Numerical air quality models, such as the Community Multiscale Air Quality (CMAQ) system, play a critical role in characterizing pollution levels at fine spatial and temporal scales, but the model outputs tend to systematically over- or under-estimate pollutants concentrations. In this work, we propose a hierarchical dynamic model that can be implemented to calibrate large-scale grid-level CMAQ model outputs using point-level observations from sparse monitoring stations. Under a Bayesian framework, our model presents a flexible quantification of uncertainties by considering deep hierarchies for key parameters and can also be used to describe the dynamic nature of data structural changes. In addition, we adopt several newly developed techniques, including triangulation of research domain, tapering-based Gaussian kernel, Gaussian graphical model, variational Bayes, and ensemble Kalman smoother, which significantly speed up the entire calibration process. We demonstrate the effectiveness of our model using the daily PM2.5 datasets of China's Beijing-Tianjin-Hebei region, which consists of 68 monitoring stations and 2499 CMAQ 9-km grids. In contrast to the existing methods, our model produces more accurate calibration results, generates maps of higher-quality predictions, and operates at a higher computational efficiency. Overall, this methodology proves to be an effective calibration tool for large-scale numerical model outputs.
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