Abstract

The relationship between the uncertainty and the resolution of the mixing-ratio profiles of absorbing gases retrieved from simulated occultation data has been investigated by analyzing sets of absorber amounts, corresponding to a constituent with a constant vertical mixing-ratio profile, along atmospheric paths observed by instruments at 0, 30, and 500 km. The vertical resolution below the instrument is limited by the number of observations and the SNR; it degrades exponentially with height and is independent of the instrument altitude; it is nearly 50 times better than the resolution obtainable above the instrument. An estimate of the resolution obtained by analyzing line shapes is included for comparison.

© 1983 Optical Society of America

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  1. P. Marché, C. Meunier, Planet. Space Sci. to be published.
  2. C. P. Rinsland, M. A. H. Smith, P. L. Rinsland, A. Goldman, J. W. Brault, G. M. Stoke, J. Geophys. Res. 87, 11, 119 (1982).
  3. A. Goldman, F. G. Fernald, F. J. Murcray, F. H. Murcray, D. G. Murcray, J. Quant. Spectrosc. Radiat. Transfer 29, 189 (1983).
    [CrossRef]
  4. M. T. Coffey, W. G. Mankin, A. Goldman, J. Geophys. Res. 86, 7331 (1981).
    [CrossRef]
  5. E. Niple, W. G. Mankin, A. Goldman, D. G. Murcray, F. J. Murcray, Geophys. Res. Lett. 7, 489 (1980).
    [CrossRef]
  6. C. B. Farmer, O. F. Raper, B. D. Robbins, R. A. Toth, C. Müller, J. Geophys. Res. 85, 1621 (1980).
    [CrossRef]
  7. A. C. Aikin, B. E. Woodgate, H. J. P. Smith, Appl. Opt. 21, 2421 (1982).
    [CrossRef] [PubMed]
  8. G. Backus, F. Gilbert, Philos. Trans. R. Soc.London266, 123 (1970).
    [CrossRef]
  9. G. Backus, Proc. Natl. Acad. Sci.USA65, 281 (1970).
    [CrossRef]
  10. L. Goldberg, Astrophys. J. 113, 567 (1951).
    [CrossRef]
  11. P. Marché, Thèse, U. Reims (1981).
  12. A. L. Buijs, G. L. Vail, G. Tremblay, D. J. W. Kendall, Geophys. Res. Lett. 7, 205 (1980).
    [CrossRef]
  13. Y. S. Chang, J. H. Shaw, J. G. Calvert, W. M. Uselman, J. Quant. Spectroc. Radiat. Transfer 19, 599 (1978).
    [CrossRef]
  14. E. Niple, Appl. Opt. 19, 3481 (1980).
    [CrossRef] [PubMed]
  15. M. M. Abbas, V. G. Kunde, M. J. Mumma, T. Kostiuk, D. Buhl, J. Geophys. Res. 84, 2681 (1979).
    [CrossRef]
  16. U.S. Standard Atmosphere, 1976, NOAA-S/T 76-1562 (U.S. GPO, Washington, D.C., 1976).
  17. D. E. Snider, J. Atmos. Sci. 32, 2178 (1975).
    [CrossRef]
  18. D. E. Snider, A. Goldman, “Refractive Effects in Remote Sensing of the Atmosphere with Infrared Transmission Spectroscopy,” BRL Report 1970, Ball. Res. Lab., Aberdeen Proving Grounds, Md. (1975).
  19. J. H. Park, Appl. Opt. 21, 1356 (1982).
    [CrossRef] [PubMed]
  20. J. P. Naudet, P. Rigaud, D. Huguenin, Geophys. Res. Lett. 7, 701 (1980).
    [CrossRef]
  21. M. Brown, Ed. BMDP Statistical Software 1981, (Univ. California Press, Berkeley, 1981).
  22. C. B. Farmer, Can. J. Chem. 52, 1544 (1974).
    [CrossRef]
  23. R. A. Toth, Appl. Opt. 16, 2661 (1977).
    [CrossRef] [PubMed]

1983

A. Goldman, F. G. Fernald, F. J. Murcray, F. H. Murcray, D. G. Murcray, J. Quant. Spectrosc. Radiat. Transfer 29, 189 (1983).
[CrossRef]

1982

C. P. Rinsland, M. A. H. Smith, P. L. Rinsland, A. Goldman, J. W. Brault, G. M. Stoke, J. Geophys. Res. 87, 11, 119 (1982).

J. H. Park, Appl. Opt. 21, 1356 (1982).
[CrossRef] [PubMed]

A. C. Aikin, B. E. Woodgate, H. J. P. Smith, Appl. Opt. 21, 2421 (1982).
[CrossRef] [PubMed]

1981

M. T. Coffey, W. G. Mankin, A. Goldman, J. Geophys. Res. 86, 7331 (1981).
[CrossRef]

1980

E. Niple, W. G. Mankin, A. Goldman, D. G. Murcray, F. J. Murcray, Geophys. Res. Lett. 7, 489 (1980).
[CrossRef]

C. B. Farmer, O. F. Raper, B. D. Robbins, R. A. Toth, C. Müller, J. Geophys. Res. 85, 1621 (1980).
[CrossRef]

A. L. Buijs, G. L. Vail, G. Tremblay, D. J. W. Kendall, Geophys. Res. Lett. 7, 205 (1980).
[CrossRef]

E. Niple, Appl. Opt. 19, 3481 (1980).
[CrossRef] [PubMed]

J. P. Naudet, P. Rigaud, D. Huguenin, Geophys. Res. Lett. 7, 701 (1980).
[CrossRef]

1979

M. M. Abbas, V. G. Kunde, M. J. Mumma, T. Kostiuk, D. Buhl, J. Geophys. Res. 84, 2681 (1979).
[CrossRef]

1978

Y. S. Chang, J. H. Shaw, J. G. Calvert, W. M. Uselman, J. Quant. Spectroc. Radiat. Transfer 19, 599 (1978).
[CrossRef]

1977

1975

D. E. Snider, J. Atmos. Sci. 32, 2178 (1975).
[CrossRef]

1974

C. B. Farmer, Can. J. Chem. 52, 1544 (1974).
[CrossRef]

1951

L. Goldberg, Astrophys. J. 113, 567 (1951).
[CrossRef]

Abbas, M. M.

M. M. Abbas, V. G. Kunde, M. J. Mumma, T. Kostiuk, D. Buhl, J. Geophys. Res. 84, 2681 (1979).
[CrossRef]

Aikin, A. C.

Backus, G.

G. Backus, F. Gilbert, Philos. Trans. R. Soc.London266, 123 (1970).
[CrossRef]

G. Backus, Proc. Natl. Acad. Sci.USA65, 281 (1970).
[CrossRef]

Brault, J. W.

C. P. Rinsland, M. A. H. Smith, P. L. Rinsland, A. Goldman, J. W. Brault, G. M. Stoke, J. Geophys. Res. 87, 11, 119 (1982).

Buhl, D.

M. M. Abbas, V. G. Kunde, M. J. Mumma, T. Kostiuk, D. Buhl, J. Geophys. Res. 84, 2681 (1979).
[CrossRef]

Buijs, A. L.

A. L. Buijs, G. L. Vail, G. Tremblay, D. J. W. Kendall, Geophys. Res. Lett. 7, 205 (1980).
[CrossRef]

Calvert, J. G.

Y. S. Chang, J. H. Shaw, J. G. Calvert, W. M. Uselman, J. Quant. Spectroc. Radiat. Transfer 19, 599 (1978).
[CrossRef]

Chang, Y. S.

Y. S. Chang, J. H. Shaw, J. G. Calvert, W. M. Uselman, J. Quant. Spectroc. Radiat. Transfer 19, 599 (1978).
[CrossRef]

Coffey, M. T.

M. T. Coffey, W. G. Mankin, A. Goldman, J. Geophys. Res. 86, 7331 (1981).
[CrossRef]

Farmer, C. B.

C. B. Farmer, O. F. Raper, B. D. Robbins, R. A. Toth, C. Müller, J. Geophys. Res. 85, 1621 (1980).
[CrossRef]

C. B. Farmer, Can. J. Chem. 52, 1544 (1974).
[CrossRef]

Fernald, F. G.

A. Goldman, F. G. Fernald, F. J. Murcray, F. H. Murcray, D. G. Murcray, J. Quant. Spectrosc. Radiat. Transfer 29, 189 (1983).
[CrossRef]

Gilbert, F.

G. Backus, F. Gilbert, Philos. Trans. R. Soc.London266, 123 (1970).
[CrossRef]

Goldberg, L.

L. Goldberg, Astrophys. J. 113, 567 (1951).
[CrossRef]

Goldman, A.

A. Goldman, F. G. Fernald, F. J. Murcray, F. H. Murcray, D. G. Murcray, J. Quant. Spectrosc. Radiat. Transfer 29, 189 (1983).
[CrossRef]

C. P. Rinsland, M. A. H. Smith, P. L. Rinsland, A. Goldman, J. W. Brault, G. M. Stoke, J. Geophys. Res. 87, 11, 119 (1982).

M. T. Coffey, W. G. Mankin, A. Goldman, J. Geophys. Res. 86, 7331 (1981).
[CrossRef]

E. Niple, W. G. Mankin, A. Goldman, D. G. Murcray, F. J. Murcray, Geophys. Res. Lett. 7, 489 (1980).
[CrossRef]

D. E. Snider, A. Goldman, “Refractive Effects in Remote Sensing of the Atmosphere with Infrared Transmission Spectroscopy,” BRL Report 1970, Ball. Res. Lab., Aberdeen Proving Grounds, Md. (1975).

Huguenin, D.

J. P. Naudet, P. Rigaud, D. Huguenin, Geophys. Res. Lett. 7, 701 (1980).
[CrossRef]

Kendall, D. J. W.

A. L. Buijs, G. L. Vail, G. Tremblay, D. J. W. Kendall, Geophys. Res. Lett. 7, 205 (1980).
[CrossRef]

Kostiuk, T.

M. M. Abbas, V. G. Kunde, M. J. Mumma, T. Kostiuk, D. Buhl, J. Geophys. Res. 84, 2681 (1979).
[CrossRef]

Kunde, V. G.

M. M. Abbas, V. G. Kunde, M. J. Mumma, T. Kostiuk, D. Buhl, J. Geophys. Res. 84, 2681 (1979).
[CrossRef]

Mankin, W. G.

M. T. Coffey, W. G. Mankin, A. Goldman, J. Geophys. Res. 86, 7331 (1981).
[CrossRef]

E. Niple, W. G. Mankin, A. Goldman, D. G. Murcray, F. J. Murcray, Geophys. Res. Lett. 7, 489 (1980).
[CrossRef]

Marché, P.

P. Marché, Thèse, U. Reims (1981).

P. Marché, C. Meunier, Planet. Space Sci. to be published.

Meunier, C.

P. Marché, C. Meunier, Planet. Space Sci. to be published.

Müller, C.

C. B. Farmer, O. F. Raper, B. D. Robbins, R. A. Toth, C. Müller, J. Geophys. Res. 85, 1621 (1980).
[CrossRef]

Mumma, M. J.

M. M. Abbas, V. G. Kunde, M. J. Mumma, T. Kostiuk, D. Buhl, J. Geophys. Res. 84, 2681 (1979).
[CrossRef]

Murcray, D. G.

A. Goldman, F. G. Fernald, F. J. Murcray, F. H. Murcray, D. G. Murcray, J. Quant. Spectrosc. Radiat. Transfer 29, 189 (1983).
[CrossRef]

E. Niple, W. G. Mankin, A. Goldman, D. G. Murcray, F. J. Murcray, Geophys. Res. Lett. 7, 489 (1980).
[CrossRef]

Murcray, F. H.

A. Goldman, F. G. Fernald, F. J. Murcray, F. H. Murcray, D. G. Murcray, J. Quant. Spectrosc. Radiat. Transfer 29, 189 (1983).
[CrossRef]

Murcray, F. J.

A. Goldman, F. G. Fernald, F. J. Murcray, F. H. Murcray, D. G. Murcray, J. Quant. Spectrosc. Radiat. Transfer 29, 189 (1983).
[CrossRef]

E. Niple, W. G. Mankin, A. Goldman, D. G. Murcray, F. J. Murcray, Geophys. Res. Lett. 7, 489 (1980).
[CrossRef]

Naudet, J. P.

J. P. Naudet, P. Rigaud, D. Huguenin, Geophys. Res. Lett. 7, 701 (1980).
[CrossRef]

Niple, E.

E. Niple, Appl. Opt. 19, 3481 (1980).
[CrossRef] [PubMed]

E. Niple, W. G. Mankin, A. Goldman, D. G. Murcray, F. J. Murcray, Geophys. Res. Lett. 7, 489 (1980).
[CrossRef]

Park, J. H.

Raper, O. F.

C. B. Farmer, O. F. Raper, B. D. Robbins, R. A. Toth, C. Müller, J. Geophys. Res. 85, 1621 (1980).
[CrossRef]

Rigaud, P.

J. P. Naudet, P. Rigaud, D. Huguenin, Geophys. Res. Lett. 7, 701 (1980).
[CrossRef]

Rinsland, C. P.

C. P. Rinsland, M. A. H. Smith, P. L. Rinsland, A. Goldman, J. W. Brault, G. M. Stoke, J. Geophys. Res. 87, 11, 119 (1982).

Rinsland, P. L.

C. P. Rinsland, M. A. H. Smith, P. L. Rinsland, A. Goldman, J. W. Brault, G. M. Stoke, J. Geophys. Res. 87, 11, 119 (1982).

Robbins, B. D.

C. B. Farmer, O. F. Raper, B. D. Robbins, R. A. Toth, C. Müller, J. Geophys. Res. 85, 1621 (1980).
[CrossRef]

Shaw, J. H.

Y. S. Chang, J. H. Shaw, J. G. Calvert, W. M. Uselman, J. Quant. Spectroc. Radiat. Transfer 19, 599 (1978).
[CrossRef]

Smith, H. J. P.

Smith, M. A. H.

C. P. Rinsland, M. A. H. Smith, P. L. Rinsland, A. Goldman, J. W. Brault, G. M. Stoke, J. Geophys. Res. 87, 11, 119 (1982).

Snider, D. E.

D. E. Snider, J. Atmos. Sci. 32, 2178 (1975).
[CrossRef]

D. E. Snider, A. Goldman, “Refractive Effects in Remote Sensing of the Atmosphere with Infrared Transmission Spectroscopy,” BRL Report 1970, Ball. Res. Lab., Aberdeen Proving Grounds, Md. (1975).

Stoke, G. M.

C. P. Rinsland, M. A. H. Smith, P. L. Rinsland, A. Goldman, J. W. Brault, G. M. Stoke, J. Geophys. Res. 87, 11, 119 (1982).

Toth, R. A.

C. B. Farmer, O. F. Raper, B. D. Robbins, R. A. Toth, C. Müller, J. Geophys. Res. 85, 1621 (1980).
[CrossRef]

R. A. Toth, Appl. Opt. 16, 2661 (1977).
[CrossRef] [PubMed]

Tremblay, G.

A. L. Buijs, G. L. Vail, G. Tremblay, D. J. W. Kendall, Geophys. Res. Lett. 7, 205 (1980).
[CrossRef]

Uselman, W. M.

Y. S. Chang, J. H. Shaw, J. G. Calvert, W. M. Uselman, J. Quant. Spectroc. Radiat. Transfer 19, 599 (1978).
[CrossRef]

Vail, G. L.

A. L. Buijs, G. L. Vail, G. Tremblay, D. J. W. Kendall, Geophys. Res. Lett. 7, 205 (1980).
[CrossRef]

Woodgate, B. E.

Appl. Opt.

Astrophys. J.

L. Goldberg, Astrophys. J. 113, 567 (1951).
[CrossRef]

Can. J. Chem.

C. B. Farmer, Can. J. Chem. 52, 1544 (1974).
[CrossRef]

Geophys. Res. Lett.

J. P. Naudet, P. Rigaud, D. Huguenin, Geophys. Res. Lett. 7, 701 (1980).
[CrossRef]

A. L. Buijs, G. L. Vail, G. Tremblay, D. J. W. Kendall, Geophys. Res. Lett. 7, 205 (1980).
[CrossRef]

E. Niple, W. G. Mankin, A. Goldman, D. G. Murcray, F. J. Murcray, Geophys. Res. Lett. 7, 489 (1980).
[CrossRef]

J. Atmos. Sci.

D. E. Snider, J. Atmos. Sci. 32, 2178 (1975).
[CrossRef]

J. Geophys. Res.

M. M. Abbas, V. G. Kunde, M. J. Mumma, T. Kostiuk, D. Buhl, J. Geophys. Res. 84, 2681 (1979).
[CrossRef]

C. B. Farmer, O. F. Raper, B. D. Robbins, R. A. Toth, C. Müller, J. Geophys. Res. 85, 1621 (1980).
[CrossRef]

C. P. Rinsland, M. A. H. Smith, P. L. Rinsland, A. Goldman, J. W. Brault, G. M. Stoke, J. Geophys. Res. 87, 11, 119 (1982).

M. T. Coffey, W. G. Mankin, A. Goldman, J. Geophys. Res. 86, 7331 (1981).
[CrossRef]

J. Quant. Spectroc. Radiat. Transfer

Y. S. Chang, J. H. Shaw, J. G. Calvert, W. M. Uselman, J. Quant. Spectroc. Radiat. Transfer 19, 599 (1978).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer

A. Goldman, F. G. Fernald, F. J. Murcray, F. H. Murcray, D. G. Murcray, J. Quant. Spectrosc. Radiat. Transfer 29, 189 (1983).
[CrossRef]

Other

P. Marché, C. Meunier, Planet. Space Sci. to be published.

G. Backus, F. Gilbert, Philos. Trans. R. Soc.London266, 123 (1970).
[CrossRef]

G. Backus, Proc. Natl. Acad. Sci.USA65, 281 (1970).
[CrossRef]

P. Marché, Thèse, U. Reims (1981).

U.S. Standard Atmosphere, 1976, NOAA-S/T 76-1562 (U.S. GPO, Washington, D.C., 1976).

D. E. Snider, A. Goldman, “Refractive Effects in Remote Sensing of the Atmosphere with Infrared Transmission Spectroscopy,” BRL Report 1970, Ball. Res. Lab., Aberdeen Proving Grounds, Md. (1975).

M. Brown, Ed. BMDP Statistical Software 1981, (Univ. California Press, Berkeley, 1981).

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Figures (10)

Fig. 1
Fig. 1

Sample observer geometries used to determine the vertical resolution for observers at (A) 500 and (B) 30 km.

Fig. 2
Fig. 2

Sample absorber amount data obtained using the constant mixing-ratio profile, as a function of the angle of arrival of the rays for SNR = 100 and observer altitudes of (A) 500 and (B) 0 km.

Fig. 3
Fig. 3

Local mixing-ratio values retrieved from the data in Fig. 2(A).

Fig. 4
Fig. 4

Uncertainty in the retrieved mixing-ratio values for an observer at 500 km obtained from data with SNR = 100, N0 = 125, and NR = 100, 50, 25, 10, and 5. The straight lines are the corresponding functions from Eq. (2).

Fig. 5
Fig. 5

Average uncertainty in the retrieved mixing-ratio values for an observer at 30 km obtained from retrievals from 16 data sets with SNR = 100, N0 = 125, and NR = 50, 25, 10, and 5. The straight lines are the corresponding functions from Eq. (5).

Fig. 6
Fig. 6

Average uncertainty in the retrieved mixing-ratio values for an observer at 0 km from retrievals from 16 data sets with SNR = 100, N0 = 125, and NR = 50, 10, and 5. The straight lines are the corresponding functions from Eq. (5).

Fig. 7
Fig. 7

Vertical resolution of the retrieved profiles obtained from Eq. (8) for the region below the observer for SNR = 100, Rult = 1.0 km, and U = 25.0, 5.0, 1.0, and 0.1%.

Fig. 8
Fig. 8

Vertical resolution of the retrieved profiles obtained from Eq. (9) for the region above the observer with SNR = 100, Rult = 1.0 km, and U = 100, 25, and 5%.

Fig. 9
Fig. 9

Weak absorption line with no added noise calculated for an observer at 0 km and zenith angle of 60° for Δνn = (n − 1) · 0.004 cm−1.

Fig. 10
Fig. 10

Uncertainty in the retrieved mixing-ratio values obtained from analysis of data similar to that shown in Fig. 9 with SNR = 100, NR = 5,4, and 2.

Equations (20)

Equations on this page are rendered with MathJax. Learn more.

a ( ϕ i ) = j = 1 200 a i j + i ,
U ( h , 500 ) = 50 N R exp ( 0.15 h ) / ( SNR N 0 1 / 2 ) .
P ( h ) = P ( 0 ) exp ( h / H s ) ,
U ( h , 500 ) = [ 50 N R P ( 0 ) ] / [ SNR N 0 1 / 2 P ( h ) ] ,
U ( h , 0 ) = 45 U ( h , 500 ) .
R = 2 Δ H / N R .
R ult = 2 Δ H / N 0 .
R B ( h ) = [ 100 Δ H exp ( 0.15 h ) ] / ( N 0 1 / 2 U SNR ) .
R A ( h ) = 45 R B ( h ) .
a i j = ρ j d j δ l i j .
δ l = ( 1 + h / R e ) δ h / ( cos 2 ϕ + 2 h / R e + h 2 / R e 2 ) 1 / 2 ,
R e , δ l sec ϕ δ h .
δ l ( cos 2 ϕ + 2 h / R e ) 1 / 2 δ h .
δ l [ ( R e + D ) / 2 ( h D ) ] 1 / 2 δ h ,
δ l ( R e / 2 h ) 1 / 2 δ h ,
k ( ν ) = S α ( h ) / { π [ Δ ν 2 + α 2 ( h ) ] } ,
α ( h ) = α ( 0 ) d ( h ) / d ( 0 ) ,
A ( ν ) = 1 T ( ν ) .
A ( ν n ) j A j ( ν n ) ,
A j ( ν n ) = ρ j k j ( ν n ) d j δ l j .

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