Abstract

Several approaches to the solution of the radiative transfer equation assume either Curtis–Godson average or linear change of the source function across grid segments. When such solutions are used for calculating limb radiances, the peak radiance response to the source function perturbation at tangent point i is displaced down to the tangent point i+1. This effect is explained through a geometric argument. Temperature profile retrievals performed by applying the ratio of signals at level i+1 for correcting temperature at level i demonstrate dramatic convergence acceleration of the iterative relaxation scheme.

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References

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  1. J. C. Gille and F. B. House, “On the inversion of limb radiance measurements 1: temperature and thickness,” J. Atmos. Sci. 28, 1427–1442 (1971).
    [CrossRef]
  2. J. C. Gille and P. L. Bailey, “Inversion of infrared limb emission measurements for temperature and trace gas concentrations,” in International Interactive Workshop on Inversion Methods in Atmospheric Remote Sensing, (Academic, 1977) pp. 195–216.
  3. J. M. Russell III, M. G. Mlynczak, L. L. Gordley, J. Tansock, and R. Esplin, “An overview of the SABER experiment and preliminary calibration results,” Proc. SPIE Int. Soc. Opt. Eng. 3756, 277–288 (1999).
  4. C. J. Mertens, M. G. Mlynczak, M. López-Puertas, P. P. Wintersteiner, R. H. Picard, J. R. Winick, L. L. Gordley, and J. M. Russell III, “Retrieval of mesospheric and lower thermospheric kinetic temperature from measurements of CO215 μm Earth limb emission under non-LTE conditions,” Geophys. Res. Lett. 28, 1391–1394 (2001).
    [CrossRef]
  5. A. A. Kutepov, O. A. Gusev, and V. P Ogibalov, “Solution of the non-LTE problem for molecular gas in planetary atmospheres: Superiority of accelerated lambda iteration,” J. Quant. Spectrosc. Radiat. Transfer 60, 199–220 (1998).
    [CrossRef]
  6. O. A. Gusev and A. A. Kutepov, “Non-LTE gas in planetary atmospheres,” in Stellar Atmosphere Modeling, I.Hubeny, D.Mihalas, and K. Werner, eds., Vol. 288 in ASP Conference Series (ASP, 2003), pp. 318–331.
  7. O. Gusev, “Non-LTE diagnostics of the infrared observations of the planetary atmosphere,” Ph. D. thesis (Ludwig-Maximilians University, Munchen, 2002).
  8. G. L. Olson and B. P. Kunasz, “Short characteristic solution of the non-LTE line transfer problem by operator perturbation I. The one dimensional planar slab,” J. Quant. Spectrosc. Radiat. Transfer 39, 325–336 (1987).
    [CrossRef]
  9. D. Mihalas, Stellar Atmospheres (Freeman, 1978).
  10. J. I. Castor, P. G. Dykema, and R. I. Klein, “A new scheme for multidimensional line transfer. II—ETLA method in one dimension with application to iron K-alpha lines,” Astrophys. J. 387, 561–571 (1992).
    [CrossRef]
  11. E. Griffioen and L. Oikarinen, “LIMBTRAN: A pseudo three-dimensional radiative transfer model for the limb viewing imager OSIRIS on the ODIN satellite,” J. Geophys. Res. 105, 29717–29730 (2000).
    [CrossRef]
  12. J. M. Russell III and S. R. Drayson, “The inference of atmospheric ozone using satellite horizon measurements in the 1042 cm−1 band,” J. Atmos. Sci. 29, –(1971).
  13. M. Carlotti, “Global-fit approach to the analysis of limb-scanning atmospheric measurements,” Appl. Opt. 27, 3250–3254 (1988).
    [CrossRef] [PubMed]
  14. O. A. Gusev, M. Kaufmann, K.-U. Grossmann, F. J. Schmidlin, and M. G. Shepherd, “Atmospheric neutral temperature distribution at the mesopause altitude,” J. Atmos. Sol. Terr. Phys. 68, 1684–1697 (2006).
    [CrossRef]
  15. M. López-Puertas and F. W. Taylor, Non-LTE Radiative Transfer in the Atmosphere (World Scientific, 2001).
    [CrossRef]

2006 (1)

O. A. Gusev, M. Kaufmann, K.-U. Grossmann, F. J. Schmidlin, and M. G. Shepherd, “Atmospheric neutral temperature distribution at the mesopause altitude,” J. Atmos. Sol. Terr. Phys. 68, 1684–1697 (2006).
[CrossRef]

2001 (1)

C. J. Mertens, M. G. Mlynczak, M. López-Puertas, P. P. Wintersteiner, R. H. Picard, J. R. Winick, L. L. Gordley, and J. M. Russell III, “Retrieval of mesospheric and lower thermospheric kinetic temperature from measurements of CO215 μm Earth limb emission under non-LTE conditions,” Geophys. Res. Lett. 28, 1391–1394 (2001).
[CrossRef]

2000 (1)

E. Griffioen and L. Oikarinen, “LIMBTRAN: A pseudo three-dimensional radiative transfer model for the limb viewing imager OSIRIS on the ODIN satellite,” J. Geophys. Res. 105, 29717–29730 (2000).
[CrossRef]

1999 (1)

J. M. Russell III, M. G. Mlynczak, L. L. Gordley, J. Tansock, and R. Esplin, “An overview of the SABER experiment and preliminary calibration results,” Proc. SPIE Int. Soc. Opt. Eng. 3756, 277–288 (1999).

1998 (1)

A. A. Kutepov, O. A. Gusev, and V. P Ogibalov, “Solution of the non-LTE problem for molecular gas in planetary atmospheres: Superiority of accelerated lambda iteration,” J. Quant. Spectrosc. Radiat. Transfer 60, 199–220 (1998).
[CrossRef]

1992 (1)

J. I. Castor, P. G. Dykema, and R. I. Klein, “A new scheme for multidimensional line transfer. II—ETLA method in one dimension with application to iron K-alpha lines,” Astrophys. J. 387, 561–571 (1992).
[CrossRef]

1988 (1)

1987 (1)

G. L. Olson and B. P. Kunasz, “Short characteristic solution of the non-LTE line transfer problem by operator perturbation I. The one dimensional planar slab,” J. Quant. Spectrosc. Radiat. Transfer 39, 325–336 (1987).
[CrossRef]

1971 (2)

J. C. Gille and F. B. House, “On the inversion of limb radiance measurements 1: temperature and thickness,” J. Atmos. Sci. 28, 1427–1442 (1971).
[CrossRef]

J. M. Russell III and S. R. Drayson, “The inference of atmospheric ozone using satellite horizon measurements in the 1042 cm−1 band,” J. Atmos. Sci. 29, –(1971).

Bailey, P. C.

J. C. Gille and P. L. Bailey, “Inversion of infrared limb emission measurements for temperature and trace gas concentrations,” in International Interactive Workshop on Inversion Methods in Atmospheric Remote Sensing, (Academic, 1977) pp. 195–216.

Carlotti, M.

Castor, J. I.

J. I. Castor, P. G. Dykema, and R. I. Klein, “A new scheme for multidimensional line transfer. II—ETLA method in one dimension with application to iron K-alpha lines,” Astrophys. J. 387, 561–571 (1992).
[CrossRef]

Drayson, S. R.

J. M. Russell III and S. R. Drayson, “The inference of atmospheric ozone using satellite horizon measurements in the 1042 cm−1 band,” J. Atmos. Sci. 29, –(1971).

Dykema, P. G.

J. I. Castor, P. G. Dykema, and R. I. Klein, “A new scheme for multidimensional line transfer. II—ETLA method in one dimension with application to iron K-alpha lines,” Astrophys. J. 387, 561–571 (1992).
[CrossRef]

Esplin, R.

J. M. Russell III, M. G. Mlynczak, L. L. Gordley, J. Tansock, and R. Esplin, “An overview of the SABER experiment and preliminary calibration results,” Proc. SPIE Int. Soc. Opt. Eng. 3756, 277–288 (1999).

Gille, J. C.

J. C. Gille and F. B. House, “On the inversion of limb radiance measurements 1: temperature and thickness,” J. Atmos. Sci. 28, 1427–1442 (1971).
[CrossRef]

J. C. Gille and P. L. Bailey, “Inversion of infrared limb emission measurements for temperature and trace gas concentrations,” in International Interactive Workshop on Inversion Methods in Atmospheric Remote Sensing, (Academic, 1977) pp. 195–216.

Gordley, L. L.

C. J. Mertens, M. G. Mlynczak, M. López-Puertas, P. P. Wintersteiner, R. H. Picard, J. R. Winick, L. L. Gordley, and J. M. Russell III, “Retrieval of mesospheric and lower thermospheric kinetic temperature from measurements of CO215 μm Earth limb emission under non-LTE conditions,” Geophys. Res. Lett. 28, 1391–1394 (2001).
[CrossRef]

J. M. Russell III, M. G. Mlynczak, L. L. Gordley, J. Tansock, and R. Esplin, “An overview of the SABER experiment and preliminary calibration results,” Proc. SPIE Int. Soc. Opt. Eng. 3756, 277–288 (1999).

Griffioen, E.

E. Griffioen and L. Oikarinen, “LIMBTRAN: A pseudo three-dimensional radiative transfer model for the limb viewing imager OSIRIS on the ODIN satellite,” J. Geophys. Res. 105, 29717–29730 (2000).
[CrossRef]

Grossmann, K.-U.

O. A. Gusev, M. Kaufmann, K.-U. Grossmann, F. J. Schmidlin, and M. G. Shepherd, “Atmospheric neutral temperature distribution at the mesopause altitude,” J. Atmos. Sol. Terr. Phys. 68, 1684–1697 (2006).
[CrossRef]

Gusev, O.

O. Gusev, “Non-LTE diagnostics of the infrared observations of the planetary atmosphere,” Ph. D. thesis (Ludwig-Maximilians University, Munchen, 2002).

Gusev, O. A.

O. A. Gusev, M. Kaufmann, K.-U. Grossmann, F. J. Schmidlin, and M. G. Shepherd, “Atmospheric neutral temperature distribution at the mesopause altitude,” J. Atmos. Sol. Terr. Phys. 68, 1684–1697 (2006).
[CrossRef]

A. A. Kutepov, O. A. Gusev, and V. P Ogibalov, “Solution of the non-LTE problem for molecular gas in planetary atmospheres: Superiority of accelerated lambda iteration,” J. Quant. Spectrosc. Radiat. Transfer 60, 199–220 (1998).
[CrossRef]

O. A. Gusev and A. A. Kutepov, “Non-LTE gas in planetary atmospheres,” in Stellar Atmosphere Modeling, I.Hubeny, D.Mihalas, and K. Werner, eds., Vol. 288 in ASP Conference Series (ASP, 2003), pp. 318–331.

House, F. B.

J. C. Gille and F. B. House, “On the inversion of limb radiance measurements 1: temperature and thickness,” J. Atmos. Sci. 28, 1427–1442 (1971).
[CrossRef]

Kaufmann, M.

O. A. Gusev, M. Kaufmann, K.-U. Grossmann, F. J. Schmidlin, and M. G. Shepherd, “Atmospheric neutral temperature distribution at the mesopause altitude,” J. Atmos. Sol. Terr. Phys. 68, 1684–1697 (2006).
[CrossRef]

Klein, R. I.

J. I. Castor, P. G. Dykema, and R. I. Klein, “A new scheme for multidimensional line transfer. II—ETLA method in one dimension with application to iron K-alpha lines,” Astrophys. J. 387, 561–571 (1992).
[CrossRef]

Kunasz, B. P.

G. L. Olson and B. P. Kunasz, “Short characteristic solution of the non-LTE line transfer problem by operator perturbation I. The one dimensional planar slab,” J. Quant. Spectrosc. Radiat. Transfer 39, 325–336 (1987).
[CrossRef]

Kutepov, A. A.

A. A. Kutepov, O. A. Gusev, and V. P Ogibalov, “Solution of the non-LTE problem for molecular gas in planetary atmospheres: Superiority of accelerated lambda iteration,” J. Quant. Spectrosc. Radiat. Transfer 60, 199–220 (1998).
[CrossRef]

O. A. Gusev and A. A. Kutepov, “Non-LTE gas in planetary atmospheres,” in Stellar Atmosphere Modeling, I.Hubeny, D.Mihalas, and K. Werner, eds., Vol. 288 in ASP Conference Series (ASP, 2003), pp. 318–331.

López-Puertas, M.

C. J. Mertens, M. G. Mlynczak, M. López-Puertas, P. P. Wintersteiner, R. H. Picard, J. R. Winick, L. L. Gordley, and J. M. Russell III, “Retrieval of mesospheric and lower thermospheric kinetic temperature from measurements of CO215 μm Earth limb emission under non-LTE conditions,” Geophys. Res. Lett. 28, 1391–1394 (2001).
[CrossRef]

M. López-Puertas and F. W. Taylor, Non-LTE Radiative Transfer in the Atmosphere (World Scientific, 2001).
[CrossRef]

Mertens, C. J.

C. J. Mertens, M. G. Mlynczak, M. López-Puertas, P. P. Wintersteiner, R. H. Picard, J. R. Winick, L. L. Gordley, and J. M. Russell III, “Retrieval of mesospheric and lower thermospheric kinetic temperature from measurements of CO215 μm Earth limb emission under non-LTE conditions,” Geophys. Res. Lett. 28, 1391–1394 (2001).
[CrossRef]

Mihalas, D.

D. Mihalas, Stellar Atmospheres (Freeman, 1978).

Mlynczak, M. G.

C. J. Mertens, M. G. Mlynczak, M. López-Puertas, P. P. Wintersteiner, R. H. Picard, J. R. Winick, L. L. Gordley, and J. M. Russell III, “Retrieval of mesospheric and lower thermospheric kinetic temperature from measurements of CO215 μm Earth limb emission under non-LTE conditions,” Geophys. Res. Lett. 28, 1391–1394 (2001).
[CrossRef]

J. M. Russell III, M. G. Mlynczak, L. L. Gordley, J. Tansock, and R. Esplin, “An overview of the SABER experiment and preliminary calibration results,” Proc. SPIE Int. Soc. Opt. Eng. 3756, 277–288 (1999).

Ogibalov, V. P

A. A. Kutepov, O. A. Gusev, and V. P Ogibalov, “Solution of the non-LTE problem for molecular gas in planetary atmospheres: Superiority of accelerated lambda iteration,” J. Quant. Spectrosc. Radiat. Transfer 60, 199–220 (1998).
[CrossRef]

Oikarinen, L.

E. Griffioen and L. Oikarinen, “LIMBTRAN: A pseudo three-dimensional radiative transfer model for the limb viewing imager OSIRIS on the ODIN satellite,” J. Geophys. Res. 105, 29717–29730 (2000).
[CrossRef]

Olson, G. L.

G. L. Olson and B. P. Kunasz, “Short characteristic solution of the non-LTE line transfer problem by operator perturbation I. The one dimensional planar slab,” J. Quant. Spectrosc. Radiat. Transfer 39, 325–336 (1987).
[CrossRef]

Picard, R. H.

C. J. Mertens, M. G. Mlynczak, M. López-Puertas, P. P. Wintersteiner, R. H. Picard, J. R. Winick, L. L. Gordley, and J. M. Russell III, “Retrieval of mesospheric and lower thermospheric kinetic temperature from measurements of CO215 μm Earth limb emission under non-LTE conditions,” Geophys. Res. Lett. 28, 1391–1394 (2001).
[CrossRef]

Russell, J. M.

C. J. Mertens, M. G. Mlynczak, M. López-Puertas, P. P. Wintersteiner, R. H. Picard, J. R. Winick, L. L. Gordley, and J. M. Russell III, “Retrieval of mesospheric and lower thermospheric kinetic temperature from measurements of CO215 μm Earth limb emission under non-LTE conditions,” Geophys. Res. Lett. 28, 1391–1394 (2001).
[CrossRef]

J. M. Russell III, M. G. Mlynczak, L. L. Gordley, J. Tansock, and R. Esplin, “An overview of the SABER experiment and preliminary calibration results,” Proc. SPIE Int. Soc. Opt. Eng. 3756, 277–288 (1999).

J. M. Russell III and S. R. Drayson, “The inference of atmospheric ozone using satellite horizon measurements in the 1042 cm−1 band,” J. Atmos. Sci. 29, –(1971).

Schmidlin, F. J.

O. A. Gusev, M. Kaufmann, K.-U. Grossmann, F. J. Schmidlin, and M. G. Shepherd, “Atmospheric neutral temperature distribution at the mesopause altitude,” J. Atmos. Sol. Terr. Phys. 68, 1684–1697 (2006).
[CrossRef]

Shepherd, M. G.

O. A. Gusev, M. Kaufmann, K.-U. Grossmann, F. J. Schmidlin, and M. G. Shepherd, “Atmospheric neutral temperature distribution at the mesopause altitude,” J. Atmos. Sol. Terr. Phys. 68, 1684–1697 (2006).
[CrossRef]

Tansock, J.

J. M. Russell III, M. G. Mlynczak, L. L. Gordley, J. Tansock, and R. Esplin, “An overview of the SABER experiment and preliminary calibration results,” Proc. SPIE Int. Soc. Opt. Eng. 3756, 277–288 (1999).

Taylor, F. W.

M. López-Puertas and F. W. Taylor, Non-LTE Radiative Transfer in the Atmosphere (World Scientific, 2001).
[CrossRef]

Werner, K.

O. A. Gusev and A. A. Kutepov, “Non-LTE gas in planetary atmospheres,” in Stellar Atmosphere Modeling, I.Hubeny, D.Mihalas, and K. Werner, eds., Vol. 288 in ASP Conference Series (ASP, 2003), pp. 318–331.

Winick, J. R.

C. J. Mertens, M. G. Mlynczak, M. López-Puertas, P. P. Wintersteiner, R. H. Picard, J. R. Winick, L. L. Gordley, and J. M. Russell III, “Retrieval of mesospheric and lower thermospheric kinetic temperature from measurements of CO215 μm Earth limb emission under non-LTE conditions,” Geophys. Res. Lett. 28, 1391–1394 (2001).
[CrossRef]

Wintersteiner, P. P.

C. J. Mertens, M. G. Mlynczak, M. López-Puertas, P. P. Wintersteiner, R. H. Picard, J. R. Winick, L. L. Gordley, and J. M. Russell III, “Retrieval of mesospheric and lower thermospheric kinetic temperature from measurements of CO215 μm Earth limb emission under non-LTE conditions,” Geophys. Res. Lett. 28, 1391–1394 (2001).
[CrossRef]

Appl. Opt. (1)

Astrophys. J. (1)

J. I. Castor, P. G. Dykema, and R. I. Klein, “A new scheme for multidimensional line transfer. II—ETLA method in one dimension with application to iron K-alpha lines,” Astrophys. J. 387, 561–571 (1992).
[CrossRef]

Geophys. Res. Lett. (1)

C. J. Mertens, M. G. Mlynczak, M. López-Puertas, P. P. Wintersteiner, R. H. Picard, J. R. Winick, L. L. Gordley, and J. M. Russell III, “Retrieval of mesospheric and lower thermospheric kinetic temperature from measurements of CO215 μm Earth limb emission under non-LTE conditions,” Geophys. Res. Lett. 28, 1391–1394 (2001).
[CrossRef]

J. Atmos. Sci. (2)

J. C. Gille and F. B. House, “On the inversion of limb radiance measurements 1: temperature and thickness,” J. Atmos. Sci. 28, 1427–1442 (1971).
[CrossRef]

J. M. Russell III and S. R. Drayson, “The inference of atmospheric ozone using satellite horizon measurements in the 1042 cm−1 band,” J. Atmos. Sci. 29, –(1971).

J. Atmos. Sol. Terr. Phys. (1)

O. A. Gusev, M. Kaufmann, K.-U. Grossmann, F. J. Schmidlin, and M. G. Shepherd, “Atmospheric neutral temperature distribution at the mesopause altitude,” J. Atmos. Sol. Terr. Phys. 68, 1684–1697 (2006).
[CrossRef]

J. Geophys. Res. (1)

E. Griffioen and L. Oikarinen, “LIMBTRAN: A pseudo three-dimensional radiative transfer model for the limb viewing imager OSIRIS on the ODIN satellite,” J. Geophys. Res. 105, 29717–29730 (2000).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer (2)

G. L. Olson and B. P. Kunasz, “Short characteristic solution of the non-LTE line transfer problem by operator perturbation I. The one dimensional planar slab,” J. Quant. Spectrosc. Radiat. Transfer 39, 325–336 (1987).
[CrossRef]

A. A. Kutepov, O. A. Gusev, and V. P Ogibalov, “Solution of the non-LTE problem for molecular gas in planetary atmospheres: Superiority of accelerated lambda iteration,” J. Quant. Spectrosc. Radiat. Transfer 60, 199–220 (1998).
[CrossRef]

Proc. SPIE Int. Soc. Opt. Eng. (1)

J. M. Russell III, M. G. Mlynczak, L. L. Gordley, J. Tansock, and R. Esplin, “An overview of the SABER experiment and preliminary calibration results,” Proc. SPIE Int. Soc. Opt. Eng. 3756, 277–288 (1999).

Other (5)

M. López-Puertas and F. W. Taylor, Non-LTE Radiative Transfer in the Atmosphere (World Scientific, 2001).
[CrossRef]

O. A. Gusev and A. A. Kutepov, “Non-LTE gas in planetary atmospheres,” in Stellar Atmosphere Modeling, I.Hubeny, D.Mihalas, and K. Werner, eds., Vol. 288 in ASP Conference Series (ASP, 2003), pp. 318–331.

O. Gusev, “Non-LTE diagnostics of the infrared observations of the planetary atmosphere,” Ph. D. thesis (Ludwig-Maximilians University, Munchen, 2002).

D. Mihalas, Stellar Atmospheres (Freeman, 1978).

J. C. Gille and P. L. Bailey, “Inversion of infrared limb emission measurements for temperature and trace gas concentrations,” in International Interactive Workshop on Inversion Methods in Atmospheric Remote Sensing, (Academic, 1977) pp. 195–216.

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Figures (3)

Fig. 1
Fig. 1

(a) Vertical displacement of the peak radiance response to the T perturbation using a linear interpolation of the source function (solid curve). The dashed curve illustrates that no displacement takes place when the source function is presented as a step-function with a constant value for each shell equal to the value at the lower boundary. (b) Four Ch1 limb contribution functions for tangent heights 97, 98, 99, and 100 km .

Fig. 2
Fig. 2

Illustration of the geometrical argument. The strongest radiance sensitivity to the change of Δ T k at tangent layer, i, is experienced at tangent layer i + 1 . The numbers indicate the grid boundaries at which the source function and other atmospheric parameters are prescribed. See text for description.

Fig. 3
Fig. 3

Convergence curves for the T k retrieval. The number of iterations is on the horizontal axis and the sum of squared differences between calculated, I c , and measured, I m , radiances is on the vertical axis. The sum is taken over the entire retrieval altitude range of 65 120 km . See text for discussion.

Equations (1)

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I ( ν , h ) = ν d ν ϕ ( ν ) x d x S ( ν , x ) d t ( ν , x ) d x ,

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