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灰霾期间细颗粒物以人为沙尘为主,沙尘颗粒粒径较小,且不断受到人为活动的影响。图1给出了灰霾期间硫酸盐和沙尘混合的透射电镜(TEM)图像[15],图1(a)中黑色箭头表示矿物沙尘颗粒,可以看出灰霾期间,大量可见涂层出现在矿物沙尘颗粒表面,从图1(b)、1(c)可以看出硫酸盐、硝酸盐的壳包裹在矿物沙尘颗粒表面,并呈现极为复杂的非球形形态和混合状态。Kojima等[16]的观测研究也表明矿物沙尘颗粒会通过吸附酸性气体获得硫酸盐壳涂层。该过程会改变大气中硫酸盐和沙尘颗粒的分布特征及沙尘颗粒的表面特性,从而进一步改变它们的光散射特性[17]。
文中以沙尘为核(图2中的灰色部分),以硫酸盐为壳(图2中的白色部分),建立了沙尘-硫酸盐(D-S)的“核-壳”模型。图2给出了D-S的内混合模型示意图。当混合比为0时,为纯硫酸盐颗粒,当混合比为1时,为纯沙尘颗粒。其中混合比q和取向比α定义为:
$$ q = \frac{{{R_{in}}}}{{{R_{out}}}} = \frac{c}{b} $$ (1) $$ \alpha = \frac{a}{b} $$ (2) 以往研究中大多采用分层球形粒子研究内混合粒子模型,但实际大气颗粒有许多粒子都是近似椭球、圆柱形等非球形粒子[18],因此采取非球形模型可以提高粒子光学特性模拟精度和测量精度。Mish-chenko等[19]研究表明,沙尘粒子的光学特性可以通过取向比为1.7的椭球模型来很好地反映,这也是目前气溶胶遥感等领域应用较广的非球形模型。因此文中选取取向比为1.7建立D-S非球形模型进行研究,以得到最为接近自然状态下的研究结果。Bauer 等[20]采用GCM模式对全球硫酸盐包覆沙尘颗粒进行了模拟,结果表明,外壳占比可达到0~20%以上,因此在研究光学参数随粒子等效半径和波长变化关系时,采取混合比为0.9来表征实际灰霾大气场景下粒子混合状态并对此进行研究。沙尘和硫酸盐的复折射率实部和虚部如表1所示。
表 1 沙尘和硫酸盐气溶胶在四个给定波长下的复折射指数[9]
Table 1. Complex refractive indices of dust and sulfate aerosol at the four selected wavelengths[9]
Wavelength/μm Dust Sulfate Real Imaginary Real Imaginary 0.44 1.593 0.0046 1.415 4.1957E-8 0.670 1.553 0.00084 1.404 5.56319E-8 0.870 1.536 0.00144 1.40 1.21828E-6 1.020 1.529 0.00213 1.396 8.9583E-6 -
T矩阵方法以Maxwell方程为出发点,把粒子入射场、散射场进行矢量球面波函数展开[21-22],即
$$ \begin{gathered} {E_{inc}}(r) = \sum\limits_{n = 1}^\infty {\sum\limits_{m = - n}^n {[{a_{mn}}Rg{M_{mn}}(kr) + {b_{mn}}Rg{N_{mn}}(kr)]} } \hfill \\ {E_{sca}}(r) = \sum\limits_{n = 1}^\infty {\sum\limits_{m = - n}^n {[{p_{mn}}{M_{mn}}(kr) + {q_{mn}}{N_{mn}}(kr)]} } \hfill \\ \end{gathered} $$ (3) 式中:
$ {E_{inc}} $ ,$ {E_{sca}} $ 分别为入射场和散射场;($ {a_{mn}} $ ,$ {b_{mn}} $ )为入射场展开系数;($ {p_{mn}} $ ,$ {q_{mn}} $ )为散射场展开系数:$$ \begin{gathered} {p_{mn}} = \sum\limits_{n' = 1}^\infty {\sum\limits_{m' = - n'}^{n'} {[T_{mnm'n'}^{11}{a_{m'n'}} + T_{mnm'n'}^{12}{b_{m'n'}}]} } \hfill \\ {q_{mn}} = \sum\limits_{n' = 1}^\infty {\sum\limits_{m' = - n'}^{n'} {[T_{mnm'n'}^{21}{a_{m'n'}} + T_{mnm'n'}^{22}{b_{m'n'}}]} } \hfill \\ \end{gathered} $$ (4) 写成矩阵形式为:
$$ \left( {\begin{array}{*{20}{c}} p \\ q \end{array}} \right) = T\left( {\begin{array}{*{20}{c}} a \\ b \end{array}} \right) = \left( {\begin{array}{*{20}{c}} {{T^{11}}}&{{T^{12}}} \\ {{T^{21}}}&{{T^{22}}} \end{array}} \right)\left( {\begin{array}{*{20}{c}} a \\ b \end{array}} \right) $$ (5) 进一步简化表示为:
$$ T = - B \times {A^{ - 1}} $$ (6) 对于内层折射率为
$ {m_1} $ ,外层折射率为$ {m_2} $ 的双层粒子,T矩阵可以表示为:$$ \begin{split} T =& - B \times {A^{ - 1}} = - [{B_2} + B{B_2} \times ( - {B_1} \times A_1^{ - 1})] \times \hfill \\ &{[{A_2} + A{A_2} \times ( - {B_1} \times A_1^{ - 1})]^{ - 1}} \hfill \end{split} $$ (7) 式中:
$ - {B_1} \times A_1^{ - 1} = {T_1} $ 为核的T矩阵。计算时内层粒子的相对折射率为$ {m_1}/{m_2} $ ,外层的相对折射率取1,即相当于内核存在折射率为$ {m_2} $ 的介质中。$ {A_2} $ 、$ {B_2} $ 计算时假设粒子折射率为$ {m_2} $ ,外层的相对折射率取1。$ A{A_2} $ 、$ B{B_2} $ 计算与$ {A_2} $ 、$ {B_2} $ 类似,但是计算时需要用Hankel函数替代第一类Bessel函数。T矩阵的计算只依赖于粒子的物理特性和几何特性,包括折射率、尺度参数、形状,而与入射场无关。因此,对于每个确定的散射体,只需要计算一次T矩阵值,就可以得到所有散射参量。这种方法计算速度比多次取向平均的方法提高几十倍。消光效率因子
$ {Q_{ext}} $ 、散射效率因子$ {Q_{sca}} $ 、吸收效率因子$ {Q_{abs}} $ 为:$$ \begin{gathered} {Q_{ext}} = {{{C_{ext}}} \mathord{\left/ {\vphantom {{{C_{ext}}} {\pi {R} _{eff}^2}}} \right. } {\pi {R} _{eff}^2}} \hfill \\ {Q_{sca}} = {{{C_{sca}}} \mathord{\left/ {\vphantom {{{C_{sca}}} {\pi {R} _{eff}^2}}} \right. } {\pi {R} _{eff}^2}} \hfill \\ {Q_{abs}} = {Q_{ext}} - {Q_{sca}} \hfill \\ \end{gathered} $$ (8) 其中
$$ \begin{gathered} {C_{ext}} = \frac{{2\pi }}{{{k^2}}}{Re} \sum\limits_{n = 1}^\infty {\sum\limits_{m = - n}^n {[T_{mnn'}^{11} + T_{mnn'}^{22}]} } \hfill \\ {C_{sca}} = \frac{{2\pi }}{{{k^2}}}\sum\limits_{i,j = 1}^2 {\sum\limits_{n = 1}^\infty {\sum\limits_{n' = 1}^\infty {\sum\limits_{m = 0}^{\min (n,n')} {(2 - {\delta _{m0}}){{\left| {T_{mnn'}^{ij}} \right|}^2}} } } } \hfill \\ \end{gathered} $$ (9) 对于旋转对称的空间随机取向粒子,归一化散射相矩阵一般表示为:
$$ \left[ {\begin{array}{*{20}{c}} {{{{P}}_{11}}(\theta )}&{{{{P}}_{12}}(\theta )}&0&0 \\ {{{{P}}_{21}}(\theta )}&{{{{P}}_{22}}(\theta )}&0&0 \\ 0&0&{{{{P}}_{33}}(\theta )}&{{{{P}}_{34}}(\theta )} \\ 0&0&{{{ - }}{{{P}}_{34}}(\theta )}&{{{{P}}_{44}}(\theta )} \end{array}} \right] $$ (10) 式中:
$ \theta $ 为散射角,且$ {0^ \circ } \leqslant \theta \leqslant {180^ \circ } $ ;${{{P}}_{11}}$ 满足如下归一化条件:$$ \frac{1}{2}\int_0^\pi {{P_{11}}(\theta )\sin \theta {\text{d}}\theta } = 1 $$ (11) 式中:
$ {P_{11}}(\theta ) $ 为归一化散射相函数。文中的研究中采用Arturo Quirantes[21]发布的T矩阵方法计算随机取向沙尘-硫酸盐颗粒的散射特性,该软件通过与Aden-Kerker、Mie理论等方法进行了详细对比,验证了该方法的有效性。更多细节请参考文献[21]。
Study on the optical properties of sulfate coated dust aerosol particles during haze episodes
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摘要: 灰霾期间硫酸盐与沙尘矿物颗粒表面经过系列化学反应形成复杂的混合状态,为气溶胶光学性质模拟带来很大困难。因此,厘清硫酸盐壳对沙尘矿物颗粒光学特性的影响机制具有重要意义。文中根据灰霾期间硫酸盐与沙尘矿物颗粒反应过程中的混合结构变化,建立了沙尘-硫酸盐颗粒的核壳椭球结构模型。采用T矩阵方法,研究了四波段条件(0.44、0.675、0.87、1.02 μm)下,混合比对单分散系沙尘-硫酸盐粒子光学特性的影响。结果表明:混合比对沙尘-硫酸盐粒子光学特性的影响主要在Mie散射区,在瑞利散射区,混合比对粒子光学特性影响不大。同时研究结果还表明,当混合比小于0.3时,硫酸盐壳在粒子散射特性中占主导地位;当混合比大于0.7时,粒子散射特性主要受沙尘核的影响;在此区间内,粒子散射特性由硫酸盐与沙尘共同影响,并会出现强于(或弱于)任何一种纯颗粒物的现象。该研究对理解灰霾老化期间单颗粒气溶胶混合结构及其光学特性具有重要意义。Abstract: The complex mixing state of sulfate and mineral dust particles is formed through a series of chemical reactions, which bring great difficulties to understand the optical properties of atmosphere aerosols during haze episodes. Therefore, it is of great significance to clarify the influence mechanism of sulfate core on the optical properties of mineral dust particles. In this paper, a "core-shell" ellipsoidal structure model of dust and sulfate (D-S) aerosols was established based on the actual haze conditions according to mixing structure change in the action process between sulfate and mineral dust particles. The influence of mixing ratio on the optical properties of monodisperse dust-sulfate particles at four selected wavelength (0.44, 0.675, 0.87 and 1.02 μm) was studied by using the T-matrix method. The results show that the influence of mixing ratio on the optical properties of D-S particles is mainly in the Mie scattering region, while the effect of mixing ratio is not obvious in the Rayleigh scattering region. When the mixing ratio is less than 0.3, the sulfate shell plays a dominant role in the particle scattering characteristics, while the mixing ratio is greater than 0.7, the particle scattering characteristics are mainly affected by the dust core. In the range of 0.3-0.7, the scattering characteristics are influenced by D-S, and maybe stronger or weaker than any kind of pure particles. The research is of great significance to understand the mixing structure and optical properties of individual aerosol particles during haze aging process.
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Key words:
- haze /
- dust /
- sulfate /
- non-spherical particle /
- mixing ratio /
- optical properties
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表 1 沙尘和硫酸盐气溶胶在四个给定波长下的复折射指数[9]
Table 1. Complex refractive indices of dust and sulfate aerosol at the four selected wavelengths[9]
Wavelength/μm Dust Sulfate Real Imaginary Real Imaginary 0.44 1.593 0.0046 1.415 4.1957E-8 0.670 1.553 0.00084 1.404 5.56319E-8 0.870 1.536 0.00144 1.40 1.21828E-6 1.020 1.529 0.00213 1.396 8.9583E-6 -
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