A. J. Drummond and A. K. Ångström, "Derivation of the Photometric Flux of Daylight from Filtered Measurements of Global (Sun and Sky) Radiant Energy," Appl. Opt. 10, 2024-2030 (1971)
The study reported on here is a continuation of an earlier investigation by the same authors into the relationship between natural illumination and shortwave solar radiation. Whereas the initial approach treated the illumination of sunlight as derived from the corresponding filtered direct radiation component, the results now given extend this work to parallel determination of the (more generally applicable) illumination of integral daylight on the basis of similarly filtered global (sun and sky) radiation. Characteristics are outlined of the instrumentation employed in the investigation undertaken at different locations, viz., Newport, Jerusalem (Israel), and Mauna Loa (Hawaii), as compared with the basic work that utilized data assembled at Pretoria (South Africa). Included is an extension to recent solar radiation measurements obtained on high-altitude aircraft. In general, it is established that it is possible to derive such estimates of natural illumination from radiometric measurements with an accuracy comparable with that obtainable in the best direct photometric efforts.
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Includes correction of −2.5% for thermal emission by RG8 filter.
Table III
Example of Computation of Global (Daylight) Illumination from Filtered Measurements of Shortwave Global Radiation at Newport, 1 November 1967–29 January 1968a
Year
Month
Day
EST
Solar height (deg)
Absolute air mass (m)
Global radiation (mcal cm−2 min−1)
Daylight illumination (klux)
WG7
RG8
WG7–RG8
Computed
Measured
M-C
1967
Nov.
1
10.15
29
2.06
180
099
081
14.8
15.5
+0.7
13
13.15
28
2.12
642
347
295
53.8
54.3
+0.5
13
13.45
26
2.27
584
316
268
49.5
49.5
0.0
16
09.45
22
2.65
580
325
255
48.7
48.6
−0.1
16
12.45
29
2.06
679
378
301
54.7
55.9
+ 1.2
16
13.15
27
2.19
621
351
270
49.6
51.5
+1.9
26
11.45
28
2.12
633
338
295
53.8
53.4
−0.4
26
12.15
28
2.12
621
328
293
53.5
52.6
−0.9
26
12.45
27
2.19
584
306
278
51.1
49.3
−0.8
Dec.
13
11.45
26
2.27
549
291
258
47.7
47.4
−0.3
13
12.15
26
2.27
526
280
246
45.5
45.3
−0.2
16
09.45
18
3.21
472
273
199
39.6
38.8
−0.8
16
12.45
25
2.36
563
317
246
45.9
46.0
+0.1
17
10.45
23
2.55
569
314
255
48.2
47.7
−0.5
17
11.15
24
2.45
600
338
262
49.1
50.1
+1.0
18
11.45
25
2.36
144
070
074
13.8
13.9
+0.1
1968
Jan.
18
11.15
27
2.19
590
331
259
47.6
49.5
+1.9
18
12.15
29
2.06
616
339
277
50.3
50.4
+0.1
18
12.45
27
2.19
592
326
266
48.9
48.7
−0.2
19
10.45
25
2.36
569
319
250
46.6
46.9
+0.3
20
11.15
28
2.12
661
354
307
55.9
53.9
−2.0
20
11.45
29
2.06
673
369
304
55.2
54.7
−0.5
20
12.15
29
2.06
667
370
297
53.9
54.4
+0.5
26
11.45
30
2.00
743
411
332
60.0
60.5
+0.5
26
12.45
30
2.00
741
409
332
60.0
60.2
+0.2
26
12.45
29
2.06
716
395
321
58.3
57.9
−0.4
27
09.45
22
2.65
505
280
225
42.9
44.5
+1.6
27
11.45
30
2.00
711
381
330
59.6
59.9
+0.3
29
10.1.
25
2.36
170
080
090
16.8
16.5
−0.3
Period = 30 min centered EST; Formula: Illumination = 150(1 + 0.102m) × W(WG7–RG8).
Table IV
Comparison Between Computed and Measured Fluxes of Daylight Illumination Under Varying Atmospheric Conditions at Newport, Jerusalem, and Mauna Loa, 4 October 1966–29 January 1968
Location
Year
Month
Series
Range solar height (deg)
Mean absolute air mass (m)
General sky cover
Daylight illumination (klux)
Computed
Measured
M-C
(1) Jerusalem (31.8°N, 800 m)
1966
Oct.
3
34–35
1.6
cloudless
58.5
58.6
+0.1
(2) Mauna Loa (19.5°N, 3400 m)
1966
Nov.
5
69–73
0.7
cloudless
97.4
96.1
−1.3
(3) Newport (41.5°N, 20 m)
1967
Mar.
21
16–50
1.7
cloudless
65.9
65.2
−0.7
4
47–49
1.3
partly cloudy
78.5
78.4
−0.1
5
40–49
1.5
overcast
40.9
41.6
+0.7
Nov.
7
26–29
2.2
cloudless
52.1
52.2
+0.2
1
22
2.7
partly cloudy
48.4
48.6
+0.2
1
29
2.1
overcast
14.8
15.5
+0.7
Dec.
4
18–25
2.6
cloudless
44.6
44.4
−0.2
2
23
2.5
partly cloudy
49.0
48.9
−0.1
1
25
2.4
overcast
13.7
13.9
+0.2
1968
Jan.
6
27–29
2.1
cloudless
51.9
52.0
+0.1
6
22–30
2.2
partly cloudy
54.4
54.9
+0.5
1
29
2.4
overcast
16.8
16.5
−0.3
Mean
49.1
49.1
±0.4
Table V
Typical Values of the Illumination Ratio: Surface/Extraterrestrial for Different Locations and Atmospheric Conditions
Location
Year
Month
Day
Sky cover
Solar height (deg)
Eh (klux)
E0 sinh (klux)
Newport
1967
Mar.
25
cloudless
50
89.8
86.7
104
0.835
19
cloudless
49
86.7
21
overcast
49
47.9
104
0.460
19
cloudless
43
75.9
93.5
0.811
21
overcast
43
50.0
93.5
0.535
Dec.
13
cloudless
25
46.3
46.2
58.0
0.796
16
cloudless
25
46.0
18
overcast
25
13.9
15.2
56.9
0.267
1968
Jan.
29
overcast
24
16.5
Jerusalem
1966
Oct.
4
cloudless
35
58.6
78.6
0.746
Mauna Loa
1966
Nov.
28
cloudless
72
97.4
130
0.750
Table VI
Computed Values of Sunlight/Daylight Illumination from Aircraft Pyrheliometric (Sun Only) and Pyranometric (Global) Measurements of Solar Radiationa
Aircraft altitude (× 103 m)
Absolute air mass
Period
Measurement series
Solar radiation (cal cm−2 min−1)
Sunlight/daylight illumination (klux)
Quartz
RG8
Quartz–RG8
(a) Sunlight: E = 150(1 + 0.032m) × W(Q–RG8)
Oct. 1967
1
1.952
1.053
0.899
135 (137)
13.2
0.20
July–Aug. 1966
21
1.842
1.002
0.840
127
Mar. 1967
12.2
0.21
July–Aug. 1968
7
1.788
0.961
0.827
125
10.0
0.35
Aug. 1966
4
1.780
0.975
0.805
122
March 1967
7.5
0.50
Aug. 1966
4
1.729
0.953
0.776
118
March 1967
5.0
0.70
Aug. 1966
4
1.620
0.882
0.738
113
March 1967
(b) Daylight–cloudless: E = 150(1 + 0. 102m) × W(Q–RG8)
10.6
0.26
June 1968
1
1.725
0.925
0.800
123
10.1
0.28
July 1969
2
1.706
0.915
0.791
122
7.0
0.45
June 1968
1
1.652
0.876
0.776
121
4.5
0.61
June 1968
1
1.587
0.835
0.752
120
3.2
0.73
June 1968
1
1.526
0.802
0.724
117
1.5
0.89
June 1968
1
1.478
0.780
0.698
114
All solar radiation (and hence illumination) values refer to mean sun–earth distance.
Tables (6)
Table I
General Operational Characteristics
Pyranometer
Illuminometer
Linearity
(0–2 cal cm−2 min−1 0–100 klux)
< ±0.5%
±1%
Temperature dependence
(−20°C to +30°C)
±0.5%
−0.15%/1°C rise in temp.
Cosine error (10–90° solar elevation)
±0.5%
±1.5%
Response time (1/e signal)
1 sec
msec
Sensitivity and stability
(See below)
Table II
Basic Newport Pyranometer and Illuminometer Calibration Data
Includes correction of −2.5% for thermal emission by RG8 filter.
Table III
Example of Computation of Global (Daylight) Illumination from Filtered Measurements of Shortwave Global Radiation at Newport, 1 November 1967–29 January 1968a
Year
Month
Day
EST
Solar height (deg)
Absolute air mass (m)
Global radiation (mcal cm−2 min−1)
Daylight illumination (klux)
WG7
RG8
WG7–RG8
Computed
Measured
M-C
1967
Nov.
1
10.15
29
2.06
180
099
081
14.8
15.5
+0.7
13
13.15
28
2.12
642
347
295
53.8
54.3
+0.5
13
13.45
26
2.27
584
316
268
49.5
49.5
0.0
16
09.45
22
2.65
580
325
255
48.7
48.6
−0.1
16
12.45
29
2.06
679
378
301
54.7
55.9
+ 1.2
16
13.15
27
2.19
621
351
270
49.6
51.5
+1.9
26
11.45
28
2.12
633
338
295
53.8
53.4
−0.4
26
12.15
28
2.12
621
328
293
53.5
52.6
−0.9
26
12.45
27
2.19
584
306
278
51.1
49.3
−0.8
Dec.
13
11.45
26
2.27
549
291
258
47.7
47.4
−0.3
13
12.15
26
2.27
526
280
246
45.5
45.3
−0.2
16
09.45
18
3.21
472
273
199
39.6
38.8
−0.8
16
12.45
25
2.36
563
317
246
45.9
46.0
+0.1
17
10.45
23
2.55
569
314
255
48.2
47.7
−0.5
17
11.15
24
2.45
600
338
262
49.1
50.1
+1.0
18
11.45
25
2.36
144
070
074
13.8
13.9
+0.1
1968
Jan.
18
11.15
27
2.19
590
331
259
47.6
49.5
+1.9
18
12.15
29
2.06
616
339
277
50.3
50.4
+0.1
18
12.45
27
2.19
592
326
266
48.9
48.7
−0.2
19
10.45
25
2.36
569
319
250
46.6
46.9
+0.3
20
11.15
28
2.12
661
354
307
55.9
53.9
−2.0
20
11.45
29
2.06
673
369
304
55.2
54.7
−0.5
20
12.15
29
2.06
667
370
297
53.9
54.4
+0.5
26
11.45
30
2.00
743
411
332
60.0
60.5
+0.5
26
12.45
30
2.00
741
409
332
60.0
60.2
+0.2
26
12.45
29
2.06
716
395
321
58.3
57.9
−0.4
27
09.45
22
2.65
505
280
225
42.9
44.5
+1.6
27
11.45
30
2.00
711
381
330
59.6
59.9
+0.3
29
10.1.
25
2.36
170
080
090
16.8
16.5
−0.3
Period = 30 min centered EST; Formula: Illumination = 150(1 + 0.102m) × W(WG7–RG8).
Table IV
Comparison Between Computed and Measured Fluxes of Daylight Illumination Under Varying Atmospheric Conditions at Newport, Jerusalem, and Mauna Loa, 4 October 1966–29 January 1968
Location
Year
Month
Series
Range solar height (deg)
Mean absolute air mass (m)
General sky cover
Daylight illumination (klux)
Computed
Measured
M-C
(1) Jerusalem (31.8°N, 800 m)
1966
Oct.
3
34–35
1.6
cloudless
58.5
58.6
+0.1
(2) Mauna Loa (19.5°N, 3400 m)
1966
Nov.
5
69–73
0.7
cloudless
97.4
96.1
−1.3
(3) Newport (41.5°N, 20 m)
1967
Mar.
21
16–50
1.7
cloudless
65.9
65.2
−0.7
4
47–49
1.3
partly cloudy
78.5
78.4
−0.1
5
40–49
1.5
overcast
40.9
41.6
+0.7
Nov.
7
26–29
2.2
cloudless
52.1
52.2
+0.2
1
22
2.7
partly cloudy
48.4
48.6
+0.2
1
29
2.1
overcast
14.8
15.5
+0.7
Dec.
4
18–25
2.6
cloudless
44.6
44.4
−0.2
2
23
2.5
partly cloudy
49.0
48.9
−0.1
1
25
2.4
overcast
13.7
13.9
+0.2
1968
Jan.
6
27–29
2.1
cloudless
51.9
52.0
+0.1
6
22–30
2.2
partly cloudy
54.4
54.9
+0.5
1
29
2.4
overcast
16.8
16.5
−0.3
Mean
49.1
49.1
±0.4
Table V
Typical Values of the Illumination Ratio: Surface/Extraterrestrial for Different Locations and Atmospheric Conditions
Location
Year
Month
Day
Sky cover
Solar height (deg)
Eh (klux)
E0 sinh (klux)
Newport
1967
Mar.
25
cloudless
50
89.8
86.7
104
0.835
19
cloudless
49
86.7
21
overcast
49
47.9
104
0.460
19
cloudless
43
75.9
93.5
0.811
21
overcast
43
50.0
93.5
0.535
Dec.
13
cloudless
25
46.3
46.2
58.0
0.796
16
cloudless
25
46.0
18
overcast
25
13.9
15.2
56.9
0.267
1968
Jan.
29
overcast
24
16.5
Jerusalem
1966
Oct.
4
cloudless
35
58.6
78.6
0.746
Mauna Loa
1966
Nov.
28
cloudless
72
97.4
130
0.750
Table VI
Computed Values of Sunlight/Daylight Illumination from Aircraft Pyrheliometric (Sun Only) and Pyranometric (Global) Measurements of Solar Radiationa
Aircraft altitude (× 103 m)
Absolute air mass
Period
Measurement series
Solar radiation (cal cm−2 min−1)
Sunlight/daylight illumination (klux)
Quartz
RG8
Quartz–RG8
(a) Sunlight: E = 150(1 + 0.032m) × W(Q–RG8)
Oct. 1967
1
1.952
1.053
0.899
135 (137)
13.2
0.20
July–Aug. 1966
21
1.842
1.002
0.840
127
Mar. 1967
12.2
0.21
July–Aug. 1968
7
1.788
0.961
0.827
125
10.0
0.35
Aug. 1966
4
1.780
0.975
0.805
122
March 1967
7.5
0.50
Aug. 1966
4
1.729
0.953
0.776
118
March 1967
5.0
0.70
Aug. 1966
4
1.620
0.882
0.738
113
March 1967
(b) Daylight–cloudless: E = 150(1 + 0. 102m) × W(Q–RG8)
10.6
0.26
June 1968
1
1.725
0.925
0.800
123
10.1
0.28
July 1969
2
1.706
0.915
0.791
122
7.0
0.45
June 1968
1
1.652
0.876
0.776
121
4.5
0.61
June 1968
1
1.587
0.835
0.752
120
3.2
0.73
June 1968
1
1.526
0.802
0.724
117
1.5
0.89
June 1968
1
1.478
0.780
0.698
114
All solar radiation (and hence illumination) values refer to mean sun–earth distance.
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