## 4 Conclusions  
A research method based on a combination of Monte Carlo simulations and the numerical solution was proposed to study the mechanism of the formation of the atmospheric vertical electric field of the short-term precursor signals of EQs. An innovative Monte Carlo simulation method was established to calculate the ionization rate at different heights from data on the variation of radon concentration with height before an EQ. Next, the ionization rate data were combined with the partial differential equations describing the motion of positive and negative particles to numerically solve for the variation of positive and negative particles and radon concentration with height. Finally, the model was validated with the 2008 Wenchuan EQ in China, which had both radon concentration data and atmospheric electric field data before the EQ. In addition, the ionization of alpha and beta particles at different heights, which were the main decay stabilization products of radon, was considered in the model. Alpha particles were the best ionized of the radon decay products, and their fitted ionization rates decayed exponentially with height. The results showed that the atmospheric electric field results obtained from the simulations compounded well with the atmospheric electric field data detected before the Wenchuan EQ. The atmospheric electric field measured by the Wenchuan EQ is direct evidence of the correctness of the model. Moreover, our atmospheric electric field simulations' results were consistent with those obtained by [PERSON], [PERSON], and [PERSON]. In this paper, [PERSON]'s experiments on the atmospheric electric field effects of nuclear explosions in 1972 fundamentally proved the feasibility of the atmospheric electric field anomalies generated by radon ionization. Therefore, the mechanism model can effectively explain the mechanism of atmospheric electric field anomalies before EQ.  
Conceptualization, R.H., M.C., T.C. and J.H.; methodology, R.H., M.C. and T.C.; software, T.Y., L.X. and X.J.; validation, R.H., M.C. and J.H.; formal analysis, R.H. and Q.X.; investigation, R.H., M.C. and T.C.; resources, M.C., T.C. and J.H.; data curation, T.Y.; writing--original draft preparation, R.H.; writing--review and editing, R.H. and M.C.; visualization, R.H.; supervision, T.C. and J.H.; project administration, M.C. and J.H.; funding acquisition, M.C. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the National Space Science Center director fund (Grant No.E0 PD41A11S); \"Climbing Plan\" of National Space Science Center, Chinese Academy of Sciences(Grant No.E1 PD30047S); and Strategic Priority Research Program of Chinese Academy of Sciences (Grant No.XDA17010301).  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The data used to support the findings of this study are available from the corresponding author upon request.  
**Acknowledgments:** We acknowledge for the data resources from \"National Space Science Data Center, National Science & Technology Infrastructure of China ([[https://www.nssdc.ac.cn](https://www.nssdc.ac.cn)]([https://www.nssdc.ac.cn](https://www.nssdc.ac.cn)))\".  
**Conflicts of Interest:** The authors declare no conflict of interest.