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To simulate the atmospheric polarization pattern for small solar elevation angle, we develop a the vector radiative transfer model VSPART (vector pseudo-spherical radiative transfer model considering refraction), and use it to calculate the polarization state of downwelling diffuse light. In this model, the propagation trajectory, transmittance rate and polarization states of directly transmitted light are tracked by ray-tracing method for spherical refractive atmosphere. Based on the matrix algorithm, an improved method to solve the radiative transfer equation is proposed. Output of this model includes not only the Stokes vector and degree of polarization of diffuse light, but also the polarized irradiance. The precision of VSPART is validated against the benchmark results, literature results and SPDISORT, and excellent agreement is achieved. DOP (degree of polarization) and AOP (angle of polarization) are simulated for pure Rayleigh scattering atmosphere and atmosphere with aerosol, and the characteristics of their angular distributions are analyzed. In addition, the influences of atmospheric spherical geometry and refraction effect on the sky DOP are discussed as well. Simulation results show that for low solar elevation angle, with the increasing of wavelength, DOP increases gradually, and the Arago and Babinet neutral points move towards the horizon when Rayleigh scattering atmosphere is considered. Although the existence of aerosol does not change the basic distribution of DOP, it has a significant influence on AOP. With the increasing of aerosol optical depth, DOP decreases gradually, and the distribution of AOP changes dramatically. By comparing the sky distribution of DOP, it could also be concluded that the neutral points might arise from low order scattering. The area affected by atmospheric spherical geometry and atmospheric refraction effect mainly includes the area near horizontal directions, the area near the neutral points and the area perpendicular to the ground. For pure Rayleigh scattering atmosphere, the influence is reduced with the increasing of the wavelength of incident light, especially for the areas near the neutral points, where the influence gradually disappears as wavelength increases. For atmosphere with aerosol, with their optical depth increasing, the effects of atmospheric spherical geometry and atmospheric refraction are gradually enhanced.
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Keywords:
- sky polarization pattern /
- atmospheric refraction effect /
- atmospheric spherical geometry /
- vector radiative transfer
[1] Rozanov V V, Rozanov A V, Kokhanovsky A A, Burrows J P 2014 J. Quant. Spectrosc. Radiat. Transfer 133 13
[2] Emde C, Buras R, Mayer B, Blumthaler M 2010 Atmos. Chem. Phys. 10 383
[3] Wu L H, Zhang J, Fan Z G, Gao J 2014 Acta Phys. Sin. 63 114201 (in Chinese) [吴良海, 张骏, 范之国, 高隽 2014 物理学报 63 114201]
[4] Cui Y, Gao Q S, Chu J K, Chen C 2013 Opt. Precis. Eng. 21 34 (in Chinese) [崔岩, 高启升, 褚金奎, 陈辰 2013 光学精密工程 21 34]
[5] Guan G X, Yan L, Chen J B, Wu T X, Wu B 2011 Acta Armament. 32 459 (in Chinese) [关桂霞, 晏磊, 陈家斌, 吴太夏, 吴波 2011 兵工学报 32 459]
[6] Pust N J, Shaw J A 2011 J. Appl. Remote Sens. 5 053529
[7] Pust N J, Shaw J A 2007 Proc. SPIE 6682 668204
[8] Pust N J 2007 Ph. D. Dissertation (Montana: Montana state university)
[9] Horvath G, Barta A, Gal J, Suhai B, Haiman O 2002 Appl. Opt. 41 543
[10] Liu Q, Chu J K, Wang J, Guan L 2014 Acta Opt. Sin. 34 0301004 (in Chinese) [刘琦, 褚金奎, 王兢, 关乐 2014 光学学报 34 0301004]
[11] Wang W, Chu J K, Cui Y, Zhi W 2013 Chin. J. Lasers 40 0513001 (in Chinese) [王威, 褚金奎, 崔岩, 支炜 2013 中国激光 40 0513001]
[12] Wu L H 2010 M. S. Dissertation (Hefei: Hefei University of Technology) (in Chinese) [吴良海 2010 硕士学位论文(合肥: 合肥工业大学)]
[13] Evans K F, Stephens G L 1991 J. Quant. Spectrosc. Radiat. Transfer 46 413
[14] Schulz F M, Stamnes K 2000 J. Quant. Spectrosc. Radiat. Transfer 65 609
[15] Min Q L, Duan M Z 2004 J. Quant. Spectrosc. Radiat. Transfer 87 243
[16] Lenoble J, Herman J, Deuz M, Lafrance J L, Santer B, Tanr R 2007 J. Quant. Spectrosc. Radiat. Transfer 107 479
[17] Evans K F 1998 J. Atmos. Sci. 55 429
[18] Doicu A, Efremenko D, Trautmann T 2013 J. Quant. Spectrosc. Radiat. Transfer 118 121
[19] Whitney B A 2011 Bull. Astr. Soc. India 39 1
[20] Cornet C, Labonnote L C, Szczap F 2010 J. Quant. Spectrosc. Radiat. Transfer 111 174
[21] Emde C, Mayer B 2007 Atmos. Chem. Phys. 7 2259
[22] Ben X, Yi H L, Tan H P 2014 Chin. Phys. B 23 099501
[23] Li J, Shibata K 2006 J. Atmos. Sci. 63 1365
[24] Spurr R J D 2006 J. Quant. Spectrosc. Radiat. Transfer 102 316
[25] Natraj V, Spurr R J D 2007 J. Quant. Spectrosc. Radiat. Transfer 107 263
[26] Spurr R J D, Christi M J 2007 J. Quant. Spectrosc. Radiat. Transfer 103 431
[27] Hu S, Gao T C, Li H, Liu L, Cheng T J, Zhang T 2015 Acta Phys. Sin. 64 184203 (in Chinese) [胡帅, 高太长, 李浩, 刘磊, 程天际, 张婷 2015 物理学报 64 184203]
[28] Rao R Z 2012 Modern Optics (Beijing: Scientific Express) p123 (in Chinese) [饶瑞中 2012 现代大气光学 (北京: 科学出版社) 第123页]
[29] de Haan J F, Bosma P B, Hovenier J W 1987 Astron. Astrophys. 183 371
[30] de Rooij W A, van der Stap C C A H 1984 Astron. Astrophys. 131 237
[31] Dahlback A, Stamnes K 1991 Planet Space Sci. 39 671
[32] Hess M, Koepke P, Schult I 1998 Bull. Am. Meteor. Soc. 79 831
[33] Mayer B, Kyllig A 2005 Atmos. Chem. Phys. 5 1855
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[1] Rozanov V V, Rozanov A V, Kokhanovsky A A, Burrows J P 2014 J. Quant. Spectrosc. Radiat. Transfer 133 13
[2] Emde C, Buras R, Mayer B, Blumthaler M 2010 Atmos. Chem. Phys. 10 383
[3] Wu L H, Zhang J, Fan Z G, Gao J 2014 Acta Phys. Sin. 63 114201 (in Chinese) [吴良海, 张骏, 范之国, 高隽 2014 物理学报 63 114201]
[4] Cui Y, Gao Q S, Chu J K, Chen C 2013 Opt. Precis. Eng. 21 34 (in Chinese) [崔岩, 高启升, 褚金奎, 陈辰 2013 光学精密工程 21 34]
[5] Guan G X, Yan L, Chen J B, Wu T X, Wu B 2011 Acta Armament. 32 459 (in Chinese) [关桂霞, 晏磊, 陈家斌, 吴太夏, 吴波 2011 兵工学报 32 459]
[6] Pust N J, Shaw J A 2011 J. Appl. Remote Sens. 5 053529
[7] Pust N J, Shaw J A 2007 Proc. SPIE 6682 668204
[8] Pust N J 2007 Ph. D. Dissertation (Montana: Montana state university)
[9] Horvath G, Barta A, Gal J, Suhai B, Haiman O 2002 Appl. Opt. 41 543
[10] Liu Q, Chu J K, Wang J, Guan L 2014 Acta Opt. Sin. 34 0301004 (in Chinese) [刘琦, 褚金奎, 王兢, 关乐 2014 光学学报 34 0301004]
[11] Wang W, Chu J K, Cui Y, Zhi W 2013 Chin. J. Lasers 40 0513001 (in Chinese) [王威, 褚金奎, 崔岩, 支炜 2013 中国激光 40 0513001]
[12] Wu L H 2010 M. S. Dissertation (Hefei: Hefei University of Technology) (in Chinese) [吴良海 2010 硕士学位论文(合肥: 合肥工业大学)]
[13] Evans K F, Stephens G L 1991 J. Quant. Spectrosc. Radiat. Transfer 46 413
[14] Schulz F M, Stamnes K 2000 J. Quant. Spectrosc. Radiat. Transfer 65 609
[15] Min Q L, Duan M Z 2004 J. Quant. Spectrosc. Radiat. Transfer 87 243
[16] Lenoble J, Herman J, Deuz M, Lafrance J L, Santer B, Tanr R 2007 J. Quant. Spectrosc. Radiat. Transfer 107 479
[17] Evans K F 1998 J. Atmos. Sci. 55 429
[18] Doicu A, Efremenko D, Trautmann T 2013 J. Quant. Spectrosc. Radiat. Transfer 118 121
[19] Whitney B A 2011 Bull. Astr. Soc. India 39 1
[20] Cornet C, Labonnote L C, Szczap F 2010 J. Quant. Spectrosc. Radiat. Transfer 111 174
[21] Emde C, Mayer B 2007 Atmos. Chem. Phys. 7 2259
[22] Ben X, Yi H L, Tan H P 2014 Chin. Phys. B 23 099501
[23] Li J, Shibata K 2006 J. Atmos. Sci. 63 1365
[24] Spurr R J D 2006 J. Quant. Spectrosc. Radiat. Transfer 102 316
[25] Natraj V, Spurr R J D 2007 J. Quant. Spectrosc. Radiat. Transfer 107 263
[26] Spurr R J D, Christi M J 2007 J. Quant. Spectrosc. Radiat. Transfer 103 431
[27] Hu S, Gao T C, Li H, Liu L, Cheng T J, Zhang T 2015 Acta Phys. Sin. 64 184203 (in Chinese) [胡帅, 高太长, 李浩, 刘磊, 程天际, 张婷 2015 物理学报 64 184203]
[28] Rao R Z 2012 Modern Optics (Beijing: Scientific Express) p123 (in Chinese) [饶瑞中 2012 现代大气光学 (北京: 科学出版社) 第123页]
[29] de Haan J F, Bosma P B, Hovenier J W 1987 Astron. Astrophys. 183 371
[30] de Rooij W A, van der Stap C C A H 1984 Astron. Astrophys. 131 237
[31] Dahlback A, Stamnes K 1991 Planet Space Sci. 39 671
[32] Hess M, Koepke P, Schult I 1998 Bull. Am. Meteor. Soc. 79 831
[33] Mayer B, Kyllig A 2005 Atmos. Chem. Phys. 5 1855
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