A new method is described for obtaining the temperature profile in the stratosphere and lower mesosphere from observations of the absorption spectrum of the high J lines of carbon dioxide at 4.3 μm. This concept is based upon the measurement of the integrated absorption of individual CO2 lines whose strengths depend strongly on temperature and that the absorption of these lines are obtained from measurements of the solar or stellar spectrum through an atmospheric path. The technique involves a rapidly converging iterative process in which the equivalent widths of the individual vibration–rotation lines of CO2 are used. Theoretical calculations are presented for balloon and satellite observations using a model atmosphere. Experimental results are given from spectra obtained with a balloon-borne Fourier interferometer spectrometer in which the sun was observed at low zenith angles. The experimental results are compared to rocketsonde data.
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See Ref. 6. Line positions and ground state energies (E″) in cm−1. Line strengths (S) in cm−2 atm−1. Air broadened widths (bco) in cm−1 atm−1. Values given for 296 K.
Table II
Calculated Values of Equivalent Widths and Temperatures for Balloon Observations a
Base altitude (km)
Zenith angle (θ)
CO2 line
W × 104 (cm−1)
Ā (km)
(K)
ΔT (K)
Ā (km)
(K)
ΔT (K)
30
90.0
R76
149.
32.4
230.6
0.1
34.3
235.2
−0.3
30
90.0
R88
11.1
32.4
237.1
−6.4
35.4
237.3
0.3
30
91.6
R76
221.
29.2
224.4
0.3
30.6
227.9
−0.9
30
91.6
R88
15.2
29.2
230.0
−5.3
31.7
230.2
−0.9
30
92.4
R78
221.
26.3
220.8
0.4
27.4
223.1
−0.6
30
92.4
R88
17.6
26.3
224.4
−3.2
28.0
224.5
−1.2
30
93.0
R78
315.
23.3
217.6
1.2
24.1
219.4
−0.3
30
93.0
R88
22.2
23.3
220.8
−2.0
24.6
220.9
−1.5
30
93.3
R78
392.
21.6
216.3
1.1
22.2
217.7
0.1
30
93.3
R88
25.6
21.6
219.0
−1.6
22.5
219.1
−1.0
50
90.0
R70
109.
52.4
265.3
0.2
51.8
263.7
3.3
50
90.0
R84
15.7
52.4
264.6
0.9
51.5
264.5
3.5
50
91.0
R70
124.
50.7
266.9
3.1
50.4
265.8
4.6
50
91.0
R84
26.1
50.7
267.1
2.8
50.3
267.1
3.5
50
92.0
R76
102.
47.9
264.8
4.0
47.7
264.6
3.7
50
92.0
R84
40.3
47.9
266.5
2.3
47.7
266.5
1.7
50
93.0
R80
89.2
43.3
256.7
3.3
43.7
257.2
3.8
50
93.0
R88
19.4
43.3
259.7
0.4
43.8
259.7
1.6
50
94.0
R80
109.
36.7
242.3
−1.1
38.1
244.8
0.4
50
94.0
R88
22.8
36.7
245.4
−4.2
38.6
245.5
1.1
50
95.0
R80
178.
28.1
223.6
−0.2
29.5
227.1
−2.0
50
95.0
R88
25.5
28.1
227.6
−4.2
30.2
227.9
−1.8
Calculations for midlatitude, spring, and fall. The mixing ratio of CO2 was 320 ppm/v.
Table III
Uncertainties in Temperature due to Uncertainties in Equivalent Width, Effective Pressure, Optical Density, and Molecular Parameters of CO2; for Balloon Observations; Temperatures in Kelvin
Calculated Values of Equivalent Widths and Temperatures for Satellite Observations a
Tangent height (km)
CO2 line
W × 104 (cm−1)
Ā (km)
(K)
ΔT (K)
Ā (km)
(K)
ΔT (K)
60
R64
104.
62.3
242.6
−1.0
68.8
241.3
1.9
60
R76
33.7
62.3
241.6
−0.0
61.6
241.6
2.0
55
R72
91.7
57.4
253.1
0.2
56.7
252.1
3.1
55
R80
35.6
57.4
253.0
0.3
56.6
252.9
2.6
50
R70
124.
52.4
265.3
0.2
51.8
263.7
3.3
50
R80
62.3
52.4
265.0
0.5
51.6
264.8
3.0
45
R74
119.
47.4
262.7
5.1
47.2
262.3
5.3
45
R86
27.3
47.4
265.4
2.4
47.2
265.4
2.2
40
R76
120.
42.3
252.9
4.6
43.0
254.8
4.0
40
R86
32.9
42.3
257.8
−0.3
43.2
257.8
1.4
35
R76
144.
37.4
242.4
0.8
38.7
245.7
1.3
35
R88
19.3
37.4
247.4
−4.3
39.5
247.4
1.8
30
R76
195.
32.4
230.6
0.1
34.3
235.2
−0.3
30
R88
20.6
32.4
237.1
−6.4
35.4
237.3
0.3
25
R76
311.
27.4
221.5
0.9
29.2
226.3
−1.6
25
R90
11.6
27.4
229.1
−6.7
30.9
229.8
−2.2
20
R78
391.
22.4
216.8
1.2
23.9
220.2
−1.2
20
R90
15.2
22.4
222.8
−4.9
25.2
223.0
−3.2
Calculations for midlatitude, Spring and Fall. The mixing ratio of CO2 was 320 ppm/v.
Table V
Uncertainties in Temperature due to Uncertainties in Equivalent Width, Effective Pressure, Optical Density, and Molecular Parameters of CO2; for Satellite Observations; Temperatures in Kelvin
Due to ±ΔW/W = ±0.10.
Due to ±Δbco/bco or
.
Due to ±ΔS/S or ±ΔX/X = ±0.10.
Table VI
Calculated and Observed Values of Equivalent Widths and Effective Temperatures for Balloon Observations at an Altitude of 37 km a
Solar zenith angle (θ)
CO2 line
W calculated (cm−1)
W measured (cm−1)
Ā
ΔT
Ā
ΔT
90.8
R76
0.0152
0.0153
38.1
260.3
3.1
39.1
264.5
3.1
90.8
R78
0.0126
0.0127
38.1
261.9
2.1
39.2
265.3
3.1
90.8
R80
0.0105
0.0104
38.1
261.0
1.8
39.3
263.8
3.1
91.3
R76
0.0168
0.0170
37.1
256.6
5.0
38.2
261.8
2.9
91.3
R78
0.0138
0.0139
37.1
259.2
2.7
38.3
263.3
3.5
91.3
R80
0.0113
0.0108
37.1
256.2
1.2
38.3
258.8
2.9
91.8
R76
0.0178
0.0182
35.7
252.3
2.1
37.1
254.5
5.6
91.8
R78
0.0141
0.0140
35.7
251.1
1.2
37.2
253.2
5.4
91.8
R80
0.0115
0.0116
35.7
253.4
0.1
37.3
255.3
4.8
91.8
R84
0.0073
0.0070
35.7
254.1
−2.8
37.6
254.9
4.4
92.3
R76
0.0192
0.0200
33.8
242.4
−0.8
35.6
248.4
5.0
92.3
R78
0.0149
0.0145
33.8
240.3
−1.9
35.7
245.2
5.0
92.3
R80
0.0118
0.0113
33.8
240.8
−3.2
35.9
244.5
5.9
92.3
R84
0.0071
0.0073
33.8
247.7
−7.1
36.3
249.3
5.8
92.9
R76
0.0252
0.0263
31.0
236.7
−0.1
33.1
242.3
0.3
92.9
R78
0.0186
0.0183
31.0
234.7
−0.8
33.3
240.2
0.1
92.9
R80
0.0142
0.0140
31.0
236.1
−2.0
33.5
241.1
−0.1
93.5
R78
0.0241
0.0235
27.6
226.3
1.2
30.0
232.7
−0.5
93.5
R80
0.0176
0.0184
27.6
229.8
0.3
30.3
236.5
−0.7
93.5
R84
0.0093
0.0090
27.6
231.8
−4.2
31.0
235.2
−0.2
94.0
R78
0.0307
0.0305
24.1
218.5
0.5
25.9
222.8
−1.0
94.0
R80
0.0212
0.0216
24.1
219.7
−0.1
26.1
223.9
−1.1
94.0
R84
0.0095
0.0094
24.1
222.2
−3.3
26.6
224.1
−1.1
Mixing ratio of CO2 was assumed to be 320 ppm/v.
Table VII
Uncertainties in Temperature due to Uncertainties in Equivalent Width, Effective Pressure, Optical Density, and Molecular Parameters of CO2; for Balloon Observations at Altitude of 37 km; Temperatures in Kelvin
See Ref. 6. Line positions and ground state energies (E″) in cm−1. Line strengths (S) in cm−2 atm−1. Air broadened widths (bco) in cm−1 atm−1. Values given for 296 K.
Table II
Calculated Values of Equivalent Widths and Temperatures for Balloon Observations a
Base altitude (km)
Zenith angle (θ)
CO2 line
W × 104 (cm−1)
Ā (km)
(K)
ΔT (K)
Ā (km)
(K)
ΔT (K)
30
90.0
R76
149.
32.4
230.6
0.1
34.3
235.2
−0.3
30
90.0
R88
11.1
32.4
237.1
−6.4
35.4
237.3
0.3
30
91.6
R76
221.
29.2
224.4
0.3
30.6
227.9
−0.9
30
91.6
R88
15.2
29.2
230.0
−5.3
31.7
230.2
−0.9
30
92.4
R78
221.
26.3
220.8
0.4
27.4
223.1
−0.6
30
92.4
R88
17.6
26.3
224.4
−3.2
28.0
224.5
−1.2
30
93.0
R78
315.
23.3
217.6
1.2
24.1
219.4
−0.3
30
93.0
R88
22.2
23.3
220.8
−2.0
24.6
220.9
−1.5
30
93.3
R78
392.
21.6
216.3
1.1
22.2
217.7
0.1
30
93.3
R88
25.6
21.6
219.0
−1.6
22.5
219.1
−1.0
50
90.0
R70
109.
52.4
265.3
0.2
51.8
263.7
3.3
50
90.0
R84
15.7
52.4
264.6
0.9
51.5
264.5
3.5
50
91.0
R70
124.
50.7
266.9
3.1
50.4
265.8
4.6
50
91.0
R84
26.1
50.7
267.1
2.8
50.3
267.1
3.5
50
92.0
R76
102.
47.9
264.8
4.0
47.7
264.6
3.7
50
92.0
R84
40.3
47.9
266.5
2.3
47.7
266.5
1.7
50
93.0
R80
89.2
43.3
256.7
3.3
43.7
257.2
3.8
50
93.0
R88
19.4
43.3
259.7
0.4
43.8
259.7
1.6
50
94.0
R80
109.
36.7
242.3
−1.1
38.1
244.8
0.4
50
94.0
R88
22.8
36.7
245.4
−4.2
38.6
245.5
1.1
50
95.0
R80
178.
28.1
223.6
−0.2
29.5
227.1
−2.0
50
95.0
R88
25.5
28.1
227.6
−4.2
30.2
227.9
−1.8
Calculations for midlatitude, spring, and fall. The mixing ratio of CO2 was 320 ppm/v.
Table III
Uncertainties in Temperature due to Uncertainties in Equivalent Width, Effective Pressure, Optical Density, and Molecular Parameters of CO2; for Balloon Observations; Temperatures in Kelvin
Calculated Values of Equivalent Widths and Temperatures for Satellite Observations a
Tangent height (km)
CO2 line
W × 104 (cm−1)
Ā (km)
(K)
ΔT (K)
Ā (km)
(K)
ΔT (K)
60
R64
104.
62.3
242.6
−1.0
68.8
241.3
1.9
60
R76
33.7
62.3
241.6
−0.0
61.6
241.6
2.0
55
R72
91.7
57.4
253.1
0.2
56.7
252.1
3.1
55
R80
35.6
57.4
253.0
0.3
56.6
252.9
2.6
50
R70
124.
52.4
265.3
0.2
51.8
263.7
3.3
50
R80
62.3
52.4
265.0
0.5
51.6
264.8
3.0
45
R74
119.
47.4
262.7
5.1
47.2
262.3
5.3
45
R86
27.3
47.4
265.4
2.4
47.2
265.4
2.2
40
R76
120.
42.3
252.9
4.6
43.0
254.8
4.0
40
R86
32.9
42.3
257.8
−0.3
43.2
257.8
1.4
35
R76
144.
37.4
242.4
0.8
38.7
245.7
1.3
35
R88
19.3
37.4
247.4
−4.3
39.5
247.4
1.8
30
R76
195.
32.4
230.6
0.1
34.3
235.2
−0.3
30
R88
20.6
32.4
237.1
−6.4
35.4
237.3
0.3
25
R76
311.
27.4
221.5
0.9
29.2
226.3
−1.6
25
R90
11.6
27.4
229.1
−6.7
30.9
229.8
−2.2
20
R78
391.
22.4
216.8
1.2
23.9
220.2
−1.2
20
R90
15.2
22.4
222.8
−4.9
25.2
223.0
−3.2
Calculations for midlatitude, Spring and Fall. The mixing ratio of CO2 was 320 ppm/v.
Table V
Uncertainties in Temperature due to Uncertainties in Equivalent Width, Effective Pressure, Optical Density, and Molecular Parameters of CO2; for Satellite Observations; Temperatures in Kelvin
Due to ±ΔW/W = ±0.10.
Due to ±Δbco/bco or
.
Due to ±ΔS/S or ±ΔX/X = ±0.10.
Table VI
Calculated and Observed Values of Equivalent Widths and Effective Temperatures for Balloon Observations at an Altitude of 37 km a
Solar zenith angle (θ)
CO2 line
W calculated (cm−1)
W measured (cm−1)
Ā
ΔT
Ā
ΔT
90.8
R76
0.0152
0.0153
38.1
260.3
3.1
39.1
264.5
3.1
90.8
R78
0.0126
0.0127
38.1
261.9
2.1
39.2
265.3
3.1
90.8
R80
0.0105
0.0104
38.1
261.0
1.8
39.3
263.8
3.1
91.3
R76
0.0168
0.0170
37.1
256.6
5.0
38.2
261.8
2.9
91.3
R78
0.0138
0.0139
37.1
259.2
2.7
38.3
263.3
3.5
91.3
R80
0.0113
0.0108
37.1
256.2
1.2
38.3
258.8
2.9
91.8
R76
0.0178
0.0182
35.7
252.3
2.1
37.1
254.5
5.6
91.8
R78
0.0141
0.0140
35.7
251.1
1.2
37.2
253.2
5.4
91.8
R80
0.0115
0.0116
35.7
253.4
0.1
37.3
255.3
4.8
91.8
R84
0.0073
0.0070
35.7
254.1
−2.8
37.6
254.9
4.4
92.3
R76
0.0192
0.0200
33.8
242.4
−0.8
35.6
248.4
5.0
92.3
R78
0.0149
0.0145
33.8
240.3
−1.9
35.7
245.2
5.0
92.3
R80
0.0118
0.0113
33.8
240.8
−3.2
35.9
244.5
5.9
92.3
R84
0.0071
0.0073
33.8
247.7
−7.1
36.3
249.3
5.8
92.9
R76
0.0252
0.0263
31.0
236.7
−0.1
33.1
242.3
0.3
92.9
R78
0.0186
0.0183
31.0
234.7
−0.8
33.3
240.2
0.1
92.9
R80
0.0142
0.0140
31.0
236.1
−2.0
33.5
241.1
−0.1
93.5
R78
0.0241
0.0235
27.6
226.3
1.2
30.0
232.7
−0.5
93.5
R80
0.0176
0.0184
27.6
229.8
0.3
30.3
236.5
−0.7
93.5
R84
0.0093
0.0090
27.6
231.8
−4.2
31.0
235.2
−0.2
94.0
R78
0.0307
0.0305
24.1
218.5
0.5
25.9
222.8
−1.0
94.0
R80
0.0212
0.0216
24.1
219.7
−0.1
26.1
223.9
−1.1
94.0
R84
0.0095
0.0094
24.1
222.2
−3.3
26.6
224.1
−1.1
Mixing ratio of CO2 was assumed to be 320 ppm/v.
Table VII
Uncertainties in Temperature due to Uncertainties in Equivalent Width, Effective Pressure, Optical Density, and Molecular Parameters of CO2; for Balloon Observations at Altitude of 37 km; Temperatures in Kelvin