# Uncertainty Quantification for Infrasound Propagation in the Atmospheric Environment
## 4 Quantitative Results Presentation and Analysis Based on the Actual Atmospheric Data
### Uncertainty Quantification Analysis for the Maximum Height of Infrasound Propagation  
The sensitivity analysis of the atmospheric physical parameters affecting the maximum propagation height of infrasound is performed using the Sobol sensitivity analysis method. The maximum propagation distance \(z_{max}\) is chosen as the output of the tau-p model. The source position of the tau-p model is set to the ground at an altitude of 0; the ray emission angle is set to a fixed value of \(30^{\circ}\); the azimuth angle is \(20^{\circ}\). The first-order Sobol index convergence curves and the total Sobol index convergence curves for each atmospheric parameter are shown in (a) and (b) of Figure 8, respectively. The range of Sobol sampling times \(N\) is from 500 to 5000.  
It can be seen from the above figures that the two indices tend to converge as the sampling times increase. The results of the first-order Sobol index and the total Sobol (5000 Sobol samples) for each atmospheric physical parameter are plotted in Figure 9. The sensitivity index values corresponding to the degree of influence of each atmospheric physical parameter on the maximum height of infrasound propagation are shown in Table 3.  
Figure 8: **(a)** Five atmospheric parameters’ first-order Sobol index convergence lines for the maximum height of infrasound propagation \(z_{max}\); **(b)** Five atmospheric parameters’ total Sobol index convergence lines for the maximum height of infrasound propagation \(z_{max}\) (the blue, dark red, yellow, purple, and light green curves indicate temperature \(T\), zonal wind \(w_{z}\), meridional wind \(w_{m}\), mean atmospheric molar mass \(m\), and specific heat ratio \(\gamma\), respectively).  
In Table 3, it can be seen that the parameters that have a large influence on the maximum height of infrasound propagation have been ranked as follows:  
(1) The first-order influence indices in descending order are the thermodynamic temperature, meridional wind, mean atmospheric molar mass, zonal wind, and specific heat ratio;  
(2) The total impact indices in descending order are the thermodynamic temperature, meridional wind, mean atmospheric molar mass, zonal wind, and specific heat ratio. From these two sensitivity indices, it can be seen that the atmospheric environmental parameter with the greatest influence on the infrasound propagation distance is the thermodynamic temperature.  
The maximum height of infrasound propagation \(z_{max}\) is mainly influenced by the infrasound propagation velocity in the direction perpendicular to the ground. It can be seen in Figure 2 that the component of infrasound propagation velocity perpendicular to the ground is \(c\cdot\cos\theta\), where \(c=\sqrt{(rt)/m}\). Through Equation (1), it can be seen that temperature can affect the velocity of infrasound propagation in the vertical ground direction, ultimately affecting the maximum height of infrasound propagation. The zonal and meridional winds in this paper are horizontal winds, which mainly affect the propagation distance of infrasound in the horizontal direction. It has little effect on the maximum height of infrasound propagation.