F. Miskolczi and R. Guzzi, "Effect of nonuniform spectral dome transmittance on the accuracy of infrared radiation measurements using shielded pyrradiometers and pyrgeometers," Appl. Opt. 32, 3257-3265 (1993)
We discuss the problem arising from the nonuniform distribution of spectral transmittance of the instrument’s shielding dome. Recently, by using high-resolution atmospheric radiation software, it became possible to evaluate both the real downward IR spectral flux density and the transmitted spectral flux density of the instrument’s dome. By using a simplified model we obtained a theoretical formula that describes the effect of dome transmittance on the instrument’s response. By the formula, the effective dome transmittance (average dome transmittance weighted by the spectral flux density) is directly proportional to the calibration constant of the instrument. In order to obtain a quantitative relationship we computed the effective dome transmittance for several domes and model atmospheres. According to our results the maximum difference in effective dome transmittance of individual domes is 20% for Eppley-type silicon domes and 10% for polyethylene domes. These relatively large differences must be corrected when the domes are replaced. The effective dome transmittance shows strong correlation with precipitable water and the total downward IR flux density. The combined effect on the calibration factor is a maximum 2% for the Eppley domes and 5% for the polyethylene domes. By using the linear regression method these types of error can be minimized.
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Precipitable Water (u in g/cm2), Surface Air Temperature (TA in K), and the Downward Flux Density (F in W/m2) of the Different Atmospheresa
Profile
Remarks
u
TA
F
ΔF
P-S1
Denver, 31 October 1988, 14:00 GMT
0.637
277.8
241.3
−93.82
P-S2
Denver, 31 October 1988, 20:00 GMT
0.403
294.4
269.8
−153.4
P-S3
Denver, 1 November 1988, 11:00 GMT
0.377
278.0
233.2
−102.9
P-TR
Tropical
4.170
299.7
396.5
−58.07
P-MS
Mid-latitude summer
2.960
294.2
351.6
−70.40
P-MW
Mid-latitude winter
0.860
272.2
223.2
−85.60
P-AS
Subarctic summer
2.100
287.2
301.9
−82.67
P-AW
Subarctic winter
0.420
257.2
172.3
−71.70
P-US
Standard, USST-1976
1.430
288.2
287.7
−100.8
In the last column ΔF = F − σTA4 and σ = 5.67032 × 10−8 W/(m2 K4). The product of ΔF with the instrument response is equal to the measured signal. GMT, Greenwich mean time; USST, U.S. Standard Atmosphere.
Table 2
Average Measured Dome Transmittance
, Nonuniformity Factors κD, and the Dome Transmittance τD at Two Different Temperatures (250 and 290 K)a
Dome
Remarks
κD
τ250D
τ290D
ΔτD
D-1
Eppley (silicon)
29.82
9.19
33.19
33.53
.34
D-2
Eppley (silicon)
35.16
3.48
34.86
35.09
.23
D-3
Eppley (silicon)
26.05
9.41
30.14
30.37
.23
D-4
Eppley (silicon)
27.85
14.1
36.33
36.52
.19
D-5
Eppley (silicon)
35.65
2.54
34.48
34.53
.05
D-6
Eppley (silicon)
35.11
4.19
35.62
35.74
.12
D-7
Eppley (silicon)
34.43
3.51
34.06
34.21
.15
D-8
Eppley (silicon)
26.29
3.58
26.73
26.78
.05
D-A
Polyethylene (new)
74.79
17.7
84.81
82.91
−1.9
D-B
Polyethylene (new)
73.15
17.6
82.80
81.03
−1.8
D-C
Polyethylene (old)
67.72
17.0
77.56
75.08
−1.7
In the last column ΔτD = τ290D − τ250D. The values are given in percent and the wave-number interval is from 110.0 to 3390.0 cm−1.
Table 3
Computed Effective Transmittance of the Eppley Domes in Percent
Profile
D-1
D-2
D-3
D-4
D-5
D-6
D-7
D-8
P-S1
33.30
34.84
30.28
36.27
34.61
35.95
34.90
27.27
P-S2
33.48
35.02
30.44
36.40
34.73
36.13
35.12
27.46
P-S3
33.31
34.89
30.29
36.32
34.66
36.02
34.97
27.35
P-TR
33.54
35.06
30.41
36.41
34.55
35.82
34.56
26.99
P-MS
33.46
34.98
30.35
36.34
34.54
35.82
34.63
27.04
P-MW
33.23
34.79
30.22
36.25
34.59
35.90
34.78
27.21
P-AS
33.36
34.89
30.29
36.27
34.53
35.83
34.70
27.10
P-AW
33.15
34.79
30.19
36.32
34.68
35.98
34.77
27.27
P-US
33.37
34.88
30.32
36.27
34.56
35.89
34.83
27.20
Table 4
Computed Effective Transmittance of the Polyethylene Domes (in percent)
Profile
D-A
D-B
D-C
P-S1
83.85
81.72
77.71
P-S2
83.27
81.14
77.14
P-S3
83.58
81.43
77.55
P-TR
82.62
80.70
75.45
P-MS
82.91
80.95
76.01
P-MW
84.36
82.22
78.19
P-AS
83.37
81.35
76.77
P-AW
85.15
82.94
79.20
P-US
83.43
81.37
77.03
Table 5
Average Effective Dome Transmittance
, Standard Deviations σe, Maximum Difference ΔτeD, and the Regression Coefficients Related to the Water Amount and the Total Downward IR Flux Density (ru and rF, respectively)
Dome
σe
ΔτeD
ru
rF
D-1
33.36
0.1256
0.3925
0.6860
0.9013
D-2
34.90
0.0968
0.2687
0.6303
0.8240
D-3
30.31
0.0797
0.2441
0.4797
0.7506
D-4
36.32
0.0596
0.1663
0.3885
0.4807
D-5
34.60
0.0693
0.1956
−0.7489
−0.6326
D-6
35.93
0.1038
0.3107
−0.7870
−0.5862
D-7
34.81
0.1734
0.5598
−0.8253
−0.5539
D-8
27.21
0.1472
0.4604
−0.9020
−0.7102
D-A
83.62
0.7644
2.5311
−0.6990
−0.9171
D-B
81.54
0.6844
2.2400
−0.6475
−0.8873
D-C
77.23
1.1229
3.7556
−0.8487
−0.9845
Table 6
Regression Coefficients A0, A1, and A2 and the Correlation: Coefficients ruF Related to Eq. (18)
Dome
A0
A1
A2
ruF
D-1
32.60
−0.08733
0.003202
0.9729
D-2
34.38
−0.05789
0.002206
0.8849
D-3
29.78
−0.08416
0.002388
0.9192
D-4
36.15
−0.01560
0.000689
0.5006
D-5
34.59
−0.05428
0.000329
0.7516
D-6
35.75
−0.12240
0.001299
0.8553
D-7
34.27
−0.26450
0.000364
0.9773
D-8
27.01
−0.18100
0.001712
0.9539
D-A
88.27
0.53220
−0.01979
0.9882
D-B
85.90
0.55820
−0.01888
0.9852
D-C
82.72
0.30790
−0.02162
0.9952
Tables (6)
Table 1
Precipitable Water (u in g/cm2), Surface Air Temperature (TA in K), and the Downward Flux Density (F in W/m2) of the Different Atmospheresa
Profile
Remarks
u
TA
F
ΔF
P-S1
Denver, 31 October 1988, 14:00 GMT
0.637
277.8
241.3
−93.82
P-S2
Denver, 31 October 1988, 20:00 GMT
0.403
294.4
269.8
−153.4
P-S3
Denver, 1 November 1988, 11:00 GMT
0.377
278.0
233.2
−102.9
P-TR
Tropical
4.170
299.7
396.5
−58.07
P-MS
Mid-latitude summer
2.960
294.2
351.6
−70.40
P-MW
Mid-latitude winter
0.860
272.2
223.2
−85.60
P-AS
Subarctic summer
2.100
287.2
301.9
−82.67
P-AW
Subarctic winter
0.420
257.2
172.3
−71.70
P-US
Standard, USST-1976
1.430
288.2
287.7
−100.8
In the last column ΔF = F − σTA4 and σ = 5.67032 × 10−8 W/(m2 K4). The product of ΔF with the instrument response is equal to the measured signal. GMT, Greenwich mean time; USST, U.S. Standard Atmosphere.
Table 2
Average Measured Dome Transmittance
, Nonuniformity Factors κD, and the Dome Transmittance τD at Two Different Temperatures (250 and 290 K)a
Dome
Remarks
κD
τ250D
τ290D
ΔτD
D-1
Eppley (silicon)
29.82
9.19
33.19
33.53
.34
D-2
Eppley (silicon)
35.16
3.48
34.86
35.09
.23
D-3
Eppley (silicon)
26.05
9.41
30.14
30.37
.23
D-4
Eppley (silicon)
27.85
14.1
36.33
36.52
.19
D-5
Eppley (silicon)
35.65
2.54
34.48
34.53
.05
D-6
Eppley (silicon)
35.11
4.19
35.62
35.74
.12
D-7
Eppley (silicon)
34.43
3.51
34.06
34.21
.15
D-8
Eppley (silicon)
26.29
3.58
26.73
26.78
.05
D-A
Polyethylene (new)
74.79
17.7
84.81
82.91
−1.9
D-B
Polyethylene (new)
73.15
17.6
82.80
81.03
−1.8
D-C
Polyethylene (old)
67.72
17.0
77.56
75.08
−1.7
In the last column ΔτD = τ290D − τ250D. The values are given in percent and the wave-number interval is from 110.0 to 3390.0 cm−1.
Table 3
Computed Effective Transmittance of the Eppley Domes in Percent
Profile
D-1
D-2
D-3
D-4
D-5
D-6
D-7
D-8
P-S1
33.30
34.84
30.28
36.27
34.61
35.95
34.90
27.27
P-S2
33.48
35.02
30.44
36.40
34.73
36.13
35.12
27.46
P-S3
33.31
34.89
30.29
36.32
34.66
36.02
34.97
27.35
P-TR
33.54
35.06
30.41
36.41
34.55
35.82
34.56
26.99
P-MS
33.46
34.98
30.35
36.34
34.54
35.82
34.63
27.04
P-MW
33.23
34.79
30.22
36.25
34.59
35.90
34.78
27.21
P-AS
33.36
34.89
30.29
36.27
34.53
35.83
34.70
27.10
P-AW
33.15
34.79
30.19
36.32
34.68
35.98
34.77
27.27
P-US
33.37
34.88
30.32
36.27
34.56
35.89
34.83
27.20
Table 4
Computed Effective Transmittance of the Polyethylene Domes (in percent)
Profile
D-A
D-B
D-C
P-S1
83.85
81.72
77.71
P-S2
83.27
81.14
77.14
P-S3
83.58
81.43
77.55
P-TR
82.62
80.70
75.45
P-MS
82.91
80.95
76.01
P-MW
84.36
82.22
78.19
P-AS
83.37
81.35
76.77
P-AW
85.15
82.94
79.20
P-US
83.43
81.37
77.03
Table 5
Average Effective Dome Transmittance
, Standard Deviations σe, Maximum Difference ΔτeD, and the Regression Coefficients Related to the Water Amount and the Total Downward IR Flux Density (ru and rF, respectively)
Dome
σe
ΔτeD
ru
rF
D-1
33.36
0.1256
0.3925
0.6860
0.9013
D-2
34.90
0.0968
0.2687
0.6303
0.8240
D-3
30.31
0.0797
0.2441
0.4797
0.7506
D-4
36.32
0.0596
0.1663
0.3885
0.4807
D-5
34.60
0.0693
0.1956
−0.7489
−0.6326
D-6
35.93
0.1038
0.3107
−0.7870
−0.5862
D-7
34.81
0.1734
0.5598
−0.8253
−0.5539
D-8
27.21
0.1472
0.4604
−0.9020
−0.7102
D-A
83.62
0.7644
2.5311
−0.6990
−0.9171
D-B
81.54
0.6844
2.2400
−0.6475
−0.8873
D-C
77.23
1.1229
3.7556
−0.8487
−0.9845
Table 6
Regression Coefficients A0, A1, and A2 and the Correlation: Coefficients ruF Related to Eq. (18)
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