Abstract

An overview of the publicly available radiative transfer Spherical Harmonics code (SHARM) is presented. SHARM is a rigorous code, as accurate as the Discrete Ordinate Radiative Transfer (DISORT) code, yet faster. It performs simultaneous calculations for different solar zenith angles, view zenith angles, and view azimuths and allows the user to make multiwavelength calculations in one run. The Delta-M method is implemented for calculations with highly anisotropic phase functions. Rayleigh scattering is automatically included as a function of wavelength, surface elevation, and the selected vertical profile of one of the standard atmospheric models. The current version of the SHARM code does not explicitly include atmospheric gaseous absorption, which should be provided by the user. The SHARM code has several built-in models of the bidirectional reflectance of land and wind-ruffled water surfaces that are most widely used in research and satellite data processing. A modification of the SHARM code with the built-in Mie algorithm designed for calculations with spherical aerosols is also described.

© 2005 Optical Society of America

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2005 (2)

B. Mayer, A. Kylling, “Technical Note: The libRadtran software package for radiative transfer calculations: description and examples of use,” Atmos. Chem. Phys. 5. 1855–1877 (2005).
[Crossref]

C. K. Gatebe, M. D. King, A. I. Lyapustin, G. T. Arnold, J. Redemann, “Airborne spectral measurements of ocean directional reflectance,” J. Atmos. Sci. 62, 1072–1092 (2005).
[Crossref]

2003 (2)

M. D. King, W. P. Menzel, Y. J. Kaufman, D. Tanre, B. C. Gao, S. Platnick, S. A. Ackerman, L. A. Remer, R. Pincus, P. A. Hubanks, “Cloud and aerosol properties, precipitable water, and profiles of temperature and humidity from MODIS,” IEEE Trans. Geosci. Remote Sens. 41, 442–458 (2003).
[Crossref]

A. Lyapustin, “Interpolation and profile correction (IPC) method for shortwave radiative transfer in spectral intervals of gaseous absorption,” J. Atmos. Sci. 60, 865–871 (2003).
[Crossref]

2002 (2)

A. Lyapustin, “Radiative transfer code SHARM-3D for radiance simulations over a non-Lambertian nonhomogeneous surface: intercomparison study,” Appl. Opt. 41, 5607–5615 (2002).
[Crossref] [PubMed]

C. O. Justice, J. R. G. Townshend, E. F. Vermote, E. Masuoka, R. E. Wolfe, N. Saleous, D. P. Roy, J. T. Morisette, “An overview of MODIS land data processing and product status,” Remote Sens. Environ. 83, 3–15 (2002).
[Crossref]

2000 (3)

W. Lucht, C. B. Schaaf, A. H. Strahler, “An algorithm for the retrieval of albedo from space using semiempirical BRDF models,” IEEE Trans. Geosci. Remote Sens. 38, 977–998 (2000).
[Crossref]

A. I. Lyapustin, T. Z. Muldashev, “Generalization of Marshak boundary condition for non-Lambert reflection,” J. Quant. Spectrosc. Radiat. Transfer 67, 457–464 (2000).
[Crossref]

F. Gao, X. Li, A. Strahler, C. Schaaf, “Evaluation of the Li transit kernel for BRF modeling,” Remote Sens. Rev. 19, 205–224 (2000).
[Crossref]

1999 (1)

B. A. Bodhaine, N. B. Wood, E. G. Dutton, J. R. Slusser, “On Rayleigh optical depth calculations,” J. Atmos. Ocean. Technol. 16, 1854–1861 (1999).
[Crossref]

1998 (6)

D. J. Diner, J. C. Beckert, T. H. Reily, 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.-P. Muller, R. B. Myneni, P. J. Sellers, B. Pinty, M. M. Verstraete, “Multi-angle Imaging SpectroRadiometer (MISR) instrument description and experiment overview,” IEEE Trans. Geosci. Remote Sens. 36, 1072–1087 (1998).
[Crossref]

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanre, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, A. Smirnov, “AERONET—a federated instrument network and data archive for aerosol characterization,” Remote Sens. Environ. 66, 1–16 (1998).
[Crossref]

P. Ricchiazzi, S. Yang, C. Gautier, D. Sowle, “SBDART: a research and teaching software tool for plane-parallel radiative transfer in the Earth’s atmosphere,” Bull. Am. Meteor. Soc. 79, 2101–2114 (1998).
[Crossref]

T. Z. Muldashev, A. I. Lyapustin, U. M. Sultangazin, “Spherical harmonics method in the problem of radiative transfer in the atmosphere-surface system,” J. Quant. Spectrosc. Radiat. Transfer 61, 393–404 (1998).
[Crossref]

K. F. Evans, “The spherical harmonics discrete ordinate method for three-dimensional atmospheric radiative transfer,” J. Atmos. Sci. 55, 429–446 (1998).
[Crossref]

J. V. Martonchik, D. J. Diner, B. Pinty, M. M. Verstratete, R. B. Myneni, Yu. Knyazikhin, H. R. Gordon, “Determination of land and ocean reflective, radiative and biophysical properties using multiangle imaging,” IEEE Trans. Geosci. Remote Sens. 36, 1266–1281 (1998).
[Crossref]

1997 (1)

E. F. Vermote, D. Tanre, J. L. Deuze, M. Herman, J.-J. Mocrette, “Second Simulation of the Satellite Signal in the Solar Spectrum, 6S: an overview,” IEEE Trans. Geosci. Remote Sens. 35, 675–686 (1997).
[Crossref]

1993 (1)

H. Rahman, B. Pinty, M. M. Verstraete, “Coupled surface-atmosphere reflectance (CSAR) model. 2. Semiempirical surface model usable with NOAA advanced very high resolution radiometer data,” J. Geophys. Res. 98, 20,791–20,801 (1993).
[Crossref]

1992 (1)

1988 (2)

K. Stamnes, S. C. Tsay, W. Wiscombe, K. Jayaweera, “Numerically stable algorithm for discrete-ordinate-method radiative transfer in multiple scattering and emitting layered media,” Appl. Opt. 27, 2502–2509 (1988).
[Crossref] [PubMed]

T. Nakajima, M. Tanaka, “Algorithm for radiative intensity calculations in moderately thick atmospheres using a truncation approximation,” J. Quant. Spectrosc. Radiat. Transfer 40, 51–69 (1988).
[Crossref]

1983 (1)

T. Nakajima, M. Tanaka, “Effect of wind-generated waves on the transfer of solar radiation in the atmosphere–ocean system,” J. Quant. Spectrosc. Radiat. Transfer 29, 521–537 (1983).
[Crossref]

1980 (2)

W. Wiscombe, “Improved Mie scattering algorithms,” Appl. Opt. 19, 1505–1509 (1980).
[Crossref] [PubMed]

A. H. Karp, J. Greenstadt, J. A. Fillmore, “Radiative transfer through an arbitriarily thick, scattering atmosphere,” J. Quant. Spectrosc. Radiat. Transfer 24, 391–406 (1980).
[Crossref]

1977 (1)

W. J. Wiscombe, “Delta-M method–rapid yet accurate radiative flux calculations for strongly asymmetric phase functions,” J. Atmos. Sci. 34, 1408–1422 (1977).
[Crossref]

1975 (1)

J. V. Dave, “A direct solution of the spherical harmonics approximation to the radiative transfer equation for an arbitriary solar elevation,” J. Atmos. Sci. 32, 790–798 (1975).
[Crossref]

1973 (1)

1954 (1)

Abreu, L. W.

F. X. Kneizys, L. W. Abreu, G. P. Anderson, J. H. Chetwynd, E. P. Shettle, A. Berk, L. S. Bernstein, D. C. Robertson, P. Acharya, L. S. Rothman, J. E. A. Selby, W. O. Gallery, S. A. Clough, “The MODTRAN 2/3 report and LOWTRAN 7 model,” (Ontar Corporation, North Andover, Mass., 1996).

Acharya, P.

F. X. Kneizys, L. W. Abreu, G. P. Anderson, J. H. Chetwynd, E. P. Shettle, A. Berk, L. S. Bernstein, D. C. Robertson, P. Acharya, L. S. Rothman, J. E. A. Selby, W. O. Gallery, S. A. Clough, “The MODTRAN 2/3 report and LOWTRAN 7 model,” (Ontar Corporation, North Andover, Mass., 1996).

Ackerman, S. A.

M. D. King, W. P. Menzel, Y. J. Kaufman, D. Tanre, B. C. Gao, S. Platnick, S. A. Ackerman, L. A. Remer, R. Pincus, P. A. Hubanks, “Cloud and aerosol properties, precipitable water, and profiles of temperature and humidity from MODIS,” IEEE Trans. Geosci. Remote Sens. 41, 442–458 (2003).
[Crossref]

Ackerman, T. P.

D. J. Diner, J. C. Beckert, T. H. Reily, 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.-P. Muller, R. B. Myneni, P. J. Sellers, B. Pinty, M. M. Verstraete, “Multi-angle Imaging SpectroRadiometer (MISR) instrument description and experiment overview,” IEEE Trans. Geosci. Remote Sens. 36, 1072–1087 (1998).
[Crossref]

Anderson, G. P.

F. X. Kneizys, L. W. Abreu, G. P. Anderson, J. H. Chetwynd, E. P. Shettle, A. Berk, L. S. Bernstein, D. C. Robertson, P. Acharya, L. S. Rothman, J. E. A. Selby, W. O. Gallery, S. A. Clough, “The MODTRAN 2/3 report and LOWTRAN 7 model,” (Ontar Corporation, North Andover, Mass., 1996).

Arnold, G. T.

C. K. Gatebe, M. D. King, A. I. Lyapustin, G. T. Arnold, J. Redemann, “Airborne spectral measurements of ocean directional reflectance,” J. Atmos. Sci. 62, 1072–1092 (2005).
[Crossref]

Beckert, J. C.

D. J. Diner, J. C. Beckert, T. H. Reily, 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.-P. Muller, R. B. Myneni, P. J. Sellers, B. Pinty, M. M. Verstraete, “Multi-angle Imaging SpectroRadiometer (MISR) instrument description and experiment overview,” IEEE Trans. Geosci. Remote Sens. 36, 1072–1087 (1998).
[Crossref]

Berk, A.

F. X. Kneizys, L. W. Abreu, G. P. Anderson, J. H. Chetwynd, E. P. Shettle, A. Berk, L. S. Bernstein, D. C. Robertson, P. Acharya, L. S. Rothman, J. E. A. Selby, W. O. Gallery, S. A. Clough, “The MODTRAN 2/3 report and LOWTRAN 7 model,” (Ontar Corporation, North Andover, Mass., 1996).

Bernstein, L. S.

F. X. Kneizys, L. W. Abreu, G. P. Anderson, J. H. Chetwynd, E. P. Shettle, A. Berk, L. S. Bernstein, D. C. Robertson, P. Acharya, L. S. Rothman, J. E. A. Selby, W. O. Gallery, S. A. Clough, “The MODTRAN 2/3 report and LOWTRAN 7 model,” (Ontar Corporation, North Andover, Mass., 1996).

Bodhaine, B. A.

B. A. Bodhaine, N. B. Wood, E. G. Dutton, J. R. Slusser, “On Rayleigh optical depth calculations,” J. Atmos. Ocean. Technol. 16, 1854–1861 (1999).
[Crossref]

Bruegge, C. J.

D. J. Diner, J. C. Beckert, T. H. Reily, 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.-P. Muller, R. B. Myneni, P. J. Sellers, B. Pinty, M. M. Verstraete, “Multi-angle Imaging SpectroRadiometer (MISR) instrument description and experiment overview,” IEEE Trans. Geosci. Remote Sens. 36, 1072–1087 (1998).
[Crossref]

Buis, J. P.

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanre, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, A. Smirnov, “AERONET—a federated instrument network and data archive for aerosol characterization,” Remote Sens. Environ. 66, 1–16 (1998).
[Crossref]

Chandrasekhar, S.

S. Chandrasekhar, Radiative Transfer (Dover, 1960).

Chetwynd, J. H.

F. X. Kneizys, L. W. Abreu, G. P. Anderson, J. H. Chetwynd, E. P. Shettle, A. Berk, L. S. Bernstein, D. C. Robertson, P. Acharya, L. S. Rothman, J. E. A. Selby, W. O. Gallery, S. A. Clough, “The MODTRAN 2/3 report and LOWTRAN 7 model,” (Ontar Corporation, North Andover, Mass., 1996).

Clough, S. A.

F. X. Kneizys, L. W. Abreu, G. P. Anderson, J. H. Chetwynd, E. P. Shettle, A. Berk, L. S. Bernstein, D. C. Robertson, P. Acharya, L. S. Rothman, J. E. A. Selby, W. O. Gallery, S. A. Clough, “The MODTRAN 2/3 report and LOWTRAN 7 model,” (Ontar Corporation, North Andover, Mass., 1996).

Conel, J. E.

D. J. Diner, J. C. Beckert, T. H. Reily, 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.-P. Muller, R. B. Myneni, P. J. Sellers, B. Pinty, M. M. Verstraete, “Multi-angle Imaging SpectroRadiometer (MISR) instrument description and experiment overview,” IEEE Trans. Geosci. Remote Sens. 36, 1072–1087 (1998).
[Crossref]

Cox, C.

Dave, J. V.

J. V. Dave, “A direct solution of the spherical harmonics approximation to the radiative transfer equation for an arbitriary solar elevation,” J. Atmos. Sci. 32, 790–798 (1975).
[Crossref]

Davies, R.

D. J. Diner, J. C. Beckert, T. H. Reily, 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.-P. Muller, R. B. Myneni, P. J. Sellers, B. Pinty, M. M. Verstraete, “Multi-angle Imaging SpectroRadiometer (MISR) instrument description and experiment overview,” IEEE Trans. Geosci. Remote Sens. 36, 1072–1087 (1998).
[Crossref]

Deuze, J. L.

E. F. Vermote, D. Tanre, J. L. Deuze, M. Herman, J.-J. Mocrette, “Second Simulation of the Satellite Signal in the Solar Spectrum, 6S: an overview,” IEEE Trans. Geosci. Remote Sens. 35, 675–686 (1997).
[Crossref]

Diner, D. J.

D. J. Diner, J. C. Beckert, T. H. Reily, 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.-P. Muller, R. B. Myneni, P. J. Sellers, B. Pinty, M. M. Verstraete, “Multi-angle Imaging SpectroRadiometer (MISR) instrument description and experiment overview,” IEEE Trans. Geosci. Remote Sens. 36, 1072–1087 (1998).
[Crossref]

J. V. Martonchik, D. J. Diner, B. Pinty, M. M. Verstratete, R. B. Myneni, Yu. Knyazikhin, H. R. Gordon, “Determination of land and ocean reflective, radiative and biophysical properties using multiangle imaging,” IEEE Trans. Geosci. Remote Sens. 36, 1266–1281 (1998).
[Crossref]

Dutton, E. G.

B. A. Bodhaine, N. B. Wood, E. G. Dutton, J. R. Slusser, “On Rayleigh optical depth calculations,” J. Atmos. Ocean. Technol. 16, 1854–1861 (1999).
[Crossref]

Eck, T. F.

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanre, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, A. Smirnov, “AERONET—a federated instrument network and data archive for aerosol characterization,” Remote Sens. Environ. 66, 1–16 (1998).
[Crossref]

Evans, K. F.

K. F. Evans, “The spherical harmonics discrete ordinate method for three-dimensional atmospheric radiative transfer,” J. Atmos. Sci. 55, 429–446 (1998).
[Crossref]

Fillmore, J. A.

A. H. Karp, J. Greenstadt, J. A. Fillmore, “Radiative transfer through an arbitriarily thick, scattering atmosphere,” J. Quant. Spectrosc. Radiat. Transfer 24, 391–406 (1980).
[Crossref]

Gallery, W. O.

F. X. Kneizys, L. W. Abreu, G. P. Anderson, J. H. Chetwynd, E. P. Shettle, A. Berk, L. S. Bernstein, D. C. Robertson, P. Acharya, L. S. Rothman, J. E. A. Selby, W. O. Gallery, S. A. Clough, “The MODTRAN 2/3 report and LOWTRAN 7 model,” (Ontar Corporation, North Andover, Mass., 1996).

Gao, B. C.

M. D. King, W. P. Menzel, Y. J. Kaufman, D. Tanre, B. C. Gao, S. Platnick, S. A. Ackerman, L. A. Remer, R. Pincus, P. A. Hubanks, “Cloud and aerosol properties, precipitable water, and profiles of temperature and humidity from MODIS,” IEEE Trans. Geosci. Remote Sens. 41, 442–458 (2003).
[Crossref]

Gao, F.

F. Gao, X. Li, A. Strahler, C. Schaaf, “Evaluation of the Li transit kernel for BRF modeling,” Remote Sens. Rev. 19, 205–224 (2000).
[Crossref]

Gatebe, C. K.

C. K. Gatebe, M. D. King, A. I. Lyapustin, G. T. Arnold, J. Redemann, “Airborne spectral measurements of ocean directional reflectance,” J. Atmos. Sci. 62, 1072–1092 (2005).
[Crossref]

Gautier, C.

P. Ricchiazzi, S. Yang, C. Gautier, D. Sowle, “SBDART: a research and teaching software tool for plane-parallel radiative transfer in the Earth’s atmosphere,” Bull. Am. Meteor. Soc. 79, 2101–2114 (1998).
[Crossref]

Gerstl, S. A. W.

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Lyapustin, A. I.

C. K. Gatebe, M. D. King, A. I. Lyapustin, G. T. Arnold, J. Redemann, “Airborne spectral measurements of ocean directional reflectance,” J. Atmos. Sci. 62, 1072–1092 (2005).
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J. V. Martonchik, D. J. Diner, B. Pinty, M. M. Verstratete, R. B. Myneni, Yu. Knyazikhin, H. R. Gordon, “Determination of land and ocean reflective, radiative and biophysical properties using multiangle imaging,” IEEE Trans. Geosci. Remote Sens. 36, 1266–1281 (1998).
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C. O. Justice, J. R. G. Townshend, E. F. Vermote, E. Masuoka, R. E. Wolfe, N. Saleous, D. P. Roy, J. T. Morisette, “An overview of MODIS land data processing and product status,” Remote Sens. Environ. 83, 3–15 (2002).
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A. I. Lyapustin, T. Z. Muldashev, “Generalization of Marshak boundary condition for non-Lambert reflection,” J. Quant. Spectrosc. Radiat. Transfer 67, 457–464 (2000).
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J. V. Martonchik, D. J. Diner, B. Pinty, M. M. Verstratete, R. B. Myneni, Yu. Knyazikhin, H. R. Gordon, “Determination of land and ocean reflective, radiative and biophysical properties using multiangle imaging,” IEEE Trans. Geosci. Remote Sens. 36, 1266–1281 (1998).
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J. V. Martonchik, D. J. Diner, B. Pinty, M. M. Verstratete, R. B. Myneni, Yu. Knyazikhin, H. R. Gordon, “Determination of land and ocean reflective, radiative and biophysical properties using multiangle imaging,” IEEE Trans. Geosci. Remote Sens. 36, 1266–1281 (1998).
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A. Lyapustin, Y. Wang, J. Martonchik, J. Privette, B. Holben, I. Slutsker, A. Sinyuk, A. Smirnov, “Local analysis of MISR surface BRF and albedo over GSFC and Mongu AERO-NET sites,” IEEE Trans. Geosci. Remote Sens. (to be published).

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Rahman, H.

H. Rahman, B. Pinty, M. M. Verstraete, “Coupled surface-atmosphere reflectance (CSAR) model. 2. Semiempirical surface model usable with NOAA advanced very high resolution radiometer data,” J. Geophys. Res. 98, 20,791–20,801 (1993).
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C. K. Gatebe, M. D. King, A. I. Lyapustin, G. T. Arnold, J. Redemann, “Airborne spectral measurements of ocean directional reflectance,” J. Atmos. Sci. 62, 1072–1092 (2005).
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F. X. Kneizys, L. W. Abreu, G. P. Anderson, J. H. Chetwynd, E. P. Shettle, A. Berk, L. S. Bernstein, D. C. Robertson, P. Acharya, L. S. Rothman, J. E. A. Selby, W. O. Gallery, S. A. Clough, “The MODTRAN 2/3 report and LOWTRAN 7 model,” (Ontar Corporation, North Andover, Mass., 1996).

Roy, D. P.

C. O. Justice, J. R. G. Townshend, E. F. Vermote, E. Masuoka, R. E. Wolfe, N. Saleous, D. P. Roy, J. T. Morisette, “An overview of MODIS land data processing and product status,” Remote Sens. Environ. 83, 3–15 (2002).
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C. O. Justice, J. R. G. Townshend, E. F. Vermote, E. Masuoka, R. E. Wolfe, N. Saleous, D. P. Roy, J. T. Morisette, “An overview of MODIS land data processing and product status,” Remote Sens. Environ. 83, 3–15 (2002).
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F. Gao, X. Li, A. Strahler, C. Schaaf, “Evaluation of the Li transit kernel for BRF modeling,” Remote Sens. Rev. 19, 205–224 (2000).
[Crossref]

Schaaf, C. B.

W. Lucht, C. B. Schaaf, A. H. Strahler, “An algorithm for the retrieval of albedo from space using semiempirical BRDF models,” IEEE Trans. Geosci. Remote Sens. 38, 977–998 (2000).
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F. X. Kneizys, L. W. Abreu, G. P. Anderson, J. H. Chetwynd, E. P. Shettle, A. Berk, L. S. Bernstein, D. C. Robertson, P. Acharya, L. S. Rothman, J. E. A. Selby, W. O. Gallery, S. A. Clough, “The MODTRAN 2/3 report and LOWTRAN 7 model,” (Ontar Corporation, North Andover, Mass., 1996).

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D. J. Diner, J. C. Beckert, T. H. Reily, 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.-P. Muller, R. B. Myneni, P. J. Sellers, B. Pinty, M. M. Verstraete, “Multi-angle Imaging SpectroRadiometer (MISR) instrument description and experiment overview,” IEEE Trans. Geosci. Remote Sens. 36, 1072–1087 (1998).
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B. N. Holben, T. F. Eck, I. Slutsker, D. Tanre, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, A. Smirnov, “AERONET—a federated instrument network and data archive for aerosol characterization,” Remote Sens. Environ. 66, 1–16 (1998).
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F. X. Kneizys, L. W. Abreu, G. P. Anderson, J. H. Chetwynd, E. P. Shettle, A. Berk, L. S. Bernstein, D. C. Robertson, P. Acharya, L. S. Rothman, J. E. A. Selby, W. O. Gallery, S. A. Clough, “The MODTRAN 2/3 report and LOWTRAN 7 model,” (Ontar Corporation, North Andover, Mass., 1996).

Sinyuk, A.

A. Lyapustin, Y. Wang, J. Martonchik, J. Privette, B. Holben, I. Slutsker, A. Sinyuk, A. Smirnov, “Local analysis of MISR surface BRF and albedo over GSFC and Mongu AERO-NET sites,” IEEE Trans. Geosci. Remote Sens. (to be published).

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A. Lyapustin, Y. Wang, J. Martonchik, J. Privette, B. Holben, I. Slutsker, A. Sinyuk, A. Smirnov, “Local analysis of MISR surface BRF and albedo over GSFC and Mongu AERO-NET sites,” IEEE Trans. Geosci. Remote Sens. (to be published).

Smirnov, A.

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanre, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, A. Smirnov, “AERONET—a federated instrument network and data archive for aerosol characterization,” Remote Sens. Environ. 66, 1–16 (1998).
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A. Lyapustin, Y. Wang, J. Martonchik, J. Privette, B. Holben, I. Slutsker, A. Sinyuk, A. Smirnov, “Local analysis of MISR surface BRF and albedo over GSFC and Mongu AERO-NET sites,” IEEE Trans. Geosci. Remote Sens. (to be published).

Sowle, D.

P. Ricchiazzi, S. Yang, C. Gautier, D. Sowle, “SBDART: a research and teaching software tool for plane-parallel radiative transfer in the Earth’s atmosphere,” Bull. Am. Meteor. Soc. 79, 2101–2114 (1998).
[Crossref]

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Strahler, A.

F. Gao, X. Li, A. Strahler, C. Schaaf, “Evaluation of the Li transit kernel for BRF modeling,” Remote Sens. Rev. 19, 205–224 (2000).
[Crossref]

Strahler, A. H.

W. Lucht, C. B. Schaaf, A. H. Strahler, “An algorithm for the retrieval of albedo from space using semiempirical BRDF models,” IEEE Trans. Geosci. Remote Sens. 38, 977–998 (2000).
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T. Nakajima, M. Tanaka, “Algorithm for radiative intensity calculations in moderately thick atmospheres using a truncation approximation,” J. Quant. Spectrosc. Radiat. Transfer 40, 51–69 (1988).
[Crossref]

T. Nakajima, M. Tanaka, “Effect of wind-generated waves on the transfer of solar radiation in the atmosphere–ocean system,” J. Quant. Spectrosc. Radiat. Transfer 29, 521–537 (1983).
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M. D. King, W. P. Menzel, Y. J. Kaufman, D. Tanre, B. C. Gao, S. Platnick, S. A. Ackerman, L. A. Remer, R. Pincus, P. A. Hubanks, “Cloud and aerosol properties, precipitable water, and profiles of temperature and humidity from MODIS,” IEEE Trans. Geosci. Remote Sens. 41, 442–458 (2003).
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B. N. Holben, T. F. Eck, I. Slutsker, D. Tanre, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, A. Smirnov, “AERONET—a federated instrument network and data archive for aerosol characterization,” Remote Sens. Environ. 66, 1–16 (1998).
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E. F. Vermote, D. Tanre, J. L. Deuze, M. Herman, J.-J. Mocrette, “Second Simulation of the Satellite Signal in the Solar Spectrum, 6S: an overview,” IEEE Trans. Geosci. Remote Sens. 35, 675–686 (1997).
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C. O. Justice, J. R. G. Townshend, E. F. Vermote, E. Masuoka, R. E. Wolfe, N. Saleous, D. P. Roy, J. T. Morisette, “An overview of MODIS land data processing and product status,” Remote Sens. Environ. 83, 3–15 (2002).
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Vermote, E.

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanre, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, A. Smirnov, “AERONET—a federated instrument network and data archive for aerosol characterization,” Remote Sens. Environ. 66, 1–16 (1998).
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C. O. Justice, J. R. G. Townshend, E. F. Vermote, E. Masuoka, R. E. Wolfe, N. Saleous, D. P. Roy, J. T. Morisette, “An overview of MODIS land data processing and product status,” Remote Sens. Environ. 83, 3–15 (2002).
[Crossref]

E. F. Vermote, D. Tanre, J. L. Deuze, M. Herman, J.-J. Mocrette, “Second Simulation of the Satellite Signal in the Solar Spectrum, 6S: an overview,” IEEE Trans. Geosci. Remote Sens. 35, 675–686 (1997).
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D. J. Diner, J. C. Beckert, T. H. Reily, 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.-P. Muller, R. B. Myneni, P. J. Sellers, B. Pinty, M. M. Verstraete, “Multi-angle Imaging SpectroRadiometer (MISR) instrument description and experiment overview,” IEEE Trans. Geosci. Remote Sens. 36, 1072–1087 (1998).
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H. Rahman, B. Pinty, M. M. Verstraete, “Coupled surface-atmosphere reflectance (CSAR) model. 2. Semiempirical surface model usable with NOAA advanced very high resolution radiometer data,” J. Geophys. Res. 98, 20,791–20,801 (1993).
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J. V. Martonchik, D. J. Diner, B. Pinty, M. M. Verstratete, R. B. Myneni, Yu. Knyazikhin, H. R. Gordon, “Determination of land and ocean reflective, radiative and biophysical properties using multiangle imaging,” IEEE Trans. Geosci. Remote Sens. 36, 1266–1281 (1998).
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Wang, M.

Wang, Y.

A. Lyapustin, Y. Wang, J. Martonchik, J. Privette, B. Holben, I. Slutsker, A. Sinyuk, A. Smirnov, “Local analysis of MISR surface BRF and albedo over GSFC and Mongu AERO-NET sites,” IEEE Trans. Geosci. Remote Sens. (to be published).

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W. J. Wiscombe, “Delta-M method–rapid yet accurate radiative flux calculations for strongly asymmetric phase functions,” J. Atmos. Sci. 34, 1408–1422 (1977).
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C. O. Justice, J. R. G. Townshend, E. F. Vermote, E. Masuoka, R. E. Wolfe, N. Saleous, D. P. Roy, J. T. Morisette, “An overview of MODIS land data processing and product status,” Remote Sens. Environ. 83, 3–15 (2002).
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B. A. Bodhaine, N. B. Wood, E. G. Dutton, J. R. Slusser, “On Rayleigh optical depth calculations,” J. Atmos. Ocean. Technol. 16, 1854–1861 (1999).
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P. Ricchiazzi, S. Yang, C. Gautier, D. Sowle, “SBDART: a research and teaching software tool for plane-parallel radiative transfer in the Earth’s atmosphere,” Bull. Am. Meteor. Soc. 79, 2101–2114 (1998).
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P. Ricchiazzi, S. Yang, C. Gautier, D. Sowle, “SBDART: a research and teaching software tool for plane-parallel radiative transfer in the Earth’s atmosphere,” Bull. Am. Meteor. Soc. 79, 2101–2114 (1998).
[Crossref]

IEEE Trans. Geosci. Remote Sens. (5)

E. F. Vermote, D. Tanre, J. L. Deuze, M. Herman, J.-J. Mocrette, “Second Simulation of the Satellite Signal in the Solar Spectrum, 6S: an overview,” IEEE Trans. Geosci. Remote Sens. 35, 675–686 (1997).
[Crossref]

M. D. King, W. P. Menzel, Y. J. Kaufman, D. Tanre, B. C. Gao, S. Platnick, S. A. Ackerman, L. A. Remer, R. Pincus, P. A. Hubanks, “Cloud and aerosol properties, precipitable water, and profiles of temperature and humidity from MODIS,” IEEE Trans. Geosci. Remote Sens. 41, 442–458 (2003).
[Crossref]

D. J. Diner, J. C. Beckert, T. H. Reily, 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.-P. Muller, R. B. Myneni, P. J. Sellers, B. Pinty, M. M. Verstraete, “Multi-angle Imaging SpectroRadiometer (MISR) instrument description and experiment overview,” IEEE Trans. Geosci. Remote Sens. 36, 1072–1087 (1998).
[Crossref]

J. V. Martonchik, D. J. Diner, B. Pinty, M. M. Verstratete, R. B. Myneni, Yu. Knyazikhin, H. R. Gordon, “Determination of land and ocean reflective, radiative and biophysical properties using multiangle imaging,” IEEE Trans. Geosci. Remote Sens. 36, 1266–1281 (1998).
[Crossref]

W. Lucht, C. B. Schaaf, A. H. Strahler, “An algorithm for the retrieval of albedo from space using semiempirical BRDF models,” IEEE Trans. Geosci. Remote Sens. 38, 977–998 (2000).
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B. A. Bodhaine, N. B. Wood, E. G. Dutton, J. R. Slusser, “On Rayleigh optical depth calculations,” J. Atmos. Ocean. Technol. 16, 1854–1861 (1999).
[Crossref]

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K. F. Evans, “The spherical harmonics discrete ordinate method for three-dimensional atmospheric radiative transfer,” J. Atmos. Sci. 55, 429–446 (1998).
[Crossref]

W. J. Wiscombe, “Delta-M method–rapid yet accurate radiative flux calculations for strongly asymmetric phase functions,” J. Atmos. Sci. 34, 1408–1422 (1977).
[Crossref]

C. K. Gatebe, M. D. King, A. I. Lyapustin, G. T. Arnold, J. Redemann, “Airborne spectral measurements of ocean directional reflectance,” J. Atmos. Sci. 62, 1072–1092 (2005).
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H. Rahman, B. Pinty, M. M. Verstraete, “Coupled surface-atmosphere reflectance (CSAR) model. 2. Semiempirical surface model usable with NOAA advanced very high resolution radiometer data,” J. Geophys. Res. 98, 20,791–20,801 (1993).
[Crossref]

J. Opt. Soc. Am. (1)

J. Quant. Spectrosc. Radiat. Transfer (5)

T. Nakajima, M. Tanaka, “Effect of wind-generated waves on the transfer of solar radiation in the atmosphere–ocean system,” J. Quant. Spectrosc. Radiat. Transfer 29, 521–537 (1983).
[Crossref]

A. H. Karp, J. Greenstadt, J. A. Fillmore, “Radiative transfer through an arbitriarily thick, scattering atmosphere,” J. Quant. Spectrosc. Radiat. Transfer 24, 391–406 (1980).
[Crossref]

T. Nakajima, M. Tanaka, “Algorithm for radiative intensity calculations in moderately thick atmospheres using a truncation approximation,” J. Quant. Spectrosc. Radiat. Transfer 40, 51–69 (1988).
[Crossref]

T. Z. Muldashev, A. I. Lyapustin, U. M. Sultangazin, “Spherical harmonics method in the problem of radiative transfer in the atmosphere-surface system,” J. Quant. Spectrosc. Radiat. Transfer 61, 393–404 (1998).
[Crossref]

A. I. Lyapustin, T. Z. Muldashev, “Generalization of Marshak boundary condition for non-Lambert reflection,” J. Quant. Spectrosc. Radiat. Transfer 67, 457–464 (2000).
[Crossref]

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B. N. Holben, T. F. Eck, I. Slutsker, D. Tanre, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, A. Smirnov, “AERONET—a federated instrument network and data archive for aerosol characterization,” Remote Sens. Environ. 66, 1–16 (1998).
[Crossref]

C. O. Justice, J. R. G. Townshend, E. F. Vermote, E. Masuoka, R. E. Wolfe, N. Saleous, D. P. Roy, J. T. Morisette, “An overview of MODIS land data processing and product status,” Remote Sens. Environ. 83, 3–15 (2002).
[Crossref]

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A. Lyapustin, Y. Wang, J. Martonchik, J. Privette, B. Holben, I. Slutsker, A. Sinyuk, A. Smirnov, “Local analysis of MISR surface BRF and albedo over GSFC and Mongu AERO-NET sites,” IEEE Trans. Geosci. Remote Sens. (to be published).

J. R. Key, “Streamer—User’s guide” (University of Wisconsin, Madison, 2002); available at http://stratus.ssec.wisc.edu/streamer/streamer.html .

A. Lyapustin, SHARM Manual (NASA GSFC, 2005); available at ftp://ltpftp.gsf.nasa.gov/projects/asrvn .

F. X. Kneizys, L. W. Abreu, G. P. Anderson, J. H. Chetwynd, E. P. Shettle, A. Berk, L. S. Bernstein, D. C. Robertson, P. Acharya, L. S. Rothman, J. E. A. Selby, W. O. Gallery, S. A. Clough, “The MODTRAN 2/3 report and LOWTRAN 7 model,” (Ontar Corporation, North Andover, Mass., 1996).

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Figures (1)

Fig. 1
Fig. 1

Convergence of the SHARM code (left) and the SHARM with Delta-M code (right) for cirrus cloud. The results are shown as relative error (%) of SHARM radiance for different orders of MSH calculated with respect to the solution with nb = 512. Calculations were performed for τ = 0.8 and a SZA of 60°. Solid and dashed curves represent relative azimuths of 0° and 180°, respectively. The negative and positive values on the abscissa axis relate to the upward radiance at the top of the atmosphere (TOA), and to the diffuse sky radiance incident upon surface, respectively. The cirrus cloud phase function at λ = 0.66 µm corresponds to ice particles with an effective diameter of 10 µm (http://www.ssec.wisc.edu/∼baum/Cirrus/IceCloudModels.html).

Equations (39)

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τ m ( λ , z ) = 0 z σ ( λ , z ) N ( z ) d z ,
N ( z ) = N s P ( z ) P s T s T ( z )
μ I ( τ , μ , φ ) τ + I ( τ , μ , φ ) = ω 4 π 0 2 π d φ 1 1 × χ ( τ , γ ) I ( τ , μ , φ ) d μ + S λ ω 4 χ ( τ , γ 0 ) × exp ( τ μ 0 ) , I ( 0 ; μ , φ ) = 0 , μ > 0 ,
I ( τ 0 , μ , φ ) = S λ μ 0 ρ ( μ 0 , μ , φ φ 0 ) exp ( τ 0 μ 0 ) + 1 π 0 2 π d φ 0 1 ρ ( μ , μ , φ φ ) × I ( τ 0 , μ , φ ) μ d μ , μ < 0 .
x ( γ ) = n = 0 L χ n P n ( cos γ ) ,
χ k = 2 k + 1 2 1 1 χ ( y ) P k ( y ) d y .
A m d φ m ( τ ) d τ + C m φ m ( τ ) = exp ( τ / μ 0 ) f m ( τ ) .
I ( τ ; μ , φ ) = m = 0 ( 2 δ 0 , m ) I m ( τ , μ ) cos m φ , I m ( τ , μ ) = k = m L m 2 k + 1 2 φ k m ( τ ) Y k m ( μ ) .
Y k m ( μ ) = [ ( k m ) ! ( k + m ) ! ] 1 / 2 P k m ( μ )
φ od m ( 0 ) G m φ ev m ( 0 ) = 0 ,
( I 2 N od m ) φ od m ( τ 0 ) + ( G m 2 N ev m ) φ ev m ( τ 0 ) = 2 S 0 exp ( τ 0 / μ 0 ) Q m ( μ 0 ) ,
( N ev m ) l , k = ( 4 k + 2 m + 2 δ m 3 ) × 0 1 μ Q l m ( μ ) Y m + δ m + 2 k 2 m ( μ ) d μ ,
( N od m ) l , k = ( 4 k + 2 m 2 δ m 1 ) × 0 1 μ Q l m ( μ ) Y m δ m + 2 k 2 m ( μ ) d μ , l , k = 1 , 2 , , L m m + 1 2 ,
Q l m ( μ ) = 1 0 ρ m ( μ , μ ) Y m δ m + 2 l 1 m ( μ ) d μ .
I ( μ 0 , μ , φ ) = D ( μ 0 , μ , φ ) + q E 0 ( μ 0 ) T ( μ ) 1 q c 0 .
χ ( γ ) = F 2 δ ( 0 ) + ( 1 F ) χ * ( γ ) ,
χ n = F ( 2 n + 1 ) + ( 1 F ) χ n * ,
F = χ N 2 N + 1 , χ n * = χ n F ( 2 n + 1 ) ( 1 F ) .
μ I τ * + I = ω * 4 π 0 2 π d φ 1 1 χ * ( τ * , γ ) I ( τ * , μ , φ ) d μ + S λ ω * 4 χ ( τ , γ 0 ) 1 F exp [ τ * ( 1 ω F ) 1 μ 0 ] ,
τ * = τ ( 1 ω F ) , ω * = ω 1 F ( 1 ω F ) .
ρ ( μ 0 ; μ ; φ ) = ρ 0 M ( k ) F ( α ) H ( ρ 0 ) , M ( k ) = [ μ μ 0 ( μ + μ 0 ) ] k 1 , F ( α ) = 1 α 2 [ 1 2 α cos γ + α 2 ] 3 / 2 ,
H ( ρ 0 ) = ( 1 + 1 ρ 0 1 + G ) ,
cos γ = μ 0 μ + 1 μ 0 2 1 μ 2 cos ( φ φ 0 ) ,
G = [ tan 2 θ 0 + tan 2 θ + 2 tan θ 0 tan θ × cos ( φ φ 0 ) ] 1 / 2 .
ρ ( μ 0 , μ , φ ) = k L + k go f go ( μ 0 , μ , φ ) + k υ f υ ( μ 0 , μ , φ ) .
f υ = ( π / 2 γ ) cos γ + sin γ μ 0 + μ π 4 ,
f go = O ( μ 0 , μ , φ ) μ 1 μ 0 1 + 1 2 ( 1 + cos γ ) μ 1 μ 0 1 ,
O ( μ 0 , μ , φ ) = 1 π ( t sin t cos t ) ( | μ | 1 + μ 0 1 ) ,
cos t = h b { ( G ) 2 + [ tan θ 0 tan θ sin ( φ φ 0 ) ] 2 } 1 / 2 | μ | 1 + μ 0 1 ,
R ( μ , μ , φ φ ) = 1 4 μ μ n R Fr ( χ ) P ( μ n ) S ( μ , μ ) ,
P ( μ n ) = 1 π σ 2 μ n 3 exp ( 1 μ n 2 σ 2 μ n 2 ) ,
1 4 μ μ n P ( μ n ) = a 2 μ π σ 2 exp ( 1 2 a σ 2 ) ,
a = 1 + cos 2 χ ( μ + μ ) 2 , cos 2 χ = μ μ 1 μ 2 1 μ 2 × cos ( φ φ ) .
S ( μ , μ ) = 1 1 + F ( g ) + F ( g ) , g = μ σ 1 μ 2 ,
F ( g ) = 1 2 [ exp ( g 2 ) g π 2 π g exp ( t 2 ) d t ] = exp ( g 2 ) 2 g π 1 2 + Φ ( 2 g ) ; Φ ( 2 g ) = 1 2 π 0 2 g exp ( z 2 2 ) d z
ρ ( μ , μ , φ φ ) = π μ R ( μ , μ , φ φ ) .
Z x = Z / X = sin α tan β = sin θ sin φ μ + μ 0 , Z y = Z / Y = cos α tan β = sin θ cos φ sin θ 0 μ + μ 0 ,
Z u = Z y = Z y cos Δ φ w + Z x sin Δ φ w , Z c = Z x = Z y sin Δ φ w + Z x cos Δ φ w .
P ( μ n ) = 1 2 π σ u σ c μ n 3 exp ( ξ 2 + η 2 2 ) GC , η = Z u / σ u , ξ = Z c / σ c .

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