非球形气溶胶粒子散射相函数经验公式
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摘要
散射相函数是研究电磁波传输特性的重要参数,直接影响电磁波传输方程的简化程度和解的精度。基于电磁散射与辐射传输中的基本理论,对非球形粒子散射相函数的经验公式进行了研究。为了很好的模拟非球形粒子的后向散射峰值,提高辐射传输方程的简化程度和解的精度,提出了一种新的相函数经验公式。分析新的相函数对非球形粒子的适用性,以单个沙尘性气溶胶为例,计算了不同形状粒子的HenyeyGreenstein*相函数和新的相函数随角度的变化,并与T矩阵法的计算结果进行了对比,发现椭球形粒子的长短轴比和有限长圆柱形粒子的径长比大于0.5时,新的相函数在大角度后向散射部分与T矩阵法的吻合程度较高。考虑波长变化,对比了尺寸谱满足对数正态分布的四种气溶胶粒子的Henyey-Greenstein*相函数和新的相函数与T矩阵法的计算结果。研究表明,对于椭球形粒子和有限长圆柱形粒子,在大角度(大于90°)后向散射部分,除了0.694时的椭球形海洋性气溶胶,新的相函数均方根差较小的占100%,证明了新的相函数可以较好的模拟非球形粒子的后向散射特征。新的相函数对准确模拟辐射传输过程具有重要意义。
In electromagnetic radiative transfer calculations,the accuracy and the computation timeare usually determined by the representation of scattering phase function.Accurate calculations are time consuming even for non-spherical particles.In order to get a better fit to exact calculations and simulate the backward-scattering peak of non-spherical particles,we developed a new empirical expression of non-spherical based on the fundamental theory of electromagnetic scattering and radiation transmission.This empirical expression of phase function is an algebraic expression with one single free parameter(asymmetry factor),and can be expanded into Legendre polynomials.We compared the Henyey-Greenstein*phase function and the new empirical expression with the T-matrix method for dustlike aerosol with different geometric shape,and found the new empirical expression provided a more realistic description for the scattering of non-spherical particles.Furthermore,the calculated value for ratio of scattering intensity at 90 degree to the scattered intensity in the backward direction is more reasonable when the ratio of the horizontal to rotational axes and the diameter-to-length ratio is larger than 0.5.We also investigated the effectiveness in approximating scattering from polydispersed particles by comparison between the new empirical expression,the Henyey-Greenstein*phase function and the T-matrix method for four of the log normal distribution polydispersions.The results show that the new empirical expression fits the T-matrix method much better than the Henyey-Greenstein*phase function.For the new empirical expression,the RMSE is small for 100% data except for the ellipsoidal oceanic aerosol at the wavelength of 633 nm.Similarly,the effectiveness of the new empirical expression is significant when we calculate the ratio of scattered intensity at 90 degree to the scattered intensity in the backward direction of non-spherical aerosol.In summary,the new empirical expression provides more accurate calculation for scattered intensity of non-spherical particlesin the backward direction,and is helpful in electromagnetic radiative transfer calculations,and the reformatting radiative transfer models in terms of the new empirical expression should require relatively less effort.
In electromagnetic radiative transfer calculations,the accuracy and the computation timeare usually determined by the representation of scattering phase function.Accurate calculations are time consuming even for non-spherical particles.In order to get a better fit to exact calculations and simulate the backward-scattering peak of non-spherical particles,we developed a new empirical expression of non-spherical based on the fundamental theory of electromagnetic scattering and radiation transmission.This empirical expression of phase function is an algebraic expression with one single free parameter(asymmetry factor),and can be expanded into Legendre polynomials.We compared the Henyey-Greenstein*phase function and the new empirical expression with the T-matrix method for dustlike aerosol with different geometric shape,and found the new empirical expression provided a more realistic description for the scattering of non-spherical particles.Furthermore,the calculated value for ratio of scattering intensity at 90 degree to the scattered intensity in the backward direction is more reasonable when the ratio of the horizontal to rotational axes and the diameter-to-length ratio is larger than 0.5.We also investigated the effectiveness in approximating scattering from polydispersed particles by comparison between the new empirical expression,the Henyey-Greenstein*phase function and the T-matrix method for four of the log normal distribution polydispersions.The results show that the new empirical expression fits the T-matrix method much better than the Henyey-Greenstein*phase function.For the new empirical expression,the RMSE is small for 100% data except for the ellipsoidal oceanic aerosol at the wavelength of 633 nm.Similarly,the effectiveness of the new empirical expression is significant when we calculate the ratio of scattered intensity at 90 degree to the scattered intensity in the backward direction of non-spherical aerosol.In summary,the new empirical expression provides more accurate calculation for scattered intensity of non-spherical particlesin the backward direction,and is helpful in electromagnetic radiative transfer calculations,and the reformatting radiative transfer models in terms of the new empirical expression should require relatively less effort.
引文
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[3] Taflove A,Hagness S C.Computational Electrodynamics.Boston:Artech House,2000.2.
[4] Mishchenko M I.Optics and Image Science,1991,8:871.
[5] SUN Xian-ming,WANG Hai-hua,LIU Wan-qiang(孙贤明,王海华,刘万强).Acta Optica Sinica(光学学报),2010,30(5):1505.
[6] BAI Lu,TANG Shuang-qing,WU Zhen-sen(白璐,汤双庆,吴振森).Acta Phys.Sin.(物理学报),2010,59(3):1749.
[7] LUO Shuang,YIN Qiu(罗双,尹球).Acta Optica Sinica(光学学报),2017,37(2):0229002-1.
[8] Wang Z,Cui S C,Yang J,et al.J.Quant.Spectrosc.Radiat.Transfer,2017,189:283.
[9] Van de Hulst H C.Light Scattering by Small Particles.New York:Wiley,1957.8.
[10] Liou K N.An Introduction to Atmospheric Radiation.2rd ed.Beijing:China Meteorological Press,2004.181.
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[12] HU Shuai,GAO Tai-chang,LIU Lei(胡帅,高太长,刘磊).Journal of the Meteorological Sciences(气象学报),2014,34(6):612.