## 3 Airborne Balloon Sensitivity Tests  
### Airborne Balloon Radius (Volume) Sensitivity Test  
Given the above assumptions and the characteristics of FLEXPART, we selected the radius (volume) of the airborne balloon as the sensitivity factor and carried out a series of sensitivity tests by setting different radii in the input file of FLEXPART. 1. Setup  
We selected a test instance of airborne balloon movement that occurred on 29 October 2019 and lasted for a duration of 4 h. In order to compare the impact of the airborne  
Figure 2: The flow fields at 6000 m on (**a**) 06:00 28 October 2019, (**b**) 12:00 28 October 2019, (**c**) 18:00 28 October 2019, and (**d**) 00:00 29 October 2019. The red and blue markers denote the location of balloon appearance and tracking, respectively. balloon radius on its movement, six sets of simulations were conducted. By analyzing the observed radius of numbers of airborne balloons affecting China, it was found that their sizes were relatively small, ranging between 0.1 and 1 m owing to the absence of appendages. Additionally, a literature review revealed that isotropic balloons used for meteorological observations, which carry appendages and ascend higher in altitude, have larger radii reaching up to approximately 3 m [29; 30; 31]. Therefore, the simulations included airborne balloon radii ranging from 0.1 to 5 m, covering a wide range of realistic scenarios. Furthermore, since FLEXPART treats each pollutant point as a labeled particle and analyzes their trajectories through the release of numbers of particles and subsequent cluster analysis, we released a total of 1000 particles simultaneously. The specific settings are provided in Table 1.  
The results of the radius (volume) sensitivity tests of the airborne balloons are presented in Table 2. These findings indicate that there are variations in the horizontal trajectory biases of the airborne balloons at different radii. Amongst the six groups of tests, the MAE (mean absolute error) of the simulated horizontal trajectories ranged from a minimum of 9.43 km (Test 1, without considering the balloon radius) to a maximum of 10.5 km (Test 3), with only a marginal difference of 1.07 km between the largest and smallest MAE. The minimum RMSE (root mean square error) was found to be 11.5 km (Test 1), while the maximum was recorded as 12.95 km (Tests 3 and 6, with radii of 0.5 m and 5 m), indicating a gap of around 1.45 km between them. This demonstrates that although changes in the airborne balloon radius have some effect on horizontal trajectory prediction, it is not so significant and the variation in bias is pretty small. In terms of vertical direction, the biases in airborne balloon trajectories also fluctuate within a small range. Vertically, the MAE varied from 145.89 m (Tests 2 and 6, with radii of 0.1 m and 1 m, respectively) to about 155.75 m (Tests 3 and 6, with radii of 0.5 m and 5 m, respectively). The minimum bias was 246.85 m (Tests 3 and 6), and the maximum was 304.22 m (Tests 2 and 6), indicating a difference of 57.37 m.  
The findings demonstrate that the variations in the radii of airborne balloons have a minor impact on model prediction biases, both horizontally and vertically. When simplified as mass points, disregarding their radii, the simulation does not significantly amplify trajectory prediction biases. On the contrary, it occasionally yields improved results. In the horizontal direction, the simulation with the smallest bias (Test 1) surpasses the other simulations that consider the balloon radius, suggesting the limited effect of balloon radius on trajectory prediction. In summary, the airborne balloon trajectories simulated by FLEXPART show low sensitivity to balloon radius. Simplifying the balloon into a