Abstract

Through a Fredholm integral equation of the first kind, aerosol kernel functions relate the variations in radiance measured by satellites to the variations in the aerosol extinction profile and thus permit profile retrieval from radiance measurements by inversion of the set of radiative transfer equations for various spectral intervals. Previously [Appl. Opt. 36, 1328 (1997)] the kernel functions were evaluated for the red and near-infrared spectral regions outside molecular absorption bands. Here they are computed within the oxygen A band with 20-cm-1 spectral resolution. It is shown that, even with such a relatively low spectral resolution, the new set of kernels is able to provide better information on and improved accuracy of the retrieved profile.

© 1999 Optical Society of America

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  1. V. V. Badayev, M. S. Malkevich, “On the possibility of retrieval of aerosol extinction vertical profile using the satellite observation of reflected radiation in the oxygen band 760 nm,” Proc. Acad. Sci. USSR Sec. Atmos. Oceanic Phys. 14, 1022–1030 (1978), in Russian.
  2. M. Gabella, R. Guzzi, V. Kisselev, G. Perona, “Retrieval of aerosol profile variations in the visible and near infrared: theory and application of the single scattering approach,” Appl. Opt. 36, 1328–1336 (1997).
    [CrossRef] [PubMed]
  3. D. E. Burch, D. A. Gryvnak, “Strengths, widths, and shapes of the oxygen lines near 13 100 cm-1 (7620 Å),” Appl. Opt. 8, 1493–1499 (1969).
    [CrossRef] [PubMed]
  4. K. J. Ritter, T. D. Wilkerson, “High-resolution spectroscopy of the oxygen A-band,” J. Mol. Spectrosc. 121, 1–19 (1987).
    [CrossRef]
  5. D. Q. Wark, D. M. Mercer, “Absorption in the atmosphere by the oxygen A-band,” Appl. Opt. 4, 839–844 (1965).
    [CrossRef]
  6. J. Fischer, W. Cordes, A. Schmitz-Pfeiffer, W. Renger, P. Mörl, “Detection of cloud-top height from backscattered radiances within oxygen A-band. 2. Measurements,” J. Appl. Meteorol. 30, 1260–1267 (1991).
    [CrossRef]
  7. A. Berk, L. S. Bernstein, D. C. Robertson, “modtran: A moderate resolution model for lowtran-7,” (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1989).
  8. R. G. Isaacs, S. A. Clough, R. D. Warsham, J. L. Moncet, B. L. Lindner, L. D. Kaplan, “Path characterisation algorithm for fascode,” (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1990).
  9. F. X. Kneizys, E. P. Shettle, L. W. Abreu, J. H. Chetwind, G. P. Andreson, W. O. Gallery, J. E. A. Selby, S. A. Clough, “Users guide to lowtran 7,” (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1988).
  10. D. L. Phillips, “A technique for the numerical solution of certain integral equations of the first kind,” J. Assoc. Comput. Mach. 9, 84–97 (1962).
    [CrossRef]
  11. S. Twomey, “On the numerical solution of Fredholm integral equations of the first kind by the inversion of the linear system produced by quadrature,” J. Assoc. Comput. Mach. 10, 97–101 (1963).
    [CrossRef]
  12. G. E. Shaw, “Inversion of optical scattering and spectral extinction measurements to recover aerosol size spectra,” Appl. Opt. 18, 988–993 (1979).
    [CrossRef] [PubMed]
  13. S. Twomey, “Information content in remote sensing,” Appl. Opt. 13, 942–945 (1974).
    [CrossRef] [PubMed]
  14. S. Twomey, Introduction to the Mathematics of Inversion in Remote Sensing and Indirect Measurements (Elsevier, New York, 1977).
  15. B. Pflug, T. Ruppert, “Information content of measurements in the O2A- and O2B bands for monitoring of aerosols from space,” in Atmospheric Propagation and Remote Sensing II, A. Kohnle, W. B. Miller, eds., Proc. SPIE1968, 533–544 (1968).
  16. B. Pflug, “Atmospheric transmission in the O2A-band: comparison of calculations and measurements,” presented at the Atmospheric Spectroscopy Applications Workshop, the University of Reims, Champagne, France, 8–10 September 1993.

1997 (1)

1991 (1)

J. Fischer, W. Cordes, A. Schmitz-Pfeiffer, W. Renger, P. Mörl, “Detection of cloud-top height from backscattered radiances within oxygen A-band. 2. Measurements,” J. Appl. Meteorol. 30, 1260–1267 (1991).
[CrossRef]

1987 (1)

K. J. Ritter, T. D. Wilkerson, “High-resolution spectroscopy of the oxygen A-band,” J. Mol. Spectrosc. 121, 1–19 (1987).
[CrossRef]

1979 (1)

1978 (1)

V. V. Badayev, M. S. Malkevich, “On the possibility of retrieval of aerosol extinction vertical profile using the satellite observation of reflected radiation in the oxygen band 760 nm,” Proc. Acad. Sci. USSR Sec. Atmos. Oceanic Phys. 14, 1022–1030 (1978), in Russian.

1974 (1)

1969 (1)

1965 (1)

1963 (1)

S. Twomey, “On the numerical solution of Fredholm integral equations of the first kind by the inversion of the linear system produced by quadrature,” J. Assoc. Comput. Mach. 10, 97–101 (1963).
[CrossRef]

1962 (1)

D. L. Phillips, “A technique for the numerical solution of certain integral equations of the first kind,” J. Assoc. Comput. Mach. 9, 84–97 (1962).
[CrossRef]

Abreu, L. W.

F. X. Kneizys, E. P. Shettle, L. W. Abreu, J. H. Chetwind, G. P. Andreson, W. O. Gallery, J. E. A. Selby, S. A. Clough, “Users guide to lowtran 7,” (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1988).

Andreson, G. P.

F. X. Kneizys, E. P. Shettle, L. W. Abreu, J. H. Chetwind, G. P. Andreson, W. O. Gallery, J. E. A. Selby, S. A. Clough, “Users guide to lowtran 7,” (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1988).

Badayev, V. V.

V. V. Badayev, M. S. Malkevich, “On the possibility of retrieval of aerosol extinction vertical profile using the satellite observation of reflected radiation in the oxygen band 760 nm,” Proc. Acad. Sci. USSR Sec. Atmos. Oceanic Phys. 14, 1022–1030 (1978), in Russian.

Berk, A.

A. Berk, L. S. Bernstein, D. C. Robertson, “modtran: A moderate resolution model for lowtran-7,” (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1989).

Bernstein, L. S.

A. Berk, L. S. Bernstein, D. C. Robertson, “modtran: A moderate resolution model for lowtran-7,” (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1989).

Burch, D. E.

Chetwind, J. H.

F. X. Kneizys, E. P. Shettle, L. W. Abreu, J. H. Chetwind, G. P. Andreson, W. O. Gallery, J. E. A. Selby, S. A. Clough, “Users guide to lowtran 7,” (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1988).

Clough, S. A.

F. X. Kneizys, E. P. Shettle, L. W. Abreu, J. H. Chetwind, G. P. Andreson, W. O. Gallery, J. E. A. Selby, S. A. Clough, “Users guide to lowtran 7,” (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1988).

R. G. Isaacs, S. A. Clough, R. D. Warsham, J. L. Moncet, B. L. Lindner, L. D. Kaplan, “Path characterisation algorithm for fascode,” (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1990).

Cordes, W.

J. Fischer, W. Cordes, A. Schmitz-Pfeiffer, W. Renger, P. Mörl, “Detection of cloud-top height from backscattered radiances within oxygen A-band. 2. Measurements,” J. Appl. Meteorol. 30, 1260–1267 (1991).
[CrossRef]

Fischer, J.

J. Fischer, W. Cordes, A. Schmitz-Pfeiffer, W. Renger, P. Mörl, “Detection of cloud-top height from backscattered radiances within oxygen A-band. 2. Measurements,” J. Appl. Meteorol. 30, 1260–1267 (1991).
[CrossRef]

Gabella, M.

Gallery, W. O.

F. X. Kneizys, E. P. Shettle, L. W. Abreu, J. H. Chetwind, G. P. Andreson, W. O. Gallery, J. E. A. Selby, S. A. Clough, “Users guide to lowtran 7,” (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1988).

Gryvnak, D. A.

Guzzi, R.

Isaacs, R. G.

R. G. Isaacs, S. A. Clough, R. D. Warsham, J. L. Moncet, B. L. Lindner, L. D. Kaplan, “Path characterisation algorithm for fascode,” (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1990).

Kaplan, L. D.

R. G. Isaacs, S. A. Clough, R. D. Warsham, J. L. Moncet, B. L. Lindner, L. D. Kaplan, “Path characterisation algorithm for fascode,” (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1990).

Kisselev, V.

Kneizys, F. X.

F. X. Kneizys, E. P. Shettle, L. W. Abreu, J. H. Chetwind, G. P. Andreson, W. O. Gallery, J. E. A. Selby, S. A. Clough, “Users guide to lowtran 7,” (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1988).

Lindner, B. L.

R. G. Isaacs, S. A. Clough, R. D. Warsham, J. L. Moncet, B. L. Lindner, L. D. Kaplan, “Path characterisation algorithm for fascode,” (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1990).

Malkevich, M. S.

V. V. Badayev, M. S. Malkevich, “On the possibility of retrieval of aerosol extinction vertical profile using the satellite observation of reflected radiation in the oxygen band 760 nm,” Proc. Acad. Sci. USSR Sec. Atmos. Oceanic Phys. 14, 1022–1030 (1978), in Russian.

Mercer, D. M.

Moncet, J. L.

R. G. Isaacs, S. A. Clough, R. D. Warsham, J. L. Moncet, B. L. Lindner, L. D. Kaplan, “Path characterisation algorithm for fascode,” (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1990).

Mörl, P.

J. Fischer, W. Cordes, A. Schmitz-Pfeiffer, W. Renger, P. Mörl, “Detection of cloud-top height from backscattered radiances within oxygen A-band. 2. Measurements,” J. Appl. Meteorol. 30, 1260–1267 (1991).
[CrossRef]

Perona, G.

Pflug, B.

B. Pflug, “Atmospheric transmission in the O2A-band: comparison of calculations and measurements,” presented at the Atmospheric Spectroscopy Applications Workshop, the University of Reims, Champagne, France, 8–10 September 1993.

B. Pflug, T. Ruppert, “Information content of measurements in the O2A- and O2B bands for monitoring of aerosols from space,” in Atmospheric Propagation and Remote Sensing II, A. Kohnle, W. B. Miller, eds., Proc. SPIE1968, 533–544 (1968).

Phillips, D. L.

D. L. Phillips, “A technique for the numerical solution of certain integral equations of the first kind,” J. Assoc. Comput. Mach. 9, 84–97 (1962).
[CrossRef]

Renger, W.

J. Fischer, W. Cordes, A. Schmitz-Pfeiffer, W. Renger, P. Mörl, “Detection of cloud-top height from backscattered radiances within oxygen A-band. 2. Measurements,” J. Appl. Meteorol. 30, 1260–1267 (1991).
[CrossRef]

Ritter, K. J.

K. J. Ritter, T. D. Wilkerson, “High-resolution spectroscopy of the oxygen A-band,” J. Mol. Spectrosc. 121, 1–19 (1987).
[CrossRef]

Robertson, D. C.

A. Berk, L. S. Bernstein, D. C. Robertson, “modtran: A moderate resolution model for lowtran-7,” (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1989).

Ruppert, T.

B. Pflug, T. Ruppert, “Information content of measurements in the O2A- and O2B bands for monitoring of aerosols from space,” in Atmospheric Propagation and Remote Sensing II, A. Kohnle, W. B. Miller, eds., Proc. SPIE1968, 533–544 (1968).

Schmitz-Pfeiffer, A.

J. Fischer, W. Cordes, A. Schmitz-Pfeiffer, W. Renger, P. Mörl, “Detection of cloud-top height from backscattered radiances within oxygen A-band. 2. Measurements,” J. Appl. Meteorol. 30, 1260–1267 (1991).
[CrossRef]

Selby, J. E. A.

F. X. Kneizys, E. P. Shettle, L. W. Abreu, J. H. Chetwind, G. P. Andreson, W. O. Gallery, J. E. A. Selby, S. A. Clough, “Users guide to lowtran 7,” (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1988).

Shaw, G. E.

Shettle, E. P.

F. X. Kneizys, E. P. Shettle, L. W. Abreu, J. H. Chetwind, G. P. Andreson, W. O. Gallery, J. E. A. Selby, S. A. Clough, “Users guide to lowtran 7,” (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1988).

Twomey, S.

S. Twomey, “Information content in remote sensing,” Appl. Opt. 13, 942–945 (1974).
[CrossRef] [PubMed]

S. Twomey, “On the numerical solution of Fredholm integral equations of the first kind by the inversion of the linear system produced by quadrature,” J. Assoc. Comput. Mach. 10, 97–101 (1963).
[CrossRef]

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

Wark, D. Q.

Warsham, R. D.

R. G. Isaacs, S. A. Clough, R. D. Warsham, J. L. Moncet, B. L. Lindner, L. D. Kaplan, “Path characterisation algorithm for fascode,” (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1990).

Wilkerson, T. D.

K. J. Ritter, T. D. Wilkerson, “High-resolution spectroscopy of the oxygen A-band,” J. Mol. Spectrosc. 121, 1–19 (1987).
[CrossRef]

Appl. Opt. (5)

J. Appl. Meteorol. (1)

J. Fischer, W. Cordes, A. Schmitz-Pfeiffer, W. Renger, P. Mörl, “Detection of cloud-top height from backscattered radiances within oxygen A-band. 2. Measurements,” J. Appl. Meteorol. 30, 1260–1267 (1991).
[CrossRef]

J. Assoc. Comput. Mach. (2)

D. L. Phillips, “A technique for the numerical solution of certain integral equations of the first kind,” J. Assoc. Comput. Mach. 9, 84–97 (1962).
[CrossRef]

S. Twomey, “On the numerical solution of Fredholm integral equations of the first kind by the inversion of the linear system produced by quadrature,” J. Assoc. Comput. Mach. 10, 97–101 (1963).
[CrossRef]

J. Mol. Spectrosc. (1)

K. J. Ritter, T. D. Wilkerson, “High-resolution spectroscopy of the oxygen A-band,” J. Mol. Spectrosc. 121, 1–19 (1987).
[CrossRef]

Proc. Acad. Sci. USSR Sec. Atmos. Oceanic Phys. (1)

V. V. Badayev, M. S. Malkevich, “On the possibility of retrieval of aerosol extinction vertical profile using the satellite observation of reflected radiation in the oxygen band 760 nm,” Proc. Acad. Sci. USSR Sec. Atmos. Oceanic Phys. 14, 1022–1030 (1978), in Russian.

Other (6)

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

B. Pflug, T. Ruppert, “Information content of measurements in the O2A- and O2B bands for monitoring of aerosols from space,” in Atmospheric Propagation and Remote Sensing II, A. Kohnle, W. B. Miller, eds., Proc. SPIE1968, 533–544 (1968).

B. Pflug, “Atmospheric transmission in the O2A-band: comparison of calculations and measurements,” presented at the Atmospheric Spectroscopy Applications Workshop, the University of Reims, Champagne, France, 8–10 September 1993.

A. Berk, L. S. Bernstein, D. C. Robertson, “modtran: A moderate resolution model for lowtran-7,” (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1989).

R. G. Isaacs, S. A. Clough, R. D. Warsham, J. L. Moncet, B. L. Lindner, L. D. Kaplan, “Path characterisation algorithm for fascode,” (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1990).

F. X. Kneizys, E. P. Shettle, L. W. Abreu, J. H. Chetwind, G. P. Andreson, W. O. Gallery, J. E. A. Selby, S. A. Clough, “Users guide to lowtran 7,” (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1988).

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Tables (5)

Tables Icon

Table 1 Parameters That Characterize Retrieval Scheme Performance in the Lower Atmosphere (23–50-km Meteorological Range Transition) As a Function of Available Measurements within the Oxygen Absorption A Band

Tables Icon

Table 2 Parameters That Characterize Retrieval Scheme Performance in the Lower Atmosphere (23–50-km Meteorological Range Transition) As a Function of Measurements Outside Molecular Absorption Bandsa

Tables Icon

Table 3 Parameters That Characterize Retrieval Scheme Performance in the Lower Atmosphere (23–50-km Meteorological Range Transition) Mixing Measurements Both Inside and Outside the Oxygen Absorption A Band

Tables Icon

Table 4 Parameters That Characterize Retrieval Scheme Performance in the Stratosphere Mixing Measurements Both Inside and Outside the Oxygen Absorption A Band

Tables Icon

Table 5 Parameters That Characterize Retrieval Scheme Performance in the Stratosphere As a Function of Measurements Outside Molecular Absorption Bandsa

Equations (10)

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

δω0APAω0APA  1,
δLλ, γ=0 Wλ, γ; zδαAzdz,
gλ, γ=0 Kλ, γ; zfzdz,
l 0 δαAξdξ= 1,  δτAzτAz  1,
g=Af.
g+dg=Af,
fe=AtA+ζH-1Atg+dg.
Ξ=AtA+ζH-1Atg+dg-f, Ψ=AtA+ζH-1Atg-f
λi  dgf2
χill=df/fdg/gcondA=A A-1.

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