多组气溶胶预测的数值计算和分析
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摘要
大气气溶胶是固体或液体微粒悬浮于空气中形成的分散体系,其对自然环境和人类健康有着重要影响.由于大气气溶胶可以散射和吸收太阳短波辐射以及红外辐射,从而产生直接辐射强迫；与此同时,它们还可以作为凝结核改变云层性质和降水效率,影响云的辐射特性,产生间接辐射强迫.因此,大气气溶胶在大气辐射和气候变化的研究中占有重要地位.此外,细小的气溶胶颗粒可以被人吸入到身体中,造成健康问题.由空气污染形成的烟雾会降低空气的可见度,从而对交通运输产生影响.鉴于大气气溶胶的重要影响,如何准确有效的对气溶胶的时空分布进行预测,成为国际学术界的重要研究课题之一
气溶胶输运模型是一个复杂的多组分系统,描述了气溶胶的多个物理和化学过程,例如排放,输运,沉降以及气溶胶成核.凝结／蒸发,凝并以及气溶胶化学等气溶胶过程,是气溶胶预测的重要工具.人们开发了多个化学输运模型用于模拟跨区域的气溶胶浓度变化.如URM model (Odman and Russell,1991), UAM-AIM model (Sun and Wexler,1998), Models-3/CMAQ (Mebust et al.,2003)[50], PMCAMx [27],和WRF/Chem model[30]等.在WRF的模拟过程中,对向量方程在水平和垂直空间方向上对流过程的计算,是结合3阶Runge-Kutta时间迭代格式和一般的显式差分方法.为保证数值格式的数值稳定性,在计算中需要采用小时间步长,从而带来较大的计算量.在其他气溶胶输运模型中,也存在类似问题.由于气溶胶输运模型需要用于跨区域长周期的数值模拟,因此需要发展一个可以应用大时间步长进行计算的有效的数值方法.
气溶胶动力学方程是一组非线性积分微分方程([70]),描述了气溶胶在凝结,凝并和沉积过程中,气溶胶矢径分布随时间的变化.迄今已有多个数值方法用于求解气溶胶动力学方程,如区域方法(sectional method)([29],[52]),动量法(moment method)([10],[69]),模式法(nodal method)([1],[86]),随机法(stochastic method)([17],[79])和有限元方法(finite element method)([67])等.区域方法的精度数值较低并会出现数值扰动；模式方法精度较高,但是缺乏气溶胶分布的物理意义并且无法有效解决气溶胶多组分问题;动量方法是基于单组分气溶胶的物理化学属性得到气溶胶矢径分布,但是在处理多组分气溶胶问题时存在局限;随机方法无法得到令人满意的误差精度,近期的研究中,Liang ([48])提出了分裂小波算法求解关于时间,空间和气溶胶矢径的空间气溶胶动力学方程.由于对流凝结项和非线性凝并项的存在,气溶胶的矢径分布非常不均匀,是一个剧烈变化的多对数正态(]multiple log-normal)分布.因此,提出能够准确求解包含对流凝并项和非线性凝结项的气溶胶动力学方程的有效方法,具有非常重要的意义.
很多自然界的气溶胶以及由人类活动产生的气溶胶包含有多个化学组分.气溶胶化学成分和人类健康之间有着重要的联系,例如,含有较多酸性组分气溶胶粒子的降雨和大雾会对人体的呼吸道及皮肤造成伤害.并且,气溶胶粒子的化学组成与气溶胶颗粒的增长率相关,从而会影响气溶胶凝结过程的气溶胶分布变化.因此,研究多组分气溶胶系统的分布状况具有重要的意义.对于多组分气溶胶动力学方程的模拟求解,Kim, Y和Seinfeld. J提出了区域方法(sectional method)([38],[39]), Tsang., T([77])提出了移动有限元方法,Kourti, N.和Schatz, A提出了蒙特卡罗方法([42]).但是这三种方法的数值精度都较低,无法得到满意的计算结果.
气溶胶热力学平衡预测是一个复杂的多态多组分系统,包括多态(气,液.固)和多个输入输出组分.在大规模气溶胶预测中,会涉及到不同地区的多种类型气溶胶,例如城市气溶胶,非城市内陆气溶胶和海洋气溶胶等.过去的时间内,研究者们建立了多种气溶胶热力学平衡模型.例如早期阶段的EQUIL (Bassett and Seinfeld,1983), MARS (Saxena et al.,1986)和SEQUILIB (Pilinis and Seinfeld,1987)是被广泛应用的NH+-SO2--NO3-气溶胶热力学平衡模拟预测系统.在近些年,又发展了多种包含海盐组分(钠盐和氯盐)的新模型,例如SCAPE2(Kim et al.,1993a,b; Kim and Seinfeld,1995:Meng et al.,1995), AIM2(Clegg et al.,1998), ISORROPIA (Nenes et al.,1998and1999), EQUISOLV II (Jacobson et al.,1996; Jacobson,1999).GFEMN (Ansari and Pandis,1999), EQSAM (Metzger et al.,2002; Trebs et al.,2005), MESA (Zaveri et al.,2005a), ADDEM (Topping et al.,2005), UHAERO (Amundson et al.,2006),以及ISORROPIA II (Fountoukis et al.,2007).此外, MESA, EQSAM和ISORROPIA II则在模拟系统中加入了对Ca,K,Mg的处理.这些模型所采用的计算方法通常是通过迭代方式求解热力学平衡方程,会导致求解过程中大量的计算,而且在跨区域的大规模气溶胶预测中,使用传统方法会遇到计算瓶颈.
在导师王文洽教授和梁栋教授的悉心指导下,本文作者关于多组分气溶胶的预测问题做了部分研究工作.在多组分气溶胶输运模型方面,将算子分裂方法与特征线有限差分方法结合,提出了可应用大时间步长进行计算的特征有限差分算法(CFDM)在气溶胶动力学方面,提出了有效的二阶特征有限元方法,用于解决与时间和矢径分布相关的非线性气溶胶动力学方程,以及和气溶胶组分相关的多组分气溶胶动力学方程,并且给出了关于时间方向二阶精度的严格证明.另外,我们提出了多功能MC-HDMR方法,用于气溶胶热力学平衡预测,可以对跨区域的多种类型气溶胶进行有效计算,并可大幅减少CPU计算时间.数值算例的结果表明,我们所提出的方法在多组分气溶胶预测中具有很好的效果.
在第一章中,我们介绍了气溶胶的基本背景,气溶胶数值模拟的重要意义,并给出了多组分气溶胶输运问题、气溶胶动力学问题和气溶胶热力学平衡问题的描述,以及相关的模型介绍和研究现状.
在第二章中,我们给出了包含多个物理和化学过程的多组分气溶胶输运模型以及算子分裂方法的介绍,提出了用于多组分气溶胶输运模型的特征有限差分方法(CFDM),可以在气溶胶模拟中采用大时间步长进行计算.通过一个具有精确解的二维区域内的Gaussian hump传播问题的计算,对CFDM的计算效果进行测试,通过比较采用大时间步长的CFDM计算结果和采用小时间步长的Runge-Kutta方法(RKM)的计算结果以及精确解,可以看到我们的方法可以使用大时间步长进行计算并取得满意的结果.之后,我们对Pittsburgh附近区域的硫酸盐气溶胶输运问题进行了模拟计算.模拟结果表明,硫酸盐气溶胶的覆盖区域随时间而增大,并且是沿风向进行扩张.当风速增大一倍时,在同时间段内,硫酸盐气溶胶的覆盖区域大幅增加.另外,我们应用气溶胶输运模型对美国东北部及相邻区域的2400km×1800km范围内的气溶胶分布进行了模拟,在计算中CFDM的时间步长为1800s.我们给出了New York地区,一个农村地区和一个海洋地区的72-hour模拟结果,可以看到在三个地区中,New York地区的PM2.5浓度最高,海洋地区的最低.在New York地区和农村地区,硫酸盐,硝酸盐和铵盐是气溶胶的主要组成部分,而在海洋地区,海盐(钠盐和铵盐)是气溶胶的主要组成.此外,模拟结果显示了低温环境有利于硝酸盐的生成.通过包含和不包含气溶胶沉积过程的计算,可以看出沉积过程对气溶胶粒子,特别是矢径较大的气溶胶粒子的消除有着重要贡献.最后,我们对美国东南部区域的120小时模拟结果进行了研究,发现在城市及周围区域的PM2.5硫酸盐,硝酸盐和铵盐浓度较高,海盐气溶胶主要存在于沿海和海洋地区.
在第三章中,我们考虑了与时间和矢径相关的非线性气溶胶动力学方程.研究大气环境中的气溶胶动力学过程对于大气模拟非常重要.气溶胶动力学方程中包含对流项(凝结过程)和非线性项(凝并过程),因此对准确求解造成了很大困难.为得到多重对数正态气溶胶矢径分布的高精度预测结果,我们提出了气溶胶动力学方程的二阶特征线有限元方法,并给出了时间方向误差精度二阶的严格证明.相对于时间方向一阶精度的经典特征线方法,我们所提出的数值格式大大提高了计算精度.在第三章最后,我们对气溶胶的多重对数正态分布问题进行了数值实验,计算结果验证了我们的理论分析结果.
在第四章中,我们提出了多组分气溶胶动力学方程(4.1.1)的二阶特征有限元方法,利用特征线方法和二阶外推方法,分别对多组分气溶胶动力学方程中的对流项和非线性凝并项进行处理,并给出了特征线数值格式沿时间方向二阶精度的严格证明.对多组分气溶胶实际问题的数值实验计算结果验证了理论分析结果.本章中所得到的结果在多组分气溶胶动力学研究的理论分析和计算应用方面均具有重要意义.
在第五章中,对于多态多组分的高维气溶胶热力学平衡预测问题,我们提出了多功能移动切割点HDMR方法(moving-cut high-dimensional model representation (MC-HDMR))此方法基于全热力学平衡模型如ISORROPIA建立一个气溶胶预测数据库系统.所建立的气溶胶预测系统可以有效的计算高维区域内的气溶胶热力学平衡预测问题,气溶胶浓度的预测范围可从10-9mol m-3到10-5mol m-3.并可以对包含海盐组分的多种类型气溶胶进行模拟.数值算例的计算结果表明了所提出方法的有效性.与经典的气溶胶热力学平衡算法ISORROPIA相比,使用多功能MC-HDMR方法可以大幅减少计算CPU时间.进一步的,我们对城市,非城市内陆地区和海洋地区的三种类型气溶胶进行了模拟,得到了多个组分的预测结果,多功能MC-HDMR方法的计算结果与气溶胶热力学平衡模型ISORROPIA和AIM2的预测结果相符.最后,我们应用多功能MC-HDMR方法,ISORROPIA和AIM2对欧洲和亚洲城市进行了实际气溶胶模拟.三种方法的计算结果非常一致.预测结果表明,在六个欧洲城市中,HU02,IT01和NL09有较严重的交通污染;在Shanghai地区,由人类活动造成的气溶胶污染,较其他亚洲城市更为严重；此外,Hong Kong地区的气溶胶受海洋环境的影响较大.
Atmosphere aerosols are ensembles of solid, liquid, or mixed-phase fine particles suspended in air. They have significantly impact on the environ-ment and human health. Aerosols can scatter and absorb solar and infrared radiation in the atmosphere, and can change cloud properties by decreasing the precipitation efficiency of warm clouds, thus have strong radiative forc-ing. They are also associated to the formation of acid rain and acid fogs, and small aerosols can be inhaled and cause human health problems. Thus, the atmospheric aerosols take an important role in the research of aerosol radia-tion and climate change. Small aerosol particles in the air can be inhaled into people's body and cause health problem. The smokes and fogs that caused by air pollution can reduce visibility a lot and thus have great impact on transportation. As the importance of atmospheric aerosols, it is important to find efficient accurate methods to give the prediction of aerosols in spatial and size.
Aerosol transport modeling is a complex multi-component system that involves several physical and chemical processes, such as emission, advection, dispersion, deposition and aerosol processes including nucleation, condensa-tion/evaporation, coagulation and aerosol chemistry, and the area it studies usually covers a large region of the world. There has been several chemical transport models that have previously been applied to simulate the aerosol concentrations in various regions. The URM model (Odman and Russell,1991) and the UAM-AIM (Sun and Wexler,1998) models have been applied in southern California, the Models-3/CMAQ (Mebust et al.,2003)[50], the PMCAMx [27], and the WRF/Chem model[30] have been applied to the eastern United States and contiguous areas, the models are also applied to the Europe [56], the east Asia regions [87] and Yangtze River Delta region in China[80]. The WRF model uses a spatially2nd through6th order evalua-tion of the horizontal and vertical flux divergence (advection) in the scalar conservation equation coupled with the3rd-order Runge-Kutta time integra-tion scheme. In the evaluation of the WRF, small operator time step has to be chosen in order to ensure the numerical stability for the numerical schemes used for the solution of the advection process, which brings a large cost of computation. Similar problem exists in other aerosol transport models. As the aerosol transport model usually needs to simulate a long time period in a large area, thus we need to develop an efficient method which can use large time step size to fit this need.
The general aerosol dynamic equations describe the evolution of aerosol size distribution with time when the aerosol particles undergo condensation, coagulation and removal, etc, which are nonlinear differential and integral equations ([70]). Many numerical methods have been studied to solve the aerosol dynamic equations such as sectional method ([29],[52]), moment method ([10],[69]), modal method ([1],[86]), stochastic method ([17],[79]) and finite element method ([67]), etc. The sectional approach has numerical diffusion and lower accuracy, while the modal approach has the high numer-ical efficiency but less physical representation of aerosol distributions and overlap of various models. Them moment method based on the aerosol phys-ical properties tends to the chemical or physical method with single modal distribution but is not suitable to multi-modal distributions in the practical process. The stochastic method has a difficulty of obtaining a satisfied error accuracy. Recently, Liang et al.([48]) developed a splitting wavelet method for solving the spatial aerosol dynamic equations on time, particle size and vertical spatial coordinate. However, due to the advection condensation and nonlinear coagulation, the aerosol distribution is strongly uneven distributed, obeying the very sharp multiple log-normal distributions. Thus, it is an im-portant and challenge task to accurately compute the sharp distribution of aerosols in general aerosol dynamic equations that contain the condensation advection and the nonlinear coagulation.
Most aerosols in nature and aerosols generated by human activity have several chemical components. The aerosol chemical components are related to human health. For example, rainfalls and fogs which contain many acid aerosol particles will hurt peoples'respiratory and skin. The condensation rates are different due to the chemical species, thus the aerosol chemical com-positions are also related to the condensation rate of aerosol particles. Thus, it is important to compute the aerosol component distribution of the multi-component aerosol system. For the numerical solution of multi-component aerosols, Kim, Y. and Seinfeld, J. developed the sectional method ([38],[39]), Tsang., T.([77]) proposed the moving finite element method, and Kourti, N. and Schatz, A. using the Monte Carlo method to get the distribution of multi-component aerosols ([42]). But the accuracies of these three numerical method are not enough to give satisfactory numerical results. So we need to find a new numerical method which has high accuracy.
Aerosol thermodynamic equilibrium prediction is a complex multi-phase, multi-component system that involves multiple compositions outputs of liq-uid, gas and solid phases. The large scale predictions of aerosols contain simulations of different types of aerosols in multiple regions such as urban, non-urban continental and marine and at multiple levels in atmosphere. Sev-eral aerosol thermodynamic equilibrium modules have been built. In the early period, EQUIL (Bassett and Seinfeld,1983), MARS (Saxena et al.,1986) and SEQUILIB (Pilinis and Seinfeld,1987) were widely used models for NH4+-SO42--NO3-system. In the recent years, numerous new models have been developed, such as SCAPE2(Kim et al.,1993a.b; Kim and Seinfeld,1995; Meng et al.,1995), AIM2(Clegg et al.,1998), ISORROPIA (Nenes et al.,1998and1999), EQUISOLV II (Jacobson et al.,1996; Jacobson,1999), GFEMN (Ansari and Pandis,1999), EQSAM (Metzger et al.,2002; Trebs et al.,2005), MESA (Zaveri et al.,2005a), ADDEM (Topping et al.,2005), UHAERO (Amundson et al.,2006), and ISORROPIA II (Fountoukis et al.,2007). MESA solves the solid-liquid system NH4+-Na+-SO42--NO3--Cl-with addition of Ca+, while EQSAM and ISORROPIA II include the treatment of Ca, K, Mg into the system. The computational methods used in these mod-els are mostly based on solving the thermodynamic equilibrium equations by iterations, which normally lead to a large cost of computation in the solution processes, as huge calculations are required in the multi-region and large scale predictions in Air Quality (AQ) forecast of regions and atmosphere, and traditional methods are unfit and meet computational burdens.
Under the guidance of Professor Wenqia Wang and Professor Dong Liang, the author has finished this dissertation consisting of some work on the prediction of multi-component aerosols. On the aspect of multi-component aerosol transport model, by combining the operator splitting method and the finite difference method, we developed the CFDM algorithm which can use big time step in the computation. On the aspect of aerosol dynamics, we proposed an efficient second order finite element method (CFEM) for the solution of nonlinear aerosol general dynamics equation, and also the multi-component aerosol general dynamics equation. We strictly prove that the developed CFEM has second order accuracy in time. And we developed a multi-functional moving-cut high-dimensional model representation (MC-HDMR) approach for the aerosol thermodynamics equilibrium prediction, which could simulate efficiently different types of aerosols in multi-regions. The new proposed multi-functional MC-HDMR approach can greatly reduce the CPU time in the simulation.
In Chapter1, we introduce the background of atmospheric aerosols, and the importance of the numerical simulation of atmospheric aerosols. Then we give the description of the multi-component aerosol transport problem, aerosol dynamics problem and the aerosol thermodynamic equilibrium prob-lem, and the related governing models and the current work on these models.
In Chapter2. an aerosol transport model involving physical and chem- ical processes is presented, and the operator splitting method is introduced. We proposed a characteristic finite difference method (CFDM) for the so-lution of aerosol advection and dispersion processes, which can be applied in the evaluation of the model using large time step size. The performance of the method is first studied by a test of the moving of Gaussian hump with analytical solution, the results obtained by the CFDM are compared to the results calculated by Runge-Kutta method (RKM) using small time size step, as well as to the analytical solution, which shows that our approach has great advantage using large time step size. Then a simulation of sulfate transport problem is carried out in a small domain near Pittsburgh with one emission area. The sulfate pollution area increased as time goes by, and the sulfate pollution area expansion direction changes with the wind direction, and the expansion rate of the pollution area will be increased when the wind velocities are doubled. Then the aerosol transport model is used to simulate PM mass concentrations in a area which covers2400km×1800km of north-east America using the CFDM with time step size of1800s. The predicted concentration of PM2.5sulfate, ammonium, nitrate, sodium and chloride in the New York, rural and marine areas are presented, which shows that the concentrations of sulfate, ammonium, nitrate are high in New York, and low in the marine area, and sea salts of sodium and chloride are mainly exist in the marine area. It is also shown that lower temperature facilitates the formation of aerosol nitrate. The result of calculation without dry deposition process shows its importance role in the aerosol removal. At last, a120hours simulation over a domain in the southeast of America is studied, which shows high concentration of PM2.5species of nitrate, ammonium and sulfate in the areas near cities, and marine aerosols mainly exist in the coastal and marine areas.
In Chapter3, we consider the non-linear aerosol dynamic equations on time and particle size, which involve the advection condensation process and the non-linear coagulation process. Aerosol modeling is very important to study the behavior of aerosol dynamics in atmospheric environment. For solv- ing accurately the multiple sharp log-normal aerosol distributions, we study and analyze the second order characteristic finite element method for the aerosol dynamic equations. We strictly prove that the developed method has second-order accuracy in time. The scheme improves the first-order accuracy in time comparing to the classical characteristic method. Numerical experi-ments for the multiple log-normal aerosol distributions are further given to confirm the theoretical analysis.
In Chapter4, we propose a second order characteristic finite element method for solving the multi-component aerosol dynamics equations. The characteristic method and the second order extrapolation along the char-acteristic line are applied to treat the advection condensation process and the non-linear coagulation process in the multi-component aerosol dynamics equation. The proposed numerical method can obtain high accuracy results using large time step size. By using theory of variation method and the tech-nique of prior estimates, we strictly prove the error estimate of second order in time for the developed characteristic scheme. Numerical experiments re-sults for the multi-component aerosol distributions confirm the theoretical results. The results obtained are of significance in both theoretical analysis and application of the computational multi-component aerosol dynamics.
In Chapter5, a multi-functional moving-cut high-dimensional model representation (MC-HDMR) approach is developed for simulation of multi-component input and output aerosols. This method leads to an aerosol pre-diction database system based on full thermodynamic models such as ISOR-ROPIA. The developed prediction system can efficiently compute the predic-tion of aerosol thermodynamic equilibrium in high-dimensional domains with a large range of aerosol concentrations from10-9mol m-3to10-5mol m-3and for different types of aerosols including aerosols containing sea salt com-ponent. Numerical computations show the great computational efficiency of the method that its CPU-time cost is much less compared to ISORROPIA. Three types of aerosols of urban, non-urban continental and marine are con-sidered and the multi-component outputs predicted by the approach are in great agreement with those by ISORROPIA and AIM2. Actual aerosol ex-amples in European and Asian cities are simulated by the approach and ISORROPIA and AIM2. Numerical results match very well and show heav-ier traffic pollution at the areas of HU02, IT01and NL09among six European stations, more anthropogenic pollution in Shanghai than other three Asian cities, and Hong Kong's aerosols affected by the marine environment.
气溶胶输运模型是一个复杂的多组分系统,描述了气溶胶的多个物理和化学过程,例如排放,输运,沉降以及气溶胶成核.凝结／蒸发,凝并以及气溶胶化学等气溶胶过程,是气溶胶预测的重要工具.人们开发了多个化学输运模型用于模拟跨区域的气溶胶浓度变化.如URM model (Odman and Russell,1991), UAM-AIM model (Sun and Wexler,1998), Models-3/CMAQ (Mebust et al.,2003)[50], PMCAMx [27],和WRF/Chem model[30]等.在WRF的模拟过程中,对向量方程在水平和垂直空间方向上对流过程的计算,是结合3阶Runge-Kutta时间迭代格式和一般的显式差分方法.为保证数值格式的数值稳定性,在计算中需要采用小时间步长,从而带来较大的计算量.在其他气溶胶输运模型中,也存在类似问题.由于气溶胶输运模型需要用于跨区域长周期的数值模拟,因此需要发展一个可以应用大时间步长进行计算的有效的数值方法.
气溶胶动力学方程是一组非线性积分微分方程([70]),描述了气溶胶在凝结,凝并和沉积过程中,气溶胶矢径分布随时间的变化.迄今已有多个数值方法用于求解气溶胶动力学方程,如区域方法(sectional method)([29],[52]),动量法(moment method)([10],[69]),模式法(nodal method)([1],[86]),随机法(stochastic method)([17],[79])和有限元方法(finite element method)([67])等.区域方法的精度数值较低并会出现数值扰动；模式方法精度较高,但是缺乏气溶胶分布的物理意义并且无法有效解决气溶胶多组分问题;动量方法是基于单组分气溶胶的物理化学属性得到气溶胶矢径分布,但是在处理多组分气溶胶问题时存在局限;随机方法无法得到令人满意的误差精度,近期的研究中,Liang ([48])提出了分裂小波算法求解关于时间,空间和气溶胶矢径的空间气溶胶动力学方程.由于对流凝结项和非线性凝并项的存在,气溶胶的矢径分布非常不均匀,是一个剧烈变化的多对数正态(]multiple log-normal)分布.因此,提出能够准确求解包含对流凝并项和非线性凝结项的气溶胶动力学方程的有效方法,具有非常重要的意义.
很多自然界的气溶胶以及由人类活动产生的气溶胶包含有多个化学组分.气溶胶化学成分和人类健康之间有着重要的联系,例如,含有较多酸性组分气溶胶粒子的降雨和大雾会对人体的呼吸道及皮肤造成伤害.并且,气溶胶粒子的化学组成与气溶胶颗粒的增长率相关,从而会影响气溶胶凝结过程的气溶胶分布变化.因此,研究多组分气溶胶系统的分布状况具有重要的意义.对于多组分气溶胶动力学方程的模拟求解,Kim, Y和Seinfeld. J提出了区域方法(sectional method)([38],[39]), Tsang., T([77])提出了移动有限元方法,Kourti, N.和Schatz, A提出了蒙特卡罗方法([42]).但是这三种方法的数值精度都较低,无法得到满意的计算结果.
气溶胶热力学平衡预测是一个复杂的多态多组分系统,包括多态(气,液.固)和多个输入输出组分.在大规模气溶胶预测中,会涉及到不同地区的多种类型气溶胶,例如城市气溶胶,非城市内陆气溶胶和海洋气溶胶等.过去的时间内,研究者们建立了多种气溶胶热力学平衡模型.例如早期阶段的EQUIL (Bassett and Seinfeld,1983), MARS (Saxena et al.,1986)和SEQUILIB (Pilinis and Seinfeld,1987)是被广泛应用的NH+-SO2--NO3-气溶胶热力学平衡模拟预测系统.在近些年,又发展了多种包含海盐组分(钠盐和氯盐)的新模型,例如SCAPE2(Kim et al.,1993a,b; Kim and Seinfeld,1995:Meng et al.,1995), AIM2(Clegg et al.,1998), ISORROPIA (Nenes et al.,1998and1999), EQUISOLV II (Jacobson et al.,1996; Jacobson,1999).GFEMN (Ansari and Pandis,1999), EQSAM (Metzger et al.,2002; Trebs et al.,2005), MESA (Zaveri et al.,2005a), ADDEM (Topping et al.,2005), UHAERO (Amundson et al.,2006),以及ISORROPIA II (Fountoukis et al.,2007).此外, MESA, EQSAM和ISORROPIA II则在模拟系统中加入了对Ca,K,Mg的处理.这些模型所采用的计算方法通常是通过迭代方式求解热力学平衡方程,会导致求解过程中大量的计算,而且在跨区域的大规模气溶胶预测中,使用传统方法会遇到计算瓶颈.
在导师王文洽教授和梁栋教授的悉心指导下,本文作者关于多组分气溶胶的预测问题做了部分研究工作.在多组分气溶胶输运模型方面,将算子分裂方法与特征线有限差分方法结合,提出了可应用大时间步长进行计算的特征有限差分算法(CFDM)在气溶胶动力学方面,提出了有效的二阶特征有限元方法,用于解决与时间和矢径分布相关的非线性气溶胶动力学方程,以及和气溶胶组分相关的多组分气溶胶动力学方程,并且给出了关于时间方向二阶精度的严格证明.另外,我们提出了多功能MC-HDMR方法,用于气溶胶热力学平衡预测,可以对跨区域的多种类型气溶胶进行有效计算,并可大幅减少CPU计算时间.数值算例的结果表明,我们所提出的方法在多组分气溶胶预测中具有很好的效果.
在第一章中,我们介绍了气溶胶的基本背景,气溶胶数值模拟的重要意义,并给出了多组分气溶胶输运问题、气溶胶动力学问题和气溶胶热力学平衡问题的描述,以及相关的模型介绍和研究现状.
在第二章中,我们给出了包含多个物理和化学过程的多组分气溶胶输运模型以及算子分裂方法的介绍,提出了用于多组分气溶胶输运模型的特征有限差分方法(CFDM),可以在气溶胶模拟中采用大时间步长进行计算.通过一个具有精确解的二维区域内的Gaussian hump传播问题的计算,对CFDM的计算效果进行测试,通过比较采用大时间步长的CFDM计算结果和采用小时间步长的Runge-Kutta方法(RKM)的计算结果以及精确解,可以看到我们的方法可以使用大时间步长进行计算并取得满意的结果.之后,我们对Pittsburgh附近区域的硫酸盐气溶胶输运问题进行了模拟计算.模拟结果表明,硫酸盐气溶胶的覆盖区域随时间而增大,并且是沿风向进行扩张.当风速增大一倍时,在同时间段内,硫酸盐气溶胶的覆盖区域大幅增加.另外,我们应用气溶胶输运模型对美国东北部及相邻区域的2400km×1800km范围内的气溶胶分布进行了模拟,在计算中CFDM的时间步长为1800s.我们给出了New York地区,一个农村地区和一个海洋地区的72-hour模拟结果,可以看到在三个地区中,New York地区的PM2.5浓度最高,海洋地区的最低.在New York地区和农村地区,硫酸盐,硝酸盐和铵盐是气溶胶的主要组成部分,而在海洋地区,海盐(钠盐和铵盐)是气溶胶的主要组成.此外,模拟结果显示了低温环境有利于硝酸盐的生成.通过包含和不包含气溶胶沉积过程的计算,可以看出沉积过程对气溶胶粒子,特别是矢径较大的气溶胶粒子的消除有着重要贡献.最后,我们对美国东南部区域的120小时模拟结果进行了研究,发现在城市及周围区域的PM2.5硫酸盐,硝酸盐和铵盐浓度较高,海盐气溶胶主要存在于沿海和海洋地区.
在第三章中,我们考虑了与时间和矢径相关的非线性气溶胶动力学方程.研究大气环境中的气溶胶动力学过程对于大气模拟非常重要.气溶胶动力学方程中包含对流项(凝结过程)和非线性项(凝并过程),因此对准确求解造成了很大困难.为得到多重对数正态气溶胶矢径分布的高精度预测结果,我们提出了气溶胶动力学方程的二阶特征线有限元方法,并给出了时间方向误差精度二阶的严格证明.相对于时间方向一阶精度的经典特征线方法,我们所提出的数值格式大大提高了计算精度.在第三章最后,我们对气溶胶的多重对数正态分布问题进行了数值实验,计算结果验证了我们的理论分析结果.
在第四章中,我们提出了多组分气溶胶动力学方程(4.1.1)的二阶特征有限元方法,利用特征线方法和二阶外推方法,分别对多组分气溶胶动力学方程中的对流项和非线性凝并项进行处理,并给出了特征线数值格式沿时间方向二阶精度的严格证明.对多组分气溶胶实际问题的数值实验计算结果验证了理论分析结果.本章中所得到的结果在多组分气溶胶动力学研究的理论分析和计算应用方面均具有重要意义.
在第五章中,对于多态多组分的高维气溶胶热力学平衡预测问题,我们提出了多功能移动切割点HDMR方法(moving-cut high-dimensional model representation (MC-HDMR))此方法基于全热力学平衡模型如ISORROPIA建立一个气溶胶预测数据库系统.所建立的气溶胶预测系统可以有效的计算高维区域内的气溶胶热力学平衡预测问题,气溶胶浓度的预测范围可从10-9mol m-3到10-5mol m-3.并可以对包含海盐组分的多种类型气溶胶进行模拟.数值算例的计算结果表明了所提出方法的有效性.与经典的气溶胶热力学平衡算法ISORROPIA相比,使用多功能MC-HDMR方法可以大幅减少计算CPU时间.进一步的,我们对城市,非城市内陆地区和海洋地区的三种类型气溶胶进行了模拟,得到了多个组分的预测结果,多功能MC-HDMR方法的计算结果与气溶胶热力学平衡模型ISORROPIA和AIM2的预测结果相符.最后,我们应用多功能MC-HDMR方法,ISORROPIA和AIM2对欧洲和亚洲城市进行了实际气溶胶模拟.三种方法的计算结果非常一致.预测结果表明,在六个欧洲城市中,HU02,IT01和NL09有较严重的交通污染;在Shanghai地区,由人类活动造成的气溶胶污染,较其他亚洲城市更为严重；此外,Hong Kong地区的气溶胶受海洋环境的影响较大.
Atmosphere aerosols are ensembles of solid, liquid, or mixed-phase fine particles suspended in air. They have significantly impact on the environ-ment and human health. Aerosols can scatter and absorb solar and infrared radiation in the atmosphere, and can change cloud properties by decreasing the precipitation efficiency of warm clouds, thus have strong radiative forc-ing. They are also associated to the formation of acid rain and acid fogs, and small aerosols can be inhaled and cause human health problems. Thus, the atmospheric aerosols take an important role in the research of aerosol radia-tion and climate change. Small aerosol particles in the air can be inhaled into people's body and cause health problem. The smokes and fogs that caused by air pollution can reduce visibility a lot and thus have great impact on transportation. As the importance of atmospheric aerosols, it is important to find efficient accurate methods to give the prediction of aerosols in spatial and size.
Aerosol transport modeling is a complex multi-component system that involves several physical and chemical processes, such as emission, advection, dispersion, deposition and aerosol processes including nucleation, condensa-tion/evaporation, coagulation and aerosol chemistry, and the area it studies usually covers a large region of the world. There has been several chemical transport models that have previously been applied to simulate the aerosol concentrations in various regions. The URM model (Odman and Russell,1991) and the UAM-AIM (Sun and Wexler,1998) models have been applied in southern California, the Models-3/CMAQ (Mebust et al.,2003)[50], the PMCAMx [27], and the WRF/Chem model[30] have been applied to the eastern United States and contiguous areas, the models are also applied to the Europe [56], the east Asia regions [87] and Yangtze River Delta region in China[80]. The WRF model uses a spatially2nd through6th order evalua-tion of the horizontal and vertical flux divergence (advection) in the scalar conservation equation coupled with the3rd-order Runge-Kutta time integra-tion scheme. In the evaluation of the WRF, small operator time step has to be chosen in order to ensure the numerical stability for the numerical schemes used for the solution of the advection process, which brings a large cost of computation. Similar problem exists in other aerosol transport models. As the aerosol transport model usually needs to simulate a long time period in a large area, thus we need to develop an efficient method which can use large time step size to fit this need.
The general aerosol dynamic equations describe the evolution of aerosol size distribution with time when the aerosol particles undergo condensation, coagulation and removal, etc, which are nonlinear differential and integral equations ([70]). Many numerical methods have been studied to solve the aerosol dynamic equations such as sectional method ([29],[52]), moment method ([10],[69]), modal method ([1],[86]), stochastic method ([17],[79]) and finite element method ([67]), etc. The sectional approach has numerical diffusion and lower accuracy, while the modal approach has the high numer-ical efficiency but less physical representation of aerosol distributions and overlap of various models. Them moment method based on the aerosol phys-ical properties tends to the chemical or physical method with single modal distribution but is not suitable to multi-modal distributions in the practical process. The stochastic method has a difficulty of obtaining a satisfied error accuracy. Recently, Liang et al.([48]) developed a splitting wavelet method for solving the spatial aerosol dynamic equations on time, particle size and vertical spatial coordinate. However, due to the advection condensation and nonlinear coagulation, the aerosol distribution is strongly uneven distributed, obeying the very sharp multiple log-normal distributions. Thus, it is an im-portant and challenge task to accurately compute the sharp distribution of aerosols in general aerosol dynamic equations that contain the condensation advection and the nonlinear coagulation.
Most aerosols in nature and aerosols generated by human activity have several chemical components. The aerosol chemical components are related to human health. For example, rainfalls and fogs which contain many acid aerosol particles will hurt peoples'respiratory and skin. The condensation rates are different due to the chemical species, thus the aerosol chemical com-positions are also related to the condensation rate of aerosol particles. Thus, it is important to compute the aerosol component distribution of the multi-component aerosol system. For the numerical solution of multi-component aerosols, Kim, Y. and Seinfeld, J. developed the sectional method ([38],[39]), Tsang., T.([77]) proposed the moving finite element method, and Kourti, N. and Schatz, A. using the Monte Carlo method to get the distribution of multi-component aerosols ([42]). But the accuracies of these three numerical method are not enough to give satisfactory numerical results. So we need to find a new numerical method which has high accuracy.
Aerosol thermodynamic equilibrium prediction is a complex multi-phase, multi-component system that involves multiple compositions outputs of liq-uid, gas and solid phases. The large scale predictions of aerosols contain simulations of different types of aerosols in multiple regions such as urban, non-urban continental and marine and at multiple levels in atmosphere. Sev-eral aerosol thermodynamic equilibrium modules have been built. In the early period, EQUIL (Bassett and Seinfeld,1983), MARS (Saxena et al.,1986) and SEQUILIB (Pilinis and Seinfeld,1987) were widely used models for NH4+-SO42--NO3-system. In the recent years, numerous new models have been developed, such as SCAPE2(Kim et al.,1993a.b; Kim and Seinfeld,1995; Meng et al.,1995), AIM2(Clegg et al.,1998), ISORROPIA (Nenes et al.,1998and1999), EQUISOLV II (Jacobson et al.,1996; Jacobson,1999), GFEMN (Ansari and Pandis,1999), EQSAM (Metzger et al.,2002; Trebs et al.,2005), MESA (Zaveri et al.,2005a), ADDEM (Topping et al.,2005), UHAERO (Amundson et al.,2006), and ISORROPIA II (Fountoukis et al.,2007). MESA solves the solid-liquid system NH4+-Na+-SO42--NO3--Cl-with addition of Ca+, while EQSAM and ISORROPIA II include the treatment of Ca, K, Mg into the system. The computational methods used in these mod-els are mostly based on solving the thermodynamic equilibrium equations by iterations, which normally lead to a large cost of computation in the solution processes, as huge calculations are required in the multi-region and large scale predictions in Air Quality (AQ) forecast of regions and atmosphere, and traditional methods are unfit and meet computational burdens.
Under the guidance of Professor Wenqia Wang and Professor Dong Liang, the author has finished this dissertation consisting of some work on the prediction of multi-component aerosols. On the aspect of multi-component aerosol transport model, by combining the operator splitting method and the finite difference method, we developed the CFDM algorithm which can use big time step in the computation. On the aspect of aerosol dynamics, we proposed an efficient second order finite element method (CFEM) for the solution of nonlinear aerosol general dynamics equation, and also the multi-component aerosol general dynamics equation. We strictly prove that the developed CFEM has second order accuracy in time. And we developed a multi-functional moving-cut high-dimensional model representation (MC-HDMR) approach for the aerosol thermodynamics equilibrium prediction, which could simulate efficiently different types of aerosols in multi-regions. The new proposed multi-functional MC-HDMR approach can greatly reduce the CPU time in the simulation.
In Chapter1, we introduce the background of atmospheric aerosols, and the importance of the numerical simulation of atmospheric aerosols. Then we give the description of the multi-component aerosol transport problem, aerosol dynamics problem and the aerosol thermodynamic equilibrium prob-lem, and the related governing models and the current work on these models.
In Chapter2. an aerosol transport model involving physical and chem- ical processes is presented, and the operator splitting method is introduced. We proposed a characteristic finite difference method (CFDM) for the so-lution of aerosol advection and dispersion processes, which can be applied in the evaluation of the model using large time step size. The performance of the method is first studied by a test of the moving of Gaussian hump with analytical solution, the results obtained by the CFDM are compared to the results calculated by Runge-Kutta method (RKM) using small time size step, as well as to the analytical solution, which shows that our approach has great advantage using large time step size. Then a simulation of sulfate transport problem is carried out in a small domain near Pittsburgh with one emission area. The sulfate pollution area increased as time goes by, and the sulfate pollution area expansion direction changes with the wind direction, and the expansion rate of the pollution area will be increased when the wind velocities are doubled. Then the aerosol transport model is used to simulate PM mass concentrations in a area which covers2400km×1800km of north-east America using the CFDM with time step size of1800s. The predicted concentration of PM2.5sulfate, ammonium, nitrate, sodium and chloride in the New York, rural and marine areas are presented, which shows that the concentrations of sulfate, ammonium, nitrate are high in New York, and low in the marine area, and sea salts of sodium and chloride are mainly exist in the marine area. It is also shown that lower temperature facilitates the formation of aerosol nitrate. The result of calculation without dry deposition process shows its importance role in the aerosol removal. At last, a120hours simulation over a domain in the southeast of America is studied, which shows high concentration of PM2.5species of nitrate, ammonium and sulfate in the areas near cities, and marine aerosols mainly exist in the coastal and marine areas.
In Chapter3, we consider the non-linear aerosol dynamic equations on time and particle size, which involve the advection condensation process and the non-linear coagulation process. Aerosol modeling is very important to study the behavior of aerosol dynamics in atmospheric environment. For solv- ing accurately the multiple sharp log-normal aerosol distributions, we study and analyze the second order characteristic finite element method for the aerosol dynamic equations. We strictly prove that the developed method has second-order accuracy in time. The scheme improves the first-order accuracy in time comparing to the classical characteristic method. Numerical experi-ments for the multiple log-normal aerosol distributions are further given to confirm the theoretical analysis.
In Chapter4, we propose a second order characteristic finite element method for solving the multi-component aerosol dynamics equations. The characteristic method and the second order extrapolation along the char-acteristic line are applied to treat the advection condensation process and the non-linear coagulation process in the multi-component aerosol dynamics equation. The proposed numerical method can obtain high accuracy results using large time step size. By using theory of variation method and the tech-nique of prior estimates, we strictly prove the error estimate of second order in time for the developed characteristic scheme. Numerical experiments re-sults for the multi-component aerosol distributions confirm the theoretical results. The results obtained are of significance in both theoretical analysis and application of the computational multi-component aerosol dynamics.
In Chapter5, a multi-functional moving-cut high-dimensional model representation (MC-HDMR) approach is developed for simulation of multi-component input and output aerosols. This method leads to an aerosol pre-diction database system based on full thermodynamic models such as ISOR-ROPIA. The developed prediction system can efficiently compute the predic-tion of aerosol thermodynamic equilibrium in high-dimensional domains with a large range of aerosol concentrations from10-9mol m-3to10-5mol m-3and for different types of aerosols including aerosols containing sea salt com-ponent. Numerical computations show the great computational efficiency of the method that its CPU-time cost is much less compared to ISORROPIA. Three types of aerosols of urban, non-urban continental and marine are con-sidered and the multi-component outputs predicted by the approach are in great agreement with those by ISORROPIA and AIM2. Actual aerosol ex-amples in European and Asian cities are simulated by the approach and ISORROPIA and AIM2. Numerical results match very well and show heav-ier traffic pollution at the areas of HU02, IT01and NL09among six European stations, more anthropogenic pollution in Shanghai than other three Asian cities, and Hong Kong's aerosols affected by the marine environment.
引文
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