Wesley A. Traub and Mark T. Stier, "Theoretical atmospheric transmission in the mid- and far-infrared at four altitudes," Appl. Opt. 15, 364-377 (1976)
The ir transmission of the terrestrial atmosphere is calculated at four altitudes of interest: Mauna Kea at 4.2 km (2–1000 μm), aircraft at 14 km (5–1000 μm), and balloon at 28 km and 41 km (10–1000 μm). We show both high resolution spectra (0.05 cm−1) and broadband averages. The results are intended to serve both as a detailed guide to the interference that is expected from the atmosphere for astronomical spectroscopy and also as an indicator of the relative change in absorption and emission that can be expected at various observing altitudes. One salient result for the spectral region around 100 μm is that the absorption (and emissivity) of the atmosphere drops by a factor of 10 for each increase in altitude of 15 km throughout the aircraft and balloon range; thus balloon-borne astronomical photometry and spectroscopy should both enjoy a considerable advantage over aircraft observations in the 30–300-μm region.
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Molecular Abundances, Effective Pressures, and Temperatures Used in the Curtis-Godson Approximationa
4.2 km (Mauna Kea)
14 km (Aircraft)
28 km (Balloon)
41 km (Balloon)
O2
209460.0 ppmv
209460.0
209460.0
209460.0
CO2
325.0 ppmv
325.0
325.0
325.0
CH4
1.5 ppmv
1.1
0.8
0.4
N2O
0.25 ppmv
0.20
0.20
0.20
CO
0.07 ppmv
0.06
0.06
0.06
H2O
1200 μm
2.5 ppmv
2.5 ppmv
2.5 ppmv
O3
7.28 E18 cm−2
6.37 E18
1.85 E18
1.70 E17
p
600.0 mbar
141.6
16.2
2.52
p(eff)
300.0 mbar
70.8
8.10
1.26
p(H2O)
506.0 mbar
70.8
8.10
1.26
p(O3)
36.4 mbar
30.2
7.09
1.84
T(eff)
228.0 K
217.0
230.0
268.0
T(H2O)
252.0 K
217.0
230.0
268.0
T(O3)
219.0 K
221.0
233.0
260.0
The H2O abundances in the last three columns correspond to 2.25, 0.26, and 0.040 precipitable μm, respectively; the H2O at 4.2 km is assumed to have a scale height of 1.85 km. The abundances listed are for unit air mass; an additional factor of 2 is included in the actual calculations corresponding to a zenith angle of 60°. The base pressure at each altitude is given by p, and the effective pressure for collisional line broadening is indicated by p(eff), p(H2O), and p(O3) for the first five species, H2O, and O3, respectively; the temperatures at the corresponding pressure levels are also listed.
Table II
Atmospheric Emissivity (∊) and Radiated Flux (B) at Four Altitudes and for the Wavelength Range from 1000 μm to 10 μm, with Extensions down to 2 μm at Lower Altitudesa
ATMOSPHERIC EMISSIVITY AND FLUX (WATT/M2/ST)
UPPER SIGMA (CM-1)
LOWER SIGMA (CM-1)
AVERAGE WAVELENGTH (MICRON)
4.2 KM 228 KELVIN
28.0 KM 217 KELVIN
28.0 KM 230 KELVIN
41.0 KM 268 KELVIN
EMISS.
FLUX
EMISS.
FLUX
EMISS.
FLUX
EMISS.
FLUX
10
15
800.0
.7574
.00107
.0223
.00003
.0051
.00001
.0004
.00000
15
20
571.4
.9867
.00270
.0744
.00019
.0130
00004
.0013
00000
20
25
444.4
.9758
.00434
.0509
.00021
.0129
.00006
.0011
.00001
25
30
363.6
.9717
.00635
.0808
.00050
.0194
.00013
.0019
.00001
30
35
307.7
.9989
.00897
.0946
.00080
.0220
.00020
.0023
.00002
35
40
266.7
1.0000
.01176
.2362
.00263
.0327
.00039
.0039
.00005
40
45
235.3
1.0000
.01486
.1358
.00191
.0279
.00042
.0031
.00006
45
50
210.5
1.0000
.01826
.1115
.00192
.0253
.00047
.0030
.00007
50
55
190.5
1.0000
.02194
.1154
.00239
.0228
.00050
.0026
.00007
55
60
173.9
1.0000
.02588
.3678
.00897
.0588
.00154
.0076
.00024
60
65
160.0
1.0000
.03007
.1724
.00488
.0311
.00094
.0040
.00015
65
70
148.1
1.0000
.03440
.1205
.00391
.0218
.00076
.0027
.00011
70
75
137.9
1.0000
.03911
.2713
.00997
.0396
.00157
.0051
.00024
75
80
129.0
1.0000
.04394
.2635
.01087
.0397
.00176
.0056
.00030
80
85
121.2
1.0000
.04895
.1372
.00630
.0213
.00105
.0028
.00017
85
90
114.3
1.0000
.05412
.2852
.01447
.0412
.00226
.0057
.00038
90
95
108.1
1.0000
.05945
.2127
.01184
.0275
.00166
.0035
.00025
95
100
102.6
1.0000
.06492
.2459
.01494
.0380
.00250
.0055
.00044
100
110
95.2
1.0000
.14669
.2478
.03396
.0342
.00508
.0051
.00092
110
120
87.0
1.0000
.16988
.1002
.01587
.0119
.00204
.0018
.00037
120
130
80.0
1.0000
.19370
.2456
.04426
.0318
.00623
.0049
.00119
130
140
74.1
1.0000
.21799
.2250
.04554
.0290
.00641
.0047
.00128
140
150
69.0
1.0000
.24255
.1527
.03432
.0162
.00398
.0023
.00072
150
160
64.5
1.0000
.26724
.2732
.06751
.0353
.00956
.0058
.00197
160
170
60.6
1.0000
.29190
.0699
.01882
.0065
.00193
.0012
.00045
170
180
57.1
1.0000
.31640
.2377
.06924
.0301
.00967
.0048
.00196
180
190
54.1
1.0000
.34061
.0880
.02754
.0102
.00352
.0017
.00073
190
200
51.3
1.0000
.36442
.0596
.01991
.0075
.00278
.0016
.00077
200
210
48.8
1.0000
.38773
.2250
.07978
.0341
.01341
.0052
.00264
210
220
46.5
1.0000
.41045
.0703
.02634
.0087
.00361
.0017
.00095
220
230
44.4
1.0000
.43248
.2023
.07964
.0242
.01066
.0039
.00224
230
240
42.6
.9996
.45358
.0200
.00824
.0026
.00120
.0008
.00047
240
250
40.8
.9999
.47421
.1258
.05405
.0152
.00735
.0028
.00181
250
260
39.2
1.0000
.49383
.0918
.04098
.0145
.00731
.0028
.00186
260
270
37.7
.9994
.51218
.0249
.01149
.0032
.00165
.0007
.00053
270
280
36.4
.9993
.52982
.0887
.04232
.0115
.00623
.0021
.00153
280
?90
35.1
1.0000
.54693
.1053
.05168
.0132
.00733
.0024
.00186
290
300
33.9
.9976
.56130
.0148
.00748
.0018
.00102
.0005
.00036
300
310
32.8
.9986
.57645
.0724
.03734
.0106
.00627
.0023
.00188
310
320
31.7
.9756
.57645
.0198
.01041
.0024
.00146
.0005
.00045
320
330
30.8
.9993
.60301
.0766
.04105
.0106
.00650
.0022
.00193
330
340
29.9
.9927
.61042
.0294
.01604
.0034
.00216
.0006
.00057
340
350
29.0
.9859
.61649
.0321
.01774
.0042
.00271
.0011
.00098
350
360
28.2
.9993
.63419
.0597
.03339
.0076
.00494
.0020
.00182
360
370
27.4
.7443
.47855
.0028
.00157
.0009
.00061
.0003
.00026
370
380
26.7
.9583
.62303
.0295
.01680
.0035
.00235
.0011
.00109
380
390
26.0
.7715
.50642
.0178
.01021
.0022
.00146
.0005
.00053
390
400
25.3
.8514
.56328
.0295
.01702
.0041
.00278
.0014
.00141
400
410
24.7
.4265
.28400
.0038
.00222
.0006
.00042
.0002
.00023
410
420
24.1
.6166
.41262
.0252
.01465
.0034
.00234
.0010
.00105
420
430
23.5
.7595
.51001
.0061
.00356
.0009
.00059
.0004
.00037
430
440
23.0
.5331
.35876
.0052
.00301
.0007
.00050
.0003
.00027
440
450
22.5
.6198
.41751
.0099
.00574
.0014
.00094
.0004
.00047
450
460
22.0
.7166
.48255
.0148
.00853
.0022
.00152
.0007
.00077
460
470
21.5
.4415
.29684
.0010
.00055
. 0002
.00014
.0001
.00014
470
480
21.1
.5282
.35417
.0107
.00610
.0014
.00099
.0004
.00047
480
490
20.6
.4221
.28195
.0052
.00293
.0007
.00045
.0002
.00020
490
500
20.2
.2491
.16560
.0016
.00091
.0002
.00017
.0001
.00010
500
520
19.6
.5487
.72270
.0063
.00697
.0009
.00126
.0003
.00073
520
540
18.9
.2598
.33690
.0028
.00305
.0004
.00056
.0002
.00035
540
560
18.2
.3040
.38663
.0048
.00512
.0008
.00107
.0003
.00070
560
580
17.5
.3341
.41524
.0181
.01866
.0028
.00357
.0010
.00213
580
600
16.9
.5678
.68759
.1122
.11205
.0187
.02335
.0057
.01232
600
620
16.4
.7985
.93922
.2431
.23432
.0497
.06045
.0135
.02868
620
640
15.9
.9.590
1.09239
.5054
.46899
.0835
.09848
.0199
.04169
640
660
15.4
1.0000
1.10028
.9523
.84842
.2729
.31135
.0382
.11975
660
680
14.9
1.0000
1.06001
.9956
.84930
.3964
.43621
.1148
.23178
680
700
14.5
1.0000
1.01873
.8888
.72427
.2145
.22708
.0462
.09125
700
720
14.1
.9382
.91640
.4314
.33499
.0802
.08147
.0194
.03733
720
740
13.7
.7382
.68986
.2621
.19351
.0622
.06048
.0135
.02534
740
760
13.3
.4218
.37634
.1191
.08342
.0248
.02307
.0066
.01212
760
780
13.0
.0859
.07304
.0226
.01497
.0065
.00576
.0013
.00232
780
800
12.7
.0812
.06567
.0098
.00614
.0026
.00217
.0006
.00102
800
820
12.3
.0272
.02085
.0018
.00104
.0004
.00031
.0001
.00025
820
840
12.0
.0065
.00471
.0001
.00005
.0000
.00002
.0000
.00003
840
860
11.8
.0179
.01234
.0000
.00001
.0000
.00000
.0000
.00001
860
880
11.5
.0065
.00426
.0000
.00000
.0000
.00000
.0000
.00000
900
920
11.2
.0072
.00440
.0000
.00000
.0000
.00000
.0000
.00000
900
920
11.0
.0046
.00263
.0000
.00002
.0000
.00001
.0000
.00002
920
940
10.8
.0074
.00402
.0005
.00019
.0001
.00006
.0001
.00009
940
960
10.5
.0168
.00857
.0020
.00075
.0004
.00021
.0002
.00024
960
980
10.3
.0199
.00951
.0047
.00166
.0015
.00075
.0004
.00049
980
1000
10.1
.0691
.03099
.0589
.01923
.0223
.01053
.0036
.00413
1000
1050
9.76
.5245
.52284
.4398
.31572
1050
1100
9.30
.2803
.23499
.2276
.13527
1100
1150
8.89
.0617
.04321
.0321
.01570
1150
1200
8.51
.0722
.04200
.0125
.00498
1200
1250
8.16
.1450
.06974
.0178
.00580
1250
1300
7.84
.5815
.23007
.1292
.03398
1300
1350
7.55
.6624
.21452
.1218
.02581
1350
1400
7.27
.7669
.20241
.0380
.00646
1400
1450
7.02
.8748
.18746
.0235
.00320
1450
1500
6.78
.9821
.17023
.0503
.00544
1500
1550
6.56
.9998
.13970
.0884
.00759
1550
1600
6.35
.9100
.10217
.0527
.00357
1600
1650
6.15
.9776
.08793
.0539
.00288
1650
1700
5.97
.9995
.07182
.0840
.00353
1700
1750
5.80
.9921
.05679
.0638
.00210
1750
1800
5.63
.9672
.04400
.0363
.00094
1800
1850
5.48
.8092
.02918
.0187
.00038
1850
1900
5.33
.5167
.01474
.0094
.00015
1900
1950
5.19
.4827
.01087
.0221
.00027
1950
2000
5.06
.2446
.00434
.0029
.00003
2000
2100
4.88
.2313
.00572
2100
2200
4.65
.3332
.00505
2200
2300
4.44
.9421
.00871
2300
2400
4.26
.9983
.00560
2400
2500
4.08
.5366
.00181
2500
2600
3.92
.1514
.00031
2600
2700
3.77
.0147
.00002
2700
2800
3.64
.0319
.00002
2800
2900
3.51
.0392
.00002
2900
3000
3.39
.1733
.00004
3000
3100
3.28
.3658
.00005
3100
3200
3.17
.2715
.00002
3200
3300
3.08
.3241
.00002
3300
3400
2.99
.2685
.00001
3400
3500
2.90
.4373
.00001
3500
3600
2.82
.9226
.00001
3600
3700
2.74
.9979
.00001
3700
3800
2.67
.9845
.00000
3800
3900
2.60
.9962
.00000
3900
4000
2.53
.6335
.00000
4000
4100
2.47
.1559
.00000
4100
4200
2.41
.0585
.00000
4200
4300
2.35
.0092
.00000
4300
4400
2.30
.0015
.00000
4400
4500
2.25
.0031
.00000
4500
4600
2.20
.0070
.00000
4600
4700
2.15
.0050
.00000
4700
4800
2.11
.0170
.00000
4800
4900
2.06
.1871
.00000
4900
5000
2.02
.3421
.00000
5000
5100
1.98
.1838
.00000
The emissivity is 1.0 — TAV, where TAV is the atmospheric transmission along a sec z0 = 2.0 path, averaged over the indicated spectral range. The upper and lower wavenumbers (cm−1) are given for each interval, as well as the average wavelength (μm). Then at each altitude (4.2 km, 14 km, 28 km, 41 km) the corresponding temperature (228 K, 217 K, 230 K, 268 K) is used to calculate the total radiated spectral-line emission flux (W/m2/sr) for each spectral interval, using Eq. (19). The power (W) measured by a detector will then be P(det) = AΩΣB(λi).TINST(λi), where TINST is the instrumental transmission at each wavelength, AΩ is the product of area and solid angle, and the sum is over all λi for which T is greater than zero.
Tables (2)
Table I
Molecular Abundances, Effective Pressures, and Temperatures Used in the Curtis-Godson Approximationa
4.2 km (Mauna Kea)
14 km (Aircraft)
28 km (Balloon)
41 km (Balloon)
O2
209460.0 ppmv
209460.0
209460.0
209460.0
CO2
325.0 ppmv
325.0
325.0
325.0
CH4
1.5 ppmv
1.1
0.8
0.4
N2O
0.25 ppmv
0.20
0.20
0.20
CO
0.07 ppmv
0.06
0.06
0.06
H2O
1200 μm
2.5 ppmv
2.5 ppmv
2.5 ppmv
O3
7.28 E18 cm−2
6.37 E18
1.85 E18
1.70 E17
p
600.0 mbar
141.6
16.2
2.52
p(eff)
300.0 mbar
70.8
8.10
1.26
p(H2O)
506.0 mbar
70.8
8.10
1.26
p(O3)
36.4 mbar
30.2
7.09
1.84
T(eff)
228.0 K
217.0
230.0
268.0
T(H2O)
252.0 K
217.0
230.0
268.0
T(O3)
219.0 K
221.0
233.0
260.0
The H2O abundances in the last three columns correspond to 2.25, 0.26, and 0.040 precipitable μm, respectively; the H2O at 4.2 km is assumed to have a scale height of 1.85 km. The abundances listed are for unit air mass; an additional factor of 2 is included in the actual calculations corresponding to a zenith angle of 60°. The base pressure at each altitude is given by p, and the effective pressure for collisional line broadening is indicated by p(eff), p(H2O), and p(O3) for the first five species, H2O, and O3, respectively; the temperatures at the corresponding pressure levels are also listed.
Table II
Atmospheric Emissivity (∊) and Radiated Flux (B) at Four Altitudes and for the Wavelength Range from 1000 μm to 10 μm, with Extensions down to 2 μm at Lower Altitudesa
ATMOSPHERIC EMISSIVITY AND FLUX (WATT/M2/ST)
UPPER SIGMA (CM-1)
LOWER SIGMA (CM-1)
AVERAGE WAVELENGTH (MICRON)
4.2 KM 228 KELVIN
28.0 KM 217 KELVIN
28.0 KM 230 KELVIN
41.0 KM 268 KELVIN
EMISS.
FLUX
EMISS.
FLUX
EMISS.
FLUX
EMISS.
FLUX
10
15
800.0
.7574
.00107
.0223
.00003
.0051
.00001
.0004
.00000
15
20
571.4
.9867
.00270
.0744
.00019
.0130
00004
.0013
00000
20
25
444.4
.9758
.00434
.0509
.00021
.0129
.00006
.0011
.00001
25
30
363.6
.9717
.00635
.0808
.00050
.0194
.00013
.0019
.00001
30
35
307.7
.9989
.00897
.0946
.00080
.0220
.00020
.0023
.00002
35
40
266.7
1.0000
.01176
.2362
.00263
.0327
.00039
.0039
.00005
40
45
235.3
1.0000
.01486
.1358
.00191
.0279
.00042
.0031
.00006
45
50
210.5
1.0000
.01826
.1115
.00192
.0253
.00047
.0030
.00007
50
55
190.5
1.0000
.02194
.1154
.00239
.0228
.00050
.0026
.00007
55
60
173.9
1.0000
.02588
.3678
.00897
.0588
.00154
.0076
.00024
60
65
160.0
1.0000
.03007
.1724
.00488
.0311
.00094
.0040
.00015
65
70
148.1
1.0000
.03440
.1205
.00391
.0218
.00076
.0027
.00011
70
75
137.9
1.0000
.03911
.2713
.00997
.0396
.00157
.0051
.00024
75
80
129.0
1.0000
.04394
.2635
.01087
.0397
.00176
.0056
.00030
80
85
121.2
1.0000
.04895
.1372
.00630
.0213
.00105
.0028
.00017
85
90
114.3
1.0000
.05412
.2852
.01447
.0412
.00226
.0057
.00038
90
95
108.1
1.0000
.05945
.2127
.01184
.0275
.00166
.0035
.00025
95
100
102.6
1.0000
.06492
.2459
.01494
.0380
.00250
.0055
.00044
100
110
95.2
1.0000
.14669
.2478
.03396
.0342
.00508
.0051
.00092
110
120
87.0
1.0000
.16988
.1002
.01587
.0119
.00204
.0018
.00037
120
130
80.0
1.0000
.19370
.2456
.04426
.0318
.00623
.0049
.00119
130
140
74.1
1.0000
.21799
.2250
.04554
.0290
.00641
.0047
.00128
140
150
69.0
1.0000
.24255
.1527
.03432
.0162
.00398
.0023
.00072
150
160
64.5
1.0000
.26724
.2732
.06751
.0353
.00956
.0058
.00197
160
170
60.6
1.0000
.29190
.0699
.01882
.0065
.00193
.0012
.00045
170
180
57.1
1.0000
.31640
.2377
.06924
.0301
.00967
.0048
.00196
180
190
54.1
1.0000
.34061
.0880
.02754
.0102
.00352
.0017
.00073
190
200
51.3
1.0000
.36442
.0596
.01991
.0075
.00278
.0016
.00077
200
210
48.8
1.0000
.38773
.2250
.07978
.0341
.01341
.0052
.00264
210
220
46.5
1.0000
.41045
.0703
.02634
.0087
.00361
.0017
.00095
220
230
44.4
1.0000
.43248
.2023
.07964
.0242
.01066
.0039
.00224
230
240
42.6
.9996
.45358
.0200
.00824
.0026
.00120
.0008
.00047
240
250
40.8
.9999
.47421
.1258
.05405
.0152
.00735
.0028
.00181
250
260
39.2
1.0000
.49383
.0918
.04098
.0145
.00731
.0028
.00186
260
270
37.7
.9994
.51218
.0249
.01149
.0032
.00165
.0007
.00053
270
280
36.4
.9993
.52982
.0887
.04232
.0115
.00623
.0021
.00153
280
?90
35.1
1.0000
.54693
.1053
.05168
.0132
.00733
.0024
.00186
290
300
33.9
.9976
.56130
.0148
.00748
.0018
.00102
.0005
.00036
300
310
32.8
.9986
.57645
.0724
.03734
.0106
.00627
.0023
.00188
310
320
31.7
.9756
.57645
.0198
.01041
.0024
.00146
.0005
.00045
320
330
30.8
.9993
.60301
.0766
.04105
.0106
.00650
.0022
.00193
330
340
29.9
.9927
.61042
.0294
.01604
.0034
.00216
.0006
.00057
340
350
29.0
.9859
.61649
.0321
.01774
.0042
.00271
.0011
.00098
350
360
28.2
.9993
.63419
.0597
.03339
.0076
.00494
.0020
.00182
360
370
27.4
.7443
.47855
.0028
.00157
.0009
.00061
.0003
.00026
370
380
26.7
.9583
.62303
.0295
.01680
.0035
.00235
.0011
.00109
380
390
26.0
.7715
.50642
.0178
.01021
.0022
.00146
.0005
.00053
390
400
25.3
.8514
.56328
.0295
.01702
.0041
.00278
.0014
.00141
400
410
24.7
.4265
.28400
.0038
.00222
.0006
.00042
.0002
.00023
410
420
24.1
.6166
.41262
.0252
.01465
.0034
.00234
.0010
.00105
420
430
23.5
.7595
.51001
.0061
.00356
.0009
.00059
.0004
.00037
430
440
23.0
.5331
.35876
.0052
.00301
.0007
.00050
.0003
.00027
440
450
22.5
.6198
.41751
.0099
.00574
.0014
.00094
.0004
.00047
450
460
22.0
.7166
.48255
.0148
.00853
.0022
.00152
.0007
.00077
460
470
21.5
.4415
.29684
.0010
.00055
. 0002
.00014
.0001
.00014
470
480
21.1
.5282
.35417
.0107
.00610
.0014
.00099
.0004
.00047
480
490
20.6
.4221
.28195
.0052
.00293
.0007
.00045
.0002
.00020
490
500
20.2
.2491
.16560
.0016
.00091
.0002
.00017
.0001
.00010
500
520
19.6
.5487
.72270
.0063
.00697
.0009
.00126
.0003
.00073
520
540
18.9
.2598
.33690
.0028
.00305
.0004
.00056
.0002
.00035
540
560
18.2
.3040
.38663
.0048
.00512
.0008
.00107
.0003
.00070
560
580
17.5
.3341
.41524
.0181
.01866
.0028
.00357
.0010
.00213
580
600
16.9
.5678
.68759
.1122
.11205
.0187
.02335
.0057
.01232
600
620
16.4
.7985
.93922
.2431
.23432
.0497
.06045
.0135
.02868
620
640
15.9
.9.590
1.09239
.5054
.46899
.0835
.09848
.0199
.04169
640
660
15.4
1.0000
1.10028
.9523
.84842
.2729
.31135
.0382
.11975
660
680
14.9
1.0000
1.06001
.9956
.84930
.3964
.43621
.1148
.23178
680
700
14.5
1.0000
1.01873
.8888
.72427
.2145
.22708
.0462
.09125
700
720
14.1
.9382
.91640
.4314
.33499
.0802
.08147
.0194
.03733
720
740
13.7
.7382
.68986
.2621
.19351
.0622
.06048
.0135
.02534
740
760
13.3
.4218
.37634
.1191
.08342
.0248
.02307
.0066
.01212
760
780
13.0
.0859
.07304
.0226
.01497
.0065
.00576
.0013
.00232
780
800
12.7
.0812
.06567
.0098
.00614
.0026
.00217
.0006
.00102
800
820
12.3
.0272
.02085
.0018
.00104
.0004
.00031
.0001
.00025
820
840
12.0
.0065
.00471
.0001
.00005
.0000
.00002
.0000
.00003
840
860
11.8
.0179
.01234
.0000
.00001
.0000
.00000
.0000
.00001
860
880
11.5
.0065
.00426
.0000
.00000
.0000
.00000
.0000
.00000
900
920
11.2
.0072
.00440
.0000
.00000
.0000
.00000
.0000
.00000
900
920
11.0
.0046
.00263
.0000
.00002
.0000
.00001
.0000
.00002
920
940
10.8
.0074
.00402
.0005
.00019
.0001
.00006
.0001
.00009
940
960
10.5
.0168
.00857
.0020
.00075
.0004
.00021
.0002
.00024
960
980
10.3
.0199
.00951
.0047
.00166
.0015
.00075
.0004
.00049
980
1000
10.1
.0691
.03099
.0589
.01923
.0223
.01053
.0036
.00413
1000
1050
9.76
.5245
.52284
.4398
.31572
1050
1100
9.30
.2803
.23499
.2276
.13527
1100
1150
8.89
.0617
.04321
.0321
.01570
1150
1200
8.51
.0722
.04200
.0125
.00498
1200
1250
8.16
.1450
.06974
.0178
.00580
1250
1300
7.84
.5815
.23007
.1292
.03398
1300
1350
7.55
.6624
.21452
.1218
.02581
1350
1400
7.27
.7669
.20241
.0380
.00646
1400
1450
7.02
.8748
.18746
.0235
.00320
1450
1500
6.78
.9821
.17023
.0503
.00544
1500
1550
6.56
.9998
.13970
.0884
.00759
1550
1600
6.35
.9100
.10217
.0527
.00357
1600
1650
6.15
.9776
.08793
.0539
.00288
1650
1700
5.97
.9995
.07182
.0840
.00353
1700
1750
5.80
.9921
.05679
.0638
.00210
1750
1800
5.63
.9672
.04400
.0363
.00094
1800
1850
5.48
.8092
.02918
.0187
.00038
1850
1900
5.33
.5167
.01474
.0094
.00015
1900
1950
5.19
.4827
.01087
.0221
.00027
1950
2000
5.06
.2446
.00434
.0029
.00003
2000
2100
4.88
.2313
.00572
2100
2200
4.65
.3332
.00505
2200
2300
4.44
.9421
.00871
2300
2400
4.26
.9983
.00560
2400
2500
4.08
.5366
.00181
2500
2600
3.92
.1514
.00031
2600
2700
3.77
.0147
.00002
2700
2800
3.64
.0319
.00002
2800
2900
3.51
.0392
.00002
2900
3000
3.39
.1733
.00004
3000
3100
3.28
.3658
.00005
3100
3200
3.17
.2715
.00002
3200
3300
3.08
.3241
.00002
3300
3400
2.99
.2685
.00001
3400
3500
2.90
.4373
.00001
3500
3600
2.82
.9226
.00001
3600
3700
2.74
.9979
.00001
3700
3800
2.67
.9845
.00000
3800
3900
2.60
.9962
.00000
3900
4000
2.53
.6335
.00000
4000
4100
2.47
.1559
.00000
4100
4200
2.41
.0585
.00000
4200
4300
2.35
.0092
.00000
4300
4400
2.30
.0015
.00000
4400
4500
2.25
.0031
.00000
4500
4600
2.20
.0070
.00000
4600
4700
2.15
.0050
.00000
4700
4800
2.11
.0170
.00000
4800
4900
2.06
.1871
.00000
4900
5000
2.02
.3421
.00000
5000
5100
1.98
.1838
.00000
The emissivity is 1.0 — TAV, where TAV is the atmospheric transmission along a sec z0 = 2.0 path, averaged over the indicated spectral range. The upper and lower wavenumbers (cm−1) are given for each interval, as well as the average wavelength (μm). Then at each altitude (4.2 km, 14 km, 28 km, 41 km) the corresponding temperature (228 K, 217 K, 230 K, 268 K) is used to calculate the total radiated spectral-line emission flux (W/m2/sr) for each spectral interval, using Eq. (19). The power (W) measured by a detector will then be P(det) = AΩΣB(λi).TINST(λi), where TINST is the instrumental transmission at each wavelength, AΩ is the product of area and solid angle, and the sum is over all λi for which T is greater than zero.