Abstract

Building on the Markov chain formalism for scalar (intensity only) radiative transfer, this paper formulates the solution to polarized diffuse reflection from and transmission through a vertically inhomogeneous atmosphere. For verification, numerical results are compared to those obtained by the Monte Carlo method, showing deviations less than 1% when 90 streams are used to compute the radiation from two types of atmospheres, pure Rayleigh and Rayleigh plus aerosol, when they are divided into sublayers of optical thicknesses of less than 0.03.

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    [CrossRef]
  24. D. Crisp, R. Atlas, F. Breon, L. Brown, J. Burrows, P. Ciais, B. Connor, S. Doney, I. Fung, and D. Jacob, “The Orbiting Carbon Observatory (OCO) mission,” Adv. Space Res. 34(4), 700–709 (2004).
    [CrossRef]
  25. V. Natraj, R. J. D. Spurr, H. Boesch, Y. Jiang, and Y. Yung, “Evaluation of errors in neglecting polarization in the forward modeling of O2 A band measurements from space, with relevance to CO2 column retrieval from polarization sensitive instruments,” J. Quant. Spectrosc. Radiat. Transf. 103(2), 245–259 (2007).
    [CrossRef]
  26. V. Natraj and R. J. D. Spurr, “A fast linearized pseudo-spherical two orders of scattering model to account for polarization in vertically inhomogeneous scattering-absorbing media,” J. Quant. Spectrosc. Radiat. Transf. 107(2), 263–293 (2007).
    [CrossRef]

2010 (2)

A. A. Kokhanovsky, V. P. Budak, C. Cornet, M. Duan, C. Emde, I. L. Katsev, D. A. Klyukov, S. V. Korkin, L. C-Labonnote, and B. Mayer, “Benchmark results in vector atmospheric radiative transfer,” J. Quant. Spectrosc. Radiat. Transf. 111(12-13), 1931–1946 (2010).
[CrossRef]

A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, E. P. Zege, A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, and E. P. Zege, “The inter-comparison of major satellite aerosol retrieval algorithms using simulated intensity and polarization characteristics of reflected light,” Atm. Meas. Techn. 3, 909–932 (2010).
[CrossRef]

2009 (2)

2007 (3)

M. I. Mishchenko, B. Cairns, G. Kopp, C. F. Schueler, B. A. Fafaul, J. E. Hansen, R. J. Hooker, T. Itchkawich, H. B. Maring, and L. D. Travis, “Accurate monitoring of terrestrial aerosols and total solar irradiance: Introducing the Glory mission,” Bull. Am. Meteorol. Soc. 88(5), 677–691 (2007).
[CrossRef]

V. Natraj, R. J. D. Spurr, H. Boesch, Y. Jiang, and Y. Yung, “Evaluation of errors in neglecting polarization in the forward modeling of O2 A band measurements from space, with relevance to CO2 column retrieval from polarization sensitive instruments,” J. Quant. Spectrosc. Radiat. Transf. 103(2), 245–259 (2007).
[CrossRef]

V. Natraj and R. J. D. Spurr, “A fast linearized pseudo-spherical two orders of scattering model to account for polarization in vertically inhomogeneous scattering-absorbing media,” J. Quant. Spectrosc. Radiat. Transf. 107(2), 263–293 (2007).
[CrossRef]

2006 (2)

R. J. D. Spurr, “VLIDORT: A linearized pseudo-spherical vector discrete ordinate radiative transfer code for forward model and retrieval studies in multilayer multiple scattering media,” J. Quant. Spectrosc. Radiat. Transf. 102(2), 316–342 (2006).
[CrossRef]

S. Y. Kotchenova, E. F. Vermote, R. Matarrese, and F. J. Klemm., “Validation of a vector version of the 6S radiative transfer code for atmospheric correction of satellite data. Part I: path radiance,” Appl. Opt. 45(26), 6762–6774 (2006).
[CrossRef] [PubMed]

2004 (2)

D. Crisp, R. Atlas, F. Breon, L. Brown, J. Burrows, P. Ciais, B. Connor, S. Doney, I. Fung, and D. Jacob, “The Orbiting Carbon Observatory (OCO) mission,” Adv. Space Res. 34(4), 700–709 (2004).
[CrossRef]

Q. L. Min and M. Duan, “A successive order of scattering model for solving vector radiative transfer in the atmosphere,” J. Quant. Spectrosc. Radiat. Transf. 87(3-4), 243–259 (2004).
[CrossRef]

1999 (1)

F. M. Schulz, K. Stamnes, and F. Weng, “VDISORT, an improved and generalized discrete ordinate method for polarized (vector) radiative transfer,” J. Quant. Spectrosc. Radiat. Transf. 61(1), 105–122 (1999).
[CrossRef]

1998 (1)

D. J. Diner, J. C. Beckert, T. H. Reilly, C. J. Bruegge, J. E. Conel, R. A. Kahn, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, J. Muller, R. B. Myneni, P. J. Sellers, B. Pinty, and M. M. Verstraete, “Multi-angle Imaging Spectro-Radiometer (MISR) instrument description and experiment overview,” IEEE Trans. Geosci. Rem. Sens. 36(4), 1072–1087 (1998).
[CrossRef]

1994 (1)

P. Y. Deschamps, F. M. Breon, M. Leroy, A. Podaire, A. Bricaud, J. C. Buriez, and G. Seze, “The POLDER mission: Instrument characteristics and scientific objectives,” IEEE Trans. Geosci. Rem. Sens. 32(3), 598–615 (1994).
[CrossRef]

1992 (1)

F. Weng, “A multi-layer discrete-ordinate method for vector radiative transfer in a vertically-inhomogeneous, emitting and scattering atmosphere–I. Theory,” J. Quant. Spectrosc. Radiat. Transf. 47(1), 19–33 (1992).
[CrossRef]

1991 (1)

K. F. Evans and G. L. Stephens, “A new polarized atmospheric radiative transfer model,” J. Quant. Spectrosc. Radiat. Transf. 46(5), 413–423 (1991).
[CrossRef]

1982 (1)

C. E. Siewert, “On the phase matrix basic to the scattering of polarized light,” Astron. Astrophys. 109, 195–200 (1982).

1979 (1)

L. W. Esposito, “An ‘adding’ algorithm for the Markov chain formalism for radiation transfer,” Astrophys. J. 233, 661–663 (1979).
[CrossRef]

1978 (1)

L. W. Esposito and L. L. House, “Radiative transfer calculated by a Markov chain formalism,” Astrophys. J. 219, 1058–1067 (1978).
[CrossRef]

1974 (1)

J. E. Hansen and L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16(4), 527–610 (1974).
[CrossRef]

1970 (1)

1969 (1)

J. W. Hovenier, “Symmetry relations for scattering of polarized light in a slab of randomly oriented particles,” J. Atmos. Sci. 26(3), 488–499 (1969).
[CrossRef]

Ackerman, T. P.

D. J. Diner, J. C. Beckert, T. H. Reilly, C. J. Bruegge, J. E. Conel, R. A. Kahn, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, J. Muller, R. B. Myneni, P. J. Sellers, B. Pinty, and M. M. Verstraete, “Multi-angle Imaging Spectro-Radiometer (MISR) instrument description and experiment overview,” IEEE Trans. Geosci. Rem. Sens. 36(4), 1072–1087 (1998).
[CrossRef]

Atlas, R.

D. Crisp, R. Atlas, F. Breon, L. Brown, J. Burrows, P. Ciais, B. Connor, S. Doney, I. Fung, and D. Jacob, “The Orbiting Carbon Observatory (OCO) mission,” Adv. Space Res. 34(4), 700–709 (2004).
[CrossRef]

Beckert, J. C.

D. J. Diner, J. C. Beckert, T. H. Reilly, C. J. Bruegge, J. E. Conel, R. A. Kahn, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, J. Muller, R. B. Myneni, P. J. Sellers, B. Pinty, and M. M. Verstraete, “Multi-angle Imaging Spectro-Radiometer (MISR) instrument description and experiment overview,” IEEE Trans. Geosci. Rem. Sens. 36(4), 1072–1087 (1998).
[CrossRef]

Boesch, H.

V. Natraj, R. J. D. Spurr, H. Boesch, Y. Jiang, and Y. Yung, “Evaluation of errors in neglecting polarization in the forward modeling of O2 A band measurements from space, with relevance to CO2 column retrieval from polarization sensitive instruments,” J. Quant. Spectrosc. Radiat. Transf. 103(2), 245–259 (2007).
[CrossRef]

Breon, F.

D. Crisp, R. Atlas, F. Breon, L. Brown, J. Burrows, P. Ciais, B. Connor, S. Doney, I. Fung, and D. Jacob, “The Orbiting Carbon Observatory (OCO) mission,” Adv. Space Res. 34(4), 700–709 (2004).
[CrossRef]

Breon, F. M.

P. Y. Deschamps, F. M. Breon, M. Leroy, A. Podaire, A. Bricaud, J. C. Buriez, and G. Seze, “The POLDER mission: Instrument characteristics and scientific objectives,” IEEE Trans. Geosci. Rem. Sens. 32(3), 598–615 (1994).
[CrossRef]

Bricaud, A.

P. Y. Deschamps, F. M. Breon, M. Leroy, A. Podaire, A. Bricaud, J. C. Buriez, and G. Seze, “The POLDER mission: Instrument characteristics and scientific objectives,” IEEE Trans. Geosci. Rem. Sens. 32(3), 598–615 (1994).
[CrossRef]

Brown, L.

D. Crisp, R. Atlas, F. Breon, L. Brown, J. Burrows, P. Ciais, B. Connor, S. Doney, I. Fung, and D. Jacob, “The Orbiting Carbon Observatory (OCO) mission,” Adv. Space Res. 34(4), 700–709 (2004).
[CrossRef]

Bruegge, C. J.

D. J. Diner, J. C. Beckert, T. H. Reilly, C. J. Bruegge, J. E. Conel, R. A. Kahn, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, J. Muller, R. B. Myneni, P. J. Sellers, B. Pinty, and M. M. Verstraete, “Multi-angle Imaging Spectro-Radiometer (MISR) instrument description and experiment overview,” IEEE Trans. Geosci. Rem. Sens. 36(4), 1072–1087 (1998).
[CrossRef]

Budak, V. P.

A. A. Kokhanovsky, V. P. Budak, C. Cornet, M. Duan, C. Emde, I. L. Katsev, D. A. Klyukov, S. V. Korkin, L. C-Labonnote, and B. Mayer, “Benchmark results in vector atmospheric radiative transfer,” J. Quant. Spectrosc. Radiat. Transf. 111(12-13), 1931–1946 (2010).
[CrossRef]

Buriez, J. C.

P. Y. Deschamps, F. M. Breon, M. Leroy, A. Podaire, A. Bricaud, J. C. Buriez, and G. Seze, “The POLDER mission: Instrument characteristics and scientific objectives,” IEEE Trans. Geosci. Rem. Sens. 32(3), 598–615 (1994).
[CrossRef]

Burrows, J.

D. Crisp, R. Atlas, F. Breon, L. Brown, J. Burrows, P. Ciais, B. Connor, S. Doney, I. Fung, and D. Jacob, “The Orbiting Carbon Observatory (OCO) mission,” Adv. Space Res. 34(4), 700–709 (2004).
[CrossRef]

Cairns, B.

M. I. Mishchenko, B. Cairns, G. Kopp, C. F. Schueler, B. A. Fafaul, J. E. Hansen, R. J. Hooker, T. Itchkawich, H. B. Maring, and L. D. Travis, “Accurate monitoring of terrestrial aerosols and total solar irradiance: Introducing the Glory mission,” Bull. Am. Meteorol. Soc. 88(5), 677–691 (2007).
[CrossRef]

Ciais, P.

D. Crisp, R. Atlas, F. Breon, L. Brown, J. Burrows, P. Ciais, B. Connor, S. Doney, I. Fung, and D. Jacob, “The Orbiting Carbon Observatory (OCO) mission,” Adv. Space Res. 34(4), 700–709 (2004).
[CrossRef]

C-Labonnote, L.

A. A. Kokhanovsky, V. P. Budak, C. Cornet, M. Duan, C. Emde, I. L. Katsev, D. A. Klyukov, S. V. Korkin, L. C-Labonnote, and B. Mayer, “Benchmark results in vector atmospheric radiative transfer,” J. Quant. Spectrosc. Radiat. Transf. 111(12-13), 1931–1946 (2010).
[CrossRef]

Conel, J. E.

D. J. Diner, J. C. Beckert, T. H. Reilly, C. J. Bruegge, J. E. Conel, R. A. Kahn, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, J. Muller, R. B. Myneni, P. J. Sellers, B. Pinty, and M. M. Verstraete, “Multi-angle Imaging Spectro-Radiometer (MISR) instrument description and experiment overview,” IEEE Trans. Geosci. Rem. Sens. 36(4), 1072–1087 (1998).
[CrossRef]

Connor, B.

D. Crisp, R. Atlas, F. Breon, L. Brown, J. Burrows, P. Ciais, B. Connor, S. Doney, I. Fung, and D. Jacob, “The Orbiting Carbon Observatory (OCO) mission,” Adv. Space Res. 34(4), 700–709 (2004).
[CrossRef]

Cornet, C.

A. A. Kokhanovsky, V. P. Budak, C. Cornet, M. Duan, C. Emde, I. L. Katsev, D. A. Klyukov, S. V. Korkin, L. C-Labonnote, and B. Mayer, “Benchmark results in vector atmospheric radiative transfer,” J. Quant. Spectrosc. Radiat. Transf. 111(12-13), 1931–1946 (2010).
[CrossRef]

Crisp, D.

D. Crisp, R. Atlas, F. Breon, L. Brown, J. Burrows, P. Ciais, B. Connor, S. Doney, I. Fung, and D. Jacob, “The Orbiting Carbon Observatory (OCO) mission,” Adv. Space Res. 34(4), 700–709 (2004).
[CrossRef]

Dave, J. V.

Davies, R.

D. J. Diner, J. C. Beckert, T. H. Reilly, C. J. Bruegge, J. E. Conel, R. A. Kahn, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, J. Muller, R. B. Myneni, P. J. Sellers, B. Pinty, and M. M. Verstraete, “Multi-angle Imaging Spectro-Radiometer (MISR) instrument description and experiment overview,” IEEE Trans. Geosci. Rem. Sens. 36(4), 1072–1087 (1998).
[CrossRef]

Deschamps, P. Y.

P. Y. Deschamps, F. M. Breon, M. Leroy, A. Podaire, A. Bricaud, J. C. Buriez, and G. Seze, “The POLDER mission: Instrument characteristics and scientific objectives,” IEEE Trans. Geosci. Rem. Sens. 32(3), 598–615 (1994).
[CrossRef]

Deuzé, J. L.

A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, E. P. Zege, A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, and E. P. Zege, “The inter-comparison of major satellite aerosol retrieval algorithms using simulated intensity and polarization characteristics of reflected light,” Atm. Meas. Techn. 3, 909–932 (2010).
[CrossRef]

A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, E. P. Zege, A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, and E. P. Zege, “The inter-comparison of major satellite aerosol retrieval algorithms using simulated intensity and polarization characteristics of reflected light,” Atm. Meas. Techn. 3, 909–932 (2010).
[CrossRef]

Diner, D. J.

A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, E. P. Zege, A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, and E. P. Zege, “The inter-comparison of major satellite aerosol retrieval algorithms using simulated intensity and polarization characteristics of reflected light,” Atm. Meas. Techn. 3, 909–932 (2010).
[CrossRef]

A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, E. P. Zege, A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, and E. P. Zege, “The inter-comparison of major satellite aerosol retrieval algorithms using simulated intensity and polarization characteristics of reflected light,” Atm. Meas. Techn. 3, 909–932 (2010).
[CrossRef]

D. J. Diner, J. C. Beckert, T. H. Reilly, C. J. Bruegge, J. E. Conel, R. A. Kahn, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, J. Muller, R. B. Myneni, P. J. Sellers, B. Pinty, and M. M. Verstraete, “Multi-angle Imaging Spectro-Radiometer (MISR) instrument description and experiment overview,” IEEE Trans. Geosci. Rem. Sens. 36(4), 1072–1087 (1998).
[CrossRef]

Doney, S.

D. Crisp, R. Atlas, F. Breon, L. Brown, J. Burrows, P. Ciais, B. Connor, S. Doney, I. Fung, and D. Jacob, “The Orbiting Carbon Observatory (OCO) mission,” Adv. Space Res. 34(4), 700–709 (2004).
[CrossRef]

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A. A. Kokhanovsky, V. P. Budak, C. Cornet, M. Duan, C. Emde, I. L. Katsev, D. A. Klyukov, S. V. Korkin, L. C-Labonnote, and B. Mayer, “Benchmark results in vector atmospheric radiative transfer,” J. Quant. Spectrosc. Radiat. Transf. 111(12-13), 1931–1946 (2010).
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A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, E. P. Zege, A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, and E. P. Zege, “The inter-comparison of major satellite aerosol retrieval algorithms using simulated intensity and polarization characteristics of reflected light,” Atm. Meas. Techn. 3, 909–932 (2010).
[CrossRef]

A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, E. P. Zege, A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, and E. P. Zege, “The inter-comparison of major satellite aerosol retrieval algorithms using simulated intensity and polarization characteristics of reflected light,” Atm. Meas. Techn. 3, 909–932 (2010).
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Ducos, F.

A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, E. P. Zege, A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, and E. P. Zege, “The inter-comparison of major satellite aerosol retrieval algorithms using simulated intensity and polarization characteristics of reflected light,” Atm. Meas. Techn. 3, 909–932 (2010).
[CrossRef]

A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, E. P. Zege, A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, and E. P. Zege, “The inter-comparison of major satellite aerosol retrieval algorithms using simulated intensity and polarization characteristics of reflected light,” Atm. Meas. Techn. 3, 909–932 (2010).
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Emde, C.

A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, E. P. Zege, A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, and E. P. Zege, “The inter-comparison of major satellite aerosol retrieval algorithms using simulated intensity and polarization characteristics of reflected light,” Atm. Meas. Techn. 3, 909–932 (2010).
[CrossRef]

A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, E. P. Zege, A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, and E. P. Zege, “The inter-comparison of major satellite aerosol retrieval algorithms using simulated intensity and polarization characteristics of reflected light,” Atm. Meas. Techn. 3, 909–932 (2010).
[CrossRef]

A. A. Kokhanovsky, V. P. Budak, C. Cornet, M. Duan, C. Emde, I. L. Katsev, D. A. Klyukov, S. V. Korkin, L. C-Labonnote, and B. Mayer, “Benchmark results in vector atmospheric radiative transfer,” J. Quant. Spectrosc. Radiat. Transf. 111(12-13), 1931–1946 (2010).
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L. W. Esposito, “An ‘adding’ algorithm for the Markov chain formalism for radiation transfer,” Astrophys. J. 233, 661–663 (1979).
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L. W. Esposito and L. L. House, “Radiative transfer calculated by a Markov chain formalism,” Astrophys. J. 219, 1058–1067 (1978).
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M. I. Mishchenko, B. Cairns, G. Kopp, C. F. Schueler, B. A. Fafaul, J. E. Hansen, R. J. Hooker, T. Itchkawich, H. B. Maring, and L. D. Travis, “Accurate monitoring of terrestrial aerosols and total solar irradiance: Introducing the Glory mission,” Bull. Am. Meteorol. Soc. 88(5), 677–691 (2007).
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D. Crisp, R. Atlas, F. Breon, L. Brown, J. Burrows, P. Ciais, B. Connor, S. Doney, I. Fung, and D. Jacob, “The Orbiting Carbon Observatory (OCO) mission,” Adv. Space Res. 34(4), 700–709 (2004).
[CrossRef]

Garay, M. J.

A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, E. P. Zege, A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, and E. P. Zege, “The inter-comparison of major satellite aerosol retrieval algorithms using simulated intensity and polarization characteristics of reflected light,” Atm. Meas. Techn. 3, 909–932 (2010).
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A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, E. P. Zege, A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, and E. P. Zege, “The inter-comparison of major satellite aerosol retrieval algorithms using simulated intensity and polarization characteristics of reflected light,” Atm. Meas. Techn. 3, 909–932 (2010).
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D. J. Diner, J. C. Beckert, T. H. Reilly, C. J. Bruegge, J. E. Conel, R. A. Kahn, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, J. Muller, R. B. Myneni, P. J. Sellers, B. Pinty, and M. M. Verstraete, “Multi-angle Imaging Spectro-Radiometer (MISR) instrument description and experiment overview,” IEEE Trans. Geosci. Rem. Sens. 36(4), 1072–1087 (1998).
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Grainger, R. G.

A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, E. P. Zege, A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, and E. P. Zege, “The inter-comparison of major satellite aerosol retrieval algorithms using simulated intensity and polarization characteristics of reflected light,” Atm. Meas. Techn. 3, 909–932 (2010).
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A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, E. P. Zege, A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, and E. P. Zege, “The inter-comparison of major satellite aerosol retrieval algorithms using simulated intensity and polarization characteristics of reflected light,” Atm. Meas. Techn. 3, 909–932 (2010).
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Hannay, J. H.

Hansen, J. E.

M. I. Mishchenko, B. Cairns, G. Kopp, C. F. Schueler, B. A. Fafaul, J. E. Hansen, R. J. Hooker, T. Itchkawich, H. B. Maring, and L. D. Travis, “Accurate monitoring of terrestrial aerosols and total solar irradiance: Introducing the Glory mission,” Bull. Am. Meteorol. Soc. 88(5), 677–691 (2007).
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A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, E. P. Zege, A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, and E. P. Zege, “The inter-comparison of major satellite aerosol retrieval algorithms using simulated intensity and polarization characteristics of reflected light,” Atm. Meas. Techn. 3, 909–932 (2010).
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A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, E. P. Zege, A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, and E. P. Zege, “The inter-comparison of major satellite aerosol retrieval algorithms using simulated intensity and polarization characteristics of reflected light,” Atm. Meas. Techn. 3, 909–932 (2010).
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Herman, M.

A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, E. P. Zege, A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, and E. P. Zege, “The inter-comparison of major satellite aerosol retrieval algorithms using simulated intensity and polarization characteristics of reflected light,” Atm. Meas. Techn. 3, 909–932 (2010).
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A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, E. P. Zege, A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, and E. P. Zege, “The inter-comparison of major satellite aerosol retrieval algorithms using simulated intensity and polarization characteristics of reflected light,” Atm. Meas. Techn. 3, 909–932 (2010).
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M. I. Mishchenko, B. Cairns, G. Kopp, C. F. Schueler, B. A. Fafaul, J. E. Hansen, R. J. Hooker, T. Itchkawich, H. B. Maring, and L. D. Travis, “Accurate monitoring of terrestrial aerosols and total solar irradiance: Introducing the Glory mission,” Bull. Am. Meteorol. Soc. 88(5), 677–691 (2007).
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L. W. Esposito and L. L. House, “Radiative transfer calculated by a Markov chain formalism,” Astrophys. J. 219, 1058–1067 (1978).
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J. W. Hovenier, “Symmetry relations for scattering of polarized light in a slab of randomly oriented particles,” J. Atmos. Sci. 26(3), 488–499 (1969).
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Itchkawich, T.

M. I. Mishchenko, B. Cairns, G. Kopp, C. F. Schueler, B. A. Fafaul, J. E. Hansen, R. J. Hooker, T. Itchkawich, H. B. Maring, and L. D. Travis, “Accurate monitoring of terrestrial aerosols and total solar irradiance: Introducing the Glory mission,” Bull. Am. Meteorol. Soc. 88(5), 677–691 (2007).
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Jacob, D.

D. Crisp, R. Atlas, F. Breon, L. Brown, J. Burrows, P. Ciais, B. Connor, S. Doney, I. Fung, and D. Jacob, “The Orbiting Carbon Observatory (OCO) mission,” Adv. Space Res. 34(4), 700–709 (2004).
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Jiang, Y.

V. Natraj, R. J. D. Spurr, H. Boesch, Y. Jiang, and Y. Yung, “Evaluation of errors in neglecting polarization in the forward modeling of O2 A band measurements from space, with relevance to CO2 column retrieval from polarization sensitive instruments,” J. Quant. Spectrosc. Radiat. Transf. 103(2), 245–259 (2007).
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Kahn, R. A.

D. J. Diner, J. C. Beckert, T. H. Reilly, C. J. Bruegge, J. E. Conel, R. A. Kahn, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, J. Muller, R. B. Myneni, P. J. Sellers, B. Pinty, and M. M. Verstraete, “Multi-angle Imaging Spectro-Radiometer (MISR) instrument description and experiment overview,” IEEE Trans. Geosci. Rem. Sens. 36(4), 1072–1087 (1998).
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Katsev, I. L.

A. A. Kokhanovsky, V. P. Budak, C. Cornet, M. Duan, C. Emde, I. L. Katsev, D. A. Klyukov, S. V. Korkin, L. C-Labonnote, and B. Mayer, “Benchmark results in vector atmospheric radiative transfer,” J. Quant. Spectrosc. Radiat. Transf. 111(12-13), 1931–1946 (2010).
[CrossRef]

A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, E. P. Zege, A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, and E. P. Zege, “The inter-comparison of major satellite aerosol retrieval algorithms using simulated intensity and polarization characteristics of reflected light,” Atm. Meas. Techn. 3, 909–932 (2010).
[CrossRef]

A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, E. P. Zege, A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, and E. P. Zege, “The inter-comparison of major satellite aerosol retrieval algorithms using simulated intensity and polarization characteristics of reflected light,” Atm. Meas. Techn. 3, 909–932 (2010).
[CrossRef]

Keller, J.

A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, E. P. Zege, A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, and E. P. Zege, “The inter-comparison of major satellite aerosol retrieval algorithms using simulated intensity and polarization characteristics of reflected light,” Atm. Meas. Techn. 3, 909–932 (2010).
[CrossRef]

A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, E. P. Zege, A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, and E. P. Zege, “The inter-comparison of major satellite aerosol retrieval algorithms using simulated intensity and polarization characteristics of reflected light,” Atm. Meas. Techn. 3, 909–932 (2010).
[CrossRef]

Klemm, F. J.

Klyukov, D. A.

A. A. Kokhanovsky, V. P. Budak, C. Cornet, M. Duan, C. Emde, I. L. Katsev, D. A. Klyukov, S. V. Korkin, L. C-Labonnote, and B. Mayer, “Benchmark results in vector atmospheric radiative transfer,” J. Quant. Spectrosc. Radiat. Transf. 111(12-13), 1931–1946 (2010).
[CrossRef]

Kokhanovsky, A. A.

A. A. Kokhanovsky, V. P. Budak, C. Cornet, M. Duan, C. Emde, I. L. Katsev, D. A. Klyukov, S. V. Korkin, L. C-Labonnote, and B. Mayer, “Benchmark results in vector atmospheric radiative transfer,” J. Quant. Spectrosc. Radiat. Transf. 111(12-13), 1931–1946 (2010).
[CrossRef]

A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, E. P. Zege, A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, and E. P. Zege, “The inter-comparison of major satellite aerosol retrieval algorithms using simulated intensity and polarization characteristics of reflected light,” Atm. Meas. Techn. 3, 909–932 (2010).
[CrossRef]

A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, E. P. Zege, A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, and E. P. Zege, “The inter-comparison of major satellite aerosol retrieval algorithms using simulated intensity and polarization characteristics of reflected light,” Atm. Meas. Techn. 3, 909–932 (2010).
[CrossRef]

Kopp, G.

M. I. Mishchenko, B. Cairns, G. Kopp, C. F. Schueler, B. A. Fafaul, J. E. Hansen, R. J. Hooker, T. Itchkawich, H. B. Maring, and L. D. Travis, “Accurate monitoring of terrestrial aerosols and total solar irradiance: Introducing the Glory mission,” Bull. Am. Meteorol. Soc. 88(5), 677–691 (2007).
[CrossRef]

Korkin, S. V.

A. A. Kokhanovsky, V. P. Budak, C. Cornet, M. Duan, C. Emde, I. L. Katsev, D. A. Klyukov, S. V. Korkin, L. C-Labonnote, and B. Mayer, “Benchmark results in vector atmospheric radiative transfer,” J. Quant. Spectrosc. Radiat. Transf. 111(12-13), 1931–1946 (2010).
[CrossRef]

Kotchenova, S. Y.

Leroy, M.

P. Y. Deschamps, F. M. Breon, M. Leroy, A. Podaire, A. Bricaud, J. C. Buriez, and G. Seze, “The POLDER mission: Instrument characteristics and scientific objectives,” IEEE Trans. Geosci. Rem. Sens. 32(3), 598–615 (1994).
[CrossRef]

Levy, R.

A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, E. P. Zege, A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, and E. P. Zege, “The inter-comparison of major satellite aerosol retrieval algorithms using simulated intensity and polarization characteristics of reflected light,” Atm. Meas. Techn. 3, 909–932 (2010).
[CrossRef]

A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, E. P. Zege, A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, and E. P. Zege, “The inter-comparison of major satellite aerosol retrieval algorithms using simulated intensity and polarization characteristics of reflected light,” Atm. Meas. Techn. 3, 909–932 (2010).
[CrossRef]

Lucker, P. L.

Maring, H. B.

M. I. Mishchenko, B. Cairns, G. Kopp, C. F. Schueler, B. A. Fafaul, J. E. Hansen, R. J. Hooker, T. Itchkawich, H. B. Maring, and L. D. Travis, “Accurate monitoring of terrestrial aerosols and total solar irradiance: Introducing the Glory mission,” Bull. Am. Meteorol. Soc. 88(5), 677–691 (2007).
[CrossRef]

Martonchik, J. V.

D. J. Diner, J. C. Beckert, T. H. Reilly, C. J. Bruegge, J. E. Conel, R. A. Kahn, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, J. Muller, R. B. Myneni, P. J. Sellers, B. Pinty, and M. M. Verstraete, “Multi-angle Imaging Spectro-Radiometer (MISR) instrument description and experiment overview,” IEEE Trans. Geosci. Rem. Sens. 36(4), 1072–1087 (1998).
[CrossRef]

Matarrese, R.

Mayer, B.

A. A. Kokhanovsky, V. P. Budak, C. Cornet, M. Duan, C. Emde, I. L. Katsev, D. A. Klyukov, S. V. Korkin, L. C-Labonnote, and B. Mayer, “Benchmark results in vector atmospheric radiative transfer,” J. Quant. Spectrosc. Radiat. Transf. 111(12-13), 1931–1946 (2010).
[CrossRef]

Min, Q. L.

Q. L. Min and M. Duan, “A successive order of scattering model for solving vector radiative transfer in the atmosphere,” J. Quant. Spectrosc. Radiat. Transf. 87(3-4), 243–259 (2004).
[CrossRef]

Mishchenko, M. I.

M. I. Mishchenko, B. Cairns, G. Kopp, C. F. Schueler, B. A. Fafaul, J. E. Hansen, R. J. Hooker, T. Itchkawich, H. B. Maring, and L. D. Travis, “Accurate monitoring of terrestrial aerosols and total solar irradiance: Introducing the Glory mission,” Bull. Am. Meteorol. Soc. 88(5), 677–691 (2007).
[CrossRef]

Muller, J.

D. J. Diner, J. C. Beckert, T. H. Reilly, C. J. Bruegge, J. E. Conel, R. A. Kahn, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, J. Muller, R. B. Myneni, P. J. Sellers, B. Pinty, and M. M. Verstraete, “Multi-angle Imaging Spectro-Radiometer (MISR) instrument description and experiment overview,” IEEE Trans. Geosci. Rem. Sens. 36(4), 1072–1087 (1998).
[CrossRef]

Myneni, R. B.

D. J. Diner, J. C. Beckert, T. H. Reilly, C. J. Bruegge, J. E. Conel, R. A. Kahn, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, J. Muller, R. B. Myneni, P. J. Sellers, B. Pinty, and M. M. Verstraete, “Multi-angle Imaging Spectro-Radiometer (MISR) instrument description and experiment overview,” IEEE Trans. Geosci. Rem. Sens. 36(4), 1072–1087 (1998).
[CrossRef]

Natraj, V.

V. Natraj and R. J. D. Spurr, “A fast linearized pseudo-spherical two orders of scattering model to account for polarization in vertically inhomogeneous scattering-absorbing media,” J. Quant. Spectrosc. Radiat. Transf. 107(2), 263–293 (2007).
[CrossRef]

V. Natraj, R. J. D. Spurr, H. Boesch, Y. Jiang, and Y. Yung, “Evaluation of errors in neglecting polarization in the forward modeling of O2 A band measurements from space, with relevance to CO2 column retrieval from polarization sensitive instruments,” J. Quant. Spectrosc. Radiat. Transf. 103(2), 245–259 (2007).
[CrossRef]

North, P. R. J.

A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, E. P. Zege, A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, and E. P. Zege, “The inter-comparison of major satellite aerosol retrieval algorithms using simulated intensity and polarization characteristics of reflected light,” Atm. Meas. Techn. 3, 909–932 (2010).
[CrossRef]

A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, E. P. Zege, A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, and E. P. Zege, “The inter-comparison of major satellite aerosol retrieval algorithms using simulated intensity and polarization characteristics of reflected light,” Atm. Meas. Techn. 3, 909–932 (2010).
[CrossRef]

Ota, Y.

A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, E. P. Zege, A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, and E. P. Zege, “The inter-comparison of major satellite aerosol retrieval algorithms using simulated intensity and polarization characteristics of reflected light,” Atm. Meas. Techn. 3, 909–932 (2010).
[CrossRef]

A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, E. P. Zege, A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, and E. P. Zege, “The inter-comparison of major satellite aerosol retrieval algorithms using simulated intensity and polarization characteristics of reflected light,” Atm. Meas. Techn. 3, 909–932 (2010).
[CrossRef]

Pinty, B.

D. J. Diner, J. C. Beckert, T. H. Reilly, C. J. Bruegge, J. E. Conel, R. A. Kahn, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, J. Muller, R. B. Myneni, P. J. Sellers, B. Pinty, and M. M. Verstraete, “Multi-angle Imaging Spectro-Radiometer (MISR) instrument description and experiment overview,” IEEE Trans. Geosci. Rem. Sens. 36(4), 1072–1087 (1998).
[CrossRef]

Podaire, A.

P. Y. Deschamps, F. M. Breon, M. Leroy, A. Podaire, A. Bricaud, J. C. Buriez, and G. Seze, “The POLDER mission: Instrument characteristics and scientific objectives,” IEEE Trans. Geosci. Rem. Sens. 32(3), 598–615 (1994).
[CrossRef]

Prikhach, A. S.

A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, E. P. Zege, A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, and E. P. Zege, “The inter-comparison of major satellite aerosol retrieval algorithms using simulated intensity and polarization characteristics of reflected light,” Atm. Meas. Techn. 3, 909–932 (2010).
[CrossRef]

A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, E. P. Zege, A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, and E. P. Zege, “The inter-comparison of major satellite aerosol retrieval algorithms using simulated intensity and polarization characteristics of reflected light,” Atm. Meas. Techn. 3, 909–932 (2010).
[CrossRef]

Reilly, T. H.

D. J. Diner, J. C. Beckert, T. H. Reilly, C. J. Bruegge, J. E. Conel, R. A. Kahn, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, J. Muller, R. B. Myneni, P. J. Sellers, B. Pinty, and M. M. Verstraete, “Multi-angle Imaging Spectro-Radiometer (MISR) instrument description and experiment overview,” IEEE Trans. Geosci. Rem. Sens. 36(4), 1072–1087 (1998).
[CrossRef]

Rozanov, V. V.

A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, E. P. Zege, A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, and E. P. Zege, “The inter-comparison of major satellite aerosol retrieval algorithms using simulated intensity and polarization characteristics of reflected light,” Atm. Meas. Techn. 3, 909–932 (2010).
[CrossRef]

A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, E. P. Zege, A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, and E. P. Zege, “The inter-comparison of major satellite aerosol retrieval algorithms using simulated intensity and polarization characteristics of reflected light,” Atm. Meas. Techn. 3, 909–932 (2010).
[CrossRef]

Sayer, A. M.

A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, E. P. Zege, A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, and E. P. Zege, “The inter-comparison of major satellite aerosol retrieval algorithms using simulated intensity and polarization characteristics of reflected light,” Atm. Meas. Techn. 3, 909–932 (2010).
[CrossRef]

A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, E. P. Zege, A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, and E. P. Zege, “The inter-comparison of major satellite aerosol retrieval algorithms using simulated intensity and polarization characteristics of reflected light,” Atm. Meas. Techn. 3, 909–932 (2010).
[CrossRef]

Schueler, C. F.

M. I. Mishchenko, B. Cairns, G. Kopp, C. F. Schueler, B. A. Fafaul, J. E. Hansen, R. J. Hooker, T. Itchkawich, H. B. Maring, and L. D. Travis, “Accurate monitoring of terrestrial aerosols and total solar irradiance: Introducing the Glory mission,” Bull. Am. Meteorol. Soc. 88(5), 677–691 (2007).
[CrossRef]

Schulz, F. M.

F. M. Schulz, K. Stamnes, and F. Weng, “VDISORT, an improved and generalized discrete ordinate method for polarized (vector) radiative transfer,” J. Quant. Spectrosc. Radiat. Transf. 61(1), 105–122 (1999).
[CrossRef]

Sellers, P. J.

D. J. Diner, J. C. Beckert, T. H. Reilly, C. J. Bruegge, J. E. Conel, R. A. Kahn, J. V. Martonchik, T. P. Ackerman, R. Davies, S. A. W. Gerstl, H. R. Gordon, J. Muller, R. B. Myneni, P. J. Sellers, B. Pinty, and M. M. Verstraete, “Multi-angle Imaging Spectro-Radiometer (MISR) instrument description and experiment overview,” IEEE Trans. Geosci. Rem. Sens. 36(4), 1072–1087 (1998).
[CrossRef]

Seze, G.

P. Y. Deschamps, F. M. Breon, M. Leroy, A. Podaire, A. Bricaud, J. C. Buriez, and G. Seze, “The POLDER mission: Instrument characteristics and scientific objectives,” IEEE Trans. Geosci. Rem. Sens. 32(3), 598–615 (1994).
[CrossRef]

Siewert, C. E.

C. E. Siewert, “On the phase matrix basic to the scattering of polarized light,” Astron. Astrophys. 109, 195–200 (1982).

Spurr, R. J. D.

V. Natraj, R. J. D. Spurr, H. Boesch, Y. Jiang, and Y. Yung, “Evaluation of errors in neglecting polarization in the forward modeling of O2 A band measurements from space, with relevance to CO2 column retrieval from polarization sensitive instruments,” J. Quant. Spectrosc. Radiat. Transf. 103(2), 245–259 (2007).
[CrossRef]

V. Natraj and R. J. D. Spurr, “A fast linearized pseudo-spherical two orders of scattering model to account for polarization in vertically inhomogeneous scattering-absorbing media,” J. Quant. Spectrosc. Radiat. Transf. 107(2), 263–293 (2007).
[CrossRef]

R. J. D. Spurr, “VLIDORT: A linearized pseudo-spherical vector discrete ordinate radiative transfer code for forward model and retrieval studies in multilayer multiple scattering media,” J. Quant. Spectrosc. Radiat. Transf. 102(2), 316–342 (2006).
[CrossRef]

Stamnes, K.

F. M. Schulz, K. Stamnes, and F. Weng, “VDISORT, an improved and generalized discrete ordinate method for polarized (vector) radiative transfer,” J. Quant. Spectrosc. Radiat. Transf. 61(1), 105–122 (1999).
[CrossRef]

Stephens, G. L.

K. F. Evans and G. L. Stephens, “A new polarized atmospheric radiative transfer model,” J. Quant. Spectrosc. Radiat. Transf. 46(5), 413–423 (1991).
[CrossRef]

Tanré, D.

A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, E. P. Zege, A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, and E. P. Zege, “The inter-comparison of major satellite aerosol retrieval algorithms using simulated intensity and polarization characteristics of reflected light,” Atm. Meas. Techn. 3, 909–932 (2010).
[CrossRef]

A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, E. P. Zege, A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, and E. P. Zege, “The inter-comparison of major satellite aerosol retrieval algorithms using simulated intensity and polarization characteristics of reflected light,” Atm. Meas. Techn. 3, 909–932 (2010).
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Thomas, G. E.

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A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, E. P. Zege, A. A. Kokhanovsky, J. L. Deuzé, D. J. Diner, O. Dubovik, F. Ducos, C. Emde, M. J. Garay, R. G. Grainger, A. Heckel, M. Herman, I. L. Katsev, J. Keller, R. Levy, P. R. J. North, A. S. Prikhach, V. V. Rozanov, A. M. Sayer, Y. Ota, D. Tanré, G. E. Thomas, and E. P. Zege, “The inter-comparison of major satellite aerosol retrieval algorithms using simulated intensity and polarization characteristics of reflected light,” Atm. Meas. Techn. 3, 909–932 (2010).
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Figures (16)

Fig. 1
Fig. 1

The first two, three, then all, orders of scattering contributing to the diffuse reflection field (I component) in the principal plane for a homogeneous Rayleigh atmosphere of optical depth τ0 = 0.5 and unit single scattering albedo. Error bars are based on the standard deviation among 10 realizations of the Monte Carlo simulation, each with 107 histories (cf. Figures 12 and 16 for a situation with degraded precision).

Fig. 12
Fig. 12

Same as Fig. 9 but the V component of the diffusely reflected field is plotted.

Fig. 4
Fig. 4

Same as Fig. 1 but the Q component of the diffuse transmission field is plotted.

Fig. 2
Fig. 2

Same as Fig. 1 but the Q component of the diffuse reflection field is plotted.

Fig. 3
Fig. 3

Same as Fig. 1 but the I component of the diffuse transmission field is plotted.

Fig. 5
Fig. 5

Diffuse reflection field (I component) in the principal plane of the vertically inhomogeneous atmosphere described in the main text under solar illumination at 60° incidence. As in Fig. 1, the error bars are based on the standard deviation among 10 realizations of the Monte Carlo simulation, each with 107 histories.

Fig. 6
Fig. 6

Same as Fig. 5 but the Q component of the diffuse reflection field is plotted.

Fig. 7
Fig. 7

Same as Fig. 5 but the I component of the diffuse transmission field is plotted.

Fig. 8
Fig. 8

Same as Fig. 5 but the Q component of the diffuse transmission field is plotted.

Fig. 9
Fig. 9

Same as Fig. 5 but the I component of the diffusely reflected field in the perpendicular plane (ϕϕ 0 = ±90°) is plotted.

Fig. 16
Fig. 16

Same as Fig. 9 but the V component of the diffusely transmitted field is plotted.

Fig. 10
Fig. 10

Same as Fig. 9 but the Q component of the diffusely reflected field is plotted.

Fig. 11
Fig. 11

Same as Fig. 9 but the U component of the diffusely reflected field is plotted.

Fig. 13
Fig. 13

Same as Fig. 9 but the I component of the diffusely transmitted field is plotted.

Fig. 14
Fig. 14

Same as Fig. 9 but the Q component of the diffusely transmitted field is plotted.

Fig. 15
Fig. 15

Same as Fig. 9 but the U component of the diffusely transmitted field is plotted.

Tables (1)

Tables Icon

Table 1 Optical thickness and Rayleigh fraction of the atmosphere divided into 42 sublayers

Equations (72)

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cos Θ = u u 0 + ( 1 u 2 ) 1 / 2 ( 1 u 0 2 ) 1 / 2 cos ( ϕ ϕ 0 ) ,
P ( cos Θ , n ) = P ( u , u 0 , ϕ ϕ 0 ; n ) = P ( 0 ) ( u , u 0 ; n ) + 2 m = 1 P ( m ) ( u , u 0 ; n ) cos m ( ϕ ϕ 0 ) .
P r ( μ , μ 0 , ϕ ϕ 0 ; n ) = P ( μ , μ 0 , ϕ ϕ 0 ; n ) ,
P t ( μ , μ 0 , ϕ ϕ 0 ; n ) = P ( μ , μ 0 , ϕ ϕ 0 ; n ) ,
P r * ( μ , μ 0 , ϕ ϕ 0 ; n ) = P ( μ , μ 0 , ϕ ϕ 0 ; n ) ,
P t * ( μ , μ 0 , ϕ ϕ 0 ; n ) = P ( μ , μ 0 , ϕ ϕ 0 ; n ) ,
P r ( m ) ( μ , μ 0 ; n ) = P ( m ) ( μ , μ 0 ; n ) ,
P t ( m ) ( μ , μ 0 ; n ) = P ( m ) ( μ , μ 0 ; n ) ,
P r ( m ) , * ( μ , μ 0 ; n ) = P ( m ) ( μ , μ 0 ; n ) ,
P t ( m ) , * ( μ , μ 0 ; n ) = P ( m ) ( μ , μ 0 ; n ) .
I ( τ , μ , ϕ ) = I ( 0 ) ( τ , μ ) + 2 m = 1 I ( m ) ( τ , μ ) cos m ( ϕ ϕ 0 ) .
U ( n , i ) , 0 , r ( m ) = w i F 0 exp ( τ n μ 0 ) 0 Δ τ n d x μ i exp ( x μ 0 ) ω 0 ( n ) P r ( m ) ( μ i , μ 0 ; n ) 2 exp ( x μ i ) = w i F 0 exp ( τ n μ 0 ) μ 0 μ i + μ 0 ω 0 ( n ) P r ( m ) ( μ i , μ 0 ; n ) 2 { 1 exp [ Δ τ n ( 1 μ 0 + 1 μ i ) ] }
U ( n , i ) , 0 , t ( m ) = w i F 0 exp ( τ n μ 0 ) 0 Δ τ n d x μ i exp ( x μ 0 ) ω 0 ( n ) P t ( m ) ( μ i , μ 0 ; n ) 2 exp ( Δ τ n x μ i ) = w i F 0 exp ( τ n μ 0 ) μ 0 μ i μ 0 ω 0 ( n ) P t ( m ) ( μ i , μ 0 ; n ) 2 { exp ( Δ τ n μ i ) exp ( Δ τ n μ 0 ) } .
Π ( n , i ) , 0 , r / t ( m ) = U ( n , i ) , 0 , r / t ( m ) / c ( n , i ) ,
c ( n , i ) = 1 Δ τ n 0 Δ τ n exp ( x μ i ) d x = μ i Δ τ n [ 1 exp ( Δ τ n μ i ) ] .
W ( n , i ) , ( n , i ) = [ 1 Δ τ n 0 Δ τ n exp ( x μ i ) d x ] exp ( τ n τ n + 1 μ i ) [ 0 Δ τ n exp ( x μ i ) d x μ i ] ,
W ( n , i ) , ( n , i ) = μ i Δ τ n [ 1 exp ( Δ τ n μ i ) ] exp ( τ n τ n + 1 μ i ) [ 1 exp ( Δ τ n μ i ) ] .
W ( n , i ) , ( n , i ) = μ i Δ τ n [ 1 exp ( Δ τ n μ i ) ] exp ( τ n τ n + 1 μ i ) [ 1 exp ( Δ τ n μ i ) ] .
W ( n , i ) , ( n , i ) = 1 1 Δ τ n 0 Δ τ n exp ( x μ i ) d x = 1 μ i Δ τ n [ 1 exp ( Δ τ n μ i ) ] .
( 2 δ 0 m ) I ( m ) = 1 2 A ( m ) B ( m ) ,
A ( n , j ) , ( n , i ) ( m ) = ω 0 ( n ) P ( m ) ( μ j , μ i ; n ) 2 W ( n , i ) , ( n , i ) .
Q ( n , j ) , ( n , i ) ( m ) = w j A ( n , i ) , ( n , i ) ( m ) .
R e , ( n , j ) ( m ) = n = n N R ( n , e ) , ( n , j ) ( m )
T e , ( n , j ) ( m ) = n = n N T ( n , e ) , ( n , j ) ( m )
R ( n , e ) , ( n , j ) ( m ) = τ n τ n + 1 I r , ( n , μ e ) , ( n , μ j ) ( m ) , d ( τ ) d τ μ e ,
T ( n , e ) , ( n , j ) ( m ) = τ n τ n + 1 I t , ( n , μ e ) , ( n , μ j ) ( m ) , d ( τ ) d τ μ e ,
I r , ( n , μ e ) , ( n , μ j ) ( m ) , d ( τ ) = 1 2 1 Δ τ n τ n τ n + 1 d x μ j exp ( τ μ e ) ω 0 ( n ) P r ( m ) ( μ e , μ j ; n ) 2 exp ( τ x μ j ) = 1 2 1 Δ τ n ω 0 ( n ) P r ( m ) ( μ e , μ j ; n ) 2 { exp [ ( τ n + 1 τ μ j τ μ e ) ] exp [ ( τ n τ μ j τ μ e ) ] } ,
I t , ( n , μ e ) , ( n , μ j ) ( m ) , d ( τ ) = 1 2 1 Δ τ n τ n τ n + 1 d x μ j exp ( τ 0 τ μ e ) ω 0 ( n ) P t ( m ) ( μ e , μ j ; n ) 2 exp ( τ x μ j ) = 1 2 1 Δ τ n ω 0 ( n ) P t ( m ) ( μ e , μ j ; n ) 2 { exp [ ( τ n + 1 τ μ j τ 0 τ μ e ) ] exp [ ( τ n τ μ j τ 0 τ μ e ) ] } .
R ( n , e ) , ( n , j ) ( m ) = 1 2 1 Δ τ n μ j μ e + μ j ω 0 ( n ) P r ( m ) ( μ e , μ j ; n ) 2 { [ exp ( τ n + 1 τ n μ j τ n μ e ) exp ( τ n τ n μ j τ n μ e ) ] [ exp ( τ n + 1 τ n + 1 μ j τ n + 1 μ e ) exp ( τ n τ n + 1 μ j τ n + 1 μ e ) ] } ,
T ( n , e ) , ( n , j ) ( m ) = 1 2 1 Δ τ n exp ( τ 0 μ e ) μ j μ e μ j ω 0 ( n ) P t ( m ) ( μ e , μ j ; n ) 2 { [ exp ( τ n + 1 τ n μ j + τ n μ e ) exp ( τ n τ n μ j + τ n μ e ) ] [ exp ( τ n + 1 τ n + 1 μ j + τ n + 1 μ e ) exp ( τ n τ n + 1 μ j + τ n + 1 μ e ) ] } .
R ( n , e ) , ( n , j ) ( m ) = 0 Δ τ n I r , ( n , μ e ) , ( n , μ j ) ( m ) , d ( τ ) exp ( τ n + 1 τ μ e ) d τ μ e
T ( n , e ) , ( n , j ) ( m ) = 0 Δ τ n I t , ( n , μ e ) , ( n , μ j ) ( m ) , d ( τ ) exp ( τ 0 τ n τ μ e ) d τ μ e ,
I r , ( n , μ e ) , ( n , μ j ) ( m ) , d ( τ ) = 1 2 1 Δ τ n 0 τ d x μ e exp ( τ μ e ) ω 0 ( n ) P r ( m ) ( μ e , μ j ; n ) 2 exp ( x μ j ) = 1 2 1 Δ τ n μ j μ j + μ e ω 0 ( n ) P r ( m ) ( μ e , μ j ; n ) 2 { 1 exp [ τ ( 1 μ j + 1 μ e ) ] }
I t , ( n , μ e ) , ( n , μ j ) ( m ) , d ( τ ) = 1 2 1 Δ τ n 0 τ d x μ e exp ( τ x μ e ) ω 0 ( n ) P t ( m ) ( μ e , μ j ; n ) 2 exp ( x μ j ) = 1 2 1 Δ τ n μ j μ j μ e ω 0 ( n ) P t ( m ) ( μ e , μ j ; n ) 2 [ exp ( τ μ j ) exp ( τ μ e ) ] .
R ( n , e ) , ( n , j ) ( m ) = 1 2 1 Δ τ n 1 μ j + μ e ω 0 ( n ) P r ( m ) ( μ e , μ j ; n ) 2 { μ e [ exp ( τ n μ e ) exp ( τ n + 1 μ e ) ] μ j exp ( τ n + 1 μ e ) [ 1 exp ( Δ τ n μ j ) ] } ,
T ( n , e ) , ( n , j ) ( m ) = 1 2 1 Δ τ n 1 μ j μ e ω 0 ( n ) P t ( m ) ( μ e , μ j ; n ) 2 exp ( τ 0 τ n μ e ) { μ j μ e μ j μ e [ exp ( μ j μ e μ j μ e Δ τ n ) 1 ] Δ τ n } .
R e , ( n , j ) ( m ) = n = 1 n ' R ( n , e ) , ( n , j ) ( m )
T e , ( n , j ) ( m ) = n = 1 n ' T ( n , e ) , ( n , j ) ( m ) .
R ( n , e ) , ( n , j ) ( m ) = τ n τ n + 1 I t , ( n , μ e ) , ( n , μ j ) ( m ) , u ( τ ) d τ μ e
T ( n , e ) , ( n , j ) ( m ) = τ n τ n + 1 I r , ( n , μ e ) , ( n , μ j ) ( m ) , u ( τ ) d τ μ e ,
I t , ( n , μ e ) , ( n , μ j ) ( m ) , u ( τ ) = 1 2 1 Δ τ n τ n τ n + 1 d x μ j exp ( τ μ e ) ω 0 ( n ) P t ( m ) , * ( μ e , μ j ; n ) 2 exp ( x τ μ j ) = 1 2 1 Δ τ n ω 0 ( n ) P t ( m ) , * ( μ e , μ j ; n ) 2 [ exp ( τ τ n μ j τ μ e ) exp ( τ τ n + 1 μ j τ μ e ) ]
I r , ( n , μ e ) , ( n , μ j ) ( m ) , u ( τ ) = 1 2 1 Δ τ n τ n τ n + 1 d x μ j exp ( τ 0 τ μ e ) ω 0 ( n ) P r ( m ) , * ( μ e , μ j ; n ) 2 exp ( x τ μ j ) = 1 2 1 Δ τ n ω 0 ( n ) P r ( m ) , * ( μ e , μ j ; n ) 2 [ exp ( τ τ n μ j τ 0 τ μ e ) exp ( τ τ n + 1 μ j τ 0 τ μ e ) ] .
R ( n , e ) , ( n , j ) ( m ) = 1 2 1 Δ τ n μ j μ e μ j ω 0 ( n ) P t ( m ) , * ( μ e , μ j ; n ) 2 { [ exp ( τ n + 1 τ n μ j τ n + 1 μ e ) exp ( τ n + 1 τ n + 1 μ j τ n + 1 μ e ) ] [ exp ( τ n τ n μ j τ n μ e ) exp ( τ n τ n + 1 μ j τ n μ e ) ] }
T ( n , e ) , ( n , j ) ( m ) = 1 2 1 Δ τ n μ j μ e + μ j exp ( τ 0 μ e ) ω 0 ( n ) P r ( m ) , * ( μ e , μ j ; n ) 2 { [ exp ( τ n + 1 τ n μ j + τ n + 1 μ e ) exp ( τ n + 1 τ n + 1 μ j + τ n + 1 μ e ) ] [ exp ( τ n τ n μ j + τ n μ e ) exp ( τ n τ n + 1 μ j + τ n μ e ) ] } .
R ( n , e ) , ( n , j ) ( m ) = 0 Δ τ n I t , ( n , μ e ) , ( n , μ j ) ( m ) , d ( τ ) exp ( τ n μ e ) d τ μ e
T ( n , e ) , ( n , j ) ( m ) = 0 Δ τ n I r , ( n , μ e ) , ( n , μ j ) ( m ) , d ( τ ) exp ( τ 0 τ n + 1 μ e ) d τ μ e ,
R ( n , e ) , ( n , j ) ( m ) = 1 2 1 Δ τ n 1 μ j μ e ω 0 ( n ) P t ( m ) , * ( μ e , μ j ; n ) 2 { μ j exp ( τ n μ e ) [ 1 exp ( Δ τ n μ j ) ] μ e [ exp ( τ n μ e ) exp ( τ n + 1 μ e ) ] }
T ( n , e ) , ( n , j ) ( m ) = 1 2 1 Δ τ n μ j μ j + μ e ω 0 ( n ) P r ( m ) , * ( μ e , μ j ; n ) 2 exp ( τ 0 τ n + 1 μ e ) ( Δ τ n μ j + μ e μ j + μ e { exp [ ( 1 μ j + 1 μ e ) Δ τ n ] 1 } ) .
( 1 + δ 0 m ) I r ( m ) ( τ = 0 ) = R eI ( m ) Π I0 ( m ) + R eJ ( m ) Q JI ( m ) Π I0 ( m ) + R eK ( m ) Q KJ ( m ) Q JI ( m ) Π I0 ( m ) + R eL ( m ) Q LK ( m ) Q KJ ( m ) Q JI ( m ) Π I0 ( m ) +
( 1 + δ 0 m ) I t ( m ) ( τ = τ 0 ) = T eI ( m ) Π I0 ( m ) + T eJ ( m ) Q JI ( m ) Π I0 ( m ) + T eK ( m ) Q KJ ( m ) Q JI ( m ) Π I0 ( m ) + T eL ( m ) Q LK ( m ) Q KJ ( m ) Q JI ( m ) Π I0 ( m ) +
( 2 δ 0 m ) I r ( m ) ( τ = 0 ) = R ( m ) ( E Q ( m ) ) 1 Π 0 ( m ) ,
( 2 δ 0 m ) I t ( m ) ( τ = τ 0 ) = T ( m ) ( E Q ( m ) ) 1 Π 0 ( m ) ,
I r / t , s = n = 1 N I r / t , s , n ,
I r , s , n ( τ = 0 , μ e , ϕ e ) = ω 0 ( n ) 4 τ n τ n + 1 d x μ e exp ( x μ e ) P r ( μ e , ϕ e ; μ 0 , ϕ 0 , n ) exp ( x μ 0 ) = ω 0 ( n ) 4 μ 0 μ e + μ 0 P r ( μ e , ϕ e ; μ 0 , ϕ 0 , n ) { exp [ τ n ( 1 μ e + 1 μ 0 ) ] exp [ τ n + 1 ( 1 μ e + 1 μ 0 ) ] } ,
I t , s , n ( τ = τ 0 , μ e , ϕ e ) = ω 0 ( n ) 4 τ n τ n + 1 d x μ e exp ( τ 0 x μ e ) P t ( μ e , ϕ e ; μ 0 , ϕ 0 , n ) exp ( x μ 0 ) = ω 0 ( n ) 4 μ 0 μ 0 μ e P t ( μ e , ϕ e ; μ 0 , ϕ 0 , n ) [ exp ( τ 0 τ n + 1 μ e ) exp ( τ n + 1 μ 0 ) exp ( τ 0 τ n μ e ) exp ( τ n μ 0 ) ] .
I r / s , d i f = I r / t , s + I r / t ( 0 ) + 2 m = 1 I r / t ( m ) .
P ( u , u 0 , ϕ ϕ 0 , n ) = L ( π i 2 ) P ( cos Θ , n ) L ( i 1 ) .
P ( u , u 0 , ϕ ϕ 0 , n ) = P c ( 0 ) ( u , u 0 ) + 2 m = 1 [ P c ( m ) ( u , u 0 , n ) cos m ( ϕ ϕ 0 ) + P s ( m ) ( u , u 0 , n ) sin m ( ϕ ϕ 0 ) ] ,
P c ( m ) ( μ , μ 0 ) = [ P 11 , c ( m ) P 12 , c ( m ) 0 0 P 21 , c ( m ) P 22 , c ( m ) 0 0 0 0 P 33 , c ( m ) P 34 , c ( m ) 0 0 P 43 , c ( m ) P 44 , c ( m ) ]
P s ( m ) ( μ , μ 0 ) = [ 0 0 P 13 , s ( m ) P 14 , s ( m ) 0 0 P 23 , s ( m ) P 24 , s ( m ) P 31 , s ( m ) P 32 , s ( m ) 0 0 P 41 , s ( m ) P 42 , s ( m ) 0 0 ] .
I ( τ , μ , ϕ ) = I c ( m ) ( τ , μ ) + 2 m = 1 [ I c ( m ) ( τ , μ ) cos m ( ϕ ϕ 0 ) + I s ( m ) ( τ , μ ) sin m ( ϕ ϕ 0 ) ] ,
[ 2 I r,c ( m ) ( τ = 0 ) 2 I r,s ( m ) ( τ = 0 ) ] = [ R c ( m ) R s ( m ) R s ( m ) R c ( m ) ] [ Π 0 , c ( m ) Π 0 , s ( m ) ] + [ R c ( m ) R s ( m ) R s ( m ) R c ( m ) ] [ Q c ( m ) Q s ( m ) Q s ( m ) Q c ( m ) ] [ Π 0 , c ( m ) Π 0 , s ( m ) ] + ...
[ 2 I t , c ( m ) ( τ = τ 0 ) 2 I t , s ( m ) ( τ = τ 0 ) ] = [ T c ( m ) T s ( m ) T s ( m ) T c ( m ) ] [ Π 0 , c ( m ) Π 0 , s ( m ) ] + [ T c ( m ) T s ( m ) T s ( m ) T c ( m ) ] [ Q c ( m ) Q s ( m ) Q s ( m ) Q c ( m ) ] [ Π 0 , c ( m ) Π 0 , s ( m ) ] + ...
I r,c ( m ) ( τ = 0 ) = R c ( m ) Π 0 , c ( m ) + R c ( m ) Q c ( m ) Π 0 , c ( m ) + ...
I t , c ( m ) ( τ = τ 0 ) = T c ( m ) Π 0 , c ( m ) + T c ( m ) Q c ( m ) Π 0 , c ( m ) + ...
[ Π ( n , i ) , 0 , r , c ( m ) Π ( n , i ) , 0 , r , s ( m ) ] = w i c ( n , i ) exp ( τ n μ 0 ) μ 0 μ i + μ 0 ω 0 ( n ) { 1 exp [ Δ τ n ( 1 μ 0 + 1 μ i ) ] } [ P r , c ( m ) ( μ 0 , μ e , n ) 2 P r , s ( m ) ( μ 0 , μ e , n ) 2 ] F 0
[ Π ( n , i ) , 0 , t , c ( m ) Π ( n , i ) , 0 , t , s ( m ) ] = w i c ( n , i ) exp ( τ n μ 0 ) μ 0 μ i μ 0 ω 0 ( n ) { exp ( Δ τ n μ i ) exp ( Δ τ n μ 0 ) } [ P t , c ( m ) ( μ 0 , μ e , n ) 2 P t , s ( m ) ( μ 0 , μ e , n ) 2 ] F 0 .
Π 0 ( m ) = [ Π 0 , c ( m ) ( 1 δ 0 m ) Π 0 , s ( m ) ] ,
Q ( m ) = [ Q c ( m ) ( 1 δ 0 m ) Q s ( m ) ( 1 δ 0 m ) Q s ( m ) ( 1 δ 0 m ) Q c ( m ) ] ,
R ( m ) = [ R c ( m ) ( 1 δ 0 m ) R s ( m ) ( 1 δ 0 m ) R s ( m ) ( 1 δ 0 m ) R c ( m ) ] ,
T ( m ) = [ T c ( m ) ( 1 δ 0 m ) T s ( m ) ( 1 δ 0 m ) T s ( m ) ( 1 δ 0 m ) T c ( m ) ] .
f ( a ) = 1 2 π ( s a ) exp { 1 2 [ ln ( a / a 0 ) s ] 2 } .

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