Corrections for atmospheric refractivity in satellite laser ranging

R. S. Iyer; J. L. Bufton

doi:10.1364/AO.16.001997

Applied Optics
Vol. 16,
Issue 7,
pp. 1997-2003
(1977)
•https://doi.org/10.1364/AO.16.001997

Corrections for atmospheric refractivity in satellite laser ranging

R. S. Iyer and J. L. Bufton

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R. S. Iyer and J. L. Bufton, "Corrections for atmospheric refractivity in satellite laser ranging," Appl. Opt. 16, 1997-2003 (1977)

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Abstract

The range correction calculated from ground-level meteorological measurements is shown to consist of a series of terms. The zeroth order term of this series corresponds to the correction obtained under the assumption of a spherically symmetric refractivity profile. The higher order terms arise due to departures from the spherical-symmetry assumption. The range correction is also shown to have residual errors, and an analytic expression for these errors is derived. Pertinent surface data are analyzed to obtain the magnitudes of the higher order corrections and the residual errors.

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1-D fit
Linear		Quadratic
a₁		a₁		a₂

Mean	S. D.	Mean	S. D.	Mean	S. D.
(a) Eight stations
0.009	0.009	0.005	0.021	1.2 × 10⁻⁵	5.3 × 10⁻⁵
(b) Five stations
0.011	0.012	0.009	0.03	1 × 10⁻⁵	1.3 × 10⁻⁴

2-D fit
a_x		a_y

Mean	S. D.	Mean	S. D.
−0.0007	0.028	0.0033	0.021

Elev. angle in deg.	Marini and Murray correction term.(m)	Plane earth model N_s = 313, C = 0.144 (m)
10	13.32	12.55
15	9.08	8.42
20	6.91	6.37
40	3.70	3.39
80	2.42	2.21
90	2.4	2.18

Elev. angle	Mean bias	S.D.
(a) Linear eight stations
10°	1.42	1.42
20°	0.35	0.35
40°	0.08	0.08
80°	0.01	0.01
(b) Linear five stations
10°	1.73	1.89
20°	0.43	0.46
40°	0.10	0.11
80°	0.01	0.01

	Linear bias		Quadratic bias

	Mean	S. D.	Mean	S. D.
(c) Quadratic eight stations
10°	0.79	3.30	0.15	0.66
20°	0.19	0.81	0.02	0.078
40°	0.05	0.19	0.002	0.008
80°	0.004	0.02	—	—
(d) Quadratic five stations
10°	1.42	4.73	0.12	1.61
20°	0.35	1.16	0.015	0.19
40°	0.08	0.27	0.002	0.02
80°	0.007	0.023	—	—

Elev. angle	Mean bias	S.D.
(a) ϕ^a = 0°
10°	−0.110	4.418
20°	−0.027	1.089
40°	−0.006	0.249
80°	−0.001	0.031
(b) ϕ = 45°
10°	0.291	3.905
20°	0.071	0.963
40°	0.016	0.220
80°	0.002	0.027
(c) ϕ = 90°
10°	0.521	3.313
20°	0.128	0.817
40°	0.029	0.187
80°	0.004	0.023
(d) ϕ = 135°
10°	0.446	3.905
20°	0.110	0.963
40°	0.025	0.220
80°	0.003	0.027

	Five stations			Eight stations

		Error			Error
Stn.	σ_a	10°	80°	σ_a	10°	80°
1-D, linear fit
1	2.5 × 10⁻³	3.33	0.61	3.05 × 10⁻³	4.06	0.74
3	2.56 × 10⁻³	3.41	0.62	2.84 × 10⁻³	3.78	0.69
5	1.42 × 10⁻³	1.89	0.34	3.44 × 10⁻³	4.58	0.83
1-D, quadratic fit
1	1.66 × 10⁻³	2.21	0.40	2.76 × 10⁻³	3.76	0.67
3	2.31 × 10⁻³	3.08	0.56	2.75 × 10⁻³	3.66	0.67
5	0.23 × 10⁻³	0.31	0.06	2.57 × 10⁻³	3.42	0.62

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Applied Optics