The author is with the Atmosphere Watch Section Observations and Engineering Branch, Bureau of Meteorology, GPO Box 1289K, Melbourne Victoria 3001, Australia
A general method for calibrating Sun photometers that relaxes the constraints on atmospheric conditions is described. Instead of requiring constant extinction conditions the method requires only that the relative aerosol size distribution remains constant during observations over a range of air masses during a morning or afternoon. Provided that the relative aerosol extinction component [ma(t)δ (t, λ0)] can be obtained at wavelength λ0, the calibration at wavelength channel λ can be calculated with simple least-squares techniques. A variant of the method in which a Sun photometer is used to provide [ma(t)δ(t, λ0)] is detailed and is verified with both model atmospheres and Sun-photometer data for 1988-1991 from Cape Grim, Tasmania (41° S). The method produces calibration data having sample variances more than 5 times smaller than Langley method calibration results.
Beat Schmid, Paul R. Spyak, Stuart F. Biggar, Christoph Wehrli, Jörg Sekler, Thomas Ingold, Christian Mätzler, and Niklaus Kämpfer Appl. Opt. 37(18) 3923-3941 (1998)
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Airmass range 2.5–6.0, pressure 1013.25, 868-nm calibration 100.0, all other true calibrations 100.0.
Mean deviation of 18 days of data from the true intercept.
Sample standard deviation.
Table 2
Langley Method Results Expressed as a Deviation from the Correct Calibrationa
Airmass range 2.5–6.0, pressure 1013.25, all true calibrations 100.0.
Mean deviation of 18 days of data from the true intercept.
Sample standard deviation.
Table 3
Comparison of Calibration Biases (ΔV0i) and Estimates of the Standard Deviation (σ) from the 154 Samples of Langley and General Method Results for the Period January 1989-June 1991 with the CGBAPS Sun Photometer
Wavelength
Langley
General
ΔV0i (%)
ΔV0i (%)
ΔV0i (%)
σ ΔV0i (%)
A. All data (154 points)
368
−0.1
13.2
−0.9
7.8
500
−0.8
10.2
−0.9
4.3
778
−0.9
9.2
−0.6
2.7
B. After proof-fit removal (92 points)
368
1.7
14.1
−0.5
5.6
500
0.6
10.1
−0.7
2.9
778
0.6
9.6
−0.3
2.8
C. Intersection of filtered sets (54 points)
368
1.4
7.5
0.0
4.0
500
0.7
5.4
−0.4
1.9
778
0.9
4.7
−0.1
0.8
Table 4
Summary Statistics for the 92 Sample Series of α01 Derived for Each Wavelength Paira
Wavelength Pair (nm)
Mean
Maximum
Minimum
σ
868–368
0.42
1.48
−0.12
0.38
868–500
0.34
1.53
−0.26
0.40
868–778
0.51
1.70
−0.20
0.42
σ01 values are determined from ψ01 results from the general method analysis of CGBAPS data over the period January 1989–June 1992.
Table 5
Mean Aerosol Optical Depth Derived from a Combination of the General and the Ratio–Langley Results for the January 1989–June 1991 Period at CGBAPS
Wavelength (nm)
368
500
778
868
Aerosol optical depth
0.069
0.064
0.050
0.48
Table 6
Extinction Model Parameters for the 29 Cases Used in the Testing of the General and the Langley Methods
Model
β(t)
α(t)
00
0.050
0.5
01
0.075 + 0.025 sin(πt)
0.5
02
0.095 + 0.045 sin(πt)
0.5
03
0.040 − 0.010 sin(πt)
0.5
04
0.060 + 0.010 sin(πt)
0.5
05
0.095 − 0.045 sin(πt)
0.5
06
0.075 − 0.025 sin(πt)
0.5
07
0.075 − 0.025 sin(πt)
1.0
08
0.095 − 0.045 sin(πt)
1.0
09
0.050 − 0.010 sir(πt)
1.0
10
0.050 + 0.010 sin(πt)
1.0
11
0.095 + 0.045 sin(πt)
1.0
12
0.075 + 0.025 sin(πt)
1.0
13
0.075 + 0.025 sin(πt)
0.0
14
0.095 + 0.045 sin(πt)
0.0
15
0.050 + 0.010 sin(πt)
0.0
16
0.050 − 0.010 sin(πt)
0.0
17
0.075 − 0.025 sin(πt)
0.0
18
0.095 − 0.045 sin(πt)
0.0
20
0.050
0.45 + 0.1 sin(πt)
21
0.050
0.55 − 0.1 sm(πt)
22
0.050
1.05 − 0.1 sin(πt)
23
0.050
0.95 + 0.1 sin(πt)
24
0.050
−0.05 + 0.1 sin(πt)
25
0.050
+0.05 − 0.1 sin(πt)
26
0.050 + 0.010 sin(πt)
0.5 exp(−0.5 t)
27
0.050 − 0.010 sin(πt)
0.5 exp(−0.5 t)
28
0.050 + 0.010 sin(πt)
0.5 exp(+0.5 t)
29
0.050 − 0.010 sin(πt)
0.5 exp(+0.5 t)
Tables (6)
Table 1
General Method Results Expressed as Deviation from the Correct Calibrationa
Airmass range 2.5–6.0, pressure 1013.25, 868-nm calibration 100.0, all other true calibrations 100.0.
Mean deviation of 18 days of data from the true intercept.
Sample standard deviation.
Table 2
Langley Method Results Expressed as a Deviation from the Correct Calibrationa
Airmass range 2.5–6.0, pressure 1013.25, all true calibrations 100.0.
Mean deviation of 18 days of data from the true intercept.
Sample standard deviation.
Table 3
Comparison of Calibration Biases (ΔV0i) and Estimates of the Standard Deviation (σ) from the 154 Samples of Langley and General Method Results for the Period January 1989-June 1991 with the CGBAPS Sun Photometer
Wavelength
Langley
General
ΔV0i (%)
ΔV0i (%)
ΔV0i (%)
σ ΔV0i (%)
A. All data (154 points)
368
−0.1
13.2
−0.9
7.8
500
−0.8
10.2
−0.9
4.3
778
−0.9
9.2
−0.6
2.7
B. After proof-fit removal (92 points)
368
1.7
14.1
−0.5
5.6
500
0.6
10.1
−0.7
2.9
778
0.6
9.6
−0.3
2.8
C. Intersection of filtered sets (54 points)
368
1.4
7.5
0.0
4.0
500
0.7
5.4
−0.4
1.9
778
0.9
4.7
−0.1
0.8
Table 4
Summary Statistics for the 92 Sample Series of α01 Derived for Each Wavelength Paira
Wavelength Pair (nm)
Mean
Maximum
Minimum
σ
868–368
0.42
1.48
−0.12
0.38
868–500
0.34
1.53
−0.26
0.40
868–778
0.51
1.70
−0.20
0.42
σ01 values are determined from ψ01 results from the general method analysis of CGBAPS data over the period January 1989–June 1992.
Table 5
Mean Aerosol Optical Depth Derived from a Combination of the General and the Ratio–Langley Results for the January 1989–June 1991 Period at CGBAPS
Wavelength (nm)
368
500
778
868
Aerosol optical depth
0.069
0.064
0.050
0.48
Table 6
Extinction Model Parameters for the 29 Cases Used in the Testing of the General and the Langley Methods
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