Without loss of generality, in our implementation, ∆p must be an integer multiple of ∆t. Although our fast Gaussian puff algorithm efficiently manages the associated computational demands for using very small ∆t and ∆p at sub-second level, optimizing these parameters to reduce computational costs without compromising accuracy is useful, especially for lengthy simulations spanning several days. ∆t is critical for ensuring sufficient overlap of a puff across consecutive evaluation time steps, as these evaluations will later be upsampled to match the observation resolution. The choice of ∆t is influenced by wind speed; higher wind speeds necessitate a smaller ∆t to maintain adequate overlap, defined as the puff center at time step t i being within an effective region with a radius of 2σ y,ti+1 corresponding to the evaluation at t i+1 . For a given wind speed, while the distance between puff centers of adjacent time steps remains constant, the effective size of the puff increases, leading to overlap only beyond a certain downwind distance. Fig. shows a schematic of the transport of a single puff under a constant wind condition. Here, puffs begin to overlap adequately (i.e., the distance between the centers of two adjacent puffs is within the 2σ y radius) only past the red dashed line, which marks the region of insufficient overlap. This region could lead to underestimations in puff simulations. The maximum extent of this insufficient overlap region thus serves as a criterion for selecting the optimal ∆t for a specified wind speed. For instance, at a wind speed of 1 m/s, a ∆t of 1 s results in a distance of 2 m, whereas a ∆t of 2 s leads to a distance of 4 m. Whereas, at a wind speed of 5 m/s, these distances increase to 20 m and 40 m, respectively. Users may adjust ∆t based on their specific application needs, considering the highest wind speed within the emission duration.