Atmospheric transmittance of an absorbing gas. 2: A computationally fast and accurate transmittance model for slant paths at different zenith angles

Henry E. Fleming; Larry M. McMillin

doi:10.1364/AO.16.001366

Applied Optics
Vol. 16,
Issue 5,
pp. 1366-1370
(1977)
•https://doi.org/10.1364/AO.16.001366

Atmospheric transmittance of an absorbing gas. 2: A computationally fast and accurate transmittance model for slant paths at different zenith angles

Henry E. Fleming and Larry M. McMillin

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Henry E. Fleming and Larry M. McMillin, "Atmospheric transmittance of an absorbing gas. 2: A computationally fast and accurate transmittance model for slant paths at different zenith angles," Appl. Opt. 16, 1366-1370 (1977)

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Abstract

Models exist which allow the calculation of atmospheric transmittance at a given zenith angle for an absorbing gas with a constant mixing ratio. However, many applications require transmittances at several zenith angles. A simple, fast, and accurate model for calculating the angular dependence is given. This model is computationally fast because only the four arithmetic operations are used. Details for calculating the expansion coefficients are provided. When this technique is combined with a procedure for calculating transmittances at a fixed angle, it is possible to calculate transmittances for slant paths at arbitrary zenith angles and temperature profiles, provided the mixing ratio is constant. This technique was evaluated with a method capable of calculating transmittances at zero zenith angle with an accuracy of 0.0031. For zenith angles ranging from 0° to 40°, transmittances agree with line-by-line calculations to within 0.0038.

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Equations (21)

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Temperature profile	Zenith angle	VTPR channel

		1	2	3	4	5	6
	0	0.0005	0.0004^a	0.0025	0.0031	0.0020^a	0.0019
	15°	0.0005	0.0004	0.0025	0.0032	0.0020	0.0020
Pt. Mugu	23°	0.0003	0.0003	0.0021	0.0029	0.0017	0.0019
	30°	0.0004	0.0003	0.0025	0.0035	0.0019	0.0021
	40°	0.0004	0.0003	0.0026	0.0038	0.0019	0.0021
	0°	0.0031^a	0.0013^a	0.0015^b	0.0017^a	0.0014	0.0022
	15°	0.0031	0.0013	0.0015	0.0019	0.0015	0.0021
Anomalous	23°	0.0031	0.0013	0.0015	0.0021	0.0016	0.0019
	30°	0.0030	0.0014	0.0015	0.0021	0.0016	0.0019
	40°	0.0031	0.0014	0.0014	0.0023	0.0017	0.0023

Temperature profile	Zenith angle	VTPR channel

		1	2	3	4	5	6
	0°	0.0002	0.0001	0.0008^a	0.0013^a	0.0009^a	0.0008
	15°	0.0002	0.0002	0.0009	0.0013	0.0009	0.0009
Pt. Mugu	23°	0.0001	0.0001	0.0007	0.0012	0.0008	0.0008
	30°	0.0002	0.0001	0.0008	0.0015	0.0010	0.0009
	40°	0.0002	0.0001	0.0009	0.0015	0.0010	0.0009
	0°	0.0010^a	0.0004^a	0.0005	0.0007^a	0.0005^a	0.0007
	15°	0.0010	0.0005	0.0005	0.0008	0.0005	0.0007
Anomalous	23°	0.0010	0.0005	0.0005	0.0008	0.0005	0.0007
	30°	0.0009	0.0004	0.0005	0.0009	0.0005	0.0007
	40°	0.0009	0.0005	0.0004	0.0010	0.0006	0.0007

Temperature profile	Zenith angle	VTPR channel

		1	2	3	4	5	6
	0	0.0005	0.0004^a	0.0025	0.0031	0.0020^a	0.0019
	15°	0.0005	0.0004	0.0025	0.0032	0.0020	0.0020
Pt. Mugu	23°	0.0003	0.0003	0.0021	0.0029	0.0017	0.0019
	30°	0.0004	0.0003	0.0025	0.0035	0.0019	0.0021
	40°	0.0004	0.0003	0.0026	0.0038	0.0019	0.0021
	0°	0.0031^a	0.0013^a	0.0015^b	0.0017^a	0.0014	0.0022
	15°	0.0031	0.0013	0.0015	0.0019	0.0015	0.0021
Anomalous	23°	0.0031	0.0013	0.0015	0.0021	0.0016	0.0019
	30°	0.0030	0.0014	0.0015	0.0021	0.0016	0.0019
	40°	0.0031	0.0014	0.0014	0.0023	0.0017	0.0023

Temperature profile	Zenith angle	VTPR channel

		1	2	3	4	5	6
	0°	0.0002	0.0001	0.0008^a	0.0013^a	0.0009^a	0.0008
	15°	0.0002	0.0002	0.0009	0.0013	0.0009	0.0009
Pt. Mugu	23°	0.0001	0.0001	0.0007	0.0012	0.0008	0.0008
	30°	0.0002	0.0001	0.0008	0.0015	0.0010	0.0009
	40°	0.0002	0.0001	0.0009	0.0015	0.0010	0.0009
	0°	0.0010^a	0.0004^a	0.0005	0.0007^a	0.0005^a	0.0007
	15°	0.0010	0.0005	0.0005	0.0008	0.0005	0.0007
Anomalous	23°	0.0010	0.0005	0.0005	0.0008	0.0005	0.0007
	30°	0.0009	0.0004	0.0005	0.0009	0.0005	0.0007
	40°	0.0009	0.0005	0.0004	0.0010	0.0006	0.0007

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Applied Optics