Predicting air quality: Improvements through advanced methods to integrate models and measurements

Air quality prediction plays an important role in the management of our environment. Computational power and efficiencies have advanced to the point where chemical transport models can predict pollution in an urban air shed with spatial resolution less than a kilometer, and cover the globe with a horizontal resolution of less than 50 km. Predicting air quality remains a challenge due to the complexity of the governing processes and the strong coupling across scales. While air quality prediction is closely aligned with weather prediction, there are important differences, including the role of pollution emissions and their associated large uncertainties. Improvements in air quality prediction require a close integration of observations. As more atmospheric chemical observations become available chemical data assimilation is expected to play an essential role in air quality forecasting. In this paper advances in air quality forecasting are discussed with an emphasis on data assimilation. Applications of the four-dimensional variational method (4D-Var) and the ensemble Kalman filter (EnKF) approach are presented and the computation challenges are discussed.     

A Self-Similar Crack Expansion method for three-dimensional cracks in an infinite or semi-infinite medium

The Self-Similar Crack Expansion (SSCE) method is used to calculate stress intensity factors for three-dimensional cracks in an infinite medium or semi-infinite medium by the boundary integral element technique, whereby, the stress intensity factors at crack tips are determined by calculating the crack-opening displacements over the crack surface. For elements on the crack surface, regular integrals and singular integrals are precisely evaluated based on closed form expressions, which improves the accuracy. Examples show that this method yields very accurate results for stress intensity factors of penny-shaped cracks and elliptical cracks in the full space, with errors of less than 1% as compared with analytical solutions. The stress intensity factors of subsurface cracks are in good agreement with other analytical solutions.