Abstract

The optical path length from a satellite to the earth's surface is strongly dependent on the atmospheric pressure along the propagation path. Surface pressure can be measured by using a two-color laser altimeter to observe the change with wavelength in the optical path length from a satellite to the ocean surface. The statistical characteristics of the ocean-reflected pulses and the expected measurement accuracy are evaluated in terms of the altimeter parameters. The results indicate that a pressure accuracy of a few millibars is feasible.

© 1983 Optical Society of America

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References

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  1. C. L. Korb, J. E. Kalshoven, C. Y. Weng, Trans. Am. Geophys. Union 60, 333 (1979).
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1983 (2)

1982 (2)

1979 (2)

C. L. Korb, J. E. Kalshoven, C. Y. Weng, Trans. Am. Geophys. Union 60, 333 (1979).

C. S. Gardner, Appl. Opt. 18, 3184 (1979).
[CrossRef] [PubMed]

1973 (1)

1969 (1)

I. Bar-David, IEEE Trans. Inf. Theory IT-21, 31 (1969).
[CrossRef]

1954 (1)

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Figures (4)

Fig. 1
Fig. 1

Pressure measurement sensitivity to differential path-length errors as a function of the satellite elevation angle.

Fig. 2
Fig. 2

Mean received pulse shape for reflection from an ocean wave with a height of 2 m (trough to crest). The laser altimeter is at an altitude of 400 km and the beam divergence is varied from 100 to 900 μrad.

Fig. 3
Fig. 3

Mean received pulse shape for a nadir angle of 1°. The wave height is 1 m (trough to crest) and the wave period is 10 m. The structure is caused by reflections from successive wave crests and troughs.

Fig. 4
Fig. 4

The rms timing error vs signal strength in both channels for a correlation receiver. The mean received pulse shape is plotted in Fig. 3.

Equations (42)

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R o = 2 r ocean r sat ( 1 + 10 6 N g ) sin θ d r .
R o = 2 R s + A C ,
A C = 2 r ocean r sat 10 6 N g sin θ d r + 2 [ r ocean r sat d r sin θ R s ] .
R 12 = R 1 R 2 = A C 1 A C 2 .
P = b + ( b 2 4 a d ) 1 / 2 2 a ,
a = 4.73 × 10 8 f ( λ 1 ) + f ( λ 2 ) T sin 2 E 2 3 1 / K ,
b = 2.357 × 10 3 + 1.084 × 10 8 T K tan 2 E 1.5 × 10 3 T 2 sin 4 E K 2 2 K ,
d = F ( θ , H ) R 12 sin E 2 [ f ( λ 1 ) ( f ( λ 2 ) ] 2.24 × 10 4 e ,
F ( θ , H ) = 1 + 0.0026 cos ( 2 θ ) 0.0003 ( H ) ,
K = 1.163 + 0.00968 cos ( 2 θ ) 0.00104 T + 0.00001435 P ,
f ( λ ) = 0.9650 + 0.0164 λ 2 + 0.000228 λ 4 ,
P R 12 0.212 sin E f ( λ 1 ) f ( λ 2 ) ( mbar / mm ) .
P d b 2.12 × 10 2 F ( θ , H ) sin E f ( λ 1 ) f ( λ 2 ) R 12 0.095 e .
σ p = [ ( P R 12 σ R 12 ) 2 + ( P e σ e ) 2 + ( P E σ E ) 2 ] 1 / 2 ,
P e 0.095 ( mbar / mbar ) ,
P E 10 3 P tan E ( mbar / mrad ) ;
E [ S ( t ) | ξ ] = N d 2 ρ b 2 ( ρ , z ) | f ( t ψ ) | 2 * h ( t ) ,
b n ( ρ , z ) = | a ( ρ , z ) | n β r n / 2 ( ρ ) / d 2 ρ | a ( ρ , z ) | n β r n / 2 ( ρ ) ,
ψ = 2 z c + ρ 2 c z 2 ξ ( ρ ) / c
β r = | R ( 0 ) | 2 4 π ( S 2 + 2 tan 2 θ T ) ,
S 2 = ( ξ x ) 2 + ( ξ y ) 2 = 0.003 + 0.00512 W .
τ ̂ ML = arg max τ [ dtS ( t ) ln S ( t + τ ) ] .
τ ̂ 12 = arg max τ [ d t S 1 ( t ) S 2 ( t + τ ) ] = arg max τ [ R 12 ( τ ) ] ,
var [ d d τ R 12 ( τ ) ] τ = τ 12 E 2 [ d d τ R 12 ( τ ) ] τ = τ 12 ,
σ τ 12 2 = E [ ( τ ̂ 12 τ 12 ) 2 ] = E { [ d d τ R 12 ( τ ) ] 2 } / E 2 [ d 2 d τ 2 R 12 ( τ ) ] τ = τ 12 .
σ τ 12 2 = d t 1 d t 2 R S 1 ( t 1 , t 2 ) 2 τ 1 τ 2 R S 2 ( t 1 + τ 1 , t 2 + τ 2 ) τ 1 = τ 2 = τ 12 [ d t S 1 ( t ) 2 t 2 S 2 ( t + τ ) τ = τ 12 ] 2 ,
R S i ( t 1 , t 2 ) = N i d 2 ρ b 2 ( ρ , z ) d τ | f ( τ ψ i ) | 2 × h ( t 1 τ ) h ( t 2 τ ) + N i 2 K i 1 × d 2 ρ b 4 ( ρ , z ) g ( t 1 ψ i ) g ( t 2 ψ i ) + S i ( t 1 ) S i ( t 2 ) ,
g ( t ) = | f ( t ) | 2 * h ( t ) .
K i = π A R ( 2 tan θ T λ i ) 2 .
σ τ 12 2 ( 1 N 1 + 1 N 2 + 1 K 1 + 1 K 2 ) α 2 B 2 ,
B 2 = d ω ω 2 | ϕ s ( ω ) | 2 d ω | ϕ s ( ω ) | 2 ,
α = d ω ω 2 ϕ s * ( ω ) [ ϕ s ( ω ) * ϕ s ( ω ) ] d ω ω 2 | ϕ s ( ω ) | 2 d ω | ϕ s ( ω ) | 2 ,
ϕ s ( ω ) = 1 N dtE [ S ( t ) | ξ ] exp ( i ω t ) = d 2 ρ b 2 ( ρ , z ) exp ( σ g 2 ω 2 / 2 ) exp ( i ω ψ ) .
B 2 = { Δ σ g 2 L z tan θ T Δ ( σ g 2 + 4 σ ξ 2 / C 2 ) L z tan θ T ,
Δ = γ e γ 2 π erfc ( γ ) γ 2 ,
γ = { c σ g 2 z tan θ T ( 2 σ ξ 2 / L 2 + tan 2 θ T ) 1 / 2 L z tan θ T c 2 z tan 2 θ T ( σ g 2 + 4 σ ξ 2 / c 2 ) 1 / 2 L z tan θ T .
Δ = { γ π γ 1 1 2 γ 1 .
σ τ 12 2 ( 1 N 1 + 1 N 2 + 1 K 1 + 1 K 2 ) 2 2 π α σ g σ ξ z tan θ T c L , L z tan θ T .
σ τ 12 2 ( 1 N 1 + 1 N 2 + 1 K 1 + 1 K 2 ) 8 α σ ξ 2 c 2 , L z tan θ T .
N = η h f o Q T a 2 A R z 2 | R ( 0 ) | 2 4 π ( S 2 + 2 tan 2 θ T ) .
S 2 = 2 σ ξ 2 / L 2 .
η = 0.1 , A R = 0.1 m 2 , T a 2 = 0.5 , z = 400 km , β r = 0.06 , θ T = 100 μ rad , Q = 250 mJ ,

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