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In satellite remote sensing, the relationship between bidirectional reflectance and optical depth is the foundation of the retrieval of the aerosols' optical depth. According to asymptotic integral theory, a new approach to dealing with bidirectional reflectance of atmospheric without artificial stratification in the single-scattering approximation. The results show that the accuracy of analytical solution obtained by the new method is high. We formulate the analytical bidirectional reflectance with the vertical continuity of the inherent optical properties. Moreover, analytical solution is relatively easy to explain some of most import features for radiative transfer process.
[1] Liang Z C, Jin Y Q 2002 Acta Phys. Sin. 51 2239 (in Chinese) [梁子长, 金亚秋 2002 物理学报 51 2239]
[2] Liang Z C, Jin Y Q 2003 Acta Phys. Sin. 52 247 (in Chinese) [梁子长, 金亚秋 2002 物理学报 52 247]
[3] Duan M Z, Guo X 2009 Acta Phys. Sin. 58 1353 (in Chinese) [段民征, 郭霞 2009 物理学报 58 1353]
[4] Zhang F, Zhang H, Shen Z P, Wei X D 2011 Acta Phys. Sin. 60 010702 (in Chinese) [张峰, 张华, 沈钟平, 卫晓东 2011 物理学报 60 010702]
[5] Han Y, Wang T J, Rao R Z, Wang Y J 2008 Acta Phys. Sin. 57 7396 (in Chinese) [韩永, 王体健, 饶瑞中, 王英俭 2008 物理学报 57 7396]
[6] Zuo H Y, Yang J G 2007 Acta Phys. Sin. 56 6132 (in Chinese) [左浩毅, 杨经国 2007 物理学报 56 6132]
[7] Du H D, Huang S X, Shi H Q 2008 Acta Phys. Sin. 57 7685 (in Chinese) [杜华栋, 黄思训, 石汉青 2008 物理学报 57 7685]
[8] Shen Z P, Zhang H 2009 Acta Energiae Sol. Sin. 30 1389 (in Chinese) [沈钟平, 张华 2009 太阳能学报 30 1389]
[9] Qiu J 1999 J. Atmos. Sci. 56 2955
[10] Duan M, Min Q, Lu D 2010 Adv. Atmos. Sci. 27 891
[11] Duan M, Min Q 2005 J. Quant. Spectrosc. Radiat. 95 21
[12] Lu P, H Zhang, J Li 2009 J. Quant. Spectrosc. Radiat. 110 129
[13] Zhang H, Zhang F, Fu Q, Shen Z, Lu P 2010 J. Atmos. Sci. 67 3238
[14] Liu Q, Weng F 2006 Geophys. Res. Lett. 33 L22811 doi:10.1029/ 2006GL027543
[15] Hovenier J W, Stam D M 2007 J. Quant. Spectro. Radia. Trans. 107 83
[16] Liou K N 2002 An Introduction to Atmospheric Radiation (2nd Ed.) (California: Academic Press) pp31-32, 105, 261, 272
[17] C M Bender, S A Orsazag 1978 Advanced Mathematical Methods for Scientists and Engineers (New York: McGraw-Hill Press) p258
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[1] Liang Z C, Jin Y Q 2002 Acta Phys. Sin. 51 2239 (in Chinese) [梁子长, 金亚秋 2002 物理学报 51 2239]
[2] Liang Z C, Jin Y Q 2003 Acta Phys. Sin. 52 247 (in Chinese) [梁子长, 金亚秋 2002 物理学报 52 247]
[3] Duan M Z, Guo X 2009 Acta Phys. Sin. 58 1353 (in Chinese) [段民征, 郭霞 2009 物理学报 58 1353]
[4] Zhang F, Zhang H, Shen Z P, Wei X D 2011 Acta Phys. Sin. 60 010702 (in Chinese) [张峰, 张华, 沈钟平, 卫晓东 2011 物理学报 60 010702]
[5] Han Y, Wang T J, Rao R Z, Wang Y J 2008 Acta Phys. Sin. 57 7396 (in Chinese) [韩永, 王体健, 饶瑞中, 王英俭 2008 物理学报 57 7396]
[6] Zuo H Y, Yang J G 2007 Acta Phys. Sin. 56 6132 (in Chinese) [左浩毅, 杨经国 2007 物理学报 56 6132]
[7] Du H D, Huang S X, Shi H Q 2008 Acta Phys. Sin. 57 7685 (in Chinese) [杜华栋, 黄思训, 石汉青 2008 物理学报 57 7685]
[8] Shen Z P, Zhang H 2009 Acta Energiae Sol. Sin. 30 1389 (in Chinese) [沈钟平, 张华 2009 太阳能学报 30 1389]
[9] Qiu J 1999 J. Atmos. Sci. 56 2955
[10] Duan M, Min Q, Lu D 2010 Adv. Atmos. Sci. 27 891
[11] Duan M, Min Q 2005 J. Quant. Spectrosc. Radiat. 95 21
[12] Lu P, H Zhang, J Li 2009 J. Quant. Spectrosc. Radiat. 110 129
[13] Zhang H, Zhang F, Fu Q, Shen Z, Lu P 2010 J. Atmos. Sci. 67 3238
[14] Liu Q, Weng F 2006 Geophys. Res. Lett. 33 L22811 doi:10.1029/ 2006GL027543
[15] Hovenier J W, Stam D M 2007 J. Quant. Spectro. Radia. Trans. 107 83
[16] Liou K N 2002 An Introduction to Atmospheric Radiation (2nd Ed.) (California: Academic Press) pp31-32, 105, 261, 272
[17] C M Bender, S A Orsazag 1978 Advanced Mathematical Methods for Scientists and Engineers (New York: McGraw-Hill Press) p258
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