Abstract

An original methodology to account for aerosol and cirrus cloud contributions to reflected sunlight is described. This method can be applied to the problem of retrieving greenhouse gases from satellite-observed data and is based on the equivalence theorem with further parameterization of the photon path-length probability density function (PPDF). Monte Carlo simulation was used to validate this parameterization for a vertically nonhomogeneous atmosphere including an aerosol layer and cirrus clouds. Initial approximation suggests that the PPDF depends on four parameters that can be interpreted as the effective cloud height, cloud relative reflectance, and two additional factors to account for photon path-length distribution under the cloud. We demonstrate that these parameters can be efficiently retrieved from the nadir radiance measured in the oxygen A-band and from the H2O-saturated area of the CO2 2.0μm spectral band.

© 2007 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2006 (1)

R. Bennartz and R. Preusker, "Representation of the photon path-length distribution in a cloudy atmosphere using finite elements," J. Quant. Spectrosc. Radiat. Transfer 98, 202-219 (2006).
[CrossRef]

2004 (2)

M. J. Christi and G. L. Stephens, "Retrieving profiles of atmospheric CO2 in clear sky and in the presence of thin cloud using spectroscopy from the near- and thermal infrared: A preliminary case study," J. Geophys. Res. 109, D04316, doi: (2004).
[CrossRef]

D. Crisp, R. M. Atlas, F.-M. Breon, L. R. Brown, J. P. Burrows, P. Ciais, B. J. Connor, S. C. Doney, I. Y. Fung, D. J. Jacob, C. E. Miller, D. O'Brien, S. Pawson, J. T. Randerson, P. Rayner, R. J. Salawitch, S. P. Sander, B. Sen, G. L. Stephens, P. P. Tans, G. C. Toon, P. O. Wennberg, S. C. Wofsy, Y. L. Yung, Z. Kuang, B. Chudasama, G. Sprague, B. Weiss, R. Pollock, D. Kenyon, and S. Schroll, "The Orbiting Carbon Observatory (OCO) mission," Adv. Space Res. 34, 700-709 (2004).
[CrossRef]

2003 (4)

E. Dufour and F.-M. Breon, "Spaceborne estimate of atmospheric CO2 column by use of the differential absorption method: Error analysis," Appl. Opt. 42, 3595-3609 (2003).
[CrossRef] [PubMed]

R. K. Patra, S. Maksyutov, Y. Sasano, H. Nakajima, G. Inoue, and T. Nakazawa, "An evaluation of CO2 observation with solar occultation FTS for inclined-orbit satellite sensor for surface source inversion," J. Geophys. Res. 108, 4759, doi: (2003).
[CrossRef]

O. Jourdan, S. Oshchepkov, V. Shcherbakov, J.-F. Gayet, and H. Isaka, "Assessment of cloud optical parameters in the solar region: retrievals from airborne measurements of scattering phase functions," J. Geophys. Res. 108, 4572, doi: (2003).
[CrossRef]

L. S. Rothman, A. Barbe, D. C. Benner, L. R. Brown, C. Camy-Peyret, M. R. Carleer, K. Chance, C. Clerbaux, V. Dana, V. M. Devi, A. Fayt, J.-M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, K. W. Jucks, W. J. Lafferty, J.-Y. Mandin, S. T. Massie, V. Nemtchinov, D. A. Newnham, A. Perrin, C. P. Rinsland, J. Schroeder, K. M. Smith, M. A. H. Smith, K. Tang, R. A. Toth, J. Vander Auwera, P. Varanasi, and K. Yoshino, "The HITRAN molecular spectroscopic database: edition of 2000 including updates through 2001," J. Quant Spectrosc. Radiat. Transfer 82, 5-44 (2003).
[CrossRef]

2002 (3)

Z. Kuang, J. Margolis, G. Toon, D. Crisp, and Y. Yung, "Spaceborne measurements of atmospheric CO2 by high-resolution NIR spectrometry of reflected sunlight: an introductory study," Geophys. Res. Lett. 29, 10.1029/2001GL014298 (2002).
[CrossRef]

D. M. O'Brien and P. J. Rayner, "Global observations of the carbon budget: II. CO2 column from differential absorption of reflected sunlight in the 1.61-μm band of CO2," J. Geophys. Res. 107, 4354, doi: (2002).
[CrossRef]

T. Aoki, T. Aoki, and M. Fukabori, "Path-radiance correction by polarization observation of Sun glint glitter for remote measurements of tropospheric greenhouse gases," Appl. Opt. 41, 4945-4957 (2002).
[CrossRef] [PubMed]

2001 (1)

P. J. Rayner and D. M. O'Brien, "The utility of remotely sensed CO2 concentration data in surface source inversions," Geophys. Res. Lett. 28, 175-178 (2001).
[CrossRef]

2000 (4)

M. Buchwitz, V. V. Rozanov, and J. P. Burrows "A near-infrared optimized DOAS method for the fast global retrieval of atmospheric CH4, CO, CO2, H2O, and N2O total column amounts from SCIAMACHY Envisat-1 nadir radiances," J. Geophys. Res. 105, 15231-15245 (2000).
[CrossRef]

A. K. Heidinger and G. L. Stephens, "Molecular line absorption in a scattering atmosphere. Part II: Application to remote sensing in the O2 A band," J. Atmos Sci. 57, 1615-1634 (2000).
[CrossRef]

P. T. Partain, A. K. Heidinger, and G. L. Stephens, "High spectral resolution atmospheric radiative transfer: application of the equivalence theorem," J. Geophys. Res. 105, 2163-2177 (2000).
[CrossRef]

G. L. Stephens and A. K. Heidinger, "Molecular line absorption in a scattering atmosphere. Part I: Theory," J. Atmos. Sci. 57, 1599-1614 (2000).
[CrossRef]

1998 (1)

K. Pfeilsticker, F. Erle, O. Funk, H. Veitel, and U. Platt, "First geometrical pathlengths probability density function derivation of the skylight from spectroscopically highly resolving oxygen a-band observations--1. Measurement technique, atmospheric observations, and model calculations," J. Geophys. Res. 103, 11483-11504 (1998).
[CrossRef]

1992 (1)

D. M. O'Brien and R. M. Mitchell, "Error estimates for retrieval of cloud-top pressure using absorption in the A band of oxygen," J. Appl. Meteorol. 31, 1179-1192 (1992).
[CrossRef]

1991 (1)

J. Fischer and H. Grassl, "Detection of cloud-top height from backscattered radiances within the oxygen A band. Part 1: Theoretical study," J. Appl. Meteorol. 30, 1245-1259 (1991).
[CrossRef]

1988 (1)

T. Nakajima and M. Tanaka, "Algorithms for radiative intensity calculations in moderately thick atmosphere using a truncation approximation," J. Quant Spectrosc. Radiat. Transfer 40, 51-69 (1988).
[CrossRef]

1987 (1)

R. M. Mitchell and D. M. O'Brien, "Error estimates for passive satellite measurements of surface pressure using absorption in the A band of oxygen," J. Atmos. Sci. 44, 1891-1991 (1987).
[CrossRef]

1980 (1)

J. B. Pollack and J. N. Cuzzi, "Scattering by nonspherical particles of size comparable to a wavelength: A new semi-empirical theory and its applications to tropospheric aerosols," J. Atmos. Sci. 37, 868-881 (1980).
[CrossRef]

Aoki, T.

Atlas, R. M.

D. Crisp, R. M. Atlas, F.-M. Breon, L. R. Brown, J. P. Burrows, P. Ciais, B. J. Connor, S. C. Doney, I. Y. Fung, D. J. Jacob, C. E. Miller, D. O'Brien, S. Pawson, J. T. Randerson, P. Rayner, R. J. Salawitch, S. P. Sander, B. Sen, G. L. Stephens, P. P. Tans, G. C. Toon, P. O. Wennberg, S. C. Wofsy, Y. L. Yung, Z. Kuang, B. Chudasama, G. Sprague, B. Weiss, R. Pollock, D. Kenyon, and S. Schroll, "The Orbiting Carbon Observatory (OCO) mission," Adv. Space Res. 34, 700-709 (2004).
[CrossRef]

Barbe, A.

L. S. Rothman, A. Barbe, D. C. Benner, L. R. Brown, C. Camy-Peyret, M. R. Carleer, K. Chance, C. Clerbaux, V. Dana, V. M. Devi, A. Fayt, J.-M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, K. W. Jucks, W. J. Lafferty, J.-Y. Mandin, S. T. Massie, V. Nemtchinov, D. A. Newnham, A. Perrin, C. P. Rinsland, J. Schroeder, K. M. Smith, M. A. H. Smith, K. Tang, R. A. Toth, J. Vander Auwera, P. Varanasi, and K. Yoshino, "The HITRAN molecular spectroscopic database: edition of 2000 including updates through 2001," J. Quant Spectrosc. Radiat. Transfer 82, 5-44 (2003).
[CrossRef]

Bennartz, R.

R. Bennartz and R. Preusker, "Representation of the photon path-length distribution in a cloudy atmosphere using finite elements," J. Quant. Spectrosc. Radiat. Transfer 98, 202-219 (2006).
[CrossRef]

Benner, D. C.

L. S. Rothman, A. Barbe, D. C. Benner, L. R. Brown, C. Camy-Peyret, M. R. Carleer, K. Chance, C. Clerbaux, V. Dana, V. M. Devi, A. Fayt, J.-M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, K. W. Jucks, W. J. Lafferty, J.-Y. Mandin, S. T. Massie, V. Nemtchinov, D. A. Newnham, A. Perrin, C. P. Rinsland, J. Schroeder, K. M. Smith, M. A. H. Smith, K. Tang, R. A. Toth, J. Vander Auwera, P. Varanasi, and K. Yoshino, "The HITRAN molecular spectroscopic database: edition of 2000 including updates through 2001," J. Quant Spectrosc. Radiat. Transfer 82, 5-44 (2003).
[CrossRef]

Breon, F.-M.

D. Crisp, R. M. Atlas, F.-M. Breon, L. R. Brown, J. P. Burrows, P. Ciais, B. J. Connor, S. C. Doney, I. Y. Fung, D. J. Jacob, C. E. Miller, D. O'Brien, S. Pawson, J. T. Randerson, P. Rayner, R. J. Salawitch, S. P. Sander, B. Sen, G. L. Stephens, P. P. Tans, G. C. Toon, P. O. Wennberg, S. C. Wofsy, Y. L. Yung, Z. Kuang, B. Chudasama, G. Sprague, B. Weiss, R. Pollock, D. Kenyon, and S. Schroll, "The Orbiting Carbon Observatory (OCO) mission," Adv. Space Res. 34, 700-709 (2004).
[CrossRef]

E. Dufour and F.-M. Breon, "Spaceborne estimate of atmospheric CO2 column by use of the differential absorption method: Error analysis," Appl. Opt. 42, 3595-3609 (2003).
[CrossRef] [PubMed]

Brown, L. R.

D. Crisp, R. M. Atlas, F.-M. Breon, L. R. Brown, J. P. Burrows, P. Ciais, B. J. Connor, S. C. Doney, I. Y. Fung, D. J. Jacob, C. E. Miller, D. O'Brien, S. Pawson, J. T. Randerson, P. Rayner, R. J. Salawitch, S. P. Sander, B. Sen, G. L. Stephens, P. P. Tans, G. C. Toon, P. O. Wennberg, S. C. Wofsy, Y. L. Yung, Z. Kuang, B. Chudasama, G. Sprague, B. Weiss, R. Pollock, D. Kenyon, and S. Schroll, "The Orbiting Carbon Observatory (OCO) mission," Adv. Space Res. 34, 700-709 (2004).
[CrossRef]

L. S. Rothman, A. Barbe, D. C. Benner, L. R. Brown, C. Camy-Peyret, M. R. Carleer, K. Chance, C. Clerbaux, V. Dana, V. M. Devi, A. Fayt, J.-M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, K. W. Jucks, W. J. Lafferty, J.-Y. Mandin, S. T. Massie, V. Nemtchinov, D. A. Newnham, A. Perrin, C. P. Rinsland, J. Schroeder, K. M. Smith, M. A. H. Smith, K. Tang, R. A. Toth, J. Vander Auwera, P. Varanasi, and K. Yoshino, "The HITRAN molecular spectroscopic database: edition of 2000 including updates through 2001," J. Quant Spectrosc. Radiat. Transfer 82, 5-44 (2003).
[CrossRef]

Buchwitz, M.

M. Buchwitz, V. V. Rozanov, and J. P. Burrows "A near-infrared optimized DOAS method for the fast global retrieval of atmospheric CH4, CO, CO2, H2O, and N2O total column amounts from SCIAMACHY Envisat-1 nadir radiances," J. Geophys. Res. 105, 15231-15245 (2000).
[CrossRef]

Burrows, J. P.

D. Crisp, R. M. Atlas, F.-M. Breon, L. R. Brown, J. P. Burrows, P. Ciais, B. J. Connor, S. C. Doney, I. Y. Fung, D. J. Jacob, C. E. Miller, D. O'Brien, S. Pawson, J. T. Randerson, P. Rayner, R. J. Salawitch, S. P. Sander, B. Sen, G. L. Stephens, P. P. Tans, G. C. Toon, P. O. Wennberg, S. C. Wofsy, Y. L. Yung, Z. Kuang, B. Chudasama, G. Sprague, B. Weiss, R. Pollock, D. Kenyon, and S. Schroll, "The Orbiting Carbon Observatory (OCO) mission," Adv. Space Res. 34, 700-709 (2004).
[CrossRef]

M. Buchwitz, V. V. Rozanov, and J. P. Burrows "A near-infrared optimized DOAS method for the fast global retrieval of atmospheric CH4, CO, CO2, H2O, and N2O total column amounts from SCIAMACHY Envisat-1 nadir radiances," J. Geophys. Res. 105, 15231-15245 (2000).
[CrossRef]

Camy-Peyret, C.

L. S. Rothman, A. Barbe, D. C. Benner, L. R. Brown, C. Camy-Peyret, M. R. Carleer, K. Chance, C. Clerbaux, V. Dana, V. M. Devi, A. Fayt, J.-M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, K. W. Jucks, W. J. Lafferty, J.-Y. Mandin, S. T. Massie, V. Nemtchinov, D. A. Newnham, A. Perrin, C. P. Rinsland, J. Schroeder, K. M. Smith, M. A. H. Smith, K. Tang, R. A. Toth, J. Vander Auwera, P. Varanasi, and K. Yoshino, "The HITRAN molecular spectroscopic database: edition of 2000 including updates through 2001," J. Quant Spectrosc. Radiat. Transfer 82, 5-44 (2003).
[CrossRef]

Carleer, M. R.

L. S. Rothman, A. Barbe, D. C. Benner, L. R. Brown, C. Camy-Peyret, M. R. Carleer, K. Chance, C. Clerbaux, V. Dana, V. M. Devi, A. Fayt, J.-M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, K. W. Jucks, W. J. Lafferty, J.-Y. Mandin, S. T. Massie, V. Nemtchinov, D. A. Newnham, A. Perrin, C. P. Rinsland, J. Schroeder, K. M. Smith, M. A. H. Smith, K. Tang, R. A. Toth, J. Vander Auwera, P. Varanasi, and K. Yoshino, "The HITRAN molecular spectroscopic database: edition of 2000 including updates through 2001," J. Quant Spectrosc. Radiat. Transfer 82, 5-44 (2003).
[CrossRef]

Chance, K.

L. S. Rothman, A. Barbe, D. C. Benner, L. R. Brown, C. Camy-Peyret, M. R. Carleer, K. Chance, C. Clerbaux, V. Dana, V. M. Devi, A. Fayt, J.-M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, K. W. Jucks, W. J. Lafferty, J.-Y. Mandin, S. T. Massie, V. Nemtchinov, D. A. Newnham, A. Perrin, C. P. Rinsland, J. Schroeder, K. M. Smith, M. A. H. Smith, K. Tang, R. A. Toth, J. Vander Auwera, P. Varanasi, and K. Yoshino, "The HITRAN molecular spectroscopic database: edition of 2000 including updates through 2001," J. Quant Spectrosc. Radiat. Transfer 82, 5-44 (2003).
[CrossRef]

Christi, M. J.

M. J. Christi and G. L. Stephens, "Retrieving profiles of atmospheric CO2 in clear sky and in the presence of thin cloud using spectroscopy from the near- and thermal infrared: A preliminary case study," J. Geophys. Res. 109, D04316, doi: (2004).
[CrossRef]

Chudasama, B.

D. Crisp, R. M. Atlas, F.-M. Breon, L. R. Brown, J. P. Burrows, P. Ciais, B. J. Connor, S. C. Doney, I. Y. Fung, D. J. Jacob, C. E. Miller, D. O'Brien, S. Pawson, J. T. Randerson, P. Rayner, R. J. Salawitch, S. P. Sander, B. Sen, G. L. Stephens, P. P. Tans, G. C. Toon, P. O. Wennberg, S. C. Wofsy, Y. L. Yung, Z. Kuang, B. Chudasama, G. Sprague, B. Weiss, R. Pollock, D. Kenyon, and S. Schroll, "The Orbiting Carbon Observatory (OCO) mission," Adv. Space Res. 34, 700-709 (2004).
[CrossRef]

Ciais, P.

D. Crisp, R. M. Atlas, F.-M. Breon, L. R. Brown, J. P. Burrows, P. Ciais, B. J. Connor, S. C. Doney, I. Y. Fung, D. J. Jacob, C. E. Miller, D. O'Brien, S. Pawson, J. T. Randerson, P. Rayner, R. J. Salawitch, S. P. Sander, B. Sen, G. L. Stephens, P. P. Tans, G. C. Toon, P. O. Wennberg, S. C. Wofsy, Y. L. Yung, Z. Kuang, B. Chudasama, G. Sprague, B. Weiss, R. Pollock, D. Kenyon, and S. Schroll, "The Orbiting Carbon Observatory (OCO) mission," Adv. Space Res. 34, 700-709 (2004).
[CrossRef]

Clerbaux, C.

L. S. Rothman, A. Barbe, D. C. Benner, L. R. Brown, C. Camy-Peyret, M. R. Carleer, K. Chance, C. Clerbaux, V. Dana, V. M. Devi, A. Fayt, J.-M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, K. W. Jucks, W. J. Lafferty, J.-Y. Mandin, S. T. Massie, V. Nemtchinov, D. A. Newnham, A. Perrin, C. P. Rinsland, J. Schroeder, K. M. Smith, M. A. H. Smith, K. Tang, R. A. Toth, J. Vander Auwera, P. Varanasi, and K. Yoshino, "The HITRAN molecular spectroscopic database: edition of 2000 including updates through 2001," J. Quant Spectrosc. Radiat. Transfer 82, 5-44 (2003).
[CrossRef]

Connor, B. J.

D. Crisp, R. M. Atlas, F.-M. Breon, L. R. Brown, J. P. Burrows, P. Ciais, B. J. Connor, S. C. Doney, I. Y. Fung, D. J. Jacob, C. E. Miller, D. O'Brien, S. Pawson, J. T. Randerson, P. Rayner, R. J. Salawitch, S. P. Sander, B. Sen, G. L. Stephens, P. P. Tans, G. C. Toon, P. O. Wennberg, S. C. Wofsy, Y. L. Yung, Z. Kuang, B. Chudasama, G. Sprague, B. Weiss, R. Pollock, D. Kenyon, and S. Schroll, "The Orbiting Carbon Observatory (OCO) mission," Adv. Space Res. 34, 700-709 (2004).
[CrossRef]

Crisp, D.

D. Crisp, R. M. Atlas, F.-M. Breon, L. R. Brown, J. P. Burrows, P. Ciais, B. J. Connor, S. C. Doney, I. Y. Fung, D. J. Jacob, C. E. Miller, D. O'Brien, S. Pawson, J. T. Randerson, P. Rayner, R. J. Salawitch, S. P. Sander, B. Sen, G. L. Stephens, P. P. Tans, G. C. Toon, P. O. Wennberg, S. C. Wofsy, Y. L. Yung, Z. Kuang, B. Chudasama, G. Sprague, B. Weiss, R. Pollock, D. Kenyon, and S. Schroll, "The Orbiting Carbon Observatory (OCO) mission," Adv. Space Res. 34, 700-709 (2004).
[CrossRef]

Z. Kuang, J. Margolis, G. Toon, D. Crisp, and Y. Yung, "Spaceborne measurements of atmospheric CO2 by high-resolution NIR spectrometry of reflected sunlight: an introductory study," Geophys. Res. Lett. 29, 10.1029/2001GL014298 (2002).
[CrossRef]

Cuzzi, J. N.

J. B. Pollack and J. N. Cuzzi, "Scattering by nonspherical particles of size comparable to a wavelength: A new semi-empirical theory and its applications to tropospheric aerosols," J. Atmos. Sci. 37, 868-881 (1980).
[CrossRef]

d'Almeida, G. A.

G. A. d'Almeida, P. Koepke, and E. P. Shettle, Atmospheric Aerosols. Global Climatology and Radiative Characteristics (Deepak, 1991).

Dana, V.

L. S. Rothman, A. Barbe, D. C. Benner, L. R. Brown, C. Camy-Peyret, M. R. Carleer, K. Chance, C. Clerbaux, V. Dana, V. M. Devi, A. Fayt, J.-M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, K. W. Jucks, W. J. Lafferty, J.-Y. Mandin, S. T. Massie, V. Nemtchinov, D. A. Newnham, A. Perrin, C. P. Rinsland, J. Schroeder, K. M. Smith, M. A. H. Smith, K. Tang, R. A. Toth, J. Vander Auwera, P. Varanasi, and K. Yoshino, "The HITRAN molecular spectroscopic database: edition of 2000 including updates through 2001," J. Quant Spectrosc. Radiat. Transfer 82, 5-44 (2003).
[CrossRef]

Dennis, J. E.

J. E. Dennis and R. B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Prentice-Hall, 1983).

Devi, V. M.

L. S. Rothman, A. Barbe, D. C. Benner, L. R. Brown, C. Camy-Peyret, M. R. Carleer, K. Chance, C. Clerbaux, V. Dana, V. M. Devi, A. Fayt, J.-M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, K. W. Jucks, W. J. Lafferty, J.-Y. Mandin, S. T. Massie, V. Nemtchinov, D. A. Newnham, A. Perrin, C. P. Rinsland, J. Schroeder, K. M. Smith, M. A. H. Smith, K. Tang, R. A. Toth, J. Vander Auwera, P. Varanasi, and K. Yoshino, "The HITRAN molecular spectroscopic database: edition of 2000 including updates through 2001," J. Quant Spectrosc. Radiat. Transfer 82, 5-44 (2003).
[CrossRef]

Doney, S. C.

D. Crisp, R. M. Atlas, F.-M. Breon, L. R. Brown, J. P. Burrows, P. Ciais, B. J. Connor, S. C. Doney, I. Y. Fung, D. J. Jacob, C. E. Miller, D. O'Brien, S. Pawson, J. T. Randerson, P. Rayner, R. J. Salawitch, S. P. Sander, B. Sen, G. L. Stephens, P. P. Tans, G. C. Toon, P. O. Wennberg, S. C. Wofsy, Y. L. Yung, Z. Kuang, B. Chudasama, G. Sprague, B. Weiss, R. Pollock, D. Kenyon, and S. Schroll, "The Orbiting Carbon Observatory (OCO) mission," Adv. Space Res. 34, 700-709 (2004).
[CrossRef]

Dufour, E.

Erle, F.

K. Pfeilsticker, F. Erle, O. Funk, H. Veitel, and U. Platt, "First geometrical pathlengths probability density function derivation of the skylight from spectroscopically highly resolving oxygen a-band observations--1. Measurement technique, atmospheric observations, and model calculations," J. Geophys. Res. 103, 11483-11504 (1998).
[CrossRef]

Fayt, A.

L. S. Rothman, A. Barbe, D. C. Benner, L. R. Brown, C. Camy-Peyret, M. R. Carleer, K. Chance, C. Clerbaux, V. Dana, V. M. Devi, A. Fayt, J.-M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, K. W. Jucks, W. J. Lafferty, J.-Y. Mandin, S. T. Massie, V. Nemtchinov, D. A. Newnham, A. Perrin, C. P. Rinsland, J. Schroeder, K. M. Smith, M. A. H. Smith, K. Tang, R. A. Toth, J. Vander Auwera, P. Varanasi, and K. Yoshino, "The HITRAN molecular spectroscopic database: edition of 2000 including updates through 2001," J. Quant Spectrosc. Radiat. Transfer 82, 5-44 (2003).
[CrossRef]

Fenn, R. W.

R. A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Voltz, and J. S. Garing, Optical Properties of the Atmosphere, 3rd ed. (Environmental Research Paper 354, Air Force Cambridge Research Laboratory, Hanscom Air Force Base, 1971).

Fischer, J.

J. Fischer and H. Grassl, "Detection of cloud-top height from backscattered radiances within the oxygen A band. Part 1: Theoretical study," J. Appl. Meteorol. 30, 1245-1259 (1991).
[CrossRef]

Flaud, J.-M.

L. S. Rothman, A. Barbe, D. C. Benner, L. R. Brown, C. Camy-Peyret, M. R. Carleer, K. Chance, C. Clerbaux, V. Dana, V. M. Devi, A. Fayt, J.-M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, K. W. Jucks, W. J. Lafferty, J.-Y. Mandin, S. T. Massie, V. Nemtchinov, D. A. Newnham, A. Perrin, C. P. Rinsland, J. Schroeder, K. M. Smith, M. A. H. Smith, K. Tang, R. A. Toth, J. Vander Auwera, P. Varanasi, and K. Yoshino, "The HITRAN molecular spectroscopic database: edition of 2000 including updates through 2001," J. Quant Spectrosc. Radiat. Transfer 82, 5-44 (2003).
[CrossRef]

Fukabori, M.

Fung, I. Y.

D. Crisp, R. M. Atlas, F.-M. Breon, L. R. Brown, J. P. Burrows, P. Ciais, B. J. Connor, S. C. Doney, I. Y. Fung, D. J. Jacob, C. E. Miller, D. O'Brien, S. Pawson, J. T. Randerson, P. Rayner, R. J. Salawitch, S. P. Sander, B. Sen, G. L. Stephens, P. P. Tans, G. C. Toon, P. O. Wennberg, S. C. Wofsy, Y. L. Yung, Z. Kuang, B. Chudasama, G. Sprague, B. Weiss, R. Pollock, D. Kenyon, and S. Schroll, "The Orbiting Carbon Observatory (OCO) mission," Adv. Space Res. 34, 700-709 (2004).
[CrossRef]

Funk, O.

K. Pfeilsticker, F. Erle, O. Funk, H. Veitel, and U. Platt, "First geometrical pathlengths probability density function derivation of the skylight from spectroscopically highly resolving oxygen a-band observations--1. Measurement technique, atmospheric observations, and model calculations," J. Geophys. Res. 103, 11483-11504 (1998).
[CrossRef]

Gamache, R. R.

L. S. Rothman, A. Barbe, D. C. Benner, L. R. Brown, C. Camy-Peyret, M. R. Carleer, K. Chance, C. Clerbaux, V. Dana, V. M. Devi, A. Fayt, J.-M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, K. W. Jucks, W. J. Lafferty, J.-Y. Mandin, S. T. Massie, V. Nemtchinov, D. A. Newnham, A. Perrin, C. P. Rinsland, J. Schroeder, K. M. Smith, M. A. H. Smith, K. Tang, R. A. Toth, J. Vander Auwera, P. Varanasi, and K. Yoshino, "The HITRAN molecular spectroscopic database: edition of 2000 including updates through 2001," J. Quant Spectrosc. Radiat. Transfer 82, 5-44 (2003).
[CrossRef]

Garing, J. S.

R. A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Voltz, and J. S. Garing, Optical Properties of the Atmosphere, 3rd ed. (Environmental Research Paper 354, Air Force Cambridge Research Laboratory, Hanscom Air Force Base, 1971).

Gayet, J.-F.

O. Jourdan, S. Oshchepkov, V. Shcherbakov, J.-F. Gayet, and H. Isaka, "Assessment of cloud optical parameters in the solar region: retrievals from airborne measurements of scattering phase functions," J. Geophys. Res. 108, 4572, doi: (2003).
[CrossRef]

Goldman, A.

L. S. Rothman, A. Barbe, D. C. Benner, L. R. Brown, C. Camy-Peyret, M. R. Carleer, K. Chance, C. Clerbaux, V. Dana, V. M. Devi, A. Fayt, J.-M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, K. W. Jucks, W. J. Lafferty, J.-Y. Mandin, S. T. Massie, V. Nemtchinov, D. A. Newnham, A. Perrin, C. P. Rinsland, J. Schroeder, K. M. Smith, M. A. H. Smith, K. Tang, R. A. Toth, J. Vander Auwera, P. Varanasi, and K. Yoshino, "The HITRAN molecular spectroscopic database: edition of 2000 including updates through 2001," J. Quant Spectrosc. Radiat. Transfer 82, 5-44 (2003).
[CrossRef]

Grassl, H.

J. Fischer and H. Grassl, "Detection of cloud-top height from backscattered radiances within the oxygen A band. Part 1: Theoretical study," J. Appl. Meteorol. 30, 1245-1259 (1991).
[CrossRef]

Heidinger, A. K.

G. L. Stephens and A. K. Heidinger, "Molecular line absorption in a scattering atmosphere. Part I: Theory," J. Atmos. Sci. 57, 1599-1614 (2000).
[CrossRef]

P. T. Partain, A. K. Heidinger, and G. L. Stephens, "High spectral resolution atmospheric radiative transfer: application of the equivalence theorem," J. Geophys. Res. 105, 2163-2177 (2000).
[CrossRef]

A. K. Heidinger and G. L. Stephens, "Molecular line absorption in a scattering atmosphere. Part II: Application to remote sensing in the O2 A band," J. Atmos Sci. 57, 1615-1634 (2000).
[CrossRef]

Inoue, G.

R. K. Patra, S. Maksyutov, Y. Sasano, H. Nakajima, G. Inoue, and T. Nakazawa, "An evaluation of CO2 observation with solar occultation FTS for inclined-orbit satellite sensor for surface source inversion," J. Geophys. Res. 108, 4759, doi: (2003).
[CrossRef]

T. Yokota, H. Oguma, I. Morino, and G. Inoue, "A nadir looking "SWIR" sensor to monitor CO2 column density for Japanese 'GOSAT' project," in Proceedings of the Twenty-Fourth International Symposium on Space Technology and Science (Japan Society for Aeronautical and Space Sciences and ISTS, Miyazaki, 2004), pp. 887-889.

Isaka, H.

O. Jourdan, S. Oshchepkov, V. Shcherbakov, J.-F. Gayet, and H. Isaka, "Assessment of cloud optical parameters in the solar region: retrievals from airborne measurements of scattering phase functions," J. Geophys. Res. 108, 4572, doi: (2003).
[CrossRef]

Jacob, D. J.

D. Crisp, R. M. Atlas, F.-M. Breon, L. R. Brown, J. P. Burrows, P. Ciais, B. J. Connor, S. C. Doney, I. Y. Fung, D. J. Jacob, C. E. Miller, D. O'Brien, S. Pawson, J. T. Randerson, P. Rayner, R. J. Salawitch, S. P. Sander, B. Sen, G. L. Stephens, P. P. Tans, G. C. Toon, P. O. Wennberg, S. C. Wofsy, Y. L. Yung, Z. Kuang, B. Chudasama, G. Sprague, B. Weiss, R. Pollock, D. Kenyon, and S. Schroll, "The Orbiting Carbon Observatory (OCO) mission," Adv. Space Res. 34, 700-709 (2004).
[CrossRef]

Jacquemart, D.

L. S. Rothman, A. Barbe, D. C. Benner, L. R. Brown, C. Camy-Peyret, M. R. Carleer, K. Chance, C. Clerbaux, V. Dana, V. M. Devi, A. Fayt, J.-M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, K. W. Jucks, W. J. Lafferty, J.-Y. Mandin, S. T. Massie, V. Nemtchinov, D. A. Newnham, A. Perrin, C. P. Rinsland, J. Schroeder, K. M. Smith, M. A. H. Smith, K. Tang, R. A. Toth, J. Vander Auwera, P. Varanasi, and K. Yoshino, "The HITRAN molecular spectroscopic database: edition of 2000 including updates through 2001," J. Quant Spectrosc. Radiat. Transfer 82, 5-44 (2003).
[CrossRef]

Jourdan, O.

O. Jourdan, S. Oshchepkov, V. Shcherbakov, J.-F. Gayet, and H. Isaka, "Assessment of cloud optical parameters in the solar region: retrievals from airborne measurements of scattering phase functions," J. Geophys. Res. 108, 4572, doi: (2003).
[CrossRef]

Jucks, K. W.

L. S. Rothman, A. Barbe, D. C. Benner, L. R. Brown, C. Camy-Peyret, M. R. Carleer, K. Chance, C. Clerbaux, V. Dana, V. M. Devi, A. Fayt, J.-M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, K. W. Jucks, W. J. Lafferty, J.-Y. Mandin, S. T. Massie, V. Nemtchinov, D. A. Newnham, A. Perrin, C. P. Rinsland, J. Schroeder, K. M. Smith, M. A. H. Smith, K. Tang, R. A. Toth, J. Vander Auwera, P. Varanasi, and K. Yoshino, "The HITRAN molecular spectroscopic database: edition of 2000 including updates through 2001," J. Quant Spectrosc. Radiat. Transfer 82, 5-44 (2003).
[CrossRef]

Kenyon, D.

D. Crisp, R. M. Atlas, F.-M. Breon, L. R. Brown, J. P. Burrows, P. Ciais, B. J. Connor, S. C. Doney, I. Y. Fung, D. J. Jacob, C. E. Miller, D. O'Brien, S. Pawson, J. T. Randerson, P. Rayner, R. J. Salawitch, S. P. Sander, B. Sen, G. L. Stephens, P. P. Tans, G. C. Toon, P. O. Wennberg, S. C. Wofsy, Y. L. Yung, Z. Kuang, B. Chudasama, G. Sprague, B. Weiss, R. Pollock, D. Kenyon, and S. Schroll, "The Orbiting Carbon Observatory (OCO) mission," Adv. Space Res. 34, 700-709 (2004).
[CrossRef]

Koepke, P.

G. A. d'Almeida, P. Koepke, and E. P. Shettle, Atmospheric Aerosols. Global Climatology and Radiative Characteristics (Deepak, 1991).

Kuang, Z.

D. Crisp, R. M. Atlas, F.-M. Breon, L. R. Brown, J. P. Burrows, P. Ciais, B. J. Connor, S. C. Doney, I. Y. Fung, D. J. Jacob, C. E. Miller, D. O'Brien, S. Pawson, J. T. Randerson, P. Rayner, R. J. Salawitch, S. P. Sander, B. Sen, G. L. Stephens, P. P. Tans, G. C. Toon, P. O. Wennberg, S. C. Wofsy, Y. L. Yung, Z. Kuang, B. Chudasama, G. Sprague, B. Weiss, R. Pollock, D. Kenyon, and S. Schroll, "The Orbiting Carbon Observatory (OCO) mission," Adv. Space Res. 34, 700-709 (2004).
[CrossRef]

Z. Kuang, J. Margolis, G. Toon, D. Crisp, and Y. Yung, "Spaceborne measurements of atmospheric CO2 by high-resolution NIR spectrometry of reflected sunlight: an introductory study," Geophys. Res. Lett. 29, 10.1029/2001GL014298 (2002).
[CrossRef]

Lafferty, W. J.

L. S. Rothman, A. Barbe, D. C. Benner, L. R. Brown, C. Camy-Peyret, M. R. Carleer, K. Chance, C. Clerbaux, V. Dana, V. M. Devi, A. Fayt, J.-M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, K. W. Jucks, W. J. Lafferty, J.-Y. Mandin, S. T. Massie, V. Nemtchinov, D. A. Newnham, A. Perrin, C. P. Rinsland, J. Schroeder, K. M. Smith, M. A. H. Smith, K. Tang, R. A. Toth, J. Vander Auwera, P. Varanasi, and K. Yoshino, "The HITRAN molecular spectroscopic database: edition of 2000 including updates through 2001," J. Quant Spectrosc. Radiat. Transfer 82, 5-44 (2003).
[CrossRef]

Maksyutov, S.

R. K. Patra, S. Maksyutov, Y. Sasano, H. Nakajima, G. Inoue, and T. Nakazawa, "An evaluation of CO2 observation with solar occultation FTS for inclined-orbit satellite sensor for surface source inversion," J. Geophys. Res. 108, 4759, doi: (2003).
[CrossRef]

Mandin, J.-Y.

L. S. Rothman, A. Barbe, D. C. Benner, L. R. Brown, C. Camy-Peyret, M. R. Carleer, K. Chance, C. Clerbaux, V. Dana, V. M. Devi, A. Fayt, J.-M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, K. W. Jucks, W. J. Lafferty, J.-Y. Mandin, S. T. Massie, V. Nemtchinov, D. A. Newnham, A. Perrin, C. P. Rinsland, J. Schroeder, K. M. Smith, M. A. H. Smith, K. Tang, R. A. Toth, J. Vander Auwera, P. Varanasi, and K. Yoshino, "The HITRAN molecular spectroscopic database: edition of 2000 including updates through 2001," J. Quant Spectrosc. Radiat. Transfer 82, 5-44 (2003).
[CrossRef]

Margolis, J.

Z. Kuang, J. Margolis, G. Toon, D. Crisp, and Y. Yung, "Spaceborne measurements of atmospheric CO2 by high-resolution NIR spectrometry of reflected sunlight: an introductory study," Geophys. Res. Lett. 29, 10.1029/2001GL014298 (2002).
[CrossRef]

Massie, S. T.

L. S. Rothman, A. Barbe, D. C. Benner, L. R. Brown, C. Camy-Peyret, M. R. Carleer, K. Chance, C. Clerbaux, V. Dana, V. M. Devi, A. Fayt, J.-M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, K. W. Jucks, W. J. Lafferty, J.-Y. Mandin, S. T. Massie, V. Nemtchinov, D. A. Newnham, A. Perrin, C. P. Rinsland, J. Schroeder, K. M. Smith, M. A. H. Smith, K. Tang, R. A. Toth, J. Vander Auwera, P. Varanasi, and K. Yoshino, "The HITRAN molecular spectroscopic database: edition of 2000 including updates through 2001," J. Quant Spectrosc. Radiat. Transfer 82, 5-44 (2003).
[CrossRef]

McClatchey, R. A.

R. A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Voltz, and J. S. Garing, Optical Properties of the Atmosphere, 3rd ed. (Environmental Research Paper 354, Air Force Cambridge Research Laboratory, Hanscom Air Force Base, 1971).

Miller, C. E.

D. Crisp, R. M. Atlas, F.-M. Breon, L. R. Brown, J. P. Burrows, P. Ciais, B. J. Connor, S. C. Doney, I. Y. Fung, D. J. Jacob, C. E. Miller, D. O'Brien, S. Pawson, J. T. Randerson, P. Rayner, R. J. Salawitch, S. P. Sander, B. Sen, G. L. Stephens, P. P. Tans, G. C. Toon, P. O. Wennberg, S. C. Wofsy, Y. L. Yung, Z. Kuang, B. Chudasama, G. Sprague, B. Weiss, R. Pollock, D. Kenyon, and S. Schroll, "The Orbiting Carbon Observatory (OCO) mission," Adv. Space Res. 34, 700-709 (2004).
[CrossRef]

Mitchell, R. M.

D. M. O'Brien and R. M. Mitchell, "Error estimates for retrieval of cloud-top pressure using absorption in the A band of oxygen," J. Appl. Meteorol. 31, 1179-1192 (1992).
[CrossRef]

R. M. Mitchell and D. M. O'Brien, "Error estimates for passive satellite measurements of surface pressure using absorption in the A band of oxygen," J. Atmos. Sci. 44, 1891-1991 (1987).
[CrossRef]

Morino, I.

T. Yokota, H. Oguma, I. Morino, and G. Inoue, "A nadir looking "SWIR" sensor to monitor CO2 column density for Japanese 'GOSAT' project," in Proceedings of the Twenty-Fourth International Symposium on Space Technology and Science (Japan Society for Aeronautical and Space Sciences and ISTS, Miyazaki, 2004), pp. 887-889.

Nakajima, H.

R. K. Patra, S. Maksyutov, Y. Sasano, H. Nakajima, G. Inoue, and T. Nakazawa, "An evaluation of CO2 observation with solar occultation FTS for inclined-orbit satellite sensor for surface source inversion," J. Geophys. Res. 108, 4759, doi: (2003).
[CrossRef]

Nakajima, T.

T. Nakajima and M. Tanaka, "Algorithms for radiative intensity calculations in moderately thick atmosphere using a truncation approximation," J. Quant Spectrosc. Radiat. Transfer 40, 51-69 (1988).
[CrossRef]

Nakazawa, T.

R. K. Patra, S. Maksyutov, Y. Sasano, H. Nakajima, G. Inoue, and T. Nakazawa, "An evaluation of CO2 observation with solar occultation FTS for inclined-orbit satellite sensor for surface source inversion," J. Geophys. Res. 108, 4759, doi: (2003).
[CrossRef]

Nemtchinov, V.

L. S. Rothman, A. Barbe, D. C. Benner, L. R. Brown, C. Camy-Peyret, M. R. Carleer, K. Chance, C. Clerbaux, V. Dana, V. M. Devi, A. Fayt, J.-M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, K. W. Jucks, W. J. Lafferty, J.-Y. Mandin, S. T. Massie, V. Nemtchinov, D. A. Newnham, A. Perrin, C. P. Rinsland, J. Schroeder, K. M. Smith, M. A. H. Smith, K. Tang, R. A. Toth, J. Vander Auwera, P. Varanasi, and K. Yoshino, "The HITRAN molecular spectroscopic database: edition of 2000 including updates through 2001," J. Quant Spectrosc. Radiat. Transfer 82, 5-44 (2003).
[CrossRef]

Newnham, D. A.

L. S. Rothman, A. Barbe, D. C. Benner, L. R. Brown, C. Camy-Peyret, M. R. Carleer, K. Chance, C. Clerbaux, V. Dana, V. M. Devi, A. Fayt, J.-M. Flaud, R. R. Gamache, A. Goldman, D. Jacquemart, K. W. Jucks, W. J. Lafferty, J.-Y. Mandin, S. T. Massie, V. Nemtchinov, D. A. Newnham, A. Perrin, C. P. Rinsland, J. Schroeder, K. M. Smith, M. A. H. Smith, K. Tang, R. A. Toth, J. Vander Auwera, P. Varanasi, and K. Yoshino, "The HITRAN molecular spectroscopic database: edition of 2000 including updates through 2001," J. Quant Spectrosc. Radiat. Transfer 82, 5-44 (2003).
[CrossRef]

O'Brien, D.

D. Crisp, R. M. Atlas, F.-M. Breon, L. R. Brown, J. P. Burrows, P. Ciais, B. J. Connor, S. C. Doney, I. Y. Fung, D. J. Jacob, C. E. Miller, D. O'Brien, S. Pawson, J. T. Randerson, P. Rayner, R. J. Salawitch, S. P. Sander, B. Sen, G. L. Stephens, P. P. Tans, G. C. Toon, P. O. Wennberg, S. C. Wofsy, Y. L. Yung, Z. Kuang, B. Chudasama, G. Sprague, B. Weiss, R. Pollock, D. Kenyon, and S. Schroll, "The Orbiting Carbon Observatory (OCO) mission," Adv. Space Res. 34, 700-709 (2004).
[CrossRef]

O'Brien, D. M.

D. M. O'Brien and P. J. Rayner, "Global observations of the carbon budget: II. CO2 column from differential absorption of reflected sunlight in the 1.61-μm band of CO2," J. Geophys. Res. 107, 4354, doi: (2002).
[CrossRef]

P. J. Rayner and D. M. O'Brien, "The utility of remotely sensed CO2 concentration data in surface source inversions," Geophys. Res. Lett. 28, 175-178 (2001).
[CrossRef]

D. M. O'Brien and R. M. Mitchell, "Error estimates for retrieval of cloud-top pressure using absorption in the A band of oxygen," J. Appl. Meteorol. 31, 1179-1192 (1992).
[CrossRef]

R. M. Mitchell and D. M. O'Brien, "Error estimates for passive satellite measurements of surface pressure using absorption in the A band of oxygen," J. Atmos. Sci. 44, 1891-1991 (1987).
[CrossRef]

Oguma, H.

T. Yokota, H. Oguma, I. Morino, and G. Inoue, "A nadir looking "SWIR" sensor to monitor CO2 column density for Japanese 'GOSAT' project," in Proceedings of the Twenty-Fourth International Symposium on Space Technology and Science (Japan Society for Aeronautical and Space Sciences and ISTS, Miyazaki, 2004), pp. 887-889.

Oshchepkov, S.

O. Jourdan, S. Oshchepkov, V. Shcherbakov, J.-F. Gayet, and H. Isaka, "Assessment of cloud optical parameters in the solar region: retrievals from airborne measurements of scattering phase functions," J. Geophys. Res. 108, 4572, doi: (2003).
[CrossRef]

Partain, P. T.

P. T. Partain, A. K. Heidinger, and G. L. Stephens, "High spectral resolution atmospheric radiative transfer: application of the equivalence theorem," J. Geophys. Res. 105, 2163-2177 (2000).
[CrossRef]

Patra, R. K.

R. K. Patra, S. Maksyutov, Y. Sasano, H. Nakajima, G. Inoue, and T. Nakazawa, "An evaluation of CO2 observation with solar occultation FTS for inclined-orbit satellite sensor for surface source inversion," J. Geophys. Res. 108, 4759, doi: (2003).
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Pawson, S.

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Figures (6)

Fig. 1
Fig. 1

Cirrus cloud scattering phase function at λ = 0.8   μm : (1) statistical data derived from in situ airborne measurements (Ref. [7]); (2) according to Pollack-Cuzzy approximation (Ref. [16]); (3) Henyey–Greenstein approximation with asymmetry parameter g = 0.75; (4) spherical particle approximation (Mie calculations).

Fig. 2
Fig. 2

Geometry of the problem for the modeled atmosphere. Solid lines show some important examples of light beams that traverse through the atmosphere and come to the satellite detector directly (red) and after interaction with the cloud (green and blue) due to single (solid lines) and double (dashed lines) light scattering. Some contributing photons have a zero path length under the cloud (dotted magenta lines), being scattered directly to the detector. Formulas for the path length and the structure of the PPDF in the insets are discussed in Subsection 3.D.

Fig. 3
Fig. 3

Photon path-length probability distributions for a 1 km thick sublayer under the cloud obtained with direct Monte Carlo simulation for two values of zenith angle (1) θ = 30 ° and (2) θ = 60 ° within the O 2 A-band at v = 12 , 980 cm 1 . Both aerosol and Rayleigh scattering are neglected in the model, and surface albedo Γ = 0.2 . Cirrus clouds are located between 11 and 12   km tangent heights with an optical thickness of τ = 0.5 .

Fig. 4
Fig. 4

Vertical profiles of PPDF parameters α (upper panels) and ρ (lower panels) produced by direct Monte Carlo simulations for channel 1 (left panels) and channel 3 (right panels). The atmosphere includes cirrus clouds between 11 and 12 km with an optical depth of τ = 0.5 and rural aerosol with an optical depth of τ = 0.2 . Calculations were performed for two values of the solar zenith angle, 30° and 60°, as well as with and without aerosol and Rayleigh scattering (insets in each panel).

Fig. 5
Fig. 5

PPDF parameters α (upper panel), ρ (middle panel), and h e (lower panel) retrieved from synthesized radiance data in the O 2 A-band as a function of the surface albedo for two values of cloud optical depth τ c and three values of aerosol optical depth τ a . Cirrus clouds are located between 8 and 9 km, and the solar zenith angle is 30°.

Fig. 6
Fig. 6

Residual according to Eq. (19) as a function of effective transmittance within the 2.0   μm band (4950 to 5050 cm 1 ) for two values of surface albedo, Γ = 0.2 (upper panel) and 0.1 (lower panel), at the solar zenith angle 60°. The atmosphere includes cirrus clouds between 11 and 12 km with optical depth τ = 0.5 and a model of rural aerosol with optical depth τ = 0.2 .

Tables (2)

Tables Icon

Table 1 PPDF Parameters a

Tables Icon

Table 2 PPDF Parameter α a

Equations (20)

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

I c i n i , i = 1 , 2 , , N ,
I v i n i T i , v ,
T i , v = exp ( k v L i ) ,
T e f f ( k v ) = I v / I c
T e f f ( k v ) = 0 exp ( k v L ) P ( L ) d L ,
T e f f ( k 1 , k 2 ,   . . . , k J ) = 0 0 d L 1 d L 2  .  .  .  d L J × exp ( k 1 L 1 k 2 L 2 . . . k J L J ) P ( L 1 , L 2 ,   . . . , L J ) .
T 1 = exp ( μ ¯ τ 1 ) ,
P ( L ) = P 1 ( L ) = α δ ( L ) + ( 1 α ) P 1 * ( L ) , z h e P 2 ( L ) = δ ( L L 2 G ) , h e < z H T O A ,
T e f f = α T 2 + ( 1 α ) T 1 T 2 ,
| L | k 1 1
T 1 = exp ( k 1 L 1 G ) L min L 1 G exp ( k 1 L ) P 1 * ( L ) d L exp ( k 1 L 1 G ) L min L 1 G ( 1 k 1 L ) P 1 * ( L ) d L = exp ( k 1 L 1 G ) ( 1 k 1 L ) exp [ k 1 ( L 1 G + L ) ] .
T 1 ( τ 1 ) = exp k 1 ( L 1 G + L τ ) ,
L τ = L exp ( γ τ 1 ) .
T e f f = C ( I v / I v * ) ( S v * / S v ) ,
C = exp [ ( 1 + μ ) τ ( v * ) ] .
T e f f MC ( v ) = 1 N n = 1 N Π j = 1 J exp [ k j ( v ) L n j ] ,
χ 2 = i = 1 M ω i [ T ˜ e f f * ( v i ) T ˜ e f f ( v i , α , ρ , γ , h e ) ] 2 ,
T e f f α T 2 ,
R ( v i ) = ω i 1 / 2 { T ˜ e f f * ( v i ) T ˜ e f f ( v i , α , ρ , γ , h e ) } × 100 % .
δ r ¯ = | Δ T e f f T e f f * 1 ln ( T e f f * ) | ,

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