Abstract

A method for inference of vertical ozone profiles from measurements of the limb radiance resulting from scattered solar ultraviolet radiation is described in terms of a new inversion technique using multiple wavelengths. The inversion equation for this method is based on weighting functions which correspond to the sensitivity of the limb radiance to the relative increment of ozone density at each altitude, and the equation is solved by an iteration technique. In principle, the ozone vertical profile can be recovered from the inversion of a limb scan at a single wavelength. In practice, however, much more information of a higher accuracy over a wider height range can be obtained if one uses multiple wavelengths. Computer simulations were done for 280, 300, 320, and 340 nm. These results indicate the feasibility of determining ozone profiles on a global basis from satellite platforms over the altitude range of ~20–70 km with a vertical resolution of 1–2 km. The inferred profile error is about three to four times larger than measurement error in the 20–70-km altitude region. If one uses the wavelengths down to 260 nm, the accuracy of ozone profile of the highest altitude region may be improved. Ozone densities can be inferred above 70 km from the observations, although the errors are significantly larger.

© 1982 Optical Society of America

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References

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  1. S. Twomey, J. Franklin Inst. 279, 95 (1965).
    [CrossRef]
  2. J. V. Dave, C. L. Mateer, J. Atmos. Sci. 24, 414 (1967).
    [CrossRef]
  3. V. A. lozenas, Geomagn. Aeron. 8, 403 (1968).
  4. G. P. Anderson, C. A. Barth, F. Cayla, J. London, Ann. Geophys. 25, 341 (1969).
  5. N. D. Yarger, J. Appl. Meteorol. 9, 921 (1970).
    [CrossRef]
  6. D. F. Heath, A. J. Krueger, C. L. Mateer, Pure Appl. Geophys. 106–108, 1238 (1973).
    [CrossRef]
  7. D. F. Heath, A. J. Krueger, C. L. Mateer, Pure Appl. Geophys. 106–108, 1254 (1973).
  8. T. Aruga, T. Igarashi, Appl. Opt. 15, 261 (1976); T. Aruga, D. F. Heath, J. Geomagn. Geoelectr. (1982), submitted for publication.
    [CrossRef] [PubMed]
  9. J. L. London, J. E. Frederick, G. P. Anderson, J. Geophys. Res. 82, 2543 (1977).
    [CrossRef]
  10. C. Prabhakara, Mon. Weather Rev. 97, 307 (1969).
    [CrossRef]
  11. B. G. Conrath, R. A. Hanel, V. G. Kunde, C. Prabhakara, J. Geophys. Res. 75, 5831 (1970).
    [CrossRef]
  12. J. C. Gille, P. L. Bailey, in Inversion Methods in Atmospheric Remote Sounding, A. Deepak, Ed. (Academic, New York, 1977), p. 195.
  13. W. P. Chu, M. P. McCormick, Appl. Opt. 18, 1404 (1979).
    [CrossRef] [PubMed]
  14. J. E. Frederick et al., private communications.
  15. T. Aruga, D. F. Heath, J. Opt. Soc. Am. 68, 1434 (1978); Appl. Opt.21, 3038 (1982), to be published.
    [PubMed]
  16. E. Vigroux, Ann. Phys. 8, 709 (1953).

1979 (1)

1978 (1)

T. Aruga, D. F. Heath, J. Opt. Soc. Am. 68, 1434 (1978); Appl. Opt.21, 3038 (1982), to be published.
[PubMed]

1977 (1)

J. L. London, J. E. Frederick, G. P. Anderson, J. Geophys. Res. 82, 2543 (1977).
[CrossRef]

1976 (1)

1973 (2)

D. F. Heath, A. J. Krueger, C. L. Mateer, Pure Appl. Geophys. 106–108, 1238 (1973).
[CrossRef]

D. F. Heath, A. J. Krueger, C. L. Mateer, Pure Appl. Geophys. 106–108, 1254 (1973).

1970 (2)

N. D. Yarger, J. Appl. Meteorol. 9, 921 (1970).
[CrossRef]

B. G. Conrath, R. A. Hanel, V. G. Kunde, C. Prabhakara, J. Geophys. Res. 75, 5831 (1970).
[CrossRef]

1969 (2)

C. Prabhakara, Mon. Weather Rev. 97, 307 (1969).
[CrossRef]

G. P. Anderson, C. A. Barth, F. Cayla, J. London, Ann. Geophys. 25, 341 (1969).

1968 (1)

V. A. lozenas, Geomagn. Aeron. 8, 403 (1968).

1967 (1)

J. V. Dave, C. L. Mateer, J. Atmos. Sci. 24, 414 (1967).
[CrossRef]

1965 (1)

S. Twomey, J. Franklin Inst. 279, 95 (1965).
[CrossRef]

1953 (1)

E. Vigroux, Ann. Phys. 8, 709 (1953).

Anderson, G. P.

J. L. London, J. E. Frederick, G. P. Anderson, J. Geophys. Res. 82, 2543 (1977).
[CrossRef]

G. P. Anderson, C. A. Barth, F. Cayla, J. London, Ann. Geophys. 25, 341 (1969).

Aruga, T.

Bailey, P. L.

J. C. Gille, P. L. Bailey, in Inversion Methods in Atmospheric Remote Sounding, A. Deepak, Ed. (Academic, New York, 1977), p. 195.

Barth, C. A.

G. P. Anderson, C. A. Barth, F. Cayla, J. London, Ann. Geophys. 25, 341 (1969).

Cayla, F.

G. P. Anderson, C. A. Barth, F. Cayla, J. London, Ann. Geophys. 25, 341 (1969).

Chu, W. P.

Conrath, B. G.

B. G. Conrath, R. A. Hanel, V. G. Kunde, C. Prabhakara, J. Geophys. Res. 75, 5831 (1970).
[CrossRef]

Dave, J. V.

J. V. Dave, C. L. Mateer, J. Atmos. Sci. 24, 414 (1967).
[CrossRef]

Frederick, J. E.

J. L. London, J. E. Frederick, G. P. Anderson, J. Geophys. Res. 82, 2543 (1977).
[CrossRef]

J. E. Frederick et al., private communications.

Gille, J. C.

J. C. Gille, P. L. Bailey, in Inversion Methods in Atmospheric Remote Sounding, A. Deepak, Ed. (Academic, New York, 1977), p. 195.

Hanel, R. A.

B. G. Conrath, R. A. Hanel, V. G. Kunde, C. Prabhakara, J. Geophys. Res. 75, 5831 (1970).
[CrossRef]

Heath, D. F.

T. Aruga, D. F. Heath, J. Opt. Soc. Am. 68, 1434 (1978); Appl. Opt.21, 3038 (1982), to be published.
[PubMed]

D. F. Heath, A. J. Krueger, C. L. Mateer, Pure Appl. Geophys. 106–108, 1238 (1973).
[CrossRef]

D. F. Heath, A. J. Krueger, C. L. Mateer, Pure Appl. Geophys. 106–108, 1254 (1973).

Igarashi, T.

Krueger, A. J.

D. F. Heath, A. J. Krueger, C. L. Mateer, Pure Appl. Geophys. 106–108, 1254 (1973).

D. F. Heath, A. J. Krueger, C. L. Mateer, Pure Appl. Geophys. 106–108, 1238 (1973).
[CrossRef]

Kunde, V. G.

B. G. Conrath, R. A. Hanel, V. G. Kunde, C. Prabhakara, J. Geophys. Res. 75, 5831 (1970).
[CrossRef]

London, J.

G. P. Anderson, C. A. Barth, F. Cayla, J. London, Ann. Geophys. 25, 341 (1969).

London, J. L.

J. L. London, J. E. Frederick, G. P. Anderson, J. Geophys. Res. 82, 2543 (1977).
[CrossRef]

lozenas, V. A.

V. A. lozenas, Geomagn. Aeron. 8, 403 (1968).

Mateer, C. L.

D. F. Heath, A. J. Krueger, C. L. Mateer, Pure Appl. Geophys. 106–108, 1238 (1973).
[CrossRef]

D. F. Heath, A. J. Krueger, C. L. Mateer, Pure Appl. Geophys. 106–108, 1254 (1973).

J. V. Dave, C. L. Mateer, J. Atmos. Sci. 24, 414 (1967).
[CrossRef]

McCormick, M. P.

Prabhakara, C.

B. G. Conrath, R. A. Hanel, V. G. Kunde, C. Prabhakara, J. Geophys. Res. 75, 5831 (1970).
[CrossRef]

C. Prabhakara, Mon. Weather Rev. 97, 307 (1969).
[CrossRef]

Twomey, S.

S. Twomey, J. Franklin Inst. 279, 95 (1965).
[CrossRef]

Vigroux, E.

E. Vigroux, Ann. Phys. 8, 709 (1953).

Yarger, N. D.

N. D. Yarger, J. Appl. Meteorol. 9, 921 (1970).
[CrossRef]

Ann. Geophys. (1)

G. P. Anderson, C. A. Barth, F. Cayla, J. London, Ann. Geophys. 25, 341 (1969).

Ann. Phys. (1)

E. Vigroux, Ann. Phys. 8, 709 (1953).

Appl. Opt. (2)

Geomagn. Aeron. (1)

V. A. lozenas, Geomagn. Aeron. 8, 403 (1968).

J. Appl. Meteorol. (1)

N. D. Yarger, J. Appl. Meteorol. 9, 921 (1970).
[CrossRef]

J. Atmos. Sci. (1)

J. V. Dave, C. L. Mateer, J. Atmos. Sci. 24, 414 (1967).
[CrossRef]

J. Franklin Inst. (1)

S. Twomey, J. Franklin Inst. 279, 95 (1965).
[CrossRef]

J. Geophys. Res. (2)

J. L. London, J. E. Frederick, G. P. Anderson, J. Geophys. Res. 82, 2543 (1977).
[CrossRef]

B. G. Conrath, R. A. Hanel, V. G. Kunde, C. Prabhakara, J. Geophys. Res. 75, 5831 (1970).
[CrossRef]

J. Opt. Soc. Am. (1)

T. Aruga, D. F. Heath, J. Opt. Soc. Am. 68, 1434 (1978); Appl. Opt.21, 3038 (1982), to be published.
[PubMed]

Mon. Weather Rev. (1)

C. Prabhakara, Mon. Weather Rev. 97, 307 (1969).
[CrossRef]

Pure Appl. Geophys. (2)

D. F. Heath, A. J. Krueger, C. L. Mateer, Pure Appl. Geophys. 106–108, 1238 (1973).
[CrossRef]

D. F. Heath, A. J. Krueger, C. L. Mateer, Pure Appl. Geophys. 106–108, 1254 (1973).

Other (2)

J. C. Gille, P. L. Bailey, in Inversion Methods in Atmospheric Remote Sounding, A. Deepak, Ed. (Academic, New York, 1977), p. 195.

J. E. Frederick et al., private communications.

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Figures (11)

Fig. 1
Fig. 1

Experimental geometry of the LSUV method.

Fig. 2
Fig. 2

Differential coefficients Dij for a mid-latitude standard ozone profile (0.300 atm cm). The observational tangent ray height is scanned from 20 to 70 km in discrete 1-km intervals for wavelengths (a) 3400, (b) 3200, (c) 3000, and (d) 2800 Å.

Fig. 3
Fig. 3

Normalized weighting functions Pij in the same conditions as Fig. 2 for wavelengths (a) 3400, (b) 3200, (c) 3000, and (d) 2800 Å.

Fig. 4
Fig. 4

Accuracy index of the inferred vertical distribution of ozone. The index shows approximately the error of inferred ozone profile caused by 1% measurement (or theoretical) error for the use of each wavelength. The lower cutoff of each curve corresponds to the saturated height of Pij.

Fig. 5
Fig. 5

Calculated limb radiances as a function of observational tangent ray height for 3400–2600-Å wavelengths at 200-Å intervals. The solar zenith angle θ0 = 60° and 1-km view angle are assumed.

Fig. 6
Fig. 6

Differential coefficients Dij for multiple wavelengths. Discrete limb-scanning altitude intervals of 20–30, 30–45, 45–55 and 55–70 km are selected for the wavelengths 3400, 3200, 3000, and 2800 Å, respectively.

Fig. 7
Fig. 7

Normalized weighting function Pij for multiple wavelengths in the same condition as Fig. 6.

Fig. 8
Fig. 8

Examples of the computer simulation of the vertical ozone distribution inferred using the various initial estimates: (a) the density is different from the real one, the profile remaining unchanged; (b) the upper layer’s height is largely different; (c) the profile shifts up and down; and (d) the profile has special structures.

Fig. 9
Fig. 9

Example of the computer simulation when the ozone profile has fine structures. The actual distribution which has fine structures of 1- and 2-km widths is assumed.

Fig. 10
Fig. 10

Test for measurement error dependence on the inferred ozone distribution. Bias errors of +2% and −2% are tested.

Fig. 11
Fig. 11

Error bars on the inferred ozone distribution due to ±1% measurement error.

Equations (22)

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F i = I ( h i ) - I ¯ ( h i ) ,             i = 1 , 2 , , m ,
y j = N [ j ] - N ¯ [ j ] N ¯ [ j ] ,
N [ j ] = N ¯ [ j ] ( 1 + y j ) ,             j = 1 , 2 , , n .
N * [ j ] = { N ¯ [ j ] ( j j ) , N [ j ] ( j = j ) , j = 1 , 2 , , n .             j = 1 , 2 , , n ,
F i ( y i ) = F i ( 0 , , y j , , 0 ) = I ¯ * ( h i , y j ) - I ¯ ( h i ) , F i ( 0 ) = F i ( 0 , 0 , , 0 ) = I ¯ * ( h i , 0 ) - I ¯ ( h i ) = 0 ,
F i ( y 1 ) = F i ( y 1 , 0 , , 0 ) , F i ( y 2 ) = F i ( 0 , y 2 , 0 , , 0 ) ,             F i ( y n ) = F i ( 0 , 0 , , y n ) . }
F i = F i ( y 1 , y 2 , , y n ) ,             i = 1 , 2 , , m .
F i ( y 1 , y 2 , , y n ) = j = 1 n F i ( y j ) .
F i ( y j ) = [ F i ( y j ) y j ] y j = 0 · y j .
D i j = [ F i ( y j ) y j ] y j = 0 , { i = 1 , 2 , , m , j = 1 , 2 , , n .
F i = j = 1 n D i j y j ,             i = 1 , 2 , , m .
( y ¯ ) i = F i j = 1 n D i j ,             i = 1 , 2 , , m .
P i j = D i j j = 1 n D i j , j = 1 n P i j = 1 , { i = 1 , 2 , , m , j = 1 , 2 , , n ,
y j = i = 1 m ( y ¯ ) i P i j i = 1 m P i j ,             j = 1 , 2 , , n .
R ( l ) = i = 1 m { R i ( l ) } 2 m , R i ( l ) = I ( h i ) - I ¯ ( l ) ( h i ) I ¯ ( l ) ( h i ) = F i ( l ) I ¯ ( l ) ( h i ) ,
I ¯ = I ¯ 1 ( 1 + C m ) .
I ¯ 1 = J 4 π k P ¯ k ( θ , φ ; θ 0 , φ 0 ) × { j = 1 n ω k ( j ) [ exp ( - τ j ) exp ( - τ j ) + exp ( - * τ j ) exp ( - * τ j ) ] Δ τ j } ,
ω k ( j ) = β k ( s ) ( j ) k β k ( e ) ( j ) = β k ( s ) ( j ) k [ β k ( s ) ( j ) + β k ( a ) ( j ) ] ,
D i j = D i j ( 1 ) ( 1 + C m ) .
Δ y j = i = 1 m ( E i · δ F i ) P i j i = 1 m P i j ,             j = 1 , 2 , , n .
E i = I ¯ ( h i ) j = 1 n D i j ,             i = 1 , 2 , , m .
δ F i = δ e + δ t .

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