Abstract

A method is proposed to recover stratospheric ozone and aerosol concentration profiles from satellite-borne polarimeter measurements of the ultraviolet light reflected from the earth’s atmosphere. A mathematical inversion is performed on simulated spectral polarization measurements demonstrating the recovery of ozone mixing ratio and aerosol scattering ratio profiles when large aerosol concentrations are present in the stratosphere.

© 1984 Optical Society of America

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References

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  1. H. H. Lamb, Philos. Trans. R. Soc. London Ser. A 266, 426 (1970).
  2. R. W. P. Gotz, A. R. Meetham, G. M. B. Dobson, Proc. R. Soc. London Ser. A 145, 416 (1934).
    [CrossRef]
  3. D. F. Heath, A. J. Krueger, C. L. Mateer, Pure Appl. Geophys. 106, 1238 (1973).
    [CrossRef]
  4. J. J. DeLuisi, J. Geophys. Res. 84, 1766 (1973).
    [CrossRef]
  5. D. M. Cunnold, C. R. Gray, D. C. Merritt, Pure Appl. Geophys. 106, 1264 (1973).
    [CrossRef]
  6. S. Chandrasekhar, Radiative Transfer (Dover, New York, 1980).
  7. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  8. C. E. Junge, C. W. Chagnon, J. E. Manson, J. Meteorol. 18, 81 (1961).
    [CrossRef]
  9. U.S. Standard Atmosphere, NOAA-S/T 76-1562, Washington, D.C. (1976).
  10. A. J. Fleig et al., “User’s Guide for the Solar Backscattered Ultraviolet (SBUV) Instrument First Year Ozone-S Data Set, NASA Report (Jan.1982), 53 pp.
  11. S. Twomey, J. Geophys. Res. 66, 2153 (1961).
    [CrossRef]
  12. S. Twomey, B. Herman, R. Rabinoff, J. Atmos. Sci. 34, 1085 (1977).
    [CrossRef]
  13. S. Twomey, Introduction to the Mathematics of Inversion in Remote Sensing and Indirect Measurements (Elsevier, Amsterdam, 1977).

1977 (1)

S. Twomey, B. Herman, R. Rabinoff, J. Atmos. Sci. 34, 1085 (1977).
[CrossRef]

1973 (3)

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

J. J. DeLuisi, J. Geophys. Res. 84, 1766 (1973).
[CrossRef]

D. M. Cunnold, C. R. Gray, D. C. Merritt, Pure Appl. Geophys. 106, 1264 (1973).
[CrossRef]

1970 (1)

H. H. Lamb, Philos. Trans. R. Soc. London Ser. A 266, 426 (1970).

1961 (2)

C. E. Junge, C. W. Chagnon, J. E. Manson, J. Meteorol. 18, 81 (1961).
[CrossRef]

S. Twomey, J. Geophys. Res. 66, 2153 (1961).
[CrossRef]

1934 (1)

R. W. P. Gotz, A. R. Meetham, G. M. B. Dobson, Proc. R. Soc. London Ser. A 145, 416 (1934).
[CrossRef]

Chagnon, C. W.

C. E. Junge, C. W. Chagnon, J. E. Manson, J. Meteorol. 18, 81 (1961).
[CrossRef]

Chandrasekhar, S.

S. Chandrasekhar, Radiative Transfer (Dover, New York, 1980).

Cunnold, D. M.

D. M. Cunnold, C. R. Gray, D. C. Merritt, Pure Appl. Geophys. 106, 1264 (1973).
[CrossRef]

DeLuisi, J. J.

J. J. DeLuisi, J. Geophys. Res. 84, 1766 (1973).
[CrossRef]

Dobson, G. M. B.

R. W. P. Gotz, A. R. Meetham, G. M. B. Dobson, Proc. R. Soc. London Ser. A 145, 416 (1934).
[CrossRef]

Fleig, A. J.

A. J. Fleig et al., “User’s Guide for the Solar Backscattered Ultraviolet (SBUV) Instrument First Year Ozone-S Data Set, NASA Report (Jan.1982), 53 pp.

Gotz, R. W. P.

R. W. P. Gotz, A. R. Meetham, G. M. B. Dobson, Proc. R. Soc. London Ser. A 145, 416 (1934).
[CrossRef]

Gray, C. R.

D. M. Cunnold, C. R. Gray, D. C. Merritt, Pure Appl. Geophys. 106, 1264 (1973).
[CrossRef]

Heath, D. F.

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

Herman, B.

S. Twomey, B. Herman, R. Rabinoff, J. Atmos. Sci. 34, 1085 (1977).
[CrossRef]

Junge, C. E.

C. E. Junge, C. W. Chagnon, J. E. Manson, J. Meteorol. 18, 81 (1961).
[CrossRef]

Krueger, A. J.

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

Lamb, H. H.

H. H. Lamb, Philos. Trans. R. Soc. London Ser. A 266, 426 (1970).

Manson, J. E.

C. E. Junge, C. W. Chagnon, J. E. Manson, J. Meteorol. 18, 81 (1961).
[CrossRef]

Mateer, C. L.

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

Meetham, A. R.

R. W. P. Gotz, A. R. Meetham, G. M. B. Dobson, Proc. R. Soc. London Ser. A 145, 416 (1934).
[CrossRef]

Merritt, D. C.

D. M. Cunnold, C. R. Gray, D. C. Merritt, Pure Appl. Geophys. 106, 1264 (1973).
[CrossRef]

Rabinoff, R.

S. Twomey, B. Herman, R. Rabinoff, J. Atmos. Sci. 34, 1085 (1977).
[CrossRef]

Twomey, S.

S. Twomey, B. Herman, R. Rabinoff, J. Atmos. Sci. 34, 1085 (1977).
[CrossRef]

S. Twomey, J. Geophys. Res. 66, 2153 (1961).
[CrossRef]

S. Twomey, Introduction to the Mathematics of Inversion in Remote Sensing and Indirect Measurements (Elsevier, Amsterdam, 1977).

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

J. Atmos. Sci. (1)

S. Twomey, B. Herman, R. Rabinoff, J. Atmos. Sci. 34, 1085 (1977).
[CrossRef]

J. Geophys. Res. (2)

S. Twomey, J. Geophys. Res. 66, 2153 (1961).
[CrossRef]

J. J. DeLuisi, J. Geophys. Res. 84, 1766 (1973).
[CrossRef]

J. Meteorol. (1)

C. E. Junge, C. W. Chagnon, J. E. Manson, J. Meteorol. 18, 81 (1961).
[CrossRef]

Philos. Trans. R. Soc. London Ser. A (1)

H. H. Lamb, Philos. Trans. R. Soc. London Ser. A 266, 426 (1970).

Proc. R. Soc. London Ser. A (1)

R. W. P. Gotz, A. R. Meetham, G. M. B. Dobson, Proc. R. Soc. London Ser. A 145, 416 (1934).
[CrossRef]

Pure Appl. Geophys. (2)

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

D. M. Cunnold, C. R. Gray, D. C. Merritt, Pure Appl. Geophys. 106, 1264 (1973).
[CrossRef]

Other (5)

S. Chandrasekhar, Radiative Transfer (Dover, New York, 1980).

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

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

A. J. Fleig et al., “User’s Guide for the Solar Backscattered Ultraviolet (SBUV) Instrument First Year Ozone-S Data Set, NASA Report (Jan.1982), 53 pp.

S. Twomey, Introduction to the Mathematics of Inversion in Remote Sensing and Indirect Measurements (Elsevier, Amsterdam, 1977).

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Figures (13)

Fig. 1
Fig. 1

(a) Normalized log-polar plot of the Mie phase functions P11(Θ) and P22(Θ) approximating the stratospheric aerosol. The size distribution in this example is dn/dlogrr−2 with cutoff radii rmin = 0.1 μm and rmax = 1 μm.

Fig. 2
Fig. 2

U.S. Standard Atmosphere mid-latitude ozone mixing ratio profile.

Fig. 3
Fig. 3

Relative contribution of pressure level to the backscattered irradiance components Ir(λ) and Il(λ) at 90° to the solar beam for a particulate-free atmosphere.

Fig. 4
Fig. 4

Viewing geometry of a hypothetical satellite measurement of the reflected radiance at 90° to the incident solar beam.

Fig. 5
Fig. 5

Sensitivity of the measured linear polarization of light reflected from a pure molecular atmosphere at 90° to the solar beam to instrument field of view.

Fig. 6
Fig. 6

Model altitude profile of aerosol scattering ratio with pressure for an aerosol optical depth of 0.1 at 300 nm. Aerosol scattering power at 300 nm is written in terms of scattering power relative to a millibar of air.

Fig. 7
Fig. 7

Relative contribution to the backscattered radiance components (a) Ir(λ) and (b) Il(λ) at 90° to the solar beam when stratospheric aerosol τA = 0.1 is present.

Fig. 8
Fig. 8

Sensitivity of Ir(297.6 nm) and Il(297.6 nm) to increases in stratospheric optical depth.

Fig. 9
Fig. 9

Standard A, initial guess B, and first solution (curve C) ozone mixing ratio profiles.

Fig. 10
Fig. 10

Columnar ozone corresponding to the mixing ratio profiles shown in Fig. 9. Actual A, initial guess B, and first solution C are shown.

Fig. 11
Fig. 11

Actual A and first solution B aerosol scattering ratio profiles.

Fig. 12
Fig. 12

Actual A, first B, and second solution C columnar ozone profiles showing the improvement in profile solution when aerosol scattering is taken into account.

Fig. 13
Fig. 13

Actual A and second B aerosol scattering ratio profiles demonstrate their improvement in the solution for aerosol scattering ratio when the ozone is more accurately known.

Tables (1)

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Table I External Data

Equations (27)

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1 4 Π 0 4 Π 1 2 ( P 11 + P 22 + P 12 + P 21 ) d Ω = 1 ,
P ˜ R ( Θ ) = 3 2 ( 1 + 2 γ ) [ cos 2 Θ + γ sin 2 Θ γ 0 0 γ 1 0 0 0 0 ( 1 - γ ) cos Θ 0 0 0 0 ( 1 - 3 γ ) cos Θ ] ,
P ˜ Mie ( Θ ) = [ P 11 0 0 0 0 P 22 0 0 0 0 P 33 P 34 0 0 - P 34 P 33 ] ,
[ I l I R ] scattered F 0 [ P 11 + P 12 P 12 + P 22 ] .
[ I l I r ] scattered ( θ = 90 ° ) F 0 2 ( 1 + 2 γ ) [ 2 γ 1 + γ ]
I ( λ , 90 ° ) = k R ( λ ) 4 π 0 P 0 exp [ - τ ( P ) ( 1 sin θ 0 + 1 cos θ 0 ) ] × [ P ˜ R ( θ ) + β ( λ , P ) P ˜ Mie ( λ , Θ ) ] F 0 ( λ ) d P sin θ 0 ,
τ ( P ) = 0 P { k R ( λ ) [ 1 + β ( λ , P ) ] + α ( λ ) d x ( P ) d P } d P ,
τ A ( λ ) = k R ( λ ) 0 P 0 β ( λ , P ) d P .
cos 2 ( 90 ° ) = ½ [ 1 - ( 1 + X + X 2 ) ] .
I r ( λ ) = B ( λ ) 0 P 0 [ P R ( 22 ) + P R ( 21 ) + β ( λ , P ) P Mie ( 22 ) ] × exp [ - y ( λ , P ) ] d P ,
y ( λ , P ) = τ ( λ , P ) ( 1 sin θ 0 + 1 cos θ 0 ) , B ( λ ) = F 0 ( λ ) k R ( λ ) 4 π · 2 sin θ 0 .
I r ( λ ) = B ( λ ) ( exp [ - y ( λ , P ) ] { P · [ P R ( 22 ) + P R ( 21 ) ] + τ A ( λ , P ) k R ( λ ) P Mie ( 22 ) } ) 0 P 0 + B ( λ ) 0 y ( λ , P 0 ) exp [ - y ( λ , P ) ] [ P R ( 22 ) + P R ( 21 ) + τ A ( λ , P ) k R ( λ ) P Mie ( 22 ) ] d y .
I r ( λ ) = B ( λ ) 0 P 0 exp [ - y ( λ , P ) ] [ P R ( 22 ) + P R ( 21 ) + τ A ( λ , P ) k R ( λ ) P Mie ( 22 ) ] d y d P d P .
K r ( λ , P ) = B ( λ ) exp [ - y ( λ , P ) ] [ P R ( 22 ) + P R ( 21 ) + τ A ( λ , P ) k R ( λ ) P Mie ( 22 ) ] .
I r ( λ ) = 0 P 0 K r ( λ , P ) d y d P d P .
I r ( λ ) = j = 1 25 P j Δ ln P j K r ( λ , P j ) d y d P ¯ | P j ,
d y d p | P j = ( 1 sin θ 0 + 1 cos θ 0 ) { k R ( λ ) [ 1 + β ( λ , P j ) ] + α ( λ ) d x d P | P j } .
d x d P | P j
d x d P | P j
d x d P | P j = [ A r ( i , j ) A max ( i ) δ i + ( 1 - A r ( i , j ) A max ( i ) ) ] d x d P | P j ;
d x d P | P j
I l ( λ i ) = B ( λ ) 0 P 0 exp [ - y ( λ , P ) ] [ P R ( 11 ) + P R ( 12 ) + β ( λ , P ) P Mie ( 11 ) ] d P .
I l ( λ i ) = j = 1 25 A i j [ P R ( 11 ) + P R ( 12 ) + β ( λ i , P j ) P Mie ( 11 ) ] ,
β ( λ i , P j ) = ( λ i λ 0 ) 3 β ( λ 0 , P j ) .
G i I l ( λ i ) - [ P R ( 11 ) + P R ( 12 ) ] j = 1 25 A i j P Mie ( 11 ) [ λ 0 λ i ] 3 ,
G = A ˜ · β ( 300 nm ) .
β = ( A ˜ T A ˜ + γ I ˜ ) - 1 A ˜ T G ,

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