## 2 Model Introduction and Simulation Design
### Airborne Balloon Movement Simulation Design  
The initialization database used in the WRF [24] is the NECP (National Centers for Environmental Prediction) FNL (Final Operational Global Analysis data) global atmospheric reanalysis database ([[https://rda.ucar.edu/dataset/](https://rda.ucar.edu/dataset/)]([https://rda.ucar.edu/dataset/](https://rda.ucar.edu/dataset/)), last accessed on 29 July 2024), which is produced by NEEP, the National Center for Environmental Prediction of the United States. The time interval of FNL is 6 h, with four times steps per day (00, 06, 12, 18 UTC), and the spatial resolution is \(1^{\circ}\times 1^{\circ}\). The horizontal resolution of the WRF is 5 km, with 351 \(\times\) 351 grid cells and 35 vertical layers, and the model layer top height is set as 10 hPa. The horizontal resolution and the number of vertical layers of FLEXPART are the same as those set in the WRF. Multiple variables outputted from the WRF, including potential height, air pressure, temperature, specific humidity, 10 m wind field, 2 m temperature, surface air pressure, and precipitation, serve as the inputs of the FLEXPART. In order to evaluate the accuracy of the forward motion trajectory prediction of the airborne balloon, an airborne balloon movement simulation was conducted on an airborne balloon process at 13:00 on 28 October 2019, which lasted for 11 h, i.e., from 13:00 on 28 October 2019 to 00:00 on 29 October 2019. The initial position of the balloon detected by the radar was 41.742\({}^{\circ}\) N and 111.907\({}^{\circ}\) E, with a height of 6300 m. At the end of the tracking, the final position of the balloon was determined to be at coordinates 35.663\({}^{\circ}\) N and 116.898\({}^{\circ}\) E, with a height of 6100 m (Figure 1). The meteorological field used in the simulation was provided by the WRF, starting from 12:00 on 28 October 2019, and lasting for 12 h. The meteorological data used in the backward motion trajectory forecast test of the airborne balloon were the same as those used in the forward test, except that the end time of this airborne balloon process (00:00 on 29 October 2019) was taken as the initial discovery time of the airborne balloon to track the trajectory of the airborne balloon that had passed in the past 11 h, retrospectively. Figure 2 depicts the flow field at 6000 m in the area where the balloon traversed. It is evident that during the time when the balloon was discovered, a stable northwesterly wind prevailed at 6100 m. From 28 October, 06:00, to 29 October, 0:00 h, the wind speeds escalated in the northern region, especially in the area from Inner Mongolia to Beijing, but the wind direction remained throughout the drifting course. Under the control of the northwesterly wind, the airborne balloon drifted from Inner Mongolia, crossing Hebei province, and finally arrived at the territorial air space above Shandong Province. Figure 1: Airborne balloon trajectory. Meteorological factors that impact the movement trajectory of airborne balloons encompass not only wind fields, but also thermodynamic fields, such as temperature [25]. In the simulation, it is assumed that the flight and movement of the balloon are primarily influenced by the dynamics of the particle cluster (provided by the wind fields) in which it resides. However, its flight trajectory may also be affected by variables like volume, surface area, weight, and the friction coefficient [26]. Henceforth, a sensitivity study was conducted of the variables characterizing the key physical features of the airborne balloon [27], and the factors that have the greatest influences on the simulation of the airborne balloon were selected as inputs to the Lagrangian model. Through analyzing a large amount of radar-detected airborne balloon trajectory data, it was found that the airborne balloon experiences minimal vertical changes [28]. During several hours of the flight, the trajectory of airborne balloons exhibits fluctuations of less than 1000 m vertically.