where ω j is the change rate of wind direction at time t j . The spread angle varies with wind speed, with higher speeds resulting in narrower angles. For example, a wind speed of 1 m/s in daytime yields a spread angle of 30.06 degrees, while a speed of 5 m/s in daytime results in an angle of 14.21 degrees. In practice, the maximum change in wind direction should be considered when selecting ∆p, which must then be adjusted to be an integer multiple of the chosen ∆t, as required by our model. These criteria provide guidelines for selecting the optimal ∆t and ∆p and can be easily adjusted in our implementation. Extensive testing, including scenarios with constant wind speeds ranging from 1 to 18 m/s and variable wind directions changing at rates from 1 to 180 degrees per second, indicates that a selection of ∆t = 1 s and ∆p = 4 s is suitable for most of the experimental scenarios. This recommendation complements the default settings of ∆t = 1 s and ∆p = 1 s, which are sufficient for simulating typical emission events at oil and gas sites over durations of a few hours.