Abstract

A hybrid stream PCRTM-SOLAR model has been proposed for fast and accurate radiative transfer simulation. It calculates the reflected solar (RS) radiances with a fast coarse way and then, with the help of a pre-saved matrix, transforms the results to obtain the desired high accurate RS spectrum. The methodology has been demonstrated with the hybrid stream discrete ordinate (HSDO) radiative transfer (RT) model. The HSDO method calculates the monochromatic radiances using a 4-stream discrete ordinate method, where only a small number of monochromatic radiances are simulated with both 4-stream and a larger N-stream (N ≥ 16) discrete ordinate RT algorithm. The accuracy of the obtained channel radiance is comparable to the result from N-stream moderate resolution atmospheric transmission version 5 (MODTRAN5). The root-mean-square errors are usually less than 5x 10-4 mW/cm2/sr/cm−1. The computational speed is three to four-orders of magnitude faster than the medium speed correlated-k option MODTRAN5. This method is very efficient to simulate thousands of RS spectra under multi-layer clouds/aerosols and solar radiation conditions for climate change study and numerical weather prediction applications.

© 2016 Optical Society of America

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References

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2016 (3)

Z. Jin and M. Sun, “An initial study on climate change fingerprinting using the reflected solar spectra,” J. Clim. 29(8), 2781–2796 (2016).
[Crossref]

X. Liu, Q. Yang, H. Li, Z. Jin, W. Wu, S. Kizer, D. K. Zhou, and P. Yang, “Development of a fast and accurate PCRTM radiative transfer model in the solar spectral region,” Appl. Opt. 55(29), 8236–8247 (2016).
[Crossref]

P. Kopparla, V. Natraj, R. Spurr, R. Shia, D. Crisp, and Y. Yung, “A fast and accurate PCA based radiative transfer model: Extension to the broadband shortwave region,” J. Quant. Spec. Radi. Trans. 173, 65–71 (2016).
[Crossref]

2013 (2)

C. Wang, P. Yang, S. L. Nasiri, S. Platnick, B. A. Baum, A. K. Heidinger, and X. Liu, “A fast radiative transfer model for visible through shortwave infrared spectral reflectance’s in clear and cloudy atmospheres,” J. Quant. Spectrosc. Radiat. Transf. 116, 122–131 (2013).
[Crossref]

B. A. Wielicki, D. F. Young, M. G. Mlynczak, K. J. Thome, S. Leroy, J. Corliss, J. G. Anderson, C. O. Ao, R. Bantges, F. Best, K. Bowman, H. Brindley, J. Butler, W. Collins, J. A. Dykema, D. R. Doelling, D. R. Feldman, N. Fox, X. Huang, R. Holz, Y. Huang, Z. Jin, D. Jennings, D. G. Johnson, K. Jucks, S. Kato, D. B. Kirk-Davidoff, R. Knuteson, G. Kopp, D. P. Kratz, X. Liu, C. Lukashin, A. J. Mannucci, N. Phojanamongkolkij, P. Pilewskie, V. Ramaswamy, H. Revercomb, J. Rice, Y. Roberts, C. M. Roithmayr, F. Rose, S. Sandford, E. L. Shirley, W. L. Smith, B. Soden, P. W. Speth, W. Sun, P. C. Taylor, D. Tobin, and X. Xiong, “Achieving climate change absolute accuracy in orbit,” Bull. Am. Meteorol. Soc. 94(10), 1519–1539 (2013).
[Crossref]

2011 (1)

D. R. Feldman, C. A. Algieri, J. R. Ong, and W. D. Collins, “CLARREO shortwave observing system simulation experiments of the twenty-first century: simulator design and implementation,” J. Geophys. Res. 116(D10), D10107 (2011).
[Crossref]

2006 (1)

2005 (1)

V. Natraj, X. Jiang, R. Shia, X. Huang, J. Margolis, and Y. Yung, “Application of principal component analysis to high spectral resolution radiative transfer: a case study of the O2 A band,” J. Quant. Spec. Radi. Trans. 95(4), 539–556 (2005).
[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]

1994 (1)

R. Cahalan, W. Ridgway, W. Wiscombe, S. Gollmer, and Harshvardhan, “Independent pixel and Monte Carlo estimates of stratocumulus albedo,” J. Atmos. Sci. 51(24), 3776–3790 (1994).
[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]

1988 (1)

1987 (1)

J. F. de Haan, P. B. Bosma, and J. W. Hovenier, “The adding method for multiple scattering calculations of polarized light,” Astron. Astrophys. 183, 371–391 (1987).

1974 (1)

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

1971 (1)

J. W. Hovenier, “Multiple scattering of polarized light in planetary atmospheres,” Astron. Astrophys. 13, 7–29 (1971).

Algieri, C. A.

D. R. Feldman, C. A. Algieri, J. R. Ong, and W. D. Collins, “CLARREO shortwave observing system simulation experiments of the twenty-first century: simulator design and implementation,” J. Geophys. Res. 116(D10), D10107 (2011).
[Crossref]

Anderson, J. G.

B. A. Wielicki, D. F. Young, M. G. Mlynczak, K. J. Thome, S. Leroy, J. Corliss, J. G. Anderson, C. O. Ao, R. Bantges, F. Best, K. Bowman, H. Brindley, J. Butler, W. Collins, J. A. Dykema, D. R. Doelling, D. R. Feldman, N. Fox, X. Huang, R. Holz, Y. Huang, Z. Jin, D. Jennings, D. G. Johnson, K. Jucks, S. Kato, D. B. Kirk-Davidoff, R. Knuteson, G. Kopp, D. P. Kratz, X. Liu, C. Lukashin, A. J. Mannucci, N. Phojanamongkolkij, P. Pilewskie, V. Ramaswamy, H. Revercomb, J. Rice, Y. Roberts, C. M. Roithmayr, F. Rose, S. Sandford, E. L. Shirley, W. L. Smith, B. Soden, P. W. Speth, W. Sun, P. C. Taylor, D. Tobin, and X. Xiong, “Achieving climate change absolute accuracy in orbit,” Bull. Am. Meteorol. Soc. 94(10), 1519–1539 (2013).
[Crossref]

Ao, C. O.

B. A. Wielicki, D. F. Young, M. G. Mlynczak, K. J. Thome, S. Leroy, J. Corliss, J. G. Anderson, C. O. Ao, R. Bantges, F. Best, K. Bowman, H. Brindley, J. Butler, W. Collins, J. A. Dykema, D. R. Doelling, D. R. Feldman, N. Fox, X. Huang, R. Holz, Y. Huang, Z. Jin, D. Jennings, D. G. Johnson, K. Jucks, S. Kato, D. B. Kirk-Davidoff, R. Knuteson, G. Kopp, D. P. Kratz, X. Liu, C. Lukashin, A. J. Mannucci, N. Phojanamongkolkij, P. Pilewskie, V. Ramaswamy, H. Revercomb, J. Rice, Y. Roberts, C. M. Roithmayr, F. Rose, S. Sandford, E. L. Shirley, W. L. Smith, B. Soden, P. W. Speth, W. Sun, P. C. Taylor, D. Tobin, and X. Xiong, “Achieving climate change absolute accuracy in orbit,” Bull. Am. Meteorol. Soc. 94(10), 1519–1539 (2013).
[Crossref]

Bantges, R.

B. A. Wielicki, D. F. Young, M. G. Mlynczak, K. J. Thome, S. Leroy, J. Corliss, J. G. Anderson, C. O. Ao, R. Bantges, F. Best, K. Bowman, H. Brindley, J. Butler, W. Collins, J. A. Dykema, D. R. Doelling, D. R. Feldman, N. Fox, X. Huang, R. Holz, Y. Huang, Z. Jin, D. Jennings, D. G. Johnson, K. Jucks, S. Kato, D. B. Kirk-Davidoff, R. Knuteson, G. Kopp, D. P. Kratz, X. Liu, C. Lukashin, A. J. Mannucci, N. Phojanamongkolkij, P. Pilewskie, V. Ramaswamy, H. Revercomb, J. Rice, Y. Roberts, C. M. Roithmayr, F. Rose, S. Sandford, E. L. Shirley, W. L. Smith, B. Soden, P. W. Speth, W. Sun, P. C. Taylor, D. Tobin, and X. Xiong, “Achieving climate change absolute accuracy in orbit,” Bull. Am. Meteorol. Soc. 94(10), 1519–1539 (2013).
[Crossref]

Baum, B. A.

C. Wang, P. Yang, S. L. Nasiri, S. Platnick, B. A. Baum, A. K. Heidinger, and X. Liu, “A fast radiative transfer model for visible through shortwave infrared spectral reflectance’s in clear and cloudy atmospheres,” J. Quant. Spectrosc. Radiat. Transf. 116, 122–131 (2013).
[Crossref]

Best, F.

B. A. Wielicki, D. F. Young, M. G. Mlynczak, K. J. Thome, S. Leroy, J. Corliss, J. G. Anderson, C. O. Ao, R. Bantges, F. Best, K. Bowman, H. Brindley, J. Butler, W. Collins, J. A. Dykema, D. R. Doelling, D. R. Feldman, N. Fox, X. Huang, R. Holz, Y. Huang, Z. Jin, D. Jennings, D. G. Johnson, K. Jucks, S. Kato, D. B. Kirk-Davidoff, R. Knuteson, G. Kopp, D. P. Kratz, X. Liu, C. Lukashin, A. J. Mannucci, N. Phojanamongkolkij, P. Pilewskie, V. Ramaswamy, H. Revercomb, J. Rice, Y. Roberts, C. M. Roithmayr, F. Rose, S. Sandford, E. L. Shirley, W. L. Smith, B. Soden, P. W. Speth, W. Sun, P. C. Taylor, D. Tobin, and X. Xiong, “Achieving climate change absolute accuracy in orbit,” Bull. Am. Meteorol. Soc. 94(10), 1519–1539 (2013).
[Crossref]

Bosma, P. B.

J. F. de Haan, P. B. Bosma, and J. W. Hovenier, “The adding method for multiple scattering calculations of polarized light,” Astron. Astrophys. 183, 371–391 (1987).

Bowman, K.

B. A. Wielicki, D. F. Young, M. G. Mlynczak, K. J. Thome, S. Leroy, J. Corliss, J. G. Anderson, C. O. Ao, R. Bantges, F. Best, K. Bowman, H. Brindley, J. Butler, W. Collins, J. A. Dykema, D. R. Doelling, D. R. Feldman, N. Fox, X. Huang, R. Holz, Y. Huang, Z. Jin, D. Jennings, D. G. Johnson, K. Jucks, S. Kato, D. B. Kirk-Davidoff, R. Knuteson, G. Kopp, D. P. Kratz, X. Liu, C. Lukashin, A. J. Mannucci, N. Phojanamongkolkij, P. Pilewskie, V. Ramaswamy, H. Revercomb, J. Rice, Y. Roberts, C. M. Roithmayr, F. Rose, S. Sandford, E. L. Shirley, W. L. Smith, B. Soden, P. W. Speth, W. Sun, P. C. Taylor, D. Tobin, and X. Xiong, “Achieving climate change absolute accuracy in orbit,” Bull. Am. Meteorol. Soc. 94(10), 1519–1539 (2013).
[Crossref]

Brindley, H.

B. A. Wielicki, D. F. Young, M. G. Mlynczak, K. J. Thome, S. Leroy, J. Corliss, J. G. Anderson, C. O. Ao, R. Bantges, F. Best, K. Bowman, H. Brindley, J. Butler, W. Collins, J. A. Dykema, D. R. Doelling, D. R. Feldman, N. Fox, X. Huang, R. Holz, Y. Huang, Z. Jin, D. Jennings, D. G. Johnson, K. Jucks, S. Kato, D. B. Kirk-Davidoff, R. Knuteson, G. Kopp, D. P. Kratz, X. Liu, C. Lukashin, A. J. Mannucci, N. Phojanamongkolkij, P. Pilewskie, V. Ramaswamy, H. Revercomb, J. Rice, Y. Roberts, C. M. Roithmayr, F. Rose, S. Sandford, E. L. Shirley, W. L. Smith, B. Soden, P. W. Speth, W. Sun, P. C. Taylor, D. Tobin, and X. Xiong, “Achieving climate change absolute accuracy in orbit,” Bull. Am. Meteorol. Soc. 94(10), 1519–1539 (2013).
[Crossref]

Butler, J.

B. A. Wielicki, D. F. Young, M. G. Mlynczak, K. J. Thome, S. Leroy, J. Corliss, J. G. Anderson, C. O. Ao, R. Bantges, F. Best, K. Bowman, H. Brindley, J. Butler, W. Collins, J. A. Dykema, D. R. Doelling, D. R. Feldman, N. Fox, X. Huang, R. Holz, Y. Huang, Z. Jin, D. Jennings, D. G. Johnson, K. Jucks, S. Kato, D. B. Kirk-Davidoff, R. Knuteson, G. Kopp, D. P. Kratz, X. Liu, C. Lukashin, A. J. Mannucci, N. Phojanamongkolkij, P. Pilewskie, V. Ramaswamy, H. Revercomb, J. Rice, Y. Roberts, C. M. Roithmayr, F. Rose, S. Sandford, E. L. Shirley, W. L. Smith, B. Soden, P. W. Speth, W. Sun, P. C. Taylor, D. Tobin, and X. Xiong, “Achieving climate change absolute accuracy in orbit,” Bull. Am. Meteorol. Soc. 94(10), 1519–1539 (2013).
[Crossref]

Cahalan, R.

R. Cahalan, W. Ridgway, W. Wiscombe, S. Gollmer, and Harshvardhan, “Independent pixel and Monte Carlo estimates of stratocumulus albedo,” J. Atmos. Sci. 51(24), 3776–3790 (1994).
[Crossref]

Collins, W.

B. A. Wielicki, D. F. Young, M. G. Mlynczak, K. J. Thome, S. Leroy, J. Corliss, J. G. Anderson, C. O. Ao, R. Bantges, F. Best, K. Bowman, H. Brindley, J. Butler, W. Collins, J. A. Dykema, D. R. Doelling, D. R. Feldman, N. Fox, X. Huang, R. Holz, Y. Huang, Z. Jin, D. Jennings, D. G. Johnson, K. Jucks, S. Kato, D. B. Kirk-Davidoff, R. Knuteson, G. Kopp, D. P. Kratz, X. Liu, C. Lukashin, A. J. Mannucci, N. Phojanamongkolkij, P. Pilewskie, V. Ramaswamy, H. Revercomb, J. Rice, Y. Roberts, C. M. Roithmayr, F. Rose, S. Sandford, E. L. Shirley, W. L. Smith, B. Soden, P. W. Speth, W. Sun, P. C. Taylor, D. Tobin, and X. Xiong, “Achieving climate change absolute accuracy in orbit,” Bull. Am. Meteorol. Soc. 94(10), 1519–1539 (2013).
[Crossref]

Collins, W. D.

D. R. Feldman, C. A. Algieri, J. R. Ong, and W. D. Collins, “CLARREO shortwave observing system simulation experiments of the twenty-first century: simulator design and implementation,” J. Geophys. Res. 116(D10), D10107 (2011).
[Crossref]

Corliss, J.

B. A. Wielicki, D. F. Young, M. G. Mlynczak, K. J. Thome, S. Leroy, J. Corliss, J. G. Anderson, C. O. Ao, R. Bantges, F. Best, K. Bowman, H. Brindley, J. Butler, W. Collins, J. A. Dykema, D. R. Doelling, D. R. Feldman, N. Fox, X. Huang, R. Holz, Y. Huang, Z. Jin, D. Jennings, D. G. Johnson, K. Jucks, S. Kato, D. B. Kirk-Davidoff, R. Knuteson, G. Kopp, D. P. Kratz, X. Liu, C. Lukashin, A. J. Mannucci, N. Phojanamongkolkij, P. Pilewskie, V. Ramaswamy, H. Revercomb, J. Rice, Y. Roberts, C. M. Roithmayr, F. Rose, S. Sandford, E. L. Shirley, W. L. Smith, B. Soden, P. W. Speth, W. Sun, P. C. Taylor, D. Tobin, and X. Xiong, “Achieving climate change absolute accuracy in orbit,” Bull. Am. Meteorol. Soc. 94(10), 1519–1539 (2013).
[Crossref]

Crisp, D.

P. Kopparla, V. Natraj, R. Spurr, R. Shia, D. Crisp, and Y. Yung, “A fast and accurate PCA based radiative transfer model: Extension to the broadband shortwave region,” J. Quant. Spec. Radi. Trans. 173, 65–71 (2016).
[Crossref]

de Haan, J. F.

J. F. de Haan, P. B. Bosma, and J. W. Hovenier, “The adding method for multiple scattering calculations of polarized light,” Astron. Astrophys. 183, 371–391 (1987).

Doelling, D. R.

B. A. Wielicki, D. F. Young, M. G. Mlynczak, K. J. Thome, S. Leroy, J. Corliss, J. G. Anderson, C. O. Ao, R. Bantges, F. Best, K. Bowman, H. Brindley, J. Butler, W. Collins, J. A. Dykema, D. R. Doelling, D. R. Feldman, N. Fox, X. Huang, R. Holz, Y. Huang, Z. Jin, D. Jennings, D. G. Johnson, K. Jucks, S. Kato, D. B. Kirk-Davidoff, R. Knuteson, G. Kopp, D. P. Kratz, X. Liu, C. Lukashin, A. J. Mannucci, N. Phojanamongkolkij, P. Pilewskie, V. Ramaswamy, H. Revercomb, J. Rice, Y. Roberts, C. M. Roithmayr, F. Rose, S. Sandford, E. L. Shirley, W. L. Smith, B. Soden, P. W. Speth, W. Sun, P. C. Taylor, D. Tobin, and X. Xiong, “Achieving climate change absolute accuracy in orbit,” Bull. Am. Meteorol. Soc. 94(10), 1519–1539 (2013).
[Crossref]

Dykema, J. A.

B. A. Wielicki, D. F. Young, M. G. Mlynczak, K. J. Thome, S. Leroy, J. Corliss, J. G. Anderson, C. O. Ao, R. Bantges, F. Best, K. Bowman, H. Brindley, J. Butler, W. Collins, J. A. Dykema, D. R. Doelling, D. R. Feldman, N. Fox, X. Huang, R. Holz, Y. Huang, Z. Jin, D. Jennings, D. G. Johnson, K. Jucks, S. Kato, D. B. Kirk-Davidoff, R. Knuteson, G. Kopp, D. P. Kratz, X. Liu, C. Lukashin, A. J. Mannucci, N. Phojanamongkolkij, P. Pilewskie, V. Ramaswamy, H. Revercomb, J. Rice, Y. Roberts, C. M. Roithmayr, F. Rose, S. Sandford, E. L. Shirley, W. L. Smith, B. Soden, P. W. Speth, W. Sun, P. C. Taylor, D. Tobin, and X. Xiong, “Achieving climate change absolute accuracy in orbit,” Bull. Am. Meteorol. Soc. 94(10), 1519–1539 (2013).
[Crossref]

Evans, K. F.

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]

Feldman, D. R.

B. A. Wielicki, D. F. Young, M. G. Mlynczak, K. J. Thome, S. Leroy, J. Corliss, J. G. Anderson, C. O. Ao, R. Bantges, F. Best, K. Bowman, H. Brindley, J. Butler, W. Collins, J. A. Dykema, D. R. Doelling, D. R. Feldman, N. Fox, X. Huang, R. Holz, Y. Huang, Z. Jin, D. Jennings, D. G. Johnson, K. Jucks, S. Kato, D. B. Kirk-Davidoff, R. Knuteson, G. Kopp, D. P. Kratz, X. Liu, C. Lukashin, A. J. Mannucci, N. Phojanamongkolkij, P. Pilewskie, V. Ramaswamy, H. Revercomb, J. Rice, Y. Roberts, C. M. Roithmayr, F. Rose, S. Sandford, E. L. Shirley, W. L. Smith, B. Soden, P. W. Speth, W. Sun, P. C. Taylor, D. Tobin, and X. Xiong, “Achieving climate change absolute accuracy in orbit,” Bull. Am. Meteorol. Soc. 94(10), 1519–1539 (2013).
[Crossref]

D. R. Feldman, C. A. Algieri, J. R. Ong, and W. D. Collins, “CLARREO shortwave observing system simulation experiments of the twenty-first century: simulator design and implementation,” J. Geophys. Res. 116(D10), D10107 (2011).
[Crossref]

Fox, N.

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B. A. Wielicki, D. F. Young, M. G. Mlynczak, K. J. Thome, S. Leroy, J. Corliss, J. G. Anderson, C. O. Ao, R. Bantges, F. Best, K. Bowman, H. Brindley, J. Butler, W. Collins, J. A. Dykema, D. R. Doelling, D. R. Feldman, N. Fox, X. Huang, R. Holz, Y. Huang, Z. Jin, D. Jennings, D. G. Johnson, K. Jucks, S. Kato, D. B. Kirk-Davidoff, R. Knuteson, G. Kopp, D. P. Kratz, X. Liu, C. Lukashin, A. J. Mannucci, N. Phojanamongkolkij, P. Pilewskie, V. Ramaswamy, H. Revercomb, J. Rice, Y. Roberts, C. M. Roithmayr, F. Rose, S. Sandford, E. L. Shirley, W. L. Smith, B. Soden, P. W. Speth, W. Sun, P. C. Taylor, D. Tobin, and X. Xiong, “Achieving climate change absolute accuracy in orbit,” Bull. Am. Meteorol. Soc. 94(10), 1519–1539 (2013).
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B. A. Wielicki, D. F. Young, M. G. Mlynczak, K. J. Thome, S. Leroy, J. Corliss, J. G. Anderson, C. O. Ao, R. Bantges, F. Best, K. Bowman, H. Brindley, J. Butler, W. Collins, J. A. Dykema, D. R. Doelling, D. R. Feldman, N. Fox, X. Huang, R. Holz, Y. Huang, Z. Jin, D. Jennings, D. G. Johnson, K. Jucks, S. Kato, D. B. Kirk-Davidoff, R. Knuteson, G. Kopp, D. P. Kratz, X. Liu, C. Lukashin, A. J. Mannucci, N. Phojanamongkolkij, P. Pilewskie, V. Ramaswamy, H. Revercomb, J. Rice, Y. Roberts, C. M. Roithmayr, F. Rose, S. Sandford, E. L. Shirley, W. L. Smith, B. Soden, P. W. Speth, W. Sun, P. C. Taylor, D. Tobin, and X. Xiong, “Achieving climate change absolute accuracy in orbit,” Bull. Am. Meteorol. Soc. 94(10), 1519–1539 (2013).
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Huang, Y.

B. A. Wielicki, D. F. Young, M. G. Mlynczak, K. J. Thome, S. Leroy, J. Corliss, J. G. Anderson, C. O. Ao, R. Bantges, F. Best, K. Bowman, H. Brindley, J. Butler, W. Collins, J. A. Dykema, D. R. Doelling, D. R. Feldman, N. Fox, X. Huang, R. Holz, Y. Huang, Z. Jin, D. Jennings, D. G. Johnson, K. Jucks, S. Kato, D. B. Kirk-Davidoff, R. Knuteson, G. Kopp, D. P. Kratz, X. Liu, C. Lukashin, A. J. Mannucci, N. Phojanamongkolkij, P. Pilewskie, V. Ramaswamy, H. Revercomb, J. Rice, Y. Roberts, C. M. Roithmayr, F. Rose, S. Sandford, E. L. Shirley, W. L. Smith, B. Soden, P. W. Speth, W. Sun, P. C. Taylor, D. Tobin, and X. Xiong, “Achieving climate change absolute accuracy in orbit,” Bull. Am. Meteorol. Soc. 94(10), 1519–1539 (2013).
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Jayaweera, K.

Jennings, D.

B. A. Wielicki, D. F. Young, M. G. Mlynczak, K. J. Thome, S. Leroy, J. Corliss, J. G. Anderson, C. O. Ao, R. Bantges, F. Best, K. Bowman, H. Brindley, J. Butler, W. Collins, J. A. Dykema, D. R. Doelling, D. R. Feldman, N. Fox, X. Huang, R. Holz, Y. Huang, Z. Jin, D. Jennings, D. G. Johnson, K. Jucks, S. Kato, D. B. Kirk-Davidoff, R. Knuteson, G. Kopp, D. P. Kratz, X. Liu, C. Lukashin, A. J. Mannucci, N. Phojanamongkolkij, P. Pilewskie, V. Ramaswamy, H. Revercomb, J. Rice, Y. Roberts, C. M. Roithmayr, F. Rose, S. Sandford, E. L. Shirley, W. L. Smith, B. Soden, P. W. Speth, W. Sun, P. C. Taylor, D. Tobin, and X. Xiong, “Achieving climate change absolute accuracy in orbit,” Bull. Am. Meteorol. Soc. 94(10), 1519–1539 (2013).
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Jiang, X.

V. Natraj, X. Jiang, R. Shia, X. Huang, J. Margolis, and Y. Yung, “Application of principal component analysis to high spectral resolution radiative transfer: a case study of the O2 A band,” J. Quant. Spec. Radi. Trans. 95(4), 539–556 (2005).
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B. A. Wielicki, D. F. Young, M. G. Mlynczak, K. J. Thome, S. Leroy, J. Corliss, J. G. Anderson, C. O. Ao, R. Bantges, F. Best, K. Bowman, H. Brindley, J. Butler, W. Collins, J. A. Dykema, D. R. Doelling, D. R. Feldman, N. Fox, X. Huang, R. Holz, Y. Huang, Z. Jin, D. Jennings, D. G. Johnson, K. Jucks, S. Kato, D. B. Kirk-Davidoff, R. Knuteson, G. Kopp, D. P. Kratz, X. Liu, C. Lukashin, A. J. Mannucci, N. Phojanamongkolkij, P. Pilewskie, V. Ramaswamy, H. Revercomb, J. Rice, Y. Roberts, C. M. Roithmayr, F. Rose, S. Sandford, E. L. Shirley, W. L. Smith, B. Soden, P. W. Speth, W. Sun, P. C. Taylor, D. Tobin, and X. Xiong, “Achieving climate change absolute accuracy in orbit,” Bull. Am. Meteorol. Soc. 94(10), 1519–1539 (2013).
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Johnson, D. G.

B. A. Wielicki, D. F. Young, M. G. Mlynczak, K. J. Thome, S. Leroy, J. Corliss, J. G. Anderson, C. O. Ao, R. Bantges, F. Best, K. Bowman, H. Brindley, J. Butler, W. Collins, J. A. Dykema, D. R. Doelling, D. R. Feldman, N. Fox, X. Huang, R. Holz, Y. Huang, Z. Jin, D. Jennings, D. G. Johnson, K. Jucks, S. Kato, D. B. Kirk-Davidoff, R. Knuteson, G. Kopp, D. P. Kratz, X. Liu, C. Lukashin, A. J. Mannucci, N. Phojanamongkolkij, P. Pilewskie, V. Ramaswamy, H. Revercomb, J. Rice, Y. Roberts, C. M. Roithmayr, F. Rose, S. Sandford, E. L. Shirley, W. L. Smith, B. Soden, P. W. Speth, W. Sun, P. C. Taylor, D. Tobin, and X. Xiong, “Achieving climate change absolute accuracy in orbit,” Bull. Am. Meteorol. Soc. 94(10), 1519–1539 (2013).
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Jucks, K.

B. A. Wielicki, D. F. Young, M. G. Mlynczak, K. J. Thome, S. Leroy, J. Corliss, J. G. Anderson, C. O. Ao, R. Bantges, F. Best, K. Bowman, H. Brindley, J. Butler, W. Collins, J. A. Dykema, D. R. Doelling, D. R. Feldman, N. Fox, X. Huang, R. Holz, Y. Huang, Z. Jin, D. Jennings, D. G. Johnson, K. Jucks, S. Kato, D. B. Kirk-Davidoff, R. Knuteson, G. Kopp, D. P. Kratz, X. Liu, C. Lukashin, A. J. Mannucci, N. Phojanamongkolkij, P. Pilewskie, V. Ramaswamy, H. Revercomb, J. Rice, Y. Roberts, C. M. Roithmayr, F. Rose, S. Sandford, E. L. Shirley, W. L. Smith, B. Soden, P. W. Speth, W. Sun, P. C. Taylor, D. Tobin, and X. Xiong, “Achieving climate change absolute accuracy in orbit,” Bull. Am. Meteorol. Soc. 94(10), 1519–1539 (2013).
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Kato, S.

B. A. Wielicki, D. F. Young, M. G. Mlynczak, K. J. Thome, S. Leroy, J. Corliss, J. G. Anderson, C. O. Ao, R. Bantges, F. Best, K. Bowman, H. Brindley, J. Butler, W. Collins, J. A. Dykema, D. R. Doelling, D. R. Feldman, N. Fox, X. Huang, R. Holz, Y. Huang, Z. Jin, D. Jennings, D. G. Johnson, K. Jucks, S. Kato, D. B. Kirk-Davidoff, R. Knuteson, G. Kopp, D. P. Kratz, X. Liu, C. Lukashin, A. J. Mannucci, N. Phojanamongkolkij, P. Pilewskie, V. Ramaswamy, H. Revercomb, J. Rice, Y. Roberts, C. M. Roithmayr, F. Rose, S. Sandford, E. L. Shirley, W. L. Smith, B. Soden, P. W. Speth, W. Sun, P. C. Taylor, D. Tobin, and X. Xiong, “Achieving climate change absolute accuracy in orbit,” Bull. Am. Meteorol. Soc. 94(10), 1519–1539 (2013).
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Kirk-Davidoff, D. B.

B. A. Wielicki, D. F. Young, M. G. Mlynczak, K. J. Thome, S. Leroy, J. Corliss, J. G. Anderson, C. O. Ao, R. Bantges, F. Best, K. Bowman, H. Brindley, J. Butler, W. Collins, J. A. Dykema, D. R. Doelling, D. R. Feldman, N. Fox, X. Huang, R. Holz, Y. Huang, Z. Jin, D. Jennings, D. G. Johnson, K. Jucks, S. Kato, D. B. Kirk-Davidoff, R. Knuteson, G. Kopp, D. P. Kratz, X. Liu, C. Lukashin, A. J. Mannucci, N. Phojanamongkolkij, P. Pilewskie, V. Ramaswamy, H. Revercomb, J. Rice, Y. Roberts, C. M. Roithmayr, F. Rose, S. Sandford, E. L. Shirley, W. L. Smith, B. Soden, P. W. Speth, W. Sun, P. C. Taylor, D. Tobin, and X. Xiong, “Achieving climate change absolute accuracy in orbit,” Bull. Am. Meteorol. Soc. 94(10), 1519–1539 (2013).
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Kizer, S.

Knuteson, R.

B. A. Wielicki, D. F. Young, M. G. Mlynczak, K. J. Thome, S. Leroy, J. Corliss, J. G. Anderson, C. O. Ao, R. Bantges, F. Best, K. Bowman, H. Brindley, J. Butler, W. Collins, J. A. Dykema, D. R. Doelling, D. R. Feldman, N. Fox, X. Huang, R. Holz, Y. Huang, Z. Jin, D. Jennings, D. G. Johnson, K. Jucks, S. Kato, D. B. Kirk-Davidoff, R. Knuteson, G. Kopp, D. P. Kratz, X. Liu, C. Lukashin, A. J. Mannucci, N. Phojanamongkolkij, P. Pilewskie, V. Ramaswamy, H. Revercomb, J. Rice, Y. Roberts, C. M. Roithmayr, F. Rose, S. Sandford, E. L. Shirley, W. L. Smith, B. Soden, P. W. Speth, W. Sun, P. C. Taylor, D. Tobin, and X. Xiong, “Achieving climate change absolute accuracy in orbit,” Bull. Am. Meteorol. Soc. 94(10), 1519–1539 (2013).
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Kopp, G.

B. A. Wielicki, D. F. Young, M. G. Mlynczak, K. J. Thome, S. Leroy, J. Corliss, J. G. Anderson, C. O. Ao, R. Bantges, F. Best, K. Bowman, H. Brindley, J. Butler, W. Collins, J. A. Dykema, D. R. Doelling, D. R. Feldman, N. Fox, X. Huang, R. Holz, Y. Huang, Z. Jin, D. Jennings, D. G. Johnson, K. Jucks, S. Kato, D. B. Kirk-Davidoff, R. Knuteson, G. Kopp, D. P. Kratz, X. Liu, C. Lukashin, A. J. Mannucci, N. Phojanamongkolkij, P. Pilewskie, V. Ramaswamy, H. Revercomb, J. Rice, Y. Roberts, C. M. Roithmayr, F. Rose, S. Sandford, E. L. Shirley, W. L. Smith, B. Soden, P. W. Speth, W. Sun, P. C. Taylor, D. Tobin, and X. Xiong, “Achieving climate change absolute accuracy in orbit,” Bull. Am. Meteorol. Soc. 94(10), 1519–1539 (2013).
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Kopparla, P.

P. Kopparla, V. Natraj, R. Spurr, R. Shia, D. Crisp, and Y. Yung, “A fast and accurate PCA based radiative transfer model: Extension to the broadband shortwave region,” J. Quant. Spec. Radi. Trans. 173, 65–71 (2016).
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Kratz, D. P.

B. A. Wielicki, D. F. Young, M. G. Mlynczak, K. J. Thome, S. Leroy, J. Corliss, J. G. Anderson, C. O. Ao, R. Bantges, F. Best, K. Bowman, H. Brindley, J. Butler, W. Collins, J. A. Dykema, D. R. Doelling, D. R. Feldman, N. Fox, X. Huang, R. Holz, Y. Huang, Z. Jin, D. Jennings, D. G. Johnson, K. Jucks, S. Kato, D. B. Kirk-Davidoff, R. Knuteson, G. Kopp, D. P. Kratz, X. Liu, C. Lukashin, A. J. Mannucci, N. Phojanamongkolkij, P. Pilewskie, V. Ramaswamy, H. Revercomb, J. Rice, Y. Roberts, C. M. Roithmayr, F. Rose, S. Sandford, E. L. Shirley, W. L. Smith, B. Soden, P. W. Speth, W. Sun, P. C. Taylor, D. Tobin, and X. Xiong, “Achieving climate change absolute accuracy in orbit,” Bull. Am. Meteorol. Soc. 94(10), 1519–1539 (2013).
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Larar, A.

Leroy, S.

B. A. Wielicki, D. F. Young, M. G. Mlynczak, K. J. Thome, S. Leroy, J. Corliss, J. G. Anderson, C. O. Ao, R. Bantges, F. Best, K. Bowman, H. Brindley, J. Butler, W. Collins, J. A. Dykema, D. R. Doelling, D. R. Feldman, N. Fox, X. Huang, R. Holz, Y. Huang, Z. Jin, D. Jennings, D. G. Johnson, K. Jucks, S. Kato, D. B. Kirk-Davidoff, R. Knuteson, G. Kopp, D. P. Kratz, X. Liu, C. Lukashin, A. J. Mannucci, N. Phojanamongkolkij, P. Pilewskie, V. Ramaswamy, H. Revercomb, J. Rice, Y. Roberts, C. M. Roithmayr, F. Rose, S. Sandford, E. L. Shirley, W. L. Smith, B. Soden, P. W. Speth, W. Sun, P. C. Taylor, D. Tobin, and X. Xiong, “Achieving climate change absolute accuracy in orbit,” Bull. Am. Meteorol. Soc. 94(10), 1519–1539 (2013).
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Li, H.

Liu, X.

X. Liu, Q. Yang, H. Li, Z. Jin, W. Wu, S. Kizer, D. K. Zhou, and P. Yang, “Development of a fast and accurate PCRTM radiative transfer model in the solar spectral region,” Appl. Opt. 55(29), 8236–8247 (2016).
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B. A. Wielicki, D. F. Young, M. G. Mlynczak, K. J. Thome, S. Leroy, J. Corliss, J. G. Anderson, C. O. Ao, R. Bantges, F. Best, K. Bowman, H. Brindley, J. Butler, W. Collins, J. A. Dykema, D. R. Doelling, D. R. Feldman, N. Fox, X. Huang, R. Holz, Y. Huang, Z. Jin, D. Jennings, D. G. Johnson, K. Jucks, S. Kato, D. B. Kirk-Davidoff, R. Knuteson, G. Kopp, D. P. Kratz, X. Liu, C. Lukashin, A. J. Mannucci, N. Phojanamongkolkij, P. Pilewskie, V. Ramaswamy, H. Revercomb, J. Rice, Y. Roberts, C. M. Roithmayr, F. Rose, S. Sandford, E. L. Shirley, W. L. Smith, B. Soden, P. W. Speth, W. Sun, P. C. Taylor, D. Tobin, and X. Xiong, “Achieving climate change absolute accuracy in orbit,” Bull. Am. Meteorol. Soc. 94(10), 1519–1539 (2013).
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C. Wang, P. Yang, S. L. Nasiri, S. Platnick, B. A. Baum, A. K. Heidinger, and X. Liu, “A fast radiative transfer model for visible through shortwave infrared spectral reflectance’s in clear and cloudy atmospheres,” J. Quant. Spectrosc. Radiat. Transf. 116, 122–131 (2013).
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X. Liu, W. L. Smith, D. K. Zhou, and A. Larar, “Principal component-based radiative transfer model for hyperspectral sensors: theoretical concept,” Appl. Opt. 45(1), 201–209 (2006).
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Lukashin, C.

B. A. Wielicki, D. F. Young, M. G. Mlynczak, K. J. Thome, S. Leroy, J. Corliss, J. G. Anderson, C. O. Ao, R. Bantges, F. Best, K. Bowman, H. Brindley, J. Butler, W. Collins, J. A. Dykema, D. R. Doelling, D. R. Feldman, N. Fox, X. Huang, R. Holz, Y. Huang, Z. Jin, D. Jennings, D. G. Johnson, K. Jucks, S. Kato, D. B. Kirk-Davidoff, R. Knuteson, G. Kopp, D. P. Kratz, X. Liu, C. Lukashin, A. J. Mannucci, N. Phojanamongkolkij, P. Pilewskie, V. Ramaswamy, H. Revercomb, J. Rice, Y. Roberts, C. M. Roithmayr, F. Rose, S. Sandford, E. L. Shirley, W. L. Smith, B. Soden, P. W. Speth, W. Sun, P. C. Taylor, D. Tobin, and X. Xiong, “Achieving climate change absolute accuracy in orbit,” Bull. Am. Meteorol. Soc. 94(10), 1519–1539 (2013).
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Mannucci, A. J.

B. A. Wielicki, D. F. Young, M. G. Mlynczak, K. J. Thome, S. Leroy, J. Corliss, J. G. Anderson, C. O. Ao, R. Bantges, F. Best, K. Bowman, H. Brindley, J. Butler, W. Collins, J. A. Dykema, D. R. Doelling, D. R. Feldman, N. Fox, X. Huang, R. Holz, Y. Huang, Z. Jin, D. Jennings, D. G. Johnson, K. Jucks, S. Kato, D. B. Kirk-Davidoff, R. Knuteson, G. Kopp, D. P. Kratz, X. Liu, C. Lukashin, A. J. Mannucci, N. Phojanamongkolkij, P. Pilewskie, V. Ramaswamy, H. Revercomb, J. Rice, Y. Roberts, C. M. Roithmayr, F. Rose, S. Sandford, E. L. Shirley, W. L. Smith, B. Soden, P. W. Speth, W. Sun, P. C. Taylor, D. Tobin, and X. Xiong, “Achieving climate change absolute accuracy in orbit,” Bull. Am. Meteorol. Soc. 94(10), 1519–1539 (2013).
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Margolis, J.

V. Natraj, X. Jiang, R. Shia, X. Huang, J. Margolis, and Y. Yung, “Application of principal component analysis to high spectral resolution radiative transfer: a case study of the O2 A band,” J. Quant. Spec. Radi. Trans. 95(4), 539–556 (2005).
[Crossref]

Mlynczak, M. G.

B. A. Wielicki, D. F. Young, M. G. Mlynczak, K. J. Thome, S. Leroy, J. Corliss, J. G. Anderson, C. O. Ao, R. Bantges, F. Best, K. Bowman, H. Brindley, J. Butler, W. Collins, J. A. Dykema, D. R. Doelling, D. R. Feldman, N. Fox, X. Huang, R. Holz, Y. Huang, Z. Jin, D. Jennings, D. G. Johnson, K. Jucks, S. Kato, D. B. Kirk-Davidoff, R. Knuteson, G. Kopp, D. P. Kratz, X. Liu, C. Lukashin, A. J. Mannucci, N. Phojanamongkolkij, P. Pilewskie, V. Ramaswamy, H. Revercomb, J. Rice, Y. Roberts, C. M. Roithmayr, F. Rose, S. Sandford, E. L. Shirley, W. L. Smith, B. Soden, P. W. Speth, W. Sun, P. C. Taylor, D. Tobin, and X. Xiong, “Achieving climate change absolute accuracy in orbit,” Bull. Am. Meteorol. Soc. 94(10), 1519–1539 (2013).
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Nasiri, S. L.

C. Wang, P. Yang, S. L. Nasiri, S. Platnick, B. A. Baum, A. K. Heidinger, and X. Liu, “A fast radiative transfer model for visible through shortwave infrared spectral reflectance’s in clear and cloudy atmospheres,” J. Quant. Spectrosc. Radiat. Transf. 116, 122–131 (2013).
[Crossref]

Natraj, V.

P. Kopparla, V. Natraj, R. Spurr, R. Shia, D. Crisp, and Y. Yung, “A fast and accurate PCA based radiative transfer model: Extension to the broadband shortwave region,” J. Quant. Spec. Radi. Trans. 173, 65–71 (2016).
[Crossref]

V. Natraj, X. Jiang, R. Shia, X. Huang, J. Margolis, and Y. Yung, “Application of principal component analysis to high spectral resolution radiative transfer: a case study of the O2 A band,” J. Quant. Spec. Radi. Trans. 95(4), 539–556 (2005).
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Ong, J. R.

D. R. Feldman, C. A. Algieri, J. R. Ong, and W. D. Collins, “CLARREO shortwave observing system simulation experiments of the twenty-first century: simulator design and implementation,” J. Geophys. Res. 116(D10), D10107 (2011).
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Phojanamongkolkij, N.

B. A. Wielicki, D. F. Young, M. G. Mlynczak, K. J. Thome, S. Leroy, J. Corliss, J. G. Anderson, C. O. Ao, R. Bantges, F. Best, K. Bowman, H. Brindley, J. Butler, W. Collins, J. A. Dykema, D. R. Doelling, D. R. Feldman, N. Fox, X. Huang, R. Holz, Y. Huang, Z. Jin, D. Jennings, D. G. Johnson, K. Jucks, S. Kato, D. B. Kirk-Davidoff, R. Knuteson, G. Kopp, D. P. Kratz, X. Liu, C. Lukashin, A. J. Mannucci, N. Phojanamongkolkij, P. Pilewskie, V. Ramaswamy, H. Revercomb, J. Rice, Y. Roberts, C. M. Roithmayr, F. Rose, S. Sandford, E. L. Shirley, W. L. Smith, B. Soden, P. W. Speth, W. Sun, P. C. Taylor, D. Tobin, and X. Xiong, “Achieving climate change absolute accuracy in orbit,” Bull. Am. Meteorol. Soc. 94(10), 1519–1539 (2013).
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Pilewskie, P.

B. A. Wielicki, D. F. Young, M. G. Mlynczak, K. J. Thome, S. Leroy, J. Corliss, J. G. Anderson, C. O. Ao, R. Bantges, F. Best, K. Bowman, H. Brindley, J. Butler, W. Collins, J. A. Dykema, D. R. Doelling, D. R. Feldman, N. Fox, X. Huang, R. Holz, Y. Huang, Z. Jin, D. Jennings, D. G. Johnson, K. Jucks, S. Kato, D. B. Kirk-Davidoff, R. Knuteson, G. Kopp, D. P. Kratz, X. Liu, C. Lukashin, A. J. Mannucci, N. Phojanamongkolkij, P. Pilewskie, V. Ramaswamy, H. Revercomb, J. Rice, Y. Roberts, C. M. Roithmayr, F. Rose, S. Sandford, E. L. Shirley, W. L. Smith, B. Soden, P. W. Speth, W. Sun, P. C. Taylor, D. Tobin, and X. Xiong, “Achieving climate change absolute accuracy in orbit,” Bull. Am. Meteorol. Soc. 94(10), 1519–1539 (2013).
[Crossref]

Platnick, S.

C. Wang, P. Yang, S. L. Nasiri, S. Platnick, B. A. Baum, A. K. Heidinger, and X. Liu, “A fast radiative transfer model for visible through shortwave infrared spectral reflectance’s in clear and cloudy atmospheres,” J. Quant. Spectrosc. Radiat. Transf. 116, 122–131 (2013).
[Crossref]

Ramaswamy, V.

B. A. Wielicki, D. F. Young, M. G. Mlynczak, K. J. Thome, S. Leroy, J. Corliss, J. G. Anderson, C. O. Ao, R. Bantges, F. Best, K. Bowman, H. Brindley, J. Butler, W. Collins, J. A. Dykema, D. R. Doelling, D. R. Feldman, N. Fox, X. Huang, R. Holz, Y. Huang, Z. Jin, D. Jennings, D. G. Johnson, K. Jucks, S. Kato, D. B. Kirk-Davidoff, R. Knuteson, G. Kopp, D. P. Kratz, X. Liu, C. Lukashin, A. J. Mannucci, N. Phojanamongkolkij, P. Pilewskie, V. Ramaswamy, H. Revercomb, J. Rice, Y. Roberts, C. M. Roithmayr, F. Rose, S. Sandford, E. L. Shirley, W. L. Smith, B. Soden, P. W. Speth, W. Sun, P. C. Taylor, D. Tobin, and X. Xiong, “Achieving climate change absolute accuracy in orbit,” Bull. Am. Meteorol. Soc. 94(10), 1519–1539 (2013).
[Crossref]

Revercomb, H.

B. A. Wielicki, D. F. Young, M. G. Mlynczak, K. J. Thome, S. Leroy, J. Corliss, J. G. Anderson, C. O. Ao, R. Bantges, F. Best, K. Bowman, H. Brindley, J. Butler, W. Collins, J. A. Dykema, D. R. Doelling, D. R. Feldman, N. Fox, X. Huang, R. Holz, Y. Huang, Z. Jin, D. Jennings, D. G. Johnson, K. Jucks, S. Kato, D. B. Kirk-Davidoff, R. Knuteson, G. Kopp, D. P. Kratz, X. Liu, C. Lukashin, A. J. Mannucci, N. Phojanamongkolkij, P. Pilewskie, V. Ramaswamy, H. Revercomb, J. Rice, Y. Roberts, C. M. Roithmayr, F. Rose, S. Sandford, E. L. Shirley, W. L. Smith, B. Soden, P. W. Speth, W. Sun, P. C. Taylor, D. Tobin, and X. Xiong, “Achieving climate change absolute accuracy in orbit,” Bull. Am. Meteorol. Soc. 94(10), 1519–1539 (2013).
[Crossref]

Rice, J.

B. A. Wielicki, D. F. Young, M. G. Mlynczak, K. J. Thome, S. Leroy, J. Corliss, J. G. Anderson, C. O. Ao, R. Bantges, F. Best, K. Bowman, H. Brindley, J. Butler, W. Collins, J. A. Dykema, D. R. Doelling, D. R. Feldman, N. Fox, X. Huang, R. Holz, Y. Huang, Z. Jin, D. Jennings, D. G. Johnson, K. Jucks, S. Kato, D. B. Kirk-Davidoff, R. Knuteson, G. Kopp, D. P. Kratz, X. Liu, C. Lukashin, A. J. Mannucci, N. Phojanamongkolkij, P. Pilewskie, V. Ramaswamy, H. Revercomb, J. Rice, Y. Roberts, C. M. Roithmayr, F. Rose, S. Sandford, E. L. Shirley, W. L. Smith, B. Soden, P. W. Speth, W. Sun, P. C. Taylor, D. Tobin, and X. Xiong, “Achieving climate change absolute accuracy in orbit,” Bull. Am. Meteorol. Soc. 94(10), 1519–1539 (2013).
[Crossref]

Ridgway, W.

R. Cahalan, W. Ridgway, W. Wiscombe, S. Gollmer, and Harshvardhan, “Independent pixel and Monte Carlo estimates of stratocumulus albedo,” J. Atmos. Sci. 51(24), 3776–3790 (1994).
[Crossref]

Roberts, Y.

B. A. Wielicki, D. F. Young, M. G. Mlynczak, K. J. Thome, S. Leroy, J. Corliss, J. G. Anderson, C. O. Ao, R. Bantges, F. Best, K. Bowman, H. Brindley, J. Butler, W. Collins, J. A. Dykema, D. R. Doelling, D. R. Feldman, N. Fox, X. Huang, R. Holz, Y. Huang, Z. Jin, D. Jennings, D. G. Johnson, K. Jucks, S. Kato, D. B. Kirk-Davidoff, R. Knuteson, G. Kopp, D. P. Kratz, X. Liu, C. Lukashin, A. J. Mannucci, N. Phojanamongkolkij, P. Pilewskie, V. Ramaswamy, H. Revercomb, J. Rice, Y. Roberts, C. M. Roithmayr, F. Rose, S. Sandford, E. L. Shirley, W. L. Smith, B. Soden, P. W. Speth, W. Sun, P. C. Taylor, D. Tobin, and X. Xiong, “Achieving climate change absolute accuracy in orbit,” Bull. Am. Meteorol. Soc. 94(10), 1519–1539 (2013).
[Crossref]

Roithmayr, C. M.

B. A. Wielicki, D. F. Young, M. G. Mlynczak, K. J. Thome, S. Leroy, J. Corliss, J. G. Anderson, C. O. Ao, R. Bantges, F. Best, K. Bowman, H. Brindley, J. Butler, W. Collins, J. A. Dykema, D. R. Doelling, D. R. Feldman, N. Fox, X. Huang, R. Holz, Y. Huang, Z. Jin, D. Jennings, D. G. Johnson, K. Jucks, S. Kato, D. B. Kirk-Davidoff, R. Knuteson, G. Kopp, D. P. Kratz, X. Liu, C. Lukashin, A. J. Mannucci, N. Phojanamongkolkij, P. Pilewskie, V. Ramaswamy, H. Revercomb, J. Rice, Y. Roberts, C. M. Roithmayr, F. Rose, S. Sandford, E. L. Shirley, W. L. Smith, B. Soden, P. W. Speth, W. Sun, P. C. Taylor, D. Tobin, and X. Xiong, “Achieving climate change absolute accuracy in orbit,” Bull. Am. Meteorol. Soc. 94(10), 1519–1539 (2013).
[Crossref]

Rose, F.

B. A. Wielicki, D. F. Young, M. G. Mlynczak, K. J. Thome, S. Leroy, J. Corliss, J. G. Anderson, C. O. Ao, R. Bantges, F. Best, K. Bowman, H. Brindley, J. Butler, W. Collins, J. A. Dykema, D. R. Doelling, D. R. Feldman, N. Fox, X. Huang, R. Holz, Y. Huang, Z. Jin, D. Jennings, D. G. Johnson, K. Jucks, S. Kato, D. B. Kirk-Davidoff, R. Knuteson, G. Kopp, D. P. Kratz, X. Liu, C. Lukashin, A. J. Mannucci, N. Phojanamongkolkij, P. Pilewskie, V. Ramaswamy, H. Revercomb, J. Rice, Y. Roberts, C. M. Roithmayr, F. Rose, S. Sandford, E. L. Shirley, W. L. Smith, B. Soden, P. W. Speth, W. Sun, P. C. Taylor, D. Tobin, and X. Xiong, “Achieving climate change absolute accuracy in orbit,” Bull. Am. Meteorol. Soc. 94(10), 1519–1539 (2013).
[Crossref]

Sandford, S.

B. A. Wielicki, D. F. Young, M. G. Mlynczak, K. J. Thome, S. Leroy, J. Corliss, J. G. Anderson, C. O. Ao, R. Bantges, F. Best, K. Bowman, H. Brindley, J. Butler, W. Collins, J. A. Dykema, D. R. Doelling, D. R. Feldman, N. Fox, X. Huang, R. Holz, Y. Huang, Z. Jin, D. Jennings, D. G. Johnson, K. Jucks, S. Kato, D. B. Kirk-Davidoff, R. Knuteson, G. Kopp, D. P. Kratz, X. Liu, C. Lukashin, A. J. Mannucci, N. Phojanamongkolkij, P. Pilewskie, V. Ramaswamy, H. Revercomb, J. Rice, Y. Roberts, C. M. Roithmayr, F. Rose, S. Sandford, E. L. Shirley, W. L. Smith, B. Soden, P. W. Speth, W. Sun, P. C. Taylor, D. Tobin, and X. Xiong, “Achieving climate change absolute accuracy in orbit,” Bull. Am. Meteorol. Soc. 94(10), 1519–1539 (2013).
[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]

Shia, R.

P. Kopparla, V. Natraj, R. Spurr, R. Shia, D. Crisp, and Y. Yung, “A fast and accurate PCA based radiative transfer model: Extension to the broadband shortwave region,” J. Quant. Spec. Radi. Trans. 173, 65–71 (2016).
[Crossref]

V. Natraj, X. Jiang, R. Shia, X. Huang, J. Margolis, and Y. Yung, “Application of principal component analysis to high spectral resolution radiative transfer: a case study of the O2 A band,” J. Quant. Spec. Radi. Trans. 95(4), 539–556 (2005).
[Crossref]

Shirley, E. L.

B. A. Wielicki, D. F. Young, M. G. Mlynczak, K. J. Thome, S. Leroy, J. Corliss, J. G. Anderson, C. O. Ao, R. Bantges, F. Best, K. Bowman, H. Brindley, J. Butler, W. Collins, J. A. Dykema, D. R. Doelling, D. R. Feldman, N. Fox, X. Huang, R. Holz, Y. Huang, Z. Jin, D. Jennings, D. G. Johnson, K. Jucks, S. Kato, D. B. Kirk-Davidoff, R. Knuteson, G. Kopp, D. P. Kratz, X. Liu, C. Lukashin, A. J. Mannucci, N. Phojanamongkolkij, P. Pilewskie, V. Ramaswamy, H. Revercomb, J. Rice, Y. Roberts, C. M. Roithmayr, F. Rose, S. Sandford, E. L. Shirley, W. L. Smith, B. Soden, P. W. Speth, W. Sun, P. C. Taylor, D. Tobin, and X. Xiong, “Achieving climate change absolute accuracy in orbit,” Bull. Am. Meteorol. Soc. 94(10), 1519–1539 (2013).
[Crossref]

Smith, W. L.

B. A. Wielicki, D. F. Young, M. G. Mlynczak, K. J. Thome, S. Leroy, J. Corliss, J. G. Anderson, C. O. Ao, R. Bantges, F. Best, K. Bowman, H. Brindley, J. Butler, W. Collins, J. A. Dykema, D. R. Doelling, D. R. Feldman, N. Fox, X. Huang, R. Holz, Y. Huang, Z. Jin, D. Jennings, D. G. Johnson, K. Jucks, S. Kato, D. B. Kirk-Davidoff, R. Knuteson, G. Kopp, D. P. Kratz, X. Liu, C. Lukashin, A. J. Mannucci, N. Phojanamongkolkij, P. Pilewskie, V. Ramaswamy, H. Revercomb, J. Rice, Y. Roberts, C. M. Roithmayr, F. Rose, S. Sandford, E. L. Shirley, W. L. Smith, B. Soden, P. W. Speth, W. Sun, P. C. Taylor, D. Tobin, and X. Xiong, “Achieving climate change absolute accuracy in orbit,” Bull. Am. Meteorol. Soc. 94(10), 1519–1539 (2013).
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X. Liu, W. L. Smith, D. K. Zhou, and A. Larar, “Principal component-based radiative transfer model for hyperspectral sensors: theoretical concept,” Appl. Opt. 45(1), 201–209 (2006).
[Crossref] [PubMed]

Soden, B.

B. A. Wielicki, D. F. Young, M. G. Mlynczak, K. J. Thome, S. Leroy, J. Corliss, J. G. Anderson, C. O. Ao, R. Bantges, F. Best, K. Bowman, H. Brindley, J. Butler, W. Collins, J. A. Dykema, D. R. Doelling, D. R. Feldman, N. Fox, X. Huang, R. Holz, Y. Huang, Z. Jin, D. Jennings, D. G. Johnson, K. Jucks, S. Kato, D. B. Kirk-Davidoff, R. Knuteson, G. Kopp, D. P. Kratz, X. Liu, C. Lukashin, A. J. Mannucci, N. Phojanamongkolkij, P. Pilewskie, V. Ramaswamy, H. Revercomb, J. Rice, Y. Roberts, C. M. Roithmayr, F. Rose, S. Sandford, E. L. Shirley, W. L. Smith, B. Soden, P. W. Speth, W. Sun, P. C. Taylor, D. Tobin, and X. Xiong, “Achieving climate change absolute accuracy in orbit,” Bull. Am. Meteorol. Soc. 94(10), 1519–1539 (2013).
[Crossref]

Speth, P. W.

B. A. Wielicki, D. F. Young, M. G. Mlynczak, K. J. Thome, S. Leroy, J. Corliss, J. G. Anderson, C. O. Ao, R. Bantges, F. Best, K. Bowman, H. Brindley, J. Butler, W. Collins, J. A. Dykema, D. R. Doelling, D. R. Feldman, N. Fox, X. Huang, R. Holz, Y. Huang, Z. Jin, D. Jennings, D. G. Johnson, K. Jucks, S. Kato, D. B. Kirk-Davidoff, R. Knuteson, G. Kopp, D. P. Kratz, X. Liu, C. Lukashin, A. J. Mannucci, N. Phojanamongkolkij, P. Pilewskie, V. Ramaswamy, H. Revercomb, J. Rice, Y. Roberts, C. M. Roithmayr, F. Rose, S. Sandford, E. L. Shirley, W. L. Smith, B. Soden, P. W. Speth, W. Sun, P. C. Taylor, D. Tobin, and X. Xiong, “Achieving climate change absolute accuracy in orbit,” Bull. Am. Meteorol. Soc. 94(10), 1519–1539 (2013).
[Crossref]

Spurr, R.

P. Kopparla, V. Natraj, R. Spurr, R. Shia, D. Crisp, and Y. Yung, “A fast and accurate PCA based radiative transfer model: Extension to the broadband shortwave region,” J. Quant. Spec. Radi. Trans. 173, 65–71 (2016).
[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]

K. Stamnes, S. C. Tsay, W. Wiscombe, and K. Jayaweera, “Numerically stable algorithm for discrete-ordinate-method radiative transfer in multiple scattering and emitting layered media,” Appl. Opt. 27(12), 2502–2509 (1988).
[Crossref] [PubMed]

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).
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Sun, M.

Z. Jin and M. Sun, “An initial study on climate change fingerprinting using the reflected solar spectra,” J. Clim. 29(8), 2781–2796 (2016).
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Sun, W.

B. A. Wielicki, D. F. Young, M. G. Mlynczak, K. J. Thome, S. Leroy, J. Corliss, J. G. Anderson, C. O. Ao, R. Bantges, F. Best, K. Bowman, H. Brindley, J. Butler, W. Collins, J. A. Dykema, D. R. Doelling, D. R. Feldman, N. Fox, X. Huang, R. Holz, Y. Huang, Z. Jin, D. Jennings, D. G. Johnson, K. Jucks, S. Kato, D. B. Kirk-Davidoff, R. Knuteson, G. Kopp, D. P. Kratz, X. Liu, C. Lukashin, A. J. Mannucci, N. Phojanamongkolkij, P. Pilewskie, V. Ramaswamy, H. Revercomb, J. Rice, Y. Roberts, C. M. Roithmayr, F. Rose, S. Sandford, E. L. Shirley, W. L. Smith, B. Soden, P. W. Speth, W. Sun, P. C. Taylor, D. Tobin, and X. Xiong, “Achieving climate change absolute accuracy in orbit,” Bull. Am. Meteorol. Soc. 94(10), 1519–1539 (2013).
[Crossref]

Taylor, P. C.

B. A. Wielicki, D. F. Young, M. G. Mlynczak, K. J. Thome, S. Leroy, J. Corliss, J. G. Anderson, C. O. Ao, R. Bantges, F. Best, K. Bowman, H. Brindley, J. Butler, W. Collins, J. A. Dykema, D. R. Doelling, D. R. Feldman, N. Fox, X. Huang, R. Holz, Y. Huang, Z. Jin, D. Jennings, D. G. Johnson, K. Jucks, S. Kato, D. B. Kirk-Davidoff, R. Knuteson, G. Kopp, D. P. Kratz, X. Liu, C. Lukashin, A. J. Mannucci, N. Phojanamongkolkij, P. Pilewskie, V. Ramaswamy, H. Revercomb, J. Rice, Y. Roberts, C. M. Roithmayr, F. Rose, S. Sandford, E. L. Shirley, W. L. Smith, B. Soden, P. W. Speth, W. Sun, P. C. Taylor, D. Tobin, and X. Xiong, “Achieving climate change absolute accuracy in orbit,” Bull. Am. Meteorol. Soc. 94(10), 1519–1539 (2013).
[Crossref]

Thome, K. J.

B. A. Wielicki, D. F. Young, M. G. Mlynczak, K. J. Thome, S. Leroy, J. Corliss, J. G. Anderson, C. O. Ao, R. Bantges, F. Best, K. Bowman, H. Brindley, J. Butler, W. Collins, J. A. Dykema, D. R. Doelling, D. R. Feldman, N. Fox, X. Huang, R. Holz, Y. Huang, Z. Jin, D. Jennings, D. G. Johnson, K. Jucks, S. Kato, D. B. Kirk-Davidoff, R. Knuteson, G. Kopp, D. P. Kratz, X. Liu, C. Lukashin, A. J. Mannucci, N. Phojanamongkolkij, P. Pilewskie, V. Ramaswamy, H. Revercomb, J. Rice, Y. Roberts, C. M. Roithmayr, F. Rose, S. Sandford, E. L. Shirley, W. L. Smith, B. Soden, P. W. Speth, W. Sun, P. C. Taylor, D. Tobin, and X. Xiong, “Achieving climate change absolute accuracy in orbit,” Bull. Am. Meteorol. Soc. 94(10), 1519–1539 (2013).
[Crossref]

Tobin, D.

B. A. Wielicki, D. F. Young, M. G. Mlynczak, K. J. Thome, S. Leroy, J. Corliss, J. G. Anderson, C. O. Ao, R. Bantges, F. Best, K. Bowman, H. Brindley, J. Butler, W. Collins, J. A. Dykema, D. R. Doelling, D. R. Feldman, N. Fox, X. Huang, R. Holz, Y. Huang, Z. Jin, D. Jennings, D. G. Johnson, K. Jucks, S. Kato, D. B. Kirk-Davidoff, R. Knuteson, G. Kopp, D. P. Kratz, X. Liu, C. Lukashin, A. J. Mannucci, N. Phojanamongkolkij, P. Pilewskie, V. Ramaswamy, H. Revercomb, J. Rice, Y. Roberts, C. M. Roithmayr, F. Rose, S. Sandford, E. L. Shirley, W. L. Smith, B. Soden, P. W. Speth, W. Sun, P. C. Taylor, D. Tobin, and X. Xiong, “Achieving climate change absolute accuracy in orbit,” Bull. Am. Meteorol. Soc. 94(10), 1519–1539 (2013).
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Travis, L. D.

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

Tsay, S. C.

Wang, C.

C. Wang, P. Yang, S. L. Nasiri, S. Platnick, B. A. Baum, A. K. Heidinger, and X. Liu, “A fast radiative transfer model for visible through shortwave infrared spectral reflectance’s in clear and cloudy atmospheres,” J. Quant. Spectrosc. Radiat. Transf. 116, 122–131 (2013).
[Crossref]

Weng, F.

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]

Wielicki, B. A.

B. A. Wielicki, D. F. Young, M. G. Mlynczak, K. J. Thome, S. Leroy, J. Corliss, J. G. Anderson, C. O. Ao, R. Bantges, F. Best, K. Bowman, H. Brindley, J. Butler, W. Collins, J. A. Dykema, D. R. Doelling, D. R. Feldman, N. Fox, X. Huang, R. Holz, Y. Huang, Z. Jin, D. Jennings, D. G. Johnson, K. Jucks, S. Kato, D. B. Kirk-Davidoff, R. Knuteson, G. Kopp, D. P. Kratz, X. Liu, C. Lukashin, A. J. Mannucci, N. Phojanamongkolkij, P. Pilewskie, V. Ramaswamy, H. Revercomb, J. Rice, Y. Roberts, C. M. Roithmayr, F. Rose, S. Sandford, E. L. Shirley, W. L. Smith, B. Soden, P. W. Speth, W. Sun, P. C. Taylor, D. Tobin, and X. Xiong, “Achieving climate change absolute accuracy in orbit,” Bull. Am. Meteorol. Soc. 94(10), 1519–1539 (2013).
[Crossref]

Wiscombe, W.

R. Cahalan, W. Ridgway, W. Wiscombe, S. Gollmer, and Harshvardhan, “Independent pixel and Monte Carlo estimates of stratocumulus albedo,” J. Atmos. Sci. 51(24), 3776–3790 (1994).
[Crossref]

K. Stamnes, S. C. Tsay, W. Wiscombe, and K. Jayaweera, “Numerically stable algorithm for discrete-ordinate-method radiative transfer in multiple scattering and emitting layered media,” Appl. Opt. 27(12), 2502–2509 (1988).
[Crossref] [PubMed]

Wu, W.

Xiong, X.

B. A. Wielicki, D. F. Young, M. G. Mlynczak, K. J. Thome, S. Leroy, J. Corliss, J. G. Anderson, C. O. Ao, R. Bantges, F. Best, K. Bowman, H. Brindley, J. Butler, W. Collins, J. A. Dykema, D. R. Doelling, D. R. Feldman, N. Fox, X. Huang, R. Holz, Y. Huang, Z. Jin, D. Jennings, D. G. Johnson, K. Jucks, S. Kato, D. B. Kirk-Davidoff, R. Knuteson, G. Kopp, D. P. Kratz, X. Liu, C. Lukashin, A. J. Mannucci, N. Phojanamongkolkij, P. Pilewskie, V. Ramaswamy, H. Revercomb, J. Rice, Y. Roberts, C. M. Roithmayr, F. Rose, S. Sandford, E. L. Shirley, W. L. Smith, B. Soden, P. W. Speth, W. Sun, P. C. Taylor, D. Tobin, and X. Xiong, “Achieving climate change absolute accuracy in orbit,” Bull. Am. Meteorol. Soc. 94(10), 1519–1539 (2013).
[Crossref]

Yang, P.

X. Liu, Q. Yang, H. Li, Z. Jin, W. Wu, S. Kizer, D. K. Zhou, and P. Yang, “Development of a fast and accurate PCRTM radiative transfer model in the solar spectral region,” Appl. Opt. 55(29), 8236–8247 (2016).
[Crossref]

C. Wang, P. Yang, S. L. Nasiri, S. Platnick, B. A. Baum, A. K. Heidinger, and X. Liu, “A fast radiative transfer model for visible through shortwave infrared spectral reflectance’s in clear and cloudy atmospheres,” J. Quant. Spectrosc. Radiat. Transf. 116, 122–131 (2013).
[Crossref]

Yang, Q.

Young, D. F.

B. A. Wielicki, D. F. Young, M. G. Mlynczak, K. J. Thome, S. Leroy, J. Corliss, J. G. Anderson, C. O. Ao, R. Bantges, F. Best, K. Bowman, H. Brindley, J. Butler, W. Collins, J. A. Dykema, D. R. Doelling, D. R. Feldman, N. Fox, X. Huang, R. Holz, Y. Huang, Z. Jin, D. Jennings, D. G. Johnson, K. Jucks, S. Kato, D. B. Kirk-Davidoff, R. Knuteson, G. Kopp, D. P. Kratz, X. Liu, C. Lukashin, A. J. Mannucci, N. Phojanamongkolkij, P. Pilewskie, V. Ramaswamy, H. Revercomb, J. Rice, Y. Roberts, C. M. Roithmayr, F. Rose, S. Sandford, E. L. Shirley, W. L. Smith, B. Soden, P. W. Speth, W. Sun, P. C. Taylor, D. Tobin, and X. Xiong, “Achieving climate change absolute accuracy in orbit,” Bull. Am. Meteorol. Soc. 94(10), 1519–1539 (2013).
[Crossref]

Yung, Y.

P. Kopparla, V. Natraj, R. Spurr, R. Shia, D. Crisp, and Y. Yung, “A fast and accurate PCA based radiative transfer model: Extension to the broadband shortwave region,” J. Quant. Spec. Radi. Trans. 173, 65–71 (2016).
[Crossref]

V. Natraj, X. Jiang, R. Shia, X. Huang, J. Margolis, and Y. Yung, “Application of principal component analysis to high spectral resolution radiative transfer: a case study of the O2 A band,” J. Quant. Spec. Radi. Trans. 95(4), 539–556 (2005).
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Zhou, D. K.

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Figures (10)

Fig. 1
Fig. 1 Stream number dependence of the TOA radiance calculated using MODTRAN5 for a three-layer cloud case in solar spectral range with solar radiation. The geometric parameters used in the calculation were VZA = 0.48°, SZA = 66.39°, and VAA – SAA = 110.26°. The effective size was 10.98 μm for water cloud droplets and 60.82 μm for ice cloud particles. The water droplet cloud vertical column density was 0.304 km.g/m3 while the ice particle cloud vertical column density was 0.072 km.g/m3.
Fig. 2
Fig. 2 Correlation between TOA monochromatic radiances obtained from 4-stream and 16-stream discrete ordinate methods. Each case had different atmospheric, geometric, and surface inputs.
Fig. 3
Fig. 3 Typical TOA monochromatic radiances (rMono, upper) obtained using 16-stream and 4-stream discrete ordinate methods for the same inputs. The difference between 4-stream rMono and 16-stream rMono is shown in the lower plot.
Fig. 4
Fig. 4 The training and validation RMS errors of the regular PCRTM-SOLAR algorithm for CLARREO 8 nm resolution RS spectrum for the land surface case.
Fig. 5
Fig. 5 RMS errors (upper) and bias (lower) in reproduced R 241 16 at the preselected 241 (M1) frequencies using R 23 16 at 23 (M2) selected frequencies. The B M 1 × M 2 matrix was obtained from the training. The 16-stream MODTRAN5 results are considered as the true values.
Fig. 6
Fig. 6 RMS errors (upper) and bias (lower) in reproduced R 241 32 at the preselected 241 (M1) frequencies using R 23 32 at 23 (M2) selected frequencies. The B M 1 × M 2 matrix is the same as in Fig. 5. The 32-stream MODTRAN5 results are considered as the true values.
Fig. 7
Fig. 7 RMS errors (upper) and bias (lower) in reproduced R 241 16 at the preselected 241 (M1) frequencies using R 23 16 at 23 (M2) selected frequencies and the transformation matrix B M 1 × M 2 obtained from training. The 16-stream MODTRAN5 results are considered as the true values.
Fig. 8
Fig. 8 RMS errors (upper) and bias (lower) in reproduced R 241 32 at the preselected 241 (M1) frequencies using R 23 32 at 23 (M2) selected frequencies and the transformation matrix B M 1 × M 2 obtained from training. The 32-stream MODTRAN5 results are considered as the true values.
Fig. 9
Fig. 9 RMS errors (upper) and bias (lower) in reproduced TOA channel radiances. The 16-stream MODTRAN5 results are considered as the true values.
Fig. 10
Fig. 10 RMS errors (upper) and bias (lower) in reproduced TOA channel radiances. The 32-stream MODTRAN5 results are considered as the true values.

Tables (1)

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Table 1 Speedup of the HS-PCRTM-SOLAR method compared to regular PCRTM-SOLAR and MODTRAN5.

Equations (12)

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I ( τ , μ , ϕ ) = m = 0 N I m ( τ , μ ) cos m ( ϕ 0 ϕ )
μ d I m ( τ , μ ) d τ = I m ( τ , μ ) S m ( τ , μ )
S m ( τ , μ ) = ω ( τ ) 2 1 1 D m ( τ , μ , μ ) I m ( τ , μ ) d μ + Q m ( τ , μ )
D m ( τ , μ , μ ) = l = m N ( 2 l + 1 ) g l ( τ ) Λ l m ( μ ) Λ l m ( μ )
Q m ( τ , μ ) = ω ( τ ) I 0 ( 2 δ m 0 ) 4 π e τ / μ 0 × l = m N ( 1 ) l + m ( 2 l + 1 ) g l ( τ ) Λ l m ( μ ) Λ l m ( μ 0 ) + δ m 0 Q t h e r m a l ( τ )
δ m 0 = { 1 ( m = 0 ) 0 ( m 0 )
1 1 D m ( τ , μ , μ ) I m ( τ , μ ) d μ = j = N j 0 N w j D m ( τ , μ i , μ j ) I m ( τ , μ j )
R M 1 N = R M 1 4 + ( R M 1 N R M 1 4 ) = R M 1 4 + Δ R M 1
Δ R M 1 × n s = B M 1 × M 2 Δ R M 2 × n s = B M 1 × M 2 ( R M 2 × n s N R M 2 × n s 4 )
R n c h × n s c h a n = U n c h × n p c A n p c × n s m o R n s m o × n s m o n o
R λ i c h a n = 1 n λ j = λ i λ W / 2 λ i + λ W / 2 R λ j m o n o
R λ i c h a n = j = 1 σ 2 π e ( λ j λ i ) 2 2 σ 2 R λ j m o n o Δ λ

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