漫射光化通量的二流四流混合近似算法求解
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摘要
本文利用二流近似方法解析求解源函数,最后获得四流近似的辐射强度,并把该方法应用到光化辐射通量的计算中。本文还对二流近似、四流近似、二流四流混合近似这三种算法的精度和效率进行比较,分析了在不同的太阳天顶角、大气光学厚度、地表反照率下,考虑分子、气溶胶、霾和云的漫射光化通量。主要结果如下:
(1)对于守恒或者非守恒的瑞利散射大气,δ-二流四流混合近似算法的精度接近δ-四流近似的精度,并且比δ-二流近似的精度更高。
(2)对于非吸收性气溶胶,当光学厚度τ1分别等于0.02、2.5、5的条件下,基于离散纵标的δ-二流四流混合近似算法的精度和δ-四流近似的算法的精度相当,在其他情况下,δ-四流近似的算法更好。并且基于离散纵标方案的δ-二流四流混合近似算法的精度要比基于爱丁顿、半球近似的δ-二流四流混合近似算法的精度更高。
(3)对于本文给定的云模型C1和霾模型L的光化通量计算,基于离散纵标的δ-二流四流混合近似算法比基于爱丁顿、半球近似方案的δ-二流四流混合近似算法精度要高。
(4)总体而言,对于漫射光化通量的计算,δ-二流近似的误差最大。而δ-四流近似在任何大气条件下都能得到可靠的结果。基于离散纵标的δ-二流四流混合近似算法的精度与δ-四流近似接近。从精度和效率两个方面考虑,基于离散纵标的δ-二流四流混合近似算法吸纳了二流近似精度速度快的优点和四流近似精度高的优点,它能在速度略低于二流近似的情况下达到接近四流近似的精度。因此它非常适用于光化通量的计算。
(5)另外,本文还提出了一种新的处理漫射因子的拟合方案,通过与前人提出的方案相比,该方案具有较高的拟合精度;然后,本文将该拟合方案和前人提出的方案同时放入辐射传输模式中来计算大气加热率,结果表明:新方案的结果总体上优于前人的结果,尤其是对45 km以上的中间层大气。
Abstract: In this paper, theδ-two-and four-stream combination approximations, which use a source function from the two-stream approximations and evaluate intensities in the four-stream directions, are formulated for the calculation of diffuse actinic fluxes. The accuracy and efficiency of the three computational techniques, i.e., theδ-two-stream approximations, theδ-two- and four-stream combination approximations based on various two-stream approaches, and theδ-four-stream approximation, have been investigated. The diffuse actinic fluxes are examined by considering molecular, aerosol, haze and cloud scattering over a wide range of solar zenith angles, optical depths, and surface albedos. In addition, the following conclusions are mainly achieved:
(1) In general, for a conservative or non-conservative Rayleigh scattering atmosphere, the accuracy of theδ-two- and four-stream combination approximations based on various two-stream approaches is close to that of theδ-four-stream approximation and much more accurate than that of theδ-two-stream approximations.
(2) For non-absorbing aerosols, when the optical depthτ1 is equal to 0.02, 2.5, and 5, the accuracy of theδ-two- and four-stream combination approximation based on the quadrature scheme is similar to that of theδ-four-stream approximation. In other cases, theδ-four-stream approximation performs better. Hence theδ-two- and four-stream combination approximation based on the quadrature scheme is better than those based on the Eddington and hemispheric constant schemes.
(3) For both Cloud C1 and Haze L, the accuracy ofδ-two- and four-stream combination approximation based on the Eddington hemispheric constant scheme is slightly better than or similar to that of theδ-two-stream approximation based on the Eddington and hemispheric constant schemes. In addition, theδ-two-and four-stream combination approximation based on the quadrature scheme is better than those based on the Eddington and hemispheric constant schemes.
(4) We found that for the calculation of diffuse actinic fluxes, the errors in theδ-two-stream methods were largest. For theδ-four-stream approximation, reliable results were obtained under all conditions. The accuracy of theδ-two- and four-stream combination approximations based on the quadrature scheme was close to that of theδ-four-stream approximation.In view of their accuracy and computational efficiency, theδ-two- and four-stream combination method based on the quadrature scheme takes the advantages of the speed of the two-stream approximations and the accuracy of the four-stream approximation. Hence it is well-suited to diffuse actinic flux calculations.
(5) The new scheme to deal with diffusivity factor, which is more precise in comparison with the previous studies, is presented. For diffusivity factor and the previous ones are put into a radiative transfer model to calculate the atmospheric heating rate. The results show that the new scheme is generally better than previous ones, especially in the upper atmosphere with a height of more than 45 km.
(1)对于守恒或者非守恒的瑞利散射大气,δ-二流四流混合近似算法的精度接近δ-四流近似的精度,并且比δ-二流近似的精度更高。
(2)对于非吸收性气溶胶,当光学厚度τ1分别等于0.02、2.5、5的条件下,基于离散纵标的δ-二流四流混合近似算法的精度和δ-四流近似的算法的精度相当,在其他情况下,δ-四流近似的算法更好。并且基于离散纵标方案的δ-二流四流混合近似算法的精度要比基于爱丁顿、半球近似的δ-二流四流混合近似算法的精度更高。
(3)对于本文给定的云模型C1和霾模型L的光化通量计算,基于离散纵标的δ-二流四流混合近似算法比基于爱丁顿、半球近似方案的δ-二流四流混合近似算法精度要高。
(4)总体而言,对于漫射光化通量的计算,δ-二流近似的误差最大。而δ-四流近似在任何大气条件下都能得到可靠的结果。基于离散纵标的δ-二流四流混合近似算法的精度与δ-四流近似接近。从精度和效率两个方面考虑,基于离散纵标的δ-二流四流混合近似算法吸纳了二流近似精度速度快的优点和四流近似精度高的优点,它能在速度略低于二流近似的情况下达到接近四流近似的精度。因此它非常适用于光化通量的计算。
(5)另外,本文还提出了一种新的处理漫射因子的拟合方案,通过与前人提出的方案相比,该方案具有较高的拟合精度;然后,本文将该拟合方案和前人提出的方案同时放入辐射传输模式中来计算大气加热率,结果表明:新方案的结果总体上优于前人的结果,尤其是对45 km以上的中间层大气。
Abstract: In this paper, theδ-two-and four-stream combination approximations, which use a source function from the two-stream approximations and evaluate intensities in the four-stream directions, are formulated for the calculation of diffuse actinic fluxes. The accuracy and efficiency of the three computational techniques, i.e., theδ-two-stream approximations, theδ-two- and four-stream combination approximations based on various two-stream approaches, and theδ-four-stream approximation, have been investigated. The diffuse actinic fluxes are examined by considering molecular, aerosol, haze and cloud scattering over a wide range of solar zenith angles, optical depths, and surface albedos. In addition, the following conclusions are mainly achieved:
(1) In general, for a conservative or non-conservative Rayleigh scattering atmosphere, the accuracy of theδ-two- and four-stream combination approximations based on various two-stream approaches is close to that of theδ-four-stream approximation and much more accurate than that of theδ-two-stream approximations.
(2) For non-absorbing aerosols, when the optical depthτ1 is equal to 0.02, 2.5, and 5, the accuracy of theδ-two- and four-stream combination approximation based on the quadrature scheme is similar to that of theδ-four-stream approximation. In other cases, theδ-four-stream approximation performs better. Hence theδ-two- and four-stream combination approximation based on the quadrature scheme is better than those based on the Eddington and hemispheric constant schemes.
(3) For both Cloud C1 and Haze L, the accuracy ofδ-two- and four-stream combination approximation based on the Eddington hemispheric constant scheme is slightly better than or similar to that of theδ-two-stream approximation based on the Eddington and hemispheric constant schemes. In addition, theδ-two-and four-stream combination approximation based on the quadrature scheme is better than those based on the Eddington and hemispheric constant schemes.
(4) We found that for the calculation of diffuse actinic fluxes, the errors in theδ-two-stream methods were largest. For theδ-four-stream approximation, reliable results were obtained under all conditions. The accuracy of theδ-two- and four-stream combination approximations based on the quadrature scheme was close to that of theδ-four-stream approximation.In view of their accuracy and computational efficiency, theδ-two- and four-stream combination method based on the quadrature scheme takes the advantages of the speed of the two-stream approximations and the accuracy of the four-stream approximation. Hence it is well-suited to diffuse actinic flux calculations.
(5) The new scheme to deal with diffusivity factor, which is more precise in comparison with the previous studies, is presented. For diffusivity factor and the previous ones are put into a radiative transfer model to calculate the atmospheric heating rate. The results show that the new scheme is generally better than previous ones, especially in the upper atmosphere with a height of more than 45 km.
引文
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[3]杨文.地球大气中辐射传输与粒子光散射相互作用的研究,中国科学院寒区旱区环境与工程研究所, 2004.
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[7] Wiscombe W J. Improved Mie scattering algorithms. Appl. Opt., 1980, 19: 1505-1509.
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[9] S Wolf, N V voshchinnikov. Mie Scattering by ensembles of particles with very large size parameters. Computer Physics Communications, 2004, 162: 113-123.
[10]张鹏.卫星测量反射太阳光反演气溶胶物理和光学特性的算法研究.中国科学院大气物理研究所博士论文, 1998.
[11]张华等.现代数值预报业务中第三章的3.2.1节辐射过程(初稿).
[12] Chou M D. Parameterization for the absorption of solar radiation by O2 and CO2 with application to climate studies. J. Climate, 1990, 3: 209–217.
[13] Chou M D. A solar radiation model for use in climate studies. J. Atmos. Sci., 1992, 49: 762–772.
[14] Chou M D, K T Lee. Parameterizations for the absorption of solar radiation by water vapor and ozone. J. Atmos. Sci., 1996, 53: 1203–1208.
[15] Chou M D, etal. Parameterizations for Cloud Overlapping and Shortwave Single-Scattering. Journal of Climate. 1999, 11: 202–214.
[16] Freidenreich S M, Ramaswamy V. A new multiple-band solar radiative parameterization for general circulation models. Journal of Geophysical Research, 1999, 104: 31389-31410.
[17] Lacis A A, et al. A description of the correlated k-distribution method for modeling nongray gaseous absorption, thermal emission, and multiple scattering in vertically inhomogeneous atmospheres. Journal of Geophysical Research, 1991, 96:9027-9063.
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