Under global warming, how to accurately measure and reduce ship emissions has become an important issue concerned by the transportation sector and the whole society. The diffusion concentration of continuous ship emissions is calculated by the emission concentrations at the time of observation. With the increase of observation time window, diffusion distance, and calculation accuracy, the calculation time of traditional algorithms and the requirements for computing resources increase exponentially. Therefore, this paper proposes a fast algorithm based on data translation (matrix translation and point translation algorithms), which can calculate the emission diffusion concentration of multiple ships, long distances and long duration while ensuring the accuracy. The time complexity of the traditional algorithm and the fast algorithm are $\mathrm{O}(\mathrm{k}{\mathrm{T}}^2)$ and $\mathrm{O}(\mathrm{k}\mathrm{T})$ respectively, and the fast algorithm can greatly improve the computing efficiency and save the computing time. The matrix translation algorithm is suitable for small-scale calculations with a fixed observation window, the amount of data is relatively small, and the calculation speed is the fastest. The point translation algorithm is suitable for large-scale calculations with a moving observation window and can adjust the calculation accuracy flexibly, but the data size is large and difficult to predict. Finally, in the numerical simulation on the Huangpu River, millions of emission concentrations data, based on trajectory information in 12 h over eight vessels, were calculated only in several minutes, which proves the high efficiency of the fast algorithm.

在全球变暖的背景下，如何准确计量和减少船舶排放已成为交通运输部门和全社会关注的重要问题。连续船舶排放物的扩散浓度由观测时的排放物浓度计算得出。随着观测时间窗口、扩散距离和计算精度的增加，传统算法的计算时间和对计算资源的需求呈指数级增长。因此，本文提出了一种基于数据平移的快速算法（矩阵平移和点平移算法），在保证精度的同时，可以计算多艘、长距离、长持续时间的多艘船舶的排放扩散浓度。传统算法和快速算法的时间复杂度分别为$\mathrm{○}(\mathrm{ķ}{\mathrm{吨}}^2)$和$\mathrm{○}(\mathrm{ķ}\mathrm{吨})$分别，快速算法可以大大提高计算效率，节省计算时间。矩阵平移算法适用于观测窗口固定的小规模计算，数据量比较少，计算速度最快。点平移算法适用于观测窗口移动的大规模计算，可以灵活调整计算精度，但数据量大，难以预测。最后，在黄浦江数值模拟中，基于8艘船舶12小时内的轨迹信息，仅在几分钟内即可计算出数百万个排放浓度数据，证明了快速算法的高效性。