42% -13% 45% 13% 47% -13% 43% 39% 10% 39% 2% 47% 18% 47% 34% 0% 34% 3% 38% 6% 37%
All stations: zeta > 15° without horizon normalized by Dvh.
strument has errors in the positioning of the measurem e n t head. The station of Garston is also equipped with a PRC K r o c h m a n n sky scanner. The study of Table 4 and Fig. 3 shows that the seven models give better results with the Japanese data. The better performance obtained with the Perez model on Berkeley's data is due to the correlation between the data and the model development, and to the luminance integrated value of Dvh.
7. CONCLUSION All the results presented are obtained with limited data banks, covering a small period of the year (no season, humidity, temperature, turbidity, etc., dependencies are considered here), and cannot be taken as representative of the various climates, but the aim of this study was to validate sky luminance distribution data banks. Nevertheless, from the figures and tables, one can see: • For luminance values far from the sun direction, Koto-Ku's data gave the best results. This may be due to higher atmospheric turbidity (or lower epsilon values) in this data bank. • As we did not find opaque cloud cover measurements for the tested data, we used a normalized K index ( K = D h / G h ) to apply Harrison's model. The result is a great disparity of the results depending on the data bank.
• The smallest reductions in R M S when the circumsolar region was removed were obtained for the Garston and the Geneva data banks and may be due to the better optical system of the sky scanner: the PRC K r o c h m a n n scanner has a sensitivity equal to zero at ___5°, whereas the EKO Instruments scanner's sensitivity is 60% of the m a x i m u m at _5 °, going down to zero at +9 ° [7]. Such a conclusion cannot be made from Berkeley's data, because all of the nonluminance data (except Bvn) are deduced from luminance measurements. • According to the significant change in MBE and RMS, when eliminating the horizon band in the Japanese data, we conclude that the station was surrounded by obstructions with nonnegligible height. On the whole, and without the climate's representative data, we obtained similar results, independently of the instrument and the site of measurement. We conclude that the different data banks are comparable. Acknowledgments--This study was supported by the Swiss Federal Energy Office (OFEN). We thank P. Littlefair from the BRE and N. Igawa from Takenaka Corp. for providing the data. Collaboration with the State University of New York was possible thanks to support from the U.S. National Science Foundation (INT 9002363 ). NOMENCLATURE Io, Ivo extraterrestrial irradiance and illuminance on a plane tracking the sun
P. INEICHEN,B. MOLINEAUX,and R. PEREZ
346
Z solar zenith angle Ma optical air mass Gh, Dh global and diffuse irradiances on a horizontal plane W. m -2 Bn beam irradiance on a plane tracking the sun W • m -2 Gvh, Dvh global and diffuse illuminances on a horizontal plane lux Bvn beam iUuminance on a plane tracking the sun lux Lvm, Lvm measured luminance, average Lvm, cd. m -2 Lv2 zenith luminance, cd. m -2 Kt, Kt' clearness index, enhanced clearness index [ 16 ] K, Kv Dh / Gh, Dvh / Gvh zeta angular distance between the considered point and the sun delta Perez' brightness index epsilon Perez' clearness index
REFERENCES
1. Beyer, H. G., Decker, B., Hammer, A., Luther, J., Poplawska, J., Steinberger-Willms, Stolzenburg, K., and Wieting, P., Analysis and synthesis of radiation data for the assessment of fluctuations in the power output of large PV-arrays, Proceedings of the 1lth 17.C. Photovoltaic Solar Energy Conference, Montreux, pp. 1652-1655 (1992). 2. Brunger, A. P., and Hooper, F. C., Anisotropic sky radiance model based on narrow field of view measurements of shortwave radiance, Solar Energy 51 ( 1), 53-64 (1993). 3. Combes, C. A., and Harrison, A. W., Radiometric estimation of cloud cover, J. Atm. Oc. Technol. 2(4), 482490 ( 1985 ). 4. Harrison, A. W., Directional sky luminance versus cloud cover and solar position, Solar Energy 46(1), 13-19 ( 1991 ). 5. lgawa, N., Private communication, Takenaka Corp., Japan ( 1992 ). 6. lneichen, P., and Molineaux, B., PRC sky scanner characterisation, cosime dependence, aperture angle of NPB, honeycomb on PRC 9 IOGV, GAP-CUEPE, University of Geneva, 1231 Conches (1992). 7. lneichen, P., and Molineaux, B., Characterisation and comparison of two sky scanners: PRC Krochmann and
EKO Instruments, Internal report, Groupe of Applied Physics, University of Geneva, Switzerland (1993 ). 8. Kleckner, E. W., et al., A multi-purpose computer-controlled scanning photometer, PNL-4081, Pacific Northwest Lab, Seattle/Richland, WA (1985). 9. Kittler, R., Luminance model of homogeneous skies for design and energy performance predictions, 2nd International Daylighting Conference, Long Beach, CA (1986). 10. Littlefair, P. J., Correcting for the shade ring used in diffuse daylight and radiation measurements, Proc. Daylight and Solar Radiation Measurements. CIE- WMO Symposium, Berlin (1989). I I. Littlefair, P., Private communication, BRE, Garston, GB (1992). 12. Matsuura, K., and lwata, T., A model of daylight source for the daylight illuminance calculations on all weather conditions, CIE Daylighting Conference, Moscow (1990). 13. Michalsky, J. J., Lawrence Berkeley Lab, Windows and Daylighting Group, LBL, Berkeley, CA ( 1986 ). 14. Molineaux, B., and Ineichen, P., Making use of thoroughly validated models for quality control of daylight measurements. GAP-CUEPE, University of Geneva, Switzerland (1993). 15. Perez, R., Ineichen, P., Seals, R., Michalsky, J., and Stewart, R., Modelling daylight availability and irradiance components from direct and global irradiance, Solar Energy 44(5), 271-289 (1990). 16. Perez, R., Ineichen, P., Seals, R., and Zelenka, A., Making full use of the clearness index for parametrizing hourly insolation conditions, Solar Energy 45(2), 111-114 (1990). 17. Perez, R., Michalsky, J., and Seals, R., Modelling sky luminance angular distribution for real sky conditions, Experimental evaluation of existing algorithms, J. lllumin. Engg. Soc. 21(2), 84-92 (1992). 18. Perez, R., Seals, R., and Michalsky, J., An all-weather model for sky luminance distribution, Solar Energy, 50(3), 235-245 (1993). 19. Perez, R., Seals, R., Michalsky, J., and Ineichen, P., Geostatistical properties and modeling of random clouds pattern for real skies, Solar Energy 51 ( l ), 7-18, 1993b. 20. Perraudeau, M., Daylight availability from energetic data, CIE Daylighting Conference, Moscow, Vol. I, pp. A 17 (1990). 21. Tregenza, P. R., Perez, R., Michalsky, J., and Seals, R., Guide to recommended practice of daylight measurement, CIE TC-3.07, Final draft, August 1993.
Pergamon 0038-092X(94)E0001-F
SKY LUMINANCE DATA VALIDATION: COMPARISON OF SEVEN MODELS WITH FOUR DATA BANKS PIERRE INEICHEN,** BENOTT MOLINEAUX,* and RICHARDPEREZ* * t • University of Geneva, GAP, 1231 Conches, Switzerland • *ASRC, State University of New York, Albany, NY, U.S.A. Abstract--In order to insure the comparability of the data acquired within the International Daylight Measurement Program, we made a preliminary investigationon the behavior of four daylight data banks when compared with the predictions of seven sky luminance distribution models. We present, in this study, the results of these comparisons, focusingon the performance of the models depending on the site of measurements, the position of the point source of light within the sky, and the weather conditions. We obtain on the whole very similar results, independently of the instrument and the site of measurement, even with limited data banks that cannot be taken as representative of the various climates.
l. INTRODUCTION
In the field of interior design, a good knowledge of the energy and daylight availability is essential for an efficient use of these renewable resources. Solar radiation is measured in many stations throughout the world; this is not the case for daylight. In order to provide for this lack of data, the "Commission Internationale de rEclairage" (CIE) has organized an International Daylight Measurement Program (IDMP) with the objective of collecting worldwide data on daylight availability. In January 1993, IDMP regrouped 15 "research class stations"[21] around the world: 5 in Europe, 5 in Japan, 2 in the U.S., 2 in Asia, and 1 in Australia. We operate one such a station in Geneva, Switzerland, where we measure irradiance (global, diffuse, and beam), illuminance (global, diffuse, beam, and vertical) and luminance (zenith, sky). The development and evaluation of luminous efficacy and sky luminance distribution models require measured values that are severely tested and validated. To achieve this goal, Molineaux and Ineichen [14 ] developed an effective automatic quality control procedure. In this article, we are concerned with the performance of sky luminance models and with the quality of the data used for their evaluation. We present a preliminary investigation on the behavior of daylight data banks from four different countries when compared to the predictions of seven models. The results give a good idea of the quality and comparability of the daylight measurements being collected within IDMP, in view of a large-scale exchange of data.
each data bank, we give, in Table 1, the location of the station, the number of days involved in this study, the time step of the acquisition, the measured parameters, and the type and manufacturer of the sensors. The measurements are independent (different manufacturers, different calibration of sensors, different methods of measurement, etc.) and cover a period of approximately 10 days with clear, intermediate, and overcast conditions. For Geneva, we chose a 9-day period in August 1992.
Data from Japan The station is located in Koto-Ku, at Takenaka Corporation, Technical Research Laboratories. All the Japanese instruments are manufactured by EKO in Japan. The data bank includes 8 days of data, from May 12 to May 21, 1992. The measurements are taken every 30 min and are instantaneous values. The scan duration is 2 min 35 s; irradiances and illuminances are measured at the beginning of the scan [ 5 ]. Data from the U.S. The data set was taken at Battelle Institute, Berkeley in 1985 and 1986 by J. Michalsky et al. [13] and reactualized by R. Perez et al. [16] at ASRC (Albany). The sky scanner is a homemade instrument by Kleckner et al. [ 8 ]; one scan consists of 186 points of measurement. Only the beam illuminance was simultaneously recorded during the data acquisition. The other illuminance and irradiance components are integrals or modeled values. We used 11 days of data from September 16 to September 31, 1985. Data from Great Britain The city of Garston is located 30 km northwest of London; the station is at the BRE (Building Research Establishment) and under the responsibility of P. Littlefair. As in Geneva, their sky scanner is manufactured by PRC Krochmann (During the analysis of BRE's
2. DESCRIPTIONOF THE SITES We obtained a limited set of data from three other laboratories in Japan, the U.S., and Great Britain. For * ISES members. 337
338
P. INEICHEN, B. MOLINEAUX, and R. PEREZ
Table 1. Data banks; location of the station, number of days involved in this study, time step of the acquisition, measured parameters, and type and manufacturer of the sensors Country
Japan
U.S.A.
Great Britain
Switzerland
City Institute Latitude Longitude Altitude Sky scanner No. pts. per scan No. days/no, scans Time step Dvh Bvn Gvh Bn Gh, Dh Diffuse Vertical irradiances Vertical illuminances
Koto-Ku Takenaka Corp. 35.7°N 139.8°E 22 m EKO 145 8/203 30' EKO ML-010S EKO ML-010SD EKO ML-010S EKO MS-52 EKO MS-801 Shadow band 5/50 NESW NESW
Berkeley LBL 37.9°N 122.2°W 396 m MASP (Battelle) 186 11/423 15' Scan integral Sun luminance Dvh + Bvn sin(hs) Luminous efficacy Luminous efficacy Scan integral ---
Garston BRE 51.7°N 0.4°W 80 m PRC Krochmann 145 9/257 15' LMT LiCor + NIP tube LMT NIP CM11 Shadow band 5/50 NESW NESW
Geneva University 46.2°N 6.1 °E 400 m PRC Krochmann 145 9/376 15' LiCor LiCor + NIP tube PRC 910GV NIP CMI 1 Rotating disk -NESW
data, Littlefair [11] noted the same problems as we had with our scanner described by Ineichen and Molineaux [14]). The diffuse components are measured with a 50 m m x 508 m m shadow band and are corrected using skies with nonuniform luminance distribution, including the CIE overcast and clear skies [ 11 ]. We have 9 days of data from August 20, 1991 to January 15, 1992.
Data from Geneva To use a comparable set of data, we extracted from our data bank a 9-day data set from August 22, 1992 to September 1, 1992. Our instrument is a PRC sky scanner and we are recording instantaneous values every 15 min. The duration of the scan is 30 s and we are measuring the illuminance and irradiance components during the first 15 s of the scan. Our sensors are calibrated outdoors side by side against a LiCor and a CM10 substandard, which are calibrated, respectively, at the Institut de M~trologie (Berne, Switzerland) and at the World Radiation Centre (WRC, Davos, Switzerland). 3. INTERCOMPARISON OF THE DATA
The first step of our analysis was to test the coherence of the data. We compared the horizontal diffuse illuminance, Dvh, with the integral of the luminances over the hemisphere. For the integral, we took into account all luminance measurements for which the distance to the sun was greater than 6 ° (respectively, 144 and 185 measurements / scan). Considering that illuminances are easier to measure, and illuminance sensors easier to calibrate, we made the hypothesis that the value of Dvh was correct if the three basic illuminances (direct, global, and diffuse) were coherent with each other. As we noted some disparity between Dvh and the scan integral, we normalized the integral of the scan to the corresponding diffuse horizontal illuminance.
4. DESCRIPTION OF THE SKY LUMINANCE DISTRIBUTION MODELS
All the models used in this study (except the Perez model) are summarized in a publication from Perez et al. [ 17 ], Table 2 gives the input data, the governing parameters, etc., for each model.
Brunger model The model is a three-component continuous model and was originally developed for modeling the sky radiance; it is a superposition of three distinct terms, isotropic, circumsolar, and horizontal brightening factor. The weighting parameters are Dh/Gh and the clearness index Kt [2]. Matsuzawa model This model is a combination of the three CIE standard skies: clear, intermediate, and overcast. The governing parameter is an illuminance "cloud ratio" defined as Dvh/Gvh [12]. A S R C - C I E model Perez et al. [17] modified Matsuzawa's model to take into account the high turbid intermediate skies. The interpolating parameters are Perez' epsilon and delta (clearness and brightness) coefficients. We reference here two versions of the model [ 15, ! 7 ] ; the best results are obtained with the most recent version, which was used in this study. Perez model Five coefficients describe the quality and the quantity of the luminance of the sky dome. Each of the coefficients has a specific physical effect and depends on epsilon and delta: (a) darkening or brightening of the horizon region; (b) luminance gradient near the horizon; (c) relative intensity of the circumsolar region; (d) width of the circumsolar region; and (e) the relative backscattered light [ 18 ].
Sky luminance data validation
339
Table 2. Sky luminance distribution models: Summary of the input data, governing parameters, and number of coefficients Model
Input
Geometry
Brunger Matsuzawa
Gh, Dh, Dvh Gvh, Dvh
Z, lo Z
ASRC-CIE
Gh, Bn
Z, Io
Perez Perraudeau Kittler Harrison
Gh, Bn Gh, Dh Bvn, albedo Opaque cloud cover (Gh, Dh)*
Z, Io Z Z, Ivo, Ma Z
Weighting parameter
Coefficients matrix
K, Kt Kv CIE skies Epsilon, delta CIE skies Epsilon, delta Nebulosity index Ilium. turbidity Op. cloud cover (normalized K)*
4X(9X9)=324
5 × (8 × 4) = 160 5 × 8 = 40
* When op. cloud cover not available. Kt = clearness index; K = Dh/Gh; Kv = Dvh/Gvh.
Perraudeau model The formulation of the model is a product of three functions, depending respectively on the angular distance to the sun (zeta), the height of the considered point, and the sun height. The five discrete sky conditions are parameterized with a nebulosity index, which is a normalized cloud ratio[20 ]. Harrison model The Harrison model needs an opaque cloud cover [ 3 ] to combine two basic luminance distributions: clear and cloudy sky. We used a normalized D h /G h coefficient as opaque cloud cover. Kittler model Based on the light diffusion theory, the Kittler [ 9 ] model is a complex formula that calculates the absolute or relative sky luminance pattern. The governing parameter is the atmospheric illuminance turbidity. 5. COMPARING THE MODELS The performance of each model is evaluated with the mean bias difference: M B D = 1 . ~ (computed valuei - measured valuei)
gion becomes negligible) we normalize the calculated values with an average luminance (and not an integrated illuminance). • Absolute comparison: for these comparisons, we use luminance values expressed in cd. m -2 and normalized by Dvh. The result will be a nonzero MBD, depending on the ability of the model to describe the climate. In Table 3 we give the number of occurrences in the data banks involved in this study for each model parameter, for the sun height and Linke turbidity coefficient. All sky performance We first analyzed the behavior of the models with the available parameters. Fig. 1 represents the behavior of the models with 12 geometrical and meteorological parameters. Each figure represents the difference between computed and measured values ( C - M ) expressed in cd. m -~ versus the considered parameter. The abscissa is divided into bins; for each of them we represent the M B D (point) surrounded by _+1 standard deviation (SD) (line):
SD =
•
[(C-
M)i - ( C - - M ) ]
i=1
and the root mean square difference: RMS N
=
• ~ (computed v a l u e i - m e a s u r e d valuei) 2 i=1
both expressed in relative values (%). We used two methods to compare the performances of the models described above: • Relative comparison: in this case, the sum or the average of the evaluated sky luminance points is normalized by a corresponding measured value. The mean bias difference ( M B D ) will always be zero. Considering the points near the horizon are as important as the points near the zenith (if one considers a vertical surface, the luminance from the zenith re-
All the calculated values are normalized by the mean luminance (relative comparison ); we did not take into account the points near the horizon (6 ° of elevation for Koto-Ku, Garston, and Geneva; 10 ° for Berkeley) because of the nonuniformity of the horizon. One can point out that, although the different models do not have the same overall performance, the dependence patterns are very similar and show that the bias becomes greater near the sun (cf. pt. azimuth, zeta, Lvm dependence graphs). All of these models were developed for values of zeta (angular distance between the considered point and the sun) greater than about 12 ° to 15 °. It should also be noted that some of the error may be attributed to the instruments' nonzero field of view; because of the steep luminance gradient near the sun, and because of the possible stray light, the instrument will have a tendency to overestimate for points close to the sun's position.
No. o f occurrences
Linke turbidity
Sky conditions
No. o f o c c u r r e n c e s
Sun height
Sun g e o m e t r y
No. o f occurrences
In
Perraudeau
No. o f occurrences
Kv
Matsuzawa
No. o f occurrences
Epsilon
No. o f occurrences ASRC-CIE
K
No. o f occurrences
Kt
No. of occurrences Brunger
Epsilon
Perez
0.1
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2
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0 --~ 0.05
214
0 ~
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1~
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133
0 ~
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1~
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3
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218 2.75
15 ° --~ 25 °
268
0.05 ~
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0.3 --~ 0.65
237
1.4 ~
53
0.8 ~
216
0.1 ~
39
1.065 --~ 1.23
Bin 2
0.3
1.5
764
6
26
2.75 ~
181
25 ° ~
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3.25
35 °
0.2 --~ 0.7
0.65
250
3 ~
37
0.7 --~ 0.8
172
0.2 ~
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1.23 ~
Bin 3
1.95
55
13
3.25 ~
202
35 ° ~
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0.7 ~
6
44
0.6 ~
142
3.75
45 °
0.9
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0.3 --~ 0.4
81
1.5 ~
Bin 4
328 55 °
0.6
0.5
7
3.75 --~ 4.25
287
45 ° ~
0.9
46
0.5 ~
95
0.4 ~
107
1.95 --~ 2.8
Bin 5
4.25 ~ 3
33
55 ° ~
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0.4 ~
115
0.5 ~
168
2.8 ~
4.75
65 °
0.5
0.6
4.5
Bin 6
75 °
0.4
0.7
6.2
0
4.75 --~ 5.25
42
65 ° ~
102
0.3 ~
152
0.6 ~
117
4.5 ~
Bin 7
T a b l e 3. N u m b e r o f o c c u r r e n c e s o f different sky c o n d i t i o n s for the m o d e l p a r a m e t e r s , sun height, a n d L i n k e turbidity coetficient
159
0.1--~0.2
41
0.8---~0.9
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F o r epsilon > 6
133
0.2---~0.3
193
0.7--~0.8
47
6 . 2 --~
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Sky luminance data validation Harrison
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Fig. 1. Performance of seven models versus different parameters for all the stations. The luminance values are normalized by the mean luminance. The pt. azimuth is the angular distance between the azimuth of the point and the azimuth of the sun.
Considering the overall performances, two models give slightly better results: the Perez and Brunger models. We chose these two models for further analysis. The detailed results obtained with the Perez model and data from all four sites are represented in Fig. 2. On the scatter-plot, one has the calculated values (Lvc) versus the corresponding measured values (Lvm). The diagonal line is representative of an ideal model. In order to underline the importance of the region near the sun, where the M B D and R M S become significant, we added histograms representing the number of considered points.
Performance in four regions of the sky Using the M B D and SD indicators, we analyzed the behavior of the models for four different regions in the sky vault:
• the zenith region--all the points higher than 60 ° above the horizon (pt. height > 60 °, ~ 2 0 % of the points); • the "south" region--the region in the direction of the sun (pt. azimuth < 45 ° and pt. height < 60 °, ~ 2 0 % of the points); • the " n o r t h " region--the region opposite to the sun region (pt. azimuth > 135 ° and pt. height < 60 °, ~ 2 0 % of the points); and • the "east-west" region--the region on the left-hand side and the right-hand side of the sun (45 ° < pt. azimuth < 135 ° and pt. height < 60 °, ~ 4 0 % of the points). For all these cases, we normalize the integrated value of the scan to the diffuse illuminance (Dvh); we neither consider points within 15 ° of the sun, nor the points near the horizon.
342
P. INEICHEN, B. MOLINEAUX, and R. PEREZ
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Fig. 2. Performance of the Perez model versus different parameters, for all the hemisphere and the four stations; the calculated luminance values are normalized by Dvh: (A) as in Fig. l; (B) relative number of points for each of the 33 bins; (C) distribution of the MBD around the ideal model (MBD = 0), and each histogram is a compilation of three of the above bins; and (D) overall histogram of the distribution of the MBD.
1f!
tad
All stations (1259 scans)
G e n e v a (376 scans)
G a r s t o n (257 scans)
Berkeley (423 scans)
K o t o - K u (203 scans)
Station
2%
0%
--
--
5475
5039
--
5421
5381
--
5967
5475
2%
- 1%
--
2704
5848
--
2957
5967
3%
4%
--
5088
3184
--
5448
2957
0%
0%
--
7189
5493
--
7820
5448
5%
-2%
6991
MBD
7820
Lvm
37%
43%
46%
46%
40%
44%
46%
46%
42%
43%
45%
46%
36%
41%
42%
42%
27%
40%
44%
48%
RMS
Perez
--
--
-1%
-1%
--
--
-2%
-3%
--
--
4%
1%
--
--
0%
-3%
--
--
-4%
2%
MBD
39%
44%
46%
48%
42%
45%
47%
48%
43%
46%
48%
54%
39%
45%
46%
48%
27%
37%
41%
45%
RMS
Brunger
--
--
-1%
1%
--
--
-2%
1%
--
--
2%
1%
--
--
0%
0%
--
--
-3%
3%
MBD
39%
47%
49%
51%
42%
48%
49%
52%
47%
52%
54%
54%
38%
44%
45%
45%
29%
45%
49%
53%
RMS
ASRC-C1E
--
--
-1%
0%
--
--
-2%
1%
--
--
2%
-1%
--
--
-1%
-3%
--
--
-3%
3%
MBD
42%
53%
55%
57%
43%
51%
53%
56%
52%
60%
62%
67%
43%
51%
52%
51%
31%
49%
53%
57%
RMS
Matsuzawa
--
--
0%
2%
--
--
-2%
1%
--
--
4%
5%
--
--
1%
0%
--
--
-3%
5%
MBD
43%
55%
55%
57%
45%
51%
51%
52%
58%
74%
74%
79%
42%
60%
59%
59%
33%
40%
44%
48%
RMS
Harrison
--
--
2%
8%
--
--
1%
8%
--
--
7%
11%
--
--
2%
4%
--
--
0%
14%
MBD
46%
50%
53%
60%
45%
51%
56%
63%
41%
42%
47%
53%
43%
48%
48%
52%
38%
46%
51%
65%
RMS
Perraudeau
--
--
-1%
0%
--
--
-2%
1%
--
--
4%
5%
--
--
-1%
-3%
--
--
-2%
2%
MBD
45%
55%
57%
57%
46%
53%
56%
58%
45%
48%
51%
51%
46%
54%
55%
53%
37%
53%
56%
58%
RMS
Kittler
Dvh Dvh Lvm Lvm
Dvh Dvh Lvm Lvm
>6 °
>6 ° > 15 °
Without
>6 °
>6 ° Without
Without
With
> 15 °
>6 ° Without
>6 ° Without
>6 °
>15 °
>6 °
>6 °
Without
With
Without
Without
Lvm Lyre
With Without
Dvh
Dvh
>6 ° > 15 °
Without
>6 ° Without
Lvm Lyre
>6 ° Without
With Dvh
Dvh
>6 ° > 15 °
Without Without
>6 °
Without
>6 °
With
Zeta
Dvh Lyre Lvm
Horizon Dvh
Norm.
T a b l e 4. M e a n bias difference ( M B D ) a n d root m e a n s q u a r e difference ( R M S ) b e t w e e n m o d e l a n d m e a s u r e m e n t s for t h e f o u r stations a n d t h e s e v e n m o d e l s , for different n o r m a l i z a t i o n s , a n d c u t t i n g v a l u e for zeta with a n d w i t h o u t t h e h o r i z o n p o i n t s
344
P. INEICHEN,
B. MOLINEAUX,
T h e results are presented in Table 4. O n e can see, in this table, t h a t even if some o f the models have a bias o f approximately zero for the complete sky, this is not the case if we test different regions o f the sky separately. T h e two previously selected models give the best description o f the sky vault for all the considered regions. Note that, as we previously observed, the SD rem a i n s high for all models. This is u n d e r s t a n d a b l e because of the effect of "one-of-a-kind" cloud patterns that c a n n o t be deterministically modeled. However, techniques are being developed to incorporate this " c l o u d noise" into a realistic model [1, 19].
Table 4 shows the results obtained w h e n applying the seven models to the four limited data sets, for four different conditions: • T h e scans are normalized by Dvh and evaluated over Berkeley
R.
PEREZ
the whole hemisphere. This represents the overall performance o f the model. • The scans are normalized by Dvh, but without taking into account the first series o f points above the horizon, in order to eliminate the effect of a nonideal horizon (in Geneva, we have a 6 ° high m o u n t a i n in the southeast direction). • T h e scans are normalized by the m e a n value of Lvm ( M B D is zero), without the horizon. This is the intrinsic performance of the model. • T h e same as above, but with cutting the points that are within 15 ° from the sun. This shows the circumsolar region influence o n the model. Fig. 3 is a graphical representation of the site dependence of Brunger's model. T h e graphs representing the dependence with the relative azimuth o f the considered point (pt. a z i m u t h ) show a significant degradation o f the M B D a n d the SD for the station of G a r s t o n a n d G e n e v a near the sun position (0 ° on the graphs). Concerning the data from Geneva, we k n o w that the in-
6. SITE DEPENDENCE OF THE MODELS
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Fig. 3. Performance of the Brunger model versus different parameters, for the four stations; the luminance values are normalized by the mean luminance.
Sky luminance data validation
345
Table 5. Histograms of the models' performances for different sky regions. The first bar represents the overall performance, the other bars represent the four sky regions' performances (zenith, south, north, and east-west) 100% 80% 60%
]
40%
20% 0% -20% -40% -60%
Perez Sky region All sky Zenith South North East-west
NbPt.
Lvrn MBD
153'655 5039 30'966 28'214 30'659 63'816
5025 8302 3572 4309
SD
1% 37% 0% -2% 5% 3%
Brunger MBD
SD
0% 39%
37% 3% 38% -3% 33% 2% 31% 0%
ASRC-CIE
Matsuzawa
MBD
MBD
SD
2% 39%
38% 4% 40% -1% 36% -3% 33% 4%
SD
2% 43%
38% 8% 40% -9% 34% 7% 33% 7%
Harrison MBD
SD
-3% 44%
Perraudeau MBD
SD
3% 47%
Kittler MBD
SD
2% 46%
43% -1% 43% -13% 42% 9% 46% 42% -13% 45% 13% 47% -13% 43% 39% 10% 39% 2% 47% 18% 47% 34% 0% 34% 3% 38% 6% 37%
All stations: zeta > 15° without horizon normalized by Dvh.
strument has errors in the positioning of the measurem e n t head. The station of Garston is also equipped with a PRC K r o c h m a n n sky scanner. The study of Table 4 and Fig. 3 shows that the seven models give better results with the Japanese data. The better performance obtained with the Perez model on Berkeley's data is due to the correlation between the data and the model development, and to the luminance integrated value of Dvh.
7. CONCLUSION All the results presented are obtained with limited data banks, covering a small period of the year (no season, humidity, temperature, turbidity, etc., dependencies are considered here), and cannot be taken as representative of the various climates, but the aim of this study was to validate sky luminance distribution data banks. Nevertheless, from the figures and tables, one can see: • For luminance values far from the sun direction, Koto-Ku's data gave the best results. This may be due to higher atmospheric turbidity (or lower epsilon values) in this data bank. • As we did not find opaque cloud cover measurements for the tested data, we used a normalized K index ( K = D h / G h ) to apply Harrison's model. The result is a great disparity of the results depending on the data bank.
• The smallest reductions in R M S when the circumsolar region was removed were obtained for the Garston and the Geneva data banks and may be due to the better optical system of the sky scanner: the PRC K r o c h m a n n scanner has a sensitivity equal to zero at ___5°, whereas the EKO Instruments scanner's sensitivity is 60% of the m a x i m u m at _5 °, going down to zero at +9 ° [7]. Such a conclusion cannot be made from Berkeley's data, because all of the nonluminance data (except Bvn) are deduced from luminance measurements. • According to the significant change in MBE and RMS, when eliminating the horizon band in the Japanese data, we conclude that the station was surrounded by obstructions with nonnegligible height. On the whole, and without the climate's representative data, we obtained similar results, independently of the instrument and the site of measurement. We conclude that the different data banks are comparable. Acknowledgments--This study was supported by the Swiss Federal Energy Office (OFEN). We thank P. Littlefair from the BRE and N. Igawa from Takenaka Corp. for providing the data. Collaboration with the State University of New York was possible thanks to support from the U.S. National Science Foundation (INT 9002363 ). NOMENCLATURE Io, Ivo extraterrestrial irradiance and illuminance on a plane tracking the sun
P. INEICHEN,B. MOLINEAUX,and R. PEREZ
346
Z solar zenith angle Ma optical air mass Gh, Dh global and diffuse irradiances on a horizontal plane W. m -2 Bn beam irradiance on a plane tracking the sun W • m -2 Gvh, Dvh global and diffuse illuminances on a horizontal plane lux Bvn beam iUuminance on a plane tracking the sun lux Lvm, Lvm measured luminance, average Lvm, cd. m -2 Lv2 zenith luminance, cd. m -2 Kt, Kt' clearness index, enhanced clearness index [ 16 ] K, Kv Dh / Gh, Dvh / Gvh zeta angular distance between the considered point and the sun delta Perez' brightness index epsilon Perez' clearness index
REFERENCES
1. Beyer, H. G., Decker, B., Hammer, A., Luther, J., Poplawska, J., Steinberger-Willms, Stolzenburg, K., and Wieting, P., Analysis and synthesis of radiation data for the assessment of fluctuations in the power output of large PV-arrays, Proceedings of the 1lth 17.C. Photovoltaic Solar Energy Conference, Montreux, pp. 1652-1655 (1992). 2. Brunger, A. P., and Hooper, F. C., Anisotropic sky radiance model based on narrow field of view measurements of shortwave radiance, Solar Energy 51 ( 1), 53-64 (1993). 3. Combes, C. A., and Harrison, A. W., Radiometric estimation of cloud cover, J. Atm. Oc. Technol. 2(4), 482490 ( 1985 ). 4. Harrison, A. W., Directional sky luminance versus cloud cover and solar position, Solar Energy 46(1), 13-19 ( 1991 ). 5. lgawa, N., Private communication, Takenaka Corp., Japan ( 1992 ). 6. lneichen, P., and Molineaux, B., PRC sky scanner characterisation, cosime dependence, aperture angle of NPB, honeycomb on PRC 9 IOGV, GAP-CUEPE, University of Geneva, 1231 Conches (1992). 7. lneichen, P., and Molineaux, B., Characterisation and comparison of two sky scanners: PRC Krochmann and
EKO Instruments, Internal report, Groupe of Applied Physics, University of Geneva, Switzerland (1993 ). 8. Kleckner, E. W., et al., A multi-purpose computer-controlled scanning photometer, PNL-4081, Pacific Northwest Lab, Seattle/Richland, WA (1985). 9. Kittler, R., Luminance model of homogeneous skies for design and energy performance predictions, 2nd International Daylighting Conference, Long Beach, CA (1986). 10. Littlefair, P. J., Correcting for the shade ring used in diffuse daylight and radiation measurements, Proc. Daylight and Solar Radiation Measurements. CIE- WMO Symposium, Berlin (1989). I I. Littlefair, P., Private communication, BRE, Garston, GB (1992). 12. Matsuura, K., and lwata, T., A model of daylight source for the daylight illuminance calculations on all weather conditions, CIE Daylighting Conference, Moscow (1990). 13. Michalsky, J. J., Lawrence Berkeley Lab, Windows and Daylighting Group, LBL, Berkeley, CA ( 1986 ). 14. Molineaux, B., and Ineichen, P., Making use of thoroughly validated models for quality control of daylight measurements. GAP-CUEPE, University of Geneva, Switzerland (1993). 15. Perez, R., Ineichen, P., Seals, R., Michalsky, J., and Stewart, R., Modelling daylight availability and irradiance components from direct and global irradiance, Solar Energy 44(5), 271-289 (1990). 16. Perez, R., Ineichen, P., Seals, R., and Zelenka, A., Making full use of the clearness index for parametrizing hourly insolation conditions, Solar Energy 45(2), 111-114 (1990). 17. Perez, R., Michalsky, J., and Seals, R., Modelling sky luminance angular distribution for real sky conditions, Experimental evaluation of existing algorithms, J. lllumin. Engg. Soc. 21(2), 84-92 (1992). 18. Perez, R., Seals, R., and Michalsky, J., An all-weather model for sky luminance distribution, Solar Energy, 50(3), 235-245 (1993). 19. Perez, R., Seals, R., Michalsky, J., and Ineichen, P., Geostatistical properties and modeling of random clouds pattern for real skies, Solar Energy 51 ( l ), 7-18, 1993b. 20. Perraudeau, M., Daylight availability from energetic data, CIE Daylighting Conference, Moscow, Vol. I, pp. A 17 (1990). 21. Tregenza, P. R., Perez, R., Michalsky, J., and Seals, R., Guide to recommended practice of daylight measurement, CIE TC-3.07, Final draft, August 1993.