A. K. Ångström and A. J. Drummond, "Fundamental Principles and Methods for the Calibration of Radiometers for Photometric Use," Appl. Opt. 1, 455-464 (1962)
If a photocell is calibrated by means of a source of known spectral energy distribution, employment of the cell for the measurement of the illumination produced by another source of different energy distribution will entail correction of the initial calibration constant. The basic principles for obtaining such a correction factor, applicable for the general case, of wavelength selective receivers, are set out in this paper. As an example, the case is discussed in detail of deriving the natural illumination flux from radiometric measurements of solar shortwave radiation with the aid of current standard meteorological filters. Equations are presented from which the illumination can be computed from known values of the air mass (i.e., optical path length) and the atmospheric turbidity. These equations have been applied to a comprehensive series of measurements of illumination and shortwave radiation assembled in South Africa. It is shown that the equations are valid over very wide ranges of air mass and turbidity.
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The Dependence of Sunlight Illumination (Kilolux), on a Surface Perpendicular to the Rays, on Air Mass and Turbidity, for Mean Solar Distance
βm
0
1.00
1.25
1.50
1.75
2.0
3.0
4.0
6.0
0.000
142
119
115
112
109
106
93
84
69
0.050
105
99
93
87
83
66
54
37
0.100
93
85
78
72
66
47
35
20
0.150
83
73
66
59
53
34
23
11
0.200
73
63
55
47
41
24
15
6
h(°)
90
53
42
35
30
19
14
9
Table II
Comparison between Measured (E0) and Computed (E1 and E2) Values of Illumination at Pretoria (25° 45′ S, 1370 meters) During a Period of Relatively Low Atmospheric Turbidity at the End of the Wet Season
March 1955
Solar height (deg)
m
β· 103
D
S (kilolux)
It − Ir8
It − Ir2
E1
E2
E1 − E0
E2 − E0
Day
TST
(mcal cm−2 min−1)
(kilolux)
(kilolux)
16
7.30
21.1
2.35
72
33.8
6.9
75
443
333
72
75
−3
0
9.30
46.6
1.18
100
82.4
10.9
98
570
446
89
91
−9
−7
13.30
57.4
1.01
122
95.0
10.1
101
587
450
91
94
−10
−7
15.30
34.1
1.51
90
55.3
8.0
85
530
407
84
86
−1
+1
20
7.30
20.3
2.44
112
30.9
9.7
61
355
255
58
59
−3
−2
9.30
45.7
1.19
125
79.5
13.8
92
535
407
83
85
−9
−7
11.30
62.6
0.95
107
105.2
12.8
104
618
475
96
98
−8
−6
13.30
56.1
1.02
97
95.5
10.6
102
618
475
96
98
−6
−4
15.30
33.4
1.54
83
57.2
9.1
87
545
412
86
87
−1
0
26
13.30
54.8
1.04
83
94.2
11.1
102
628
485
97
99
−5
−3
15.30
32.1
1.59
77
53.1
8.6
84
535
406
84
86
0
+2
27
7.30
19.0
2.60
77
31.4
7.6
73
406
299
66
69
−7
−4
9.30
44.5
1.21
80
79.3
9.8
99
597
460
93
96
−6
−3
11.30
60.3
0.98
79
103.3
8.8
109
643
500
100
102
−9
−7
13.30
54.6
1.05
78
91.6
8.7
102
633
490
98
100
−4
−2
15.30
31.9
1.60
65
53.0
7.4
86
556
426
87
90
+1
+4
28
9.30
44.3
1.22
82
78.0
8.8
99
597
455
93
94
−6
−5
11.30
60.1
0.98
85
103.8
11.1
107
639
490
99
100
−8
−7
13.30
54.4
1.05
82
92.0
9.5
101
623
485
97
99
−4
−2
15.30
31.7
1.63
71
53.5
8.3
86
545
412
86
87
0
+1
Mean
43.3
1.41
88
73.4
9.6
92.6
560
428
87.7
89.7
−4.9
−2.9
Table III
Comparison between Measured (E0) and Computed (E1 and E2) Values of Illumination at Pretoria (25° 45′ S, 1370 meters) During a Period of Relatively High Atmospheric Turbidity at the End of the Dry Season
September 1955
Solar height (deg)
m
β· 103
D
S (kilolux)
It − Ir8
It − Ir2
E1
E2
E1 − E0
E2 − E0
Day
TST
(mcal cm−2 min−1)
(kilolux)
(kilolux)
1
9.30
39.7
1.34
76
68.5
9.8
92
590
445
92
93
0
+1
11.30
55.1
1.04
78
89.0
10.3
96
642
490
99
99
+3
+3
13.30
48.9
1.13
65
79.9
9.0
94
642
495
99
100
+5
+6
7
7.30
17.1
2.88
92
25.3
9.1
55
350
240
57
57
+2
+2
9.30
41.1
1.30
119
67.0
12.9
82
520
392
81
82
−1
0
11.30
56.2
1.02
116
90.5
13.0
93
585
445
90
91
−3
−2
13.30
50.6
1.10
116
79.4
13.6
85
565
431
87
89
+2
+4
12
9.30
42.6
1.26
178
66.1
19.2
69
438
328
68
70
−1
+1
11.30
58.3
1.01
172
88.0
20.7
79
510
387
78
81
−1
+2
13.30
52.4
1.08
167
77.3
19.5
73
488
377
74
79
+1
+6
15.30
30.8
1.66
169
42.7
15.8
53
360
269
56
53
+3
0
20
7.30
19.4
2.55
110
27.5
9.5
54
355
240
57
56
+3
+2
9.30
44.5
1.21
166
68.5
15.6
76
462
353
72
75
−4
−1
11.30
61.1
0.97
165
91.6
16.5
86
540
402
83
83
−3
−3
13.30
54.8
1.04
161
80.8
16.4
79
510
392
79
81
0
+2
15.30
32.4
1.58
172
45.8
13.9
59
375
279
55
61
−4
+2
30
9.30
47.2
1.16
93
82.2
10.4
98
628
450
97
93
−1
−5
11.30
64.7
0.94
120
102.5
13.4
99
637
455
98
92
−1
−7
13.30
58.1
1.01
119
91.0
13.6
91
617
445
95
91
+4
0
15.30
34.3
1.51
130
53.7
12.8
73
494
343
77
74
+4
+1
Mean
45.5
1.34
129
70.9
14.2
79.3
540
383
79.7
80.0
+0.4
+0.7
Table IV
Comparison between Measured (E0) and Computed (E1 and E2) Values of Illumination at Pretoria (25° 45′ S, 1370 meters) During Periods of (a) Very High Atmospheric Turbidity (and Low Solar Height) and (b) Very Low Atmospheric Turbidity (and High Solar Height)
1955
Solar height (deg)
m
β· 103
D
S
It − Ir8
It − Ir2
E1
E2
E1 − E0
E2 − E0
Day
TST
(kilolux)
(mcal cm−2 min−1)
(kilolux)
(kilolux)
August 17
9.30
35.9
1.45
320
46.2
23.1
40
226
152
35
35
−5
−5
11.30
49.2
1.13
338
65.5
27.6
50
314
221
49
50
−1
0
12.30
49.2
1.13
338
65.2
27.1
51
324
230
50
52
−1
+1
13.30
44.5
1.21
360
57.1
26.0
45
278
196
43
45
−2
0
14.30
35.9
1.45
347
44.2
22.7
37
231
157
36
37
−1
0
31
9.30
39.2
1.35
271
53.5
22.0
50
340
245
53
55
+3
+5
11.30
53.5
1.06
270
76.1
25.7
63
386
284
58
62
−5
−1
12.30
53.5
1.06
270
76.5
25.4
63
407
304
63
66
0
+3
13.30
48.2
1.14
283
67.4
25.0
57
350
260
55
57
−2
0
14.30
39.2
1.35
287
53.3
23.1
48
288
218
45
49
−3
+1
(a)
Mean
44.8
1.23
308
60.5
24.8
50.4
314
227
48.7
50.8
−1.7
+0.4
November 6
11.30
76.4
0.88
105
116.0
8.5
109
700
490
108
(100)
−1
(−9)
12.30
76.4
0.88
101
116.2
8.9
109
689
485
106
(98)
−3
(−11)
December 2
11.30
80.9
0.86
121
118.6
10.3
110
679
480
104
(98)
−6
(−12)
12.30
80.9
0.86
109
118.1
9.6
110
694
500
107
102
−3
−8
13.30
09.0
0.91
117
109.0
9.5
107
663
475
102
(96)
−5
(−11)
11
11.30
81.7
0.86
106
119.0
9.0
111
693
500
106
102
−5
−9
(b)
Mean
77.5
0.87
110
116.1
9.3
109.3
586
488
105.5
99.3
−3.8
−10.0
Table V
Radiation Intensity of the Sun (mcal cm−2 min−1) in Relation to Air Mass and Turbidity for the Spectral Band Isolated by the Standard RG 8 Filter
a
0
1.0
1.25
1.50
1.75
2.0
3.0
4.0
5.0
6.0
0
948
771
742
716
698
662
569
499
436
387
25
726
688
652
619
588
479
396
333
282
50
682
638
596
559
522
404
321
256
206
75
642
592
546
505
466
342
260
196
152
100
604
549
500
455
415
290
208
148
111
125
557
510
460
413
370
246
168
114
81
150
535
475
421
371
330
200
136
90
60
175
503
445
386
337
295
180
110
68
45
The results are expressed in the International Pyrheliometric Scale, 1956, in accordance with the solar spectrum derived by Nicolet.10 From this table values of the direct solar illumination (E), in kilolux, as well as β can be obtained by application of Eqs. (18) and (21), viz., E = 149 (1 + 0.032m) · W when W is given in cal cm−2 min−1.
Tables (5)
Table I
The Dependence of Sunlight Illumination (Kilolux), on a Surface Perpendicular to the Rays, on Air Mass and Turbidity, for Mean Solar Distance
βm
0
1.00
1.25
1.50
1.75
2.0
3.0
4.0
6.0
0.000
142
119
115
112
109
106
93
84
69
0.050
105
99
93
87
83
66
54
37
0.100
93
85
78
72
66
47
35
20
0.150
83
73
66
59
53
34
23
11
0.200
73
63
55
47
41
24
15
6
h(°)
90
53
42
35
30
19
14
9
Table II
Comparison between Measured (E0) and Computed (E1 and E2) Values of Illumination at Pretoria (25° 45′ S, 1370 meters) During a Period of Relatively Low Atmospheric Turbidity at the End of the Wet Season
March 1955
Solar height (deg)
m
β· 103
D
S (kilolux)
It − Ir8
It − Ir2
E1
E2
E1 − E0
E2 − E0
Day
TST
(mcal cm−2 min−1)
(kilolux)
(kilolux)
16
7.30
21.1
2.35
72
33.8
6.9
75
443
333
72
75
−3
0
9.30
46.6
1.18
100
82.4
10.9
98
570
446
89
91
−9
−7
13.30
57.4
1.01
122
95.0
10.1
101
587
450
91
94
−10
−7
15.30
34.1
1.51
90
55.3
8.0
85
530
407
84
86
−1
+1
20
7.30
20.3
2.44
112
30.9
9.7
61
355
255
58
59
−3
−2
9.30
45.7
1.19
125
79.5
13.8
92
535
407
83
85
−9
−7
11.30
62.6
0.95
107
105.2
12.8
104
618
475
96
98
−8
−6
13.30
56.1
1.02
97
95.5
10.6
102
618
475
96
98
−6
−4
15.30
33.4
1.54
83
57.2
9.1
87
545
412
86
87
−1
0
26
13.30
54.8
1.04
83
94.2
11.1
102
628
485
97
99
−5
−3
15.30
32.1
1.59
77
53.1
8.6
84
535
406
84
86
0
+2
27
7.30
19.0
2.60
77
31.4
7.6
73
406
299
66
69
−7
−4
9.30
44.5
1.21
80
79.3
9.8
99
597
460
93
96
−6
−3
11.30
60.3
0.98
79
103.3
8.8
109
643
500
100
102
−9
−7
13.30
54.6
1.05
78
91.6
8.7
102
633
490
98
100
−4
−2
15.30
31.9
1.60
65
53.0
7.4
86
556
426
87
90
+1
+4
28
9.30
44.3
1.22
82
78.0
8.8
99
597
455
93
94
−6
−5
11.30
60.1
0.98
85
103.8
11.1
107
639
490
99
100
−8
−7
13.30
54.4
1.05
82
92.0
9.5
101
623
485
97
99
−4
−2
15.30
31.7
1.63
71
53.5
8.3
86
545
412
86
87
0
+1
Mean
43.3
1.41
88
73.4
9.6
92.6
560
428
87.7
89.7
−4.9
−2.9
Table III
Comparison between Measured (E0) and Computed (E1 and E2) Values of Illumination at Pretoria (25° 45′ S, 1370 meters) During a Period of Relatively High Atmospheric Turbidity at the End of the Dry Season
September 1955
Solar height (deg)
m
β· 103
D
S (kilolux)
It − Ir8
It − Ir2
E1
E2
E1 − E0
E2 − E0
Day
TST
(mcal cm−2 min−1)
(kilolux)
(kilolux)
1
9.30
39.7
1.34
76
68.5
9.8
92
590
445
92
93
0
+1
11.30
55.1
1.04
78
89.0
10.3
96
642
490
99
99
+3
+3
13.30
48.9
1.13
65
79.9
9.0
94
642
495
99
100
+5
+6
7
7.30
17.1
2.88
92
25.3
9.1
55
350
240
57
57
+2
+2
9.30
41.1
1.30
119
67.0
12.9
82
520
392
81
82
−1
0
11.30
56.2
1.02
116
90.5
13.0
93
585
445
90
91
−3
−2
13.30
50.6
1.10
116
79.4
13.6
85
565
431
87
89
+2
+4
12
9.30
42.6
1.26
178
66.1
19.2
69
438
328
68
70
−1
+1
11.30
58.3
1.01
172
88.0
20.7
79
510
387
78
81
−1
+2
13.30
52.4
1.08
167
77.3
19.5
73
488
377
74
79
+1
+6
15.30
30.8
1.66
169
42.7
15.8
53
360
269
56
53
+3
0
20
7.30
19.4
2.55
110
27.5
9.5
54
355
240
57
56
+3
+2
9.30
44.5
1.21
166
68.5
15.6
76
462
353
72
75
−4
−1
11.30
61.1
0.97
165
91.6
16.5
86
540
402
83
83
−3
−3
13.30
54.8
1.04
161
80.8
16.4
79
510
392
79
81
0
+2
15.30
32.4
1.58
172
45.8
13.9
59
375
279
55
61
−4
+2
30
9.30
47.2
1.16
93
82.2
10.4
98
628
450
97
93
−1
−5
11.30
64.7
0.94
120
102.5
13.4
99
637
455
98
92
−1
−7
13.30
58.1
1.01
119
91.0
13.6
91
617
445
95
91
+4
0
15.30
34.3
1.51
130
53.7
12.8
73
494
343
77
74
+4
+1
Mean
45.5
1.34
129
70.9
14.2
79.3
540
383
79.7
80.0
+0.4
+0.7
Table IV
Comparison between Measured (E0) and Computed (E1 and E2) Values of Illumination at Pretoria (25° 45′ S, 1370 meters) During Periods of (a) Very High Atmospheric Turbidity (and Low Solar Height) and (b) Very Low Atmospheric Turbidity (and High Solar Height)
1955
Solar height (deg)
m
β· 103
D
S
It − Ir8
It − Ir2
E1
E2
E1 − E0
E2 − E0
Day
TST
(kilolux)
(mcal cm−2 min−1)
(kilolux)
(kilolux)
August 17
9.30
35.9
1.45
320
46.2
23.1
40
226
152
35
35
−5
−5
11.30
49.2
1.13
338
65.5
27.6
50
314
221
49
50
−1
0
12.30
49.2
1.13
338
65.2
27.1
51
324
230
50
52
−1
+1
13.30
44.5
1.21
360
57.1
26.0
45
278
196
43
45
−2
0
14.30
35.9
1.45
347
44.2
22.7
37
231
157
36
37
−1
0
31
9.30
39.2
1.35
271
53.5
22.0
50
340
245
53
55
+3
+5
11.30
53.5
1.06
270
76.1
25.7
63
386
284
58
62
−5
−1
12.30
53.5
1.06
270
76.5
25.4
63
407
304
63
66
0
+3
13.30
48.2
1.14
283
67.4
25.0
57
350
260
55
57
−2
0
14.30
39.2
1.35
287
53.3
23.1
48
288
218
45
49
−3
+1
(a)
Mean
44.8
1.23
308
60.5
24.8
50.4
314
227
48.7
50.8
−1.7
+0.4
November 6
11.30
76.4
0.88
105
116.0
8.5
109
700
490
108
(100)
−1
(−9)
12.30
76.4
0.88
101
116.2
8.9
109
689
485
106
(98)
−3
(−11)
December 2
11.30
80.9
0.86
121
118.6
10.3
110
679
480
104
(98)
−6
(−12)
12.30
80.9
0.86
109
118.1
9.6
110
694
500
107
102
−3
−8
13.30
09.0
0.91
117
109.0
9.5
107
663
475
102
(96)
−5
(−11)
11
11.30
81.7
0.86
106
119.0
9.0
111
693
500
106
102
−5
−9
(b)
Mean
77.5
0.87
110
116.1
9.3
109.3
586
488
105.5
99.3
−3.8
−10.0
Table V
Radiation Intensity of the Sun (mcal cm−2 min−1) in Relation to Air Mass and Turbidity for the Spectral Band Isolated by the Standard RG 8 Filter
a
0
1.0
1.25
1.50
1.75
2.0
3.0
4.0
5.0
6.0
0
948
771
742
716
698
662
569
499
436
387
25
726
688
652
619
588
479
396
333
282
50
682
638
596
559
522
404
321
256
206
75
642
592
546
505
466
342
260
196
152
100
604
549
500
455
415
290
208
148
111
125
557
510
460
413
370
246
168
114
81
150
535
475
421
371
330
200
136
90
60
175
503
445
386
337
295
180
110
68
45
The results are expressed in the International Pyrheliometric Scale, 1956, in accordance with the solar spectrum derived by Nicolet.10 From this table values of the direct solar illumination (E), in kilolux, as well as β can be obtained by application of Eqs. (18) and (21), viz., E = 149 (1 + 0.032m) · W when W is given in cal cm−2 min−1.