## 5 Discussions and Conclusions  
This study investigates the application of FLEXPART to forecasting the trajectories of airborne balloons, with a specific focus on sensitivity tests related to the radius (volume) and density of airborne balloons. The findings obtained indicate that by simplifying airborne balloons as a point-mass model, forecasting accuracy can be greatly improved, especially in the horizontal direction. This simplification allows the model to operate more efficiently with minimal loss of high accuracy. In specific movement simulations, results from FLEXPART for both forward and backward trajectories of airborne balloons indicate that within 11 h, the RMSE and the MAE in the horizontal direction are both below 50 km, with biases in vertical motions being less than 500 m. These results highlight that despite an increase in forecasting time, FLEXPART forecasting remains reliable for short-term predictions. Furthermore, there is no significant increase observed in biases related to vertical movements, underscoring the effectiveness of FLEXPART in reproducing such movements. Meanwhile, the test results demonstrate that wind speed is a critical factor affecting the trajectory of airborne balloons, and the precision of wind speed and direction directly impacts their transport path. Aiming at improving the forecast accuracy and reliability, rapid cycling data assimilation methods can be adopted to accurately capture the changes in wind speed and direction. In addition, the accuracy of the initial observed position of the airborne balloon also affects the trajectory forecast biases. During forecasting, it is essential to promptly update the model's initial balloon position input based on real-time radar observations to minimize such biases. This measure is, in particular, important when significant initial position biases exist as it can greatly improve the forecast accuracy. Although this paper provides a preliminary discussion on the application of FLEXPART in forecasting trajectories of airborne balloons and achieves certain results, there are still some shortcomings to be emphasized. Firstly, the lack of observational data hinders the statistical validation of the forecast results over an extended period, significantly limiting the generalizability and reliability of the conclusions. Secondly, while the impact of wind speed was solely considered in forecasting biases, other factors such as turbulence were not fully resolved and addressed. Generally speaking, turbulence is recognized as one of the important factors affecting balloon trajectories, and different parameterization turbulence schemes would remarkably influence the forecasting results, necessitating further exploration. Given this, more attention should be paid to increasing observations and conducting long-term statistical tests on forecasting results to improve the robustness of conclusions. Additionally, exploring the influence of turbulence on airborne balloon trajectories and optimizing forecast models through comparative analyses of different turbulence parameterization schemes should be pursued. Finally, introducing ensemble forecasting techniques could enhance forecast accuracy and stability by aggregating multiple forecast results. Ensemble forecasting techniques effectively mitigate random biases in single forecasts and enhance the overall reliability of predictions. In general, FLEXPART has high application value in forecasting trajectories of airborne balloons, particularly in short-term predictions. However, biases gradually increase with extended forecasting duration, underscoring that the effect of forecast time on the bias needs to be considered when applying forecast results. Through further optimization, the accuracy and reliability of FLEXPART in forecasting trajectories of airborne balloons can be greatly improved to provide more scientifically effective technical support for practical applications. Writing--original draft, G.W. and L.Y. ; methodology, L.Y. ; software, G.W. and L.Y. ; writing--review and editing, Y.W.