Abstract

It is known that an infrared or a microwave remote-sensing equation is an integral equation of the first kind. As a result, it is ill-posed, the solution is unstable, and difficulties arise in its retrieval. To make the solution stable, either an a priori error covariance matrix or a smoothing factor γ is necessary as a constraint. However, if the error covariance matrix is not known or if it is estimated incorrectly, the solution will be suboptimal. The smoothing factor γ depends greatly on the observations, the observation error, the spectral coverage of channels, and the initial state or the first guess of the atmospheric profile. It is difficult to determine this factor properly during the retrieval procedure, so the factor is usually chosen empirically. We have developed a discrepancy principle (DP) to determine the γ in an objective way. An approach is formulated for achieving an optimal solution for the atmospheric profile together with the γ from satellite sounder observations. The DP method was applied to actual Geostationary Operational Environment Satellite (GOES-8) sounder data at the Southern Great Plains Cloud and Radiation Testbed site. Results show that the DP method yields a 21.7% improvement for low-level temperature and a 23.9% improvement for total precipitable water (TPW) retrievals compared with the traditional minimum-information method. The DP method is also compared with the Marquardt–Levenberg algorithm used in current operational GOES data processing. Results of the comparison show significant improvement, 6.5% for TPW and 11% for low-level water-vapor retrievals, in results obtained with the DP method compared with the Marquardt–Levenberg approach.

© 1999 Optical Society of America

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  1. H. H. Aumann, R. J. Pagano, “Atmospheric infrared sounder on the Earth Observing System,” Opt. Eng. 33, 776–784 (1994).
    [CrossRef]
  2. W. L. Smith, H. E. Revercomb, H. B. Howell, H. L. Huang, R. O. Knuteson, E. W. Koenig, D. D. LaPorte, S. Silverman, L. A. Sromovsky, H. W. Woolf, “GHIS—The GOES high-resolution interferometer sounder,” J. Appl. Meteorol. 29, 1189–1204 (1990).
    [CrossRef]
  3. C. D. Rodgers, “Retrieval of atmospheric temperature and composition from remote measurements of thermal radiation,” Rev. Geophys. Space Phys. 14, 609–624 (1976).
    [CrossRef]
  4. D. Q. Wark, H. E. Fleming, “Indirect measurements of atmospheric temperature profiles from satellites. I. Introduction,” Mon. Weather Rev. 94, 351–362 (1966).
    [CrossRef]
  5. S. Twomey, “On the numerical solution of the Fredholm integral equations of the first kind by inversion of the linear system produced by quadrature,” J. Assoc. Comput. Mach. 10, 79–101 (1963).
    [CrossRef]
  6. M. T. Chahine, “Determination of the temperature profile in an atmosphere from its outgoing radiance,” J. Opt. Soc. Am. 58, 1634–1637 (1968).
    [CrossRef]
  7. W. L. Smith, “Iterative solution of radiative transfer equation for the temperature and absorbing gas profile of an atmosphere,” Appl. Opt. 9, 1993–1999 (1970).
    [CrossRef] [PubMed]
  8. G. Bachus, F. Gilbert, “Uniqueness in the inversion of inaccurate gross earth data,” Phil. Trans. R. Soc. London Ser. A 266, 123–192 (1970).
    [CrossRef]
  9. M. T. Chahine, H. H. Aumann, M. Goldberg, E. Kalnay, L. McMillin, P. Rosenkranz, D. Staelin, L. Strow, W. Smith, J. Susskind, “AIRS-team unified retrieval for core products, algorithm theoretical basis document,” (Jet Propulsion Laboratory, National Aeronautics and Space Administration, Pasadena, Calif.1996).
  10. J. Susskind, J. Rosenfield, D. Reuter, M. T. Chahine, “Remote sensing of weather and climate parameters from HIRS2/MSU on TIROS-N,” J. Geophys. Res. 89, 4677–4697 (1984).
    [CrossRef]
  11. W. L. Smith, H. M. Woolf, C. M. Hayden, D. Q. Wark, L. M. McMillin, “TIROS-N operational vertical sounder,” Bull. Am. Meteorol. Soc. 60, 1177–1187 (1979).
  12. W. L. Smith, H. M. Woolf, C. M. Hayden, A. J. Schreiner, “The simultaneous export retrieval package,” presented at the 2nd International TOVS Study Conference, Igls, Austria, 18–22 February 1985 (Cooperative Institute for Meteorological Satellite Studies, University of Wisconsin–Madison, Madison, Wisc., 1985), pp. 224–253.
  13. C. M. Hayden, “GOES-VAS simultaneous temperature-moisture retrieval algorithm,” J. Appl. Meteorol. 27, 705–733 (1988).
    [CrossRef]
  14. J. Li, “Temperature and water vapor weighting functions from radiative transfer equation with surface emissivity and solar reflectivity,” Adv. Atmos. Sci. 11, 421–426 (1994).
    [CrossRef]
  15. V. A. Morozov, “On the solution of functional equation by the method of regularization,” Sov. Math. Dokl. 7, 414–417 (1966).
  16. W. L. Smith, H. M. Woolf, “The use of eigenvectors of statistical covariance matrices for interpreting satellite sounding radiometer observations,” J. Atmos. Sci. 33, 1127–1140 (1976).
    [CrossRef]
  17. W. P. Menzel, J. F. W. Purdom, “Introducing GOES-I: The first of a new generation of geostationary operational environmental satellites,” Bull. Am. Meteorol. Soc. 75, 757–781 (1994).
    [CrossRef]
  18. W. L. Smith, W. F. Feltz, R. O. Knuteson, H. E. Revercomb, H. M. Woolf, H. B. Howell, “The retrieval of planetary boundary layer structure using ground based infrared spectral radiance measurements,” J. Appl. Meteorol. (to be published).
  19. X. L. Ma, W. L. Smith, T. J. Schmit, “A non-linear physical retrieval algorithm—its application to the GOES-8/9 sounder,” J. Appl. Meteorol. (to be published).
  20. D. W. Marquardt, “An algorithm for least-squares estimation of nonlinear parameters,” J. Soc. Ind. Appl. Math. 11, 431–441 (1963).
    [CrossRef]
  21. K. Levenberg, “A method for the solution of certain non-linear problems in least squares,” Q. Appl. Math. 2, 2164–2168 (1944).

1994

J. Li, “Temperature and water vapor weighting functions from radiative transfer equation with surface emissivity and solar reflectivity,” Adv. Atmos. Sci. 11, 421–426 (1994).
[CrossRef]

W. P. Menzel, J. F. W. Purdom, “Introducing GOES-I: The first of a new generation of geostationary operational environmental satellites,” Bull. Am. Meteorol. Soc. 75, 757–781 (1994).
[CrossRef]

H. H. Aumann, R. J. Pagano, “Atmospheric infrared sounder on the Earth Observing System,” Opt. Eng. 33, 776–784 (1994).
[CrossRef]

1990

W. L. Smith, H. E. Revercomb, H. B. Howell, H. L. Huang, R. O. Knuteson, E. W. Koenig, D. D. LaPorte, S. Silverman, L. A. Sromovsky, H. W. Woolf, “GHIS—The GOES high-resolution interferometer sounder,” J. Appl. Meteorol. 29, 1189–1204 (1990).
[CrossRef]

1988

C. M. Hayden, “GOES-VAS simultaneous temperature-moisture retrieval algorithm,” J. Appl. Meteorol. 27, 705–733 (1988).
[CrossRef]

1984

J. Susskind, J. Rosenfield, D. Reuter, M. T. Chahine, “Remote sensing of weather and climate parameters from HIRS2/MSU on TIROS-N,” J. Geophys. Res. 89, 4677–4697 (1984).
[CrossRef]

1979

W. L. Smith, H. M. Woolf, C. M. Hayden, D. Q. Wark, L. M. McMillin, “TIROS-N operational vertical sounder,” Bull. Am. Meteorol. Soc. 60, 1177–1187 (1979).

1976

C. D. Rodgers, “Retrieval of atmospheric temperature and composition from remote measurements of thermal radiation,” Rev. Geophys. Space Phys. 14, 609–624 (1976).
[CrossRef]

W. L. Smith, H. M. Woolf, “The use of eigenvectors of statistical covariance matrices for interpreting satellite sounding radiometer observations,” J. Atmos. Sci. 33, 1127–1140 (1976).
[CrossRef]

1970

W. L. Smith, “Iterative solution of radiative transfer equation for the temperature and absorbing gas profile of an atmosphere,” Appl. Opt. 9, 1993–1999 (1970).
[CrossRef] [PubMed]

G. Bachus, F. Gilbert, “Uniqueness in the inversion of inaccurate gross earth data,” Phil. Trans. R. Soc. London Ser. A 266, 123–192 (1970).
[CrossRef]

1968

1966

D. Q. Wark, H. E. Fleming, “Indirect measurements of atmospheric temperature profiles from satellites. I. Introduction,” Mon. Weather Rev. 94, 351–362 (1966).
[CrossRef]

V. A. Morozov, “On the solution of functional equation by the method of regularization,” Sov. Math. Dokl. 7, 414–417 (1966).

1963

D. W. Marquardt, “An algorithm for least-squares estimation of nonlinear parameters,” J. Soc. Ind. Appl. Math. 11, 431–441 (1963).
[CrossRef]

S. Twomey, “On the numerical solution of the Fredholm integral equations of the first kind by inversion of the linear system produced by quadrature,” J. Assoc. Comput. Mach. 10, 79–101 (1963).
[CrossRef]

1944

K. Levenberg, “A method for the solution of certain non-linear problems in least squares,” Q. Appl. Math. 2, 2164–2168 (1944).

Aumann, H. H.

H. H. Aumann, R. J. Pagano, “Atmospheric infrared sounder on the Earth Observing System,” Opt. Eng. 33, 776–784 (1994).
[CrossRef]

M. T. Chahine, H. H. Aumann, M. Goldberg, E. Kalnay, L. McMillin, P. Rosenkranz, D. Staelin, L. Strow, W. Smith, J. Susskind, “AIRS-team unified retrieval for core products, algorithm theoretical basis document,” (Jet Propulsion Laboratory, National Aeronautics and Space Administration, Pasadena, Calif.1996).

Bachus, G.

G. Bachus, F. Gilbert, “Uniqueness in the inversion of inaccurate gross earth data,” Phil. Trans. R. Soc. London Ser. A 266, 123–192 (1970).
[CrossRef]

Chahine, M. T.

J. Susskind, J. Rosenfield, D. Reuter, M. T. Chahine, “Remote sensing of weather and climate parameters from HIRS2/MSU on TIROS-N,” J. Geophys. Res. 89, 4677–4697 (1984).
[CrossRef]

M. T. Chahine, “Determination of the temperature profile in an atmosphere from its outgoing radiance,” J. Opt. Soc. Am. 58, 1634–1637 (1968).
[CrossRef]

M. T. Chahine, H. H. Aumann, M. Goldberg, E. Kalnay, L. McMillin, P. Rosenkranz, D. Staelin, L. Strow, W. Smith, J. Susskind, “AIRS-team unified retrieval for core products, algorithm theoretical basis document,” (Jet Propulsion Laboratory, National Aeronautics and Space Administration, Pasadena, Calif.1996).

Feltz, W. F.

W. L. Smith, W. F. Feltz, R. O. Knuteson, H. E. Revercomb, H. M. Woolf, H. B. Howell, “The retrieval of planetary boundary layer structure using ground based infrared spectral radiance measurements,” J. Appl. Meteorol. (to be published).

Fleming, H. E.

D. Q. Wark, H. E. Fleming, “Indirect measurements of atmospheric temperature profiles from satellites. I. Introduction,” Mon. Weather Rev. 94, 351–362 (1966).
[CrossRef]

Gilbert, F.

G. Bachus, F. Gilbert, “Uniqueness in the inversion of inaccurate gross earth data,” Phil. Trans. R. Soc. London Ser. A 266, 123–192 (1970).
[CrossRef]

Goldberg, M.

M. T. Chahine, H. H. Aumann, M. Goldberg, E. Kalnay, L. McMillin, P. Rosenkranz, D. Staelin, L. Strow, W. Smith, J. Susskind, “AIRS-team unified retrieval for core products, algorithm theoretical basis document,” (Jet Propulsion Laboratory, National Aeronautics and Space Administration, Pasadena, Calif.1996).

Hayden, C. M.

C. M. Hayden, “GOES-VAS simultaneous temperature-moisture retrieval algorithm,” J. Appl. Meteorol. 27, 705–733 (1988).
[CrossRef]

W. L. Smith, H. M. Woolf, C. M. Hayden, D. Q. Wark, L. M. McMillin, “TIROS-N operational vertical sounder,” Bull. Am. Meteorol. Soc. 60, 1177–1187 (1979).

W. L. Smith, H. M. Woolf, C. M. Hayden, A. J. Schreiner, “The simultaneous export retrieval package,” presented at the 2nd International TOVS Study Conference, Igls, Austria, 18–22 February 1985 (Cooperative Institute for Meteorological Satellite Studies, University of Wisconsin–Madison, Madison, Wisc., 1985), pp. 224–253.

Howell, H. B.

W. L. Smith, H. E. Revercomb, H. B. Howell, H. L. Huang, R. O. Knuteson, E. W. Koenig, D. D. LaPorte, S. Silverman, L. A. Sromovsky, H. W. Woolf, “GHIS—The GOES high-resolution interferometer sounder,” J. Appl. Meteorol. 29, 1189–1204 (1990).
[CrossRef]

W. L. Smith, W. F. Feltz, R. O. Knuteson, H. E. Revercomb, H. M. Woolf, H. B. Howell, “The retrieval of planetary boundary layer structure using ground based infrared spectral radiance measurements,” J. Appl. Meteorol. (to be published).

Huang, H. L.

W. L. Smith, H. E. Revercomb, H. B. Howell, H. L. Huang, R. O. Knuteson, E. W. Koenig, D. D. LaPorte, S. Silverman, L. A. Sromovsky, H. W. Woolf, “GHIS—The GOES high-resolution interferometer sounder,” J. Appl. Meteorol. 29, 1189–1204 (1990).
[CrossRef]

Kalnay, E.

M. T. Chahine, H. H. Aumann, M. Goldberg, E. Kalnay, L. McMillin, P. Rosenkranz, D. Staelin, L. Strow, W. Smith, J. Susskind, “AIRS-team unified retrieval for core products, algorithm theoretical basis document,” (Jet Propulsion Laboratory, National Aeronautics and Space Administration, Pasadena, Calif.1996).

Knuteson, R. O.

W. L. Smith, H. E. Revercomb, H. B. Howell, H. L. Huang, R. O. Knuteson, E. W. Koenig, D. D. LaPorte, S. Silverman, L. A. Sromovsky, H. W. Woolf, “GHIS—The GOES high-resolution interferometer sounder,” J. Appl. Meteorol. 29, 1189–1204 (1990).
[CrossRef]

W. L. Smith, W. F. Feltz, R. O. Knuteson, H. E. Revercomb, H. M. Woolf, H. B. Howell, “The retrieval of planetary boundary layer structure using ground based infrared spectral radiance measurements,” J. Appl. Meteorol. (to be published).

Koenig, E. W.

W. L. Smith, H. E. Revercomb, H. B. Howell, H. L. Huang, R. O. Knuteson, E. W. Koenig, D. D. LaPorte, S. Silverman, L. A. Sromovsky, H. W. Woolf, “GHIS—The GOES high-resolution interferometer sounder,” J. Appl. Meteorol. 29, 1189–1204 (1990).
[CrossRef]

LaPorte, D. D.

W. L. Smith, H. E. Revercomb, H. B. Howell, H. L. Huang, R. O. Knuteson, E. W. Koenig, D. D. LaPorte, S. Silverman, L. A. Sromovsky, H. W. Woolf, “GHIS—The GOES high-resolution interferometer sounder,” J. Appl. Meteorol. 29, 1189–1204 (1990).
[CrossRef]

Levenberg, K.

K. Levenberg, “A method for the solution of certain non-linear problems in least squares,” Q. Appl. Math. 2, 2164–2168 (1944).

Li, J.

J. Li, “Temperature and water vapor weighting functions from radiative transfer equation with surface emissivity and solar reflectivity,” Adv. Atmos. Sci. 11, 421–426 (1994).
[CrossRef]

Ma, X. L.

X. L. Ma, W. L. Smith, T. J. Schmit, “A non-linear physical retrieval algorithm—its application to the GOES-8/9 sounder,” J. Appl. Meteorol. (to be published).

Marquardt, D. W.

D. W. Marquardt, “An algorithm for least-squares estimation of nonlinear parameters,” J. Soc. Ind. Appl. Math. 11, 431–441 (1963).
[CrossRef]

McMillin, L.

M. T. Chahine, H. H. Aumann, M. Goldberg, E. Kalnay, L. McMillin, P. Rosenkranz, D. Staelin, L. Strow, W. Smith, J. Susskind, “AIRS-team unified retrieval for core products, algorithm theoretical basis document,” (Jet Propulsion Laboratory, National Aeronautics and Space Administration, Pasadena, Calif.1996).

McMillin, L. M.

W. L. Smith, H. M. Woolf, C. M. Hayden, D. Q. Wark, L. M. McMillin, “TIROS-N operational vertical sounder,” Bull. Am. Meteorol. Soc. 60, 1177–1187 (1979).

Menzel, W. P.

W. P. Menzel, J. F. W. Purdom, “Introducing GOES-I: The first of a new generation of geostationary operational environmental satellites,” Bull. Am. Meteorol. Soc. 75, 757–781 (1994).
[CrossRef]

Morozov, V. A.

V. A. Morozov, “On the solution of functional equation by the method of regularization,” Sov. Math. Dokl. 7, 414–417 (1966).

Pagano, R. J.

H. H. Aumann, R. J. Pagano, “Atmospheric infrared sounder on the Earth Observing System,” Opt. Eng. 33, 776–784 (1994).
[CrossRef]

Purdom, J. F. W.

W. P. Menzel, J. F. W. Purdom, “Introducing GOES-I: The first of a new generation of geostationary operational environmental satellites,” Bull. Am. Meteorol. Soc. 75, 757–781 (1994).
[CrossRef]

Reuter, D.

J. Susskind, J. Rosenfield, D. Reuter, M. T. Chahine, “Remote sensing of weather and climate parameters from HIRS2/MSU on TIROS-N,” J. Geophys. Res. 89, 4677–4697 (1984).
[CrossRef]

Revercomb, H. E.

W. L. Smith, H. E. Revercomb, H. B. Howell, H. L. Huang, R. O. Knuteson, E. W. Koenig, D. D. LaPorte, S. Silverman, L. A. Sromovsky, H. W. Woolf, “GHIS—The GOES high-resolution interferometer sounder,” J. Appl. Meteorol. 29, 1189–1204 (1990).
[CrossRef]

W. L. Smith, W. F. Feltz, R. O. Knuteson, H. E. Revercomb, H. M. Woolf, H. B. Howell, “The retrieval of planetary boundary layer structure using ground based infrared spectral radiance measurements,” J. Appl. Meteorol. (to be published).

Rodgers, C. D.

C. D. Rodgers, “Retrieval of atmospheric temperature and composition from remote measurements of thermal radiation,” Rev. Geophys. Space Phys. 14, 609–624 (1976).
[CrossRef]

Rosenfield, J.

J. Susskind, J. Rosenfield, D. Reuter, M. T. Chahine, “Remote sensing of weather and climate parameters from HIRS2/MSU on TIROS-N,” J. Geophys. Res. 89, 4677–4697 (1984).
[CrossRef]

Rosenkranz, P.

M. T. Chahine, H. H. Aumann, M. Goldberg, E. Kalnay, L. McMillin, P. Rosenkranz, D. Staelin, L. Strow, W. Smith, J. Susskind, “AIRS-team unified retrieval for core products, algorithm theoretical basis document,” (Jet Propulsion Laboratory, National Aeronautics and Space Administration, Pasadena, Calif.1996).

Schmit, T. J.

X. L. Ma, W. L. Smith, T. J. Schmit, “A non-linear physical retrieval algorithm—its application to the GOES-8/9 sounder,” J. Appl. Meteorol. (to be published).

Schreiner, A. J.

W. L. Smith, H. M. Woolf, C. M. Hayden, A. J. Schreiner, “The simultaneous export retrieval package,” presented at the 2nd International TOVS Study Conference, Igls, Austria, 18–22 February 1985 (Cooperative Institute for Meteorological Satellite Studies, University of Wisconsin–Madison, Madison, Wisc., 1985), pp. 224–253.

Silverman, S.

W. L. Smith, H. E. Revercomb, H. B. Howell, H. L. Huang, R. O. Knuteson, E. W. Koenig, D. D. LaPorte, S. Silverman, L. A. Sromovsky, H. W. Woolf, “GHIS—The GOES high-resolution interferometer sounder,” J. Appl. Meteorol. 29, 1189–1204 (1990).
[CrossRef]

Smith, W.

M. T. Chahine, H. H. Aumann, M. Goldberg, E. Kalnay, L. McMillin, P. Rosenkranz, D. Staelin, L. Strow, W. Smith, J. Susskind, “AIRS-team unified retrieval for core products, algorithm theoretical basis document,” (Jet Propulsion Laboratory, National Aeronautics and Space Administration, Pasadena, Calif.1996).

Smith, W. L.

W. L. Smith, H. E. Revercomb, H. B. Howell, H. L. Huang, R. O. Knuteson, E. W. Koenig, D. D. LaPorte, S. Silverman, L. A. Sromovsky, H. W. Woolf, “GHIS—The GOES high-resolution interferometer sounder,” J. Appl. Meteorol. 29, 1189–1204 (1990).
[CrossRef]

W. L. Smith, H. M. Woolf, C. M. Hayden, D. Q. Wark, L. M. McMillin, “TIROS-N operational vertical sounder,” Bull. Am. Meteorol. Soc. 60, 1177–1187 (1979).

W. L. Smith, H. M. Woolf, “The use of eigenvectors of statistical covariance matrices for interpreting satellite sounding radiometer observations,” J. Atmos. Sci. 33, 1127–1140 (1976).
[CrossRef]

W. L. Smith, “Iterative solution of radiative transfer equation for the temperature and absorbing gas profile of an atmosphere,” Appl. Opt. 9, 1993–1999 (1970).
[CrossRef] [PubMed]

W. L. Smith, H. M. Woolf, C. M. Hayden, A. J. Schreiner, “The simultaneous export retrieval package,” presented at the 2nd International TOVS Study Conference, Igls, Austria, 18–22 February 1985 (Cooperative Institute for Meteorological Satellite Studies, University of Wisconsin–Madison, Madison, Wisc., 1985), pp. 224–253.

W. L. Smith, W. F. Feltz, R. O. Knuteson, H. E. Revercomb, H. M. Woolf, H. B. Howell, “The retrieval of planetary boundary layer structure using ground based infrared spectral radiance measurements,” J. Appl. Meteorol. (to be published).

X. L. Ma, W. L. Smith, T. J. Schmit, “A non-linear physical retrieval algorithm—its application to the GOES-8/9 sounder,” J. Appl. Meteorol. (to be published).

Sromovsky, L. A.

W. L. Smith, H. E. Revercomb, H. B. Howell, H. L. Huang, R. O. Knuteson, E. W. Koenig, D. D. LaPorte, S. Silverman, L. A. Sromovsky, H. W. Woolf, “GHIS—The GOES high-resolution interferometer sounder,” J. Appl. Meteorol. 29, 1189–1204 (1990).
[CrossRef]

Staelin, D.

M. T. Chahine, H. H. Aumann, M. Goldberg, E. Kalnay, L. McMillin, P. Rosenkranz, D. Staelin, L. Strow, W. Smith, J. Susskind, “AIRS-team unified retrieval for core products, algorithm theoretical basis document,” (Jet Propulsion Laboratory, National Aeronautics and Space Administration, Pasadena, Calif.1996).

Strow, L.

M. T. Chahine, H. H. Aumann, M. Goldberg, E. Kalnay, L. McMillin, P. Rosenkranz, D. Staelin, L. Strow, W. Smith, J. Susskind, “AIRS-team unified retrieval for core products, algorithm theoretical basis document,” (Jet Propulsion Laboratory, National Aeronautics and Space Administration, Pasadena, Calif.1996).

Susskind, J.

J. Susskind, J. Rosenfield, D. Reuter, M. T. Chahine, “Remote sensing of weather and climate parameters from HIRS2/MSU on TIROS-N,” J. Geophys. Res. 89, 4677–4697 (1984).
[CrossRef]

M. T. Chahine, H. H. Aumann, M. Goldberg, E. Kalnay, L. McMillin, P. Rosenkranz, D. Staelin, L. Strow, W. Smith, J. Susskind, “AIRS-team unified retrieval for core products, algorithm theoretical basis document,” (Jet Propulsion Laboratory, National Aeronautics and Space Administration, Pasadena, Calif.1996).

Twomey, S.

S. Twomey, “On the numerical solution of the Fredholm integral equations of the first kind by inversion of the linear system produced by quadrature,” J. Assoc. Comput. Mach. 10, 79–101 (1963).
[CrossRef]

Wark, D. Q.

W. L. Smith, H. M. Woolf, C. M. Hayden, D. Q. Wark, L. M. McMillin, “TIROS-N operational vertical sounder,” Bull. Am. Meteorol. Soc. 60, 1177–1187 (1979).

D. Q. Wark, H. E. Fleming, “Indirect measurements of atmospheric temperature profiles from satellites. I. Introduction,” Mon. Weather Rev. 94, 351–362 (1966).
[CrossRef]

Woolf, H. M.

W. L. Smith, H. M. Woolf, C. M. Hayden, D. Q. Wark, L. M. McMillin, “TIROS-N operational vertical sounder,” Bull. Am. Meteorol. Soc. 60, 1177–1187 (1979).

W. L. Smith, H. M. Woolf, “The use of eigenvectors of statistical covariance matrices for interpreting satellite sounding radiometer observations,” J. Atmos. Sci. 33, 1127–1140 (1976).
[CrossRef]

W. L. Smith, H. M. Woolf, C. M. Hayden, A. J. Schreiner, “The simultaneous export retrieval package,” presented at the 2nd International TOVS Study Conference, Igls, Austria, 18–22 February 1985 (Cooperative Institute for Meteorological Satellite Studies, University of Wisconsin–Madison, Madison, Wisc., 1985), pp. 224–253.

W. L. Smith, W. F. Feltz, R. O. Knuteson, H. E. Revercomb, H. M. Woolf, H. B. Howell, “The retrieval of planetary boundary layer structure using ground based infrared spectral radiance measurements,” J. Appl. Meteorol. (to be published).

Woolf, H. W.

W. L. Smith, H. E. Revercomb, H. B. Howell, H. L. Huang, R. O. Knuteson, E. W. Koenig, D. D. LaPorte, S. Silverman, L. A. Sromovsky, H. W. Woolf, “GHIS—The GOES high-resolution interferometer sounder,” J. Appl. Meteorol. 29, 1189–1204 (1990).
[CrossRef]

Adv. Atmos. Sci.

J. Li, “Temperature and water vapor weighting functions from radiative transfer equation with surface emissivity and solar reflectivity,” Adv. Atmos. Sci. 11, 421–426 (1994).
[CrossRef]

Appl. Opt.

Bull. Am. Meteorol. Soc.

W. L. Smith, H. M. Woolf, C. M. Hayden, D. Q. Wark, L. M. McMillin, “TIROS-N operational vertical sounder,” Bull. Am. Meteorol. Soc. 60, 1177–1187 (1979).

W. P. Menzel, J. F. W. Purdom, “Introducing GOES-I: The first of a new generation of geostationary operational environmental satellites,” Bull. Am. Meteorol. Soc. 75, 757–781 (1994).
[CrossRef]

J. Appl. Meteorol.

W. L. Smith, H. E. Revercomb, H. B. Howell, H. L. Huang, R. O. Knuteson, E. W. Koenig, D. D. LaPorte, S. Silverman, L. A. Sromovsky, H. W. Woolf, “GHIS—The GOES high-resolution interferometer sounder,” J. Appl. Meteorol. 29, 1189–1204 (1990).
[CrossRef]

C. M. Hayden, “GOES-VAS simultaneous temperature-moisture retrieval algorithm,” J. Appl. Meteorol. 27, 705–733 (1988).
[CrossRef]

J. Assoc. Comput. Mach.

S. Twomey, “On the numerical solution of the Fredholm integral equations of the first kind by inversion of the linear system produced by quadrature,” J. Assoc. Comput. Mach. 10, 79–101 (1963).
[CrossRef]

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W. L. Smith, H. M. Woolf, “The use of eigenvectors of statistical covariance matrices for interpreting satellite sounding radiometer observations,” J. Atmos. Sci. 33, 1127–1140 (1976).
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J. Susskind, J. Rosenfield, D. Reuter, M. T. Chahine, “Remote sensing of weather and climate parameters from HIRS2/MSU on TIROS-N,” J. Geophys. Res. 89, 4677–4697 (1984).
[CrossRef]

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[CrossRef]

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D. Q. Wark, H. E. Fleming, “Indirect measurements of atmospheric temperature profiles from satellites. I. Introduction,” Mon. Weather Rev. 94, 351–362 (1966).
[CrossRef]

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H. H. Aumann, R. J. Pagano, “Atmospheric infrared sounder on the Earth Observing System,” Opt. Eng. 33, 776–784 (1994).
[CrossRef]

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G. Bachus, F. Gilbert, “Uniqueness in the inversion of inaccurate gross earth data,” Phil. Trans. R. Soc. London Ser. A 266, 123–192 (1970).
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M. T. Chahine, H. H. Aumann, M. Goldberg, E. Kalnay, L. McMillin, P. Rosenkranz, D. Staelin, L. Strow, W. Smith, J. Susskind, “AIRS-team unified retrieval for core products, algorithm theoretical basis document,” (Jet Propulsion Laboratory, National Aeronautics and Space Administration, Pasadena, Calif.1996).

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W. L. Smith, W. F. Feltz, R. O. Knuteson, H. E. Revercomb, H. M. Woolf, H. B. Howell, “The retrieval of planetary boundary layer structure using ground based infrared spectral radiance measurements,” J. Appl. Meteorol. (to be published).

X. L. Ma, W. L. Smith, T. J. Schmit, “A non-linear physical retrieval algorithm—its application to the GOES-8/9 sounder,” J. Appl. Meteorol. (to be published).

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Figures (7)

Fig. 1
Fig. 1

Function G with respect to γ. D(X) = [F(X) - Y m ] T E -1[F(X) - Y m ].

Fig. 2
Fig. 2

Level-temperature RMSE distribution of all 56 retrievals from GOES-8 radiance measurements made at the CART site from 18 June to 17 July 1997 by the DP and the empirical MI methods.

Fig. 3
Fig. 3

Level relative humidity RMSE distribution of all 56 profiles from GOES-8 radiance measurements made at the CART site from 18 June to 17 July 1997 by the DP and the empirical MI methods.

Fig. 4
Fig. 4

Fifty-six γ retrievals, 800–1000-mbars mean-temperature errors, and TPW errors from GOES-8 radiance measurements based on the forecast first guess and made at the CART site from 18 June to 17 July 1997 by the DP method.

Fig. 5
Fig. 5

Plot of 800–1000-mbars mean-temperature error and TPW error from both MI and DP retrievals at the CART site.

Fig. 6
Fig. 6

Radiosonde temperature sounding and retrieved temperature profile from GOES-8 radiance measurements made at 12:00 UTC on 3 July 1997 at the CART site by the DP and the empirical MI methods.

Fig. 7
Fig. 7

Radiosonde dew-point temperature sounding and retrieved dew-point temperature profile from GOES-8 radiance measurements made at 12:00 UTC on 3 July 1997 at the CART site by the DP and the empirical MI methods.

Tables (2)

Tables Icon

Table 1 Instrument Noise for GOES-8

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Table 2 GOES-8 Retrievals versus Radiosonde Dataa

Equations (31)

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R=εBsτs-0ps Bdτ0, p+1-ε0ps Bdτp, ps+R,
Y=FX,
δY=FδX,
X=X0+FTE-1F+H-1FTE-1Ym-FX0,
Xγ=X0+FTE-1F+γI-1FTE-1Ym-FX0.
FXγ-Ym2=σ2,
FXγ-YmTE-1FXγ-Ym=N,
Gγ=FXγ-YmTE-1FXγ-Ym-N;
Gγ=0.
FX0-YmTE-1FX0-Ym-N>0.
γ=γ0-Gγ0Gγ0,
Gγ=2 dXγdγ FTE-1FXγ-Ym.
dXdγ=F0TE-1F0+γ0I-2F0TE-1FXγ0-Ym.
γ=γ0-FXγ0-YmTE-1FXγ0-Ym-N2FXγ0-YmTE-1F0F0TE-1F0+γ0I-2F0TE-1FXγ0-Ym.
γ0, X0Eq. 5γ0, X1γ0Eq. 14γ1, X1γ0Eq. 5γ1, X2γ1Eq. 14γ2, X2γ1  .
Xn+1=Xn+FnTE-1Fn+γnI-1FnTE-1Ym-FXn,
γn+1=γn-FXn+1-YmTE-1FXn+1-Ym-N2FXn+1-YmTE-1FnFnTE-1Fn+γnI-2FnTE-1FXn+1-Ym.
i=1L˜ λi=i=1L˜Ti2¯=σT2,
i=LT+1L˜ λiL˜ΔT2;
Xn-X0=ΦAn,
Φ=ΦT000Φq000ΦTs,
An+1=F˜nTE-1F˜n+γnI-1F˜nTE-1Ym-FAn,
γn+1=γn-FAn+1-YmTE-1FAn+1-Ym-N2FAn+1-YmTE-1F˜nF˜nTE-1F˜n+γnI-2F˜nTE-1FAn+1-Ym.
limγ Gγ=FX0-YmTE-1FX0-Ym-N>0.
limγ0 Gγ=-N<0.
FXγ-YmTE-1FXγ-Ym+γXγ-X0=Gγ+N+γΩγ.
γ2Ωγ1+Gγ1+Nγ2Ωγ2+Gγ2+Nγ1Ωγ2+Gγ2+Nγ1Ωγ1+Gγ1+N.
a=γ2Ωγ1+Gγ1+N,  b=γ2Ωγ2+Gγ2+N,  c=γ1Ωγ2+Gγ2+N, d=γ1Ωγ1+Gγ1+N,
abcd.
a-db-c  γ2-γ1Ωγ1γ2-γ1Ωγ2 Ωγ1Ωγ2,
cd  Gγ2Gγ1.

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