# Uncertainty Quantification for Infrasound Propagation in the Atmospheric Environment
## 1 Introduction  
Infrasound, or sound waves with frequencies below 20 Hz, is generated by human activities, including nuclear weapons tests and rocket launches as well as natural events such as earthquakes [1; 2; 3; 4; 5], volcanic eruptions [6; 7; 8; 9], thunderstorms [10], and other geological disasters [11]. Infrasound is commonly used to monitor the occurrence of natural disasters such as volcanic eruptions, earthquakes, and mudslides. Infrasound is also used to precisely identify infrasound events through array signal processing algorithms. The use of infrasound is of great, practical importance for the monitoring and localization of infrasound events, especially natural disasters. The propagation of infrasound in the atmosphere is easily disturbed by the propagation medium. The monitoring and location of infrasound events are affected by the changing atmospheric propagation medium. Therefore, it has become crucial to quantify the influence of atmospheric parameters on infrasound propagation. There are many uncertainties in infrasound propagation in the atmosphere, such as changes in temperature, atmospheric wind speed, and atmospheric density at different moments of the same location. The propagation trajectory of infrasound in a large-scale atmospheric environment are affected by these uncertainty factors because the atmospheric medium is a non-uniform medium with a non-uniform flow. The uncertain mechanism of infrasound propagation in complex atmospheric environments is analyzed to determine the parameters that have a greater influence on infrasound propagation. Quantifying the uncertainty of infrasound propagation can lay the foundation for the further realization of fast and accurate real-time localization of infrasound sources [12; 13]. The most commonly used methods in uncertainty quantification are the Sobol sensitivity analysis [14; 15; 16; 17; 18] and Monte Carlo [19] and Latin hypercube sampling (LHS) [20]. The effect of input parameters on model output parameters can be quantified by the Sobol sensitivity analysis [21; 22]. The method is applied to the uncertainty quantification of transient wave propagation in pressure pipelines [23] and to the uncertainty quantification analysis of sound source inversion methods [24]. The Sobol index method is based on the idea that the total variance and partial variance are used to express the effect of all variables on the output and the effect of univariate or multivariate analysis on the output, respectively. In the Sobol index method, the first-order Sobol index and the total Sobol index are usually used as sensitivity indicators for the input variables. The first indicator is the first-order Sobol index, which reflects the degree of contribution of a single input variable to the total variance of the model output and takes on values in the range of [0, 1]. The sensitivity of the input variables to the physical model can usually be ranked according to the value of the first-order Sobol index. A larger first-order Sobol index indicates that a change in that variable has a greater effect on the final output. The second indicator is the total Sobol index, which reflects the degree of influence of the main effects of the variables and the cross-effects of the variables with other variables on the model output variance. It takes on values in the range of [0, 1]. The total Sobol index contains the cross-effects of each variable. Supposing the value of the full-effects index of an input variable is small; this indicates that the change in the variable has a small impact on the change in the output, and the cross-effects between the variable and other variables also have a small impact on the output, i.e., the interaction effect between the two is also small. In the actual calculation, a certain number of variables can be reduced to simplify the computational model, but the variables must be those with a small total Sobol index.