Numerical Computation And Analysis Of Multi-component Aerosol Predictions

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.