Optimization of stepwise clustering algorithm in backward trajectory analysis

In recent years, the backward trajectory model has been widely used in the research of meteorological and atmospheric environmental quality. This paper presents a comprehensive study on a stepwise clustering analysis algorithm in the clustering process of backward trajectory model and an application of the clustering analysis of single-particle backward trajectory in 2016 in Changchun City. This study starts with an analysis of the original stepwise clustering algorithm and its application to a clustering process of 8784 backward trajectories during 48 h in Changchun City as a benchmark test case. Then, two improvements are made in the algorithm: First, in the process of finding the optimal classification, the algorithm complexity is improved from original O(n³) to O(log(n)*n²) through algorithm improvement. The algorithm performance is enhanced by log(n) times. Second, in the process of re-establishing the classification, the algorithm complexity is improved from the original O(m*n²) to O(m*log(n)*n), that is another algorithm performance improvement by a factor of log(n). Therefore, the accumulative execution efficiency improvement through the algorithm optimization is 2*log(n) times, which has been further verified in the practical application in Changchun City.