In this thesis, we have investigated several computational methods on data assimilation for air quality prediction, especially on the characteristic of sparse matrix and the underlying information of gradient in the concentration of pollutant species. In the first part, we have studied the ensemble Kalman filter (EnKF) for chemical species simulation in air quality forecast data assimilation. The main contribution of this paper is to study the sparse data observations and make use of the matrix structure of the Kalman filter updated equations to design an algorithm to compute the analysis of chemical species in the air quality forecast system efficiently. The proposed method can also handle the combined observations from multiple species together. We have applied the proposed method and tested its performance for real air quality data assimilation. Numerical examples have demonstrated the efficiency of the proposed computational method for Kalman filter update, and the effectiveness of the proposed method for NO2, NO, CO, SO2, O3, PM2.5 and PM10 in air quality data assimilation. Within the third part, we have set up an automatic workflow to connect the management system of the chemical transport model - CMAQ with our proposed data assimilation methods. The setup has successfully integrated the data assimilation into the management system and shown that the accuracy of the prediction has risen to a new level. This technique has transformed the system into a real-time and high-precision system. When the new observations are available, the predictions can then be estimated almost instantaneously. Then the agencies are able to make the decisions and respond to the situations immediately. In this way, citizens are able to protect themselves effectively. Meanwhile, it allows the mathematical algorithm to be industrialized implying that the improvements on data assimilation have directly positive effects on the developments of the environment, the human health and the society. Therefore, this has become an inspiring indication to encourage us to study, achieve and even devote more research into this promising method.

Particles reduce visibility, change climate, and affect human health. In 1997, the National Ambient Air Quality Standard (NAAQS) for PM2.5 (particles less than 2.5 mm) was promulgated. The annual mean PM2.5 mass concentrations in Atlanta, Georgia exceed the standard, and control is needed. The first goal of this study is to develop the control strategies of PM2.5 in Atlanta, Georgia. Based on the statistical analysis of measured data, from 22% to 40% of emission reductions are required to meet the NAAQS at 95% CI. The estimated control levels can be tested using the Community Multiscale Air Quality (CMAQ) model to better assess if the proposed levels will achieve sufficient reduction in PM2.5. The second goal of this study is to analyze various uncertainties residing in CMAQ. For the model to be used in such applications with confidence, it needs to be evaluated. The model performance is calculated by the relative agreement between volume-averaged predictions and point measurements. Up to 14% of the model error for PM2.5 mass is due to the different spatial scales of the two values. CMAQ predicts PM2.5 mass concentrations reasonably well, but CMAQ significantly underestimates PM2.5 number concentrations. Causes of the underestimation include that assumed inaccurate particle density and particle size of the primary emissions in CMAQ, in addition to the expression of the particle size with three lognormal distributions. Also, the strength and limitations of CMAQ in performing PM2.5 source apportionment are compared with those of the Chemical Mass Balance with Molecular Markers. Finally, the accuracy of emissions, one of the important inputs of CMAQ, is evaluated by the inverse modeling. Results show that base level emissions for CO and SO2 sources are relatively accurate, whereas NH3, NOx, PEC and PMFINE emissions are overestimated. The emission adjustment for POA and VOC emissions is significantly different among regions.