Masayuki Tanaka, Teruyuki Nakajima, and Masataka Shiobara, "Calibration of a sunphotometer by simultaneous measurements of direct-solar and circumsolar radiations," Appl. Opt. 25, 1170-1176 (1986)
A new method is proposed for the calibration of the sunphotometer. Well-known difficulties of the usual Langley-plot method when applied to unsteady turbidity conditions can be avoided by monitoring the circumsolar radiation. To realize this idea, an alternate of the Langley-plot method is developed, in which the logarithm of the sunphotometer reading is plotted against the ratio of intensity of singly scattered circumsolar radiation to that of direct solar radiation instead of the optical air mass in the usual Langley-plot method. Results of numerical simulations and field tests with a newly developed instrument show that the rms error of the calibration constant could be reduced to 1/5–1/10 of the usual method for wavelengths larger than 500 nm.
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Comparison of Simulated Calibration Between the Present and Langley-plot Methods for Turbidity Conditions Varying Parabolically with Time*
wavelength
369nm
500nm
862nm
τa0
0.072
0.144
0.288
0.05
0.1
0.2
0.026
0.052
0.104
α = 0.0
Present
0.9993
0.9994
0.9994
0.9995
1.0002
1.0004
1.0001
1.0000
0.9997
Langley
0.9995
0.9995
0.9993
0.9998
0.9998
0.9997
1.0000
0.9999
0.9999
α = 0.011
Present
0.9995
0.9994
0.9970
0.9998
1.0001
0.9988
0.9999
0.9998
0.9994
Langley
1.0375
1.0768
1.1600
1.0260
1.0529
1.1087
1.0135
1.0272
1.0552
α =−0.011
Present
1.0009
0.9998
1.0015
0.9997
0.9996
0.9997
1.0001
1,0000
0.9999
Langley
0.9630
0.9277
0.8609
0.9743
0.9493
0.9014
0.9866
0.9734
0.9475
τa0 is the optical thickness of aerosols at noon and a is Shaw's parabolic drift parameter. True values of the calibration constants are assumed to be unity.
Table II
Comparison of Simulated Calibration Between the Present and Langley-plot Methods for Size Distributions Differing from Assumed One*
wavelength
369nm
500nm
862nm
τa, 500
0.05
0.1
0.05
0.1
0.05
0.1
p=4.0
Present
0.9973
0.9938
0.9987
0.9971
0.9997
0.9990
Langley
0.9996
0.9996
0.9998
0.9998
1.0000
1.0000
p=4.5
Present
1.0032
1.0075
1.0016
1.0031
1.0004
1.0009
Langley
0.9996
0.9995
0.9998
0.9998
1.0000
1.0000
p=4.0→4.5
Present
0.9984
0.9956
0.9984
0.9947
0.9984
0.9965
Langley
0.9837
0.9681
0.9999
0.9998
1.0114
1.0229
p=4.5→4.0
Present
1.0066
1.0152
1.0062
1.0134
1.0051
1.0109
Langley
1.0239
1.0486
0.9998
0.9998
0.9860
0.9722
τa,500 is the optical thickness of aerosols at λ=500nm and p is the exponent of the size distribution function given in Eq.(10). The value of p is assumed to be 4.2 in the simulation.
Table III
Results of Simulated Calibration for the Complex Index of Refraction Differing from the Assumed Value of 1.5–0.01/
wavelength
369nm
500nm
862nm
τa
0.072
0.144
0.288
0.05
0.1
0.2
0.026
0.052
0.104
0.9980
0.9905
0.9703
0.9983
0.9973
0.9911
0.9996
0.9989
0.9969
1.50−0.03i
1.0036
1.0094
1.0404
1.0019
1.0037
1.0115
1.0003
1.0013
1.0034
1.45−0.01i
0.9983
0.9977
0.9944
1.0000
0.9979
0.9920
0.9994
0.9990
0.9970
1.55−0.01i
1.0013
1.0016
1.0013
1.0008
1.0018
1.0052
1.0002
1.0006
1.0017
Table IV
Specifications of the Aureolemeter
Interference filters: Koshin Kogaku Co., BWB series with wavelengths (bandwidths) of 369(7), 500(4), 675(6), 776(7), 862(8) (nm) blocking in both wings: < 0.01% in transmittance for all filters
Precision of the azimuthal-angle controller: 0.25°
Electrical dynamic range: 105
Driving: Equatorial mounted on a horizontal turntable
Table V
Calibration of the Aureolemeter by the Present and Langley-plot Methods*
Wavelength
369nm
500nm
862nm
Method
F
P
L
F
P
L
F
P
L
15 Oct. 1981
F0
13.43
13.42
14.33
3.035
3.040
3.197
5.341
5.345
5.488
σ
1.24
1.19
1.32
0.56
0.57
1.38
0.33
0.33
0.84
10 Nov. 1981
F0
14.52
14.52
13.95
3.043
3.043
3.008
5.346
5.346
5.357
σ
3.87
3.87
2.36
1.41
1.41
1.04
0.30
0.30
0.41
16 Feb. 1982
F0
13.93
13.89
13.83
3.027
3.009
3.264
5.342
5.333
5.540
σ
4.63
4.40
4.67
0.50
0.48
1.33
0.35
0.34
0.65
18 Feb. 1982
F0
14.56
14.45
12.97
3.008
2.996
2.896
5.280
5.274
5.207
σ
2.27
2.25
1.76
0.86
0.84
1.14
0.25
0.25
0.30
Mean
F0
14.11
14.07
13.77
3.028
3.022
3.091
5.327
5.325
5.398
σ
3.30
3.18
3.61
0.43
0.66
4.75
0.51
0.56
2.76
Method F: Present method with fixed p value of 4.2.
Method P: Present method with re-analyzed p value.
Method L: Langley-plot method.
F0 is the calibration constant and σ is its standard deviation in percent.
Tables (5)
Table I
Comparison of Simulated Calibration Between the Present and Langley-plot Methods for Turbidity Conditions Varying Parabolically with Time*
wavelength
369nm
500nm
862nm
τa0
0.072
0.144
0.288
0.05
0.1
0.2
0.026
0.052
0.104
α = 0.0
Present
0.9993
0.9994
0.9994
0.9995
1.0002
1.0004
1.0001
1.0000
0.9997
Langley
0.9995
0.9995
0.9993
0.9998
0.9998
0.9997
1.0000
0.9999
0.9999
α = 0.011
Present
0.9995
0.9994
0.9970
0.9998
1.0001
0.9988
0.9999
0.9998
0.9994
Langley
1.0375
1.0768
1.1600
1.0260
1.0529
1.1087
1.0135
1.0272
1.0552
α =−0.011
Present
1.0009
0.9998
1.0015
0.9997
0.9996
0.9997
1.0001
1,0000
0.9999
Langley
0.9630
0.9277
0.8609
0.9743
0.9493
0.9014
0.9866
0.9734
0.9475
τa0 is the optical thickness of aerosols at noon and a is Shaw's parabolic drift parameter. True values of the calibration constants are assumed to be unity.
Table II
Comparison of Simulated Calibration Between the Present and Langley-plot Methods for Size Distributions Differing from Assumed One*
wavelength
369nm
500nm
862nm
τa, 500
0.05
0.1
0.05
0.1
0.05
0.1
p=4.0
Present
0.9973
0.9938
0.9987
0.9971
0.9997
0.9990
Langley
0.9996
0.9996
0.9998
0.9998
1.0000
1.0000
p=4.5
Present
1.0032
1.0075
1.0016
1.0031
1.0004
1.0009
Langley
0.9996
0.9995
0.9998
0.9998
1.0000
1.0000
p=4.0→4.5
Present
0.9984
0.9956
0.9984
0.9947
0.9984
0.9965
Langley
0.9837
0.9681
0.9999
0.9998
1.0114
1.0229
p=4.5→4.0
Present
1.0066
1.0152
1.0062
1.0134
1.0051
1.0109
Langley
1.0239
1.0486
0.9998
0.9998
0.9860
0.9722
τa,500 is the optical thickness of aerosols at λ=500nm and p is the exponent of the size distribution function given in Eq.(10). The value of p is assumed to be 4.2 in the simulation.
Table III
Results of Simulated Calibration for the Complex Index of Refraction Differing from the Assumed Value of 1.5–0.01/
wavelength
369nm
500nm
862nm
τa
0.072
0.144
0.288
0.05
0.1
0.2
0.026
0.052
0.104
0.9980
0.9905
0.9703
0.9983
0.9973
0.9911
0.9996
0.9989
0.9969
1.50−0.03i
1.0036
1.0094
1.0404
1.0019
1.0037
1.0115
1.0003
1.0013
1.0034
1.45−0.01i
0.9983
0.9977
0.9944
1.0000
0.9979
0.9920
0.9994
0.9990
0.9970
1.55−0.01i
1.0013
1.0016
1.0013
1.0008
1.0018
1.0052
1.0002
1.0006
1.0017
Table IV
Specifications of the Aureolemeter
Interference filters: Koshin Kogaku Co., BWB series with wavelengths (bandwidths) of 369(7), 500(4), 675(6), 776(7), 862(8) (nm) blocking in both wings: < 0.01% in transmittance for all filters
Precision of the azimuthal-angle controller: 0.25°
Electrical dynamic range: 105
Driving: Equatorial mounted on a horizontal turntable
Table V
Calibration of the Aureolemeter by the Present and Langley-plot Methods*
Wavelength
369nm
500nm
862nm
Method
F
P
L
F
P
L
F
P
L
15 Oct. 1981
F0
13.43
13.42
14.33
3.035
3.040
3.197
5.341
5.345
5.488
σ
1.24
1.19
1.32
0.56
0.57
1.38
0.33
0.33
0.84
10 Nov. 1981
F0
14.52
14.52
13.95
3.043
3.043
3.008
5.346
5.346
5.357
σ
3.87
3.87
2.36
1.41
1.41
1.04
0.30
0.30
0.41
16 Feb. 1982
F0
13.93
13.89
13.83
3.027
3.009
3.264
5.342
5.333
5.540
σ
4.63
4.40
4.67
0.50
0.48
1.33
0.35
0.34
0.65
18 Feb. 1982
F0
14.56
14.45
12.97
3.008
2.996
2.896
5.280
5.274
5.207
σ
2.27
2.25
1.76
0.86
0.84
1.14
0.25
0.25
0.30
Mean
F0
14.11
14.07
13.77
3.028
3.022
3.091
5.327
5.325
5.398
σ
3.30
3.18
3.61
0.43
0.66
4.75
0.51
0.56
2.76
Method F: Present method with fixed p value of 4.2.
Method P: Present method with re-analyzed p value.
Method L: Langley-plot method.
F0 is the calibration constant and σ is its standard deviation in percent.
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