## 1 Introduction  
As the popularity of winter activities rises, so does the incidence of avalanche fatalities. According to European and American statistics, an average of one hundred people die annually in avalanches [1, 2]. The majority of avalanche victims succumb to airway obstruction or critical hypoxia and hypercapnia [3]. Oxygen (O\({}_{2}\)) concentration decreases while carbon dioxide (CO\({}_{2}\)) concentration increases when the same air is rebreathed in a closed environment. The rate of this process is affected mainly by the properties of the snow [4]. Numerous studies have explored the diffusion of gases through snow cover and its effects on the emission of gases from snow-covered soil [5, 6, 7, 8, 9, 10]. The diffusion coefficients (DCs) in all these studies were evaluated as so-called \"effective diffusion coefficients\" based on the correction of the DCs of gases in the air. Snow was considered to be a uniform, homogeneous, porous layer with constant porosity and tortucosity, and steady diffusion was assumed. [PERSON] et al. [10] published an equation for calculating the theoretical DC of a gas through the studied material, based on the knowledge of the material's parameters and the actual environmental conditions:  
\[D_{\mathrm{x}}=\phi\cdot\tau\cdot D_{\mathrm{xair}}\cdot\frac{P_{0}}{P}\cdot \left(\frac{T}{T_{0}}\right)^{\alpha}, \tag{1}\]where \(D_{\rm x}\) is the theorecitcall \(y\) calculated DC of the gas in the material, \(\phi\) is porosity, \(\tau\) is tortuosity, and \(D_{\rm xair}\) is the DC of the gas in air at standard temperature \(T_{0}\) and standard pressure \(P_{0}\). \(P\) is the actual pressure, \(T\) is the temperature of the material, and \(\alpha\) = 1.81 is the temperature correction coefficient [11]. The DC of O\({}_{2}\) at standard pressure and temperature in air is \(D_{\rm O_{2}}\) =17.6 mm\({}^{2}\cdot\)s\({}^{-1}\)[11]. The DC of CO\({}_{2}\) at standard pressure and temperature in air is \(D_{\rm CO_{2}}\) = 13.8 mm\({}^{2}\cdot\)s\({}^{-1}\)[12]. Since tortuosity is very difficult to measure, it is usually expressed using the relationship from the [PERSON] et al. study [9]:  
\[\tau=\phi^{\frac{1}{3}}. \tag{2}\]  
By solving the differential equation of [PERSON]'s second law, it is possible to compare the theoretical value of the DC (\(D_{\rm x}\)) and the measured DC (\(D\)) obtained from the experimental data [13]:  
\[\frac{c(x,t)-c_{0}}{c_{s}-c_{0}}=1-\mathrm{erf}\bigg{(}\frac{x}{2.\sqrt{D.t}} \bigg{)}, \tag{3}\]  
where \(c(x,t)\) is the concentration at a given time \(t\) and the distance \(x\) from the constant gas source, \(c_{0}\) is the ambient concentration, \(c_{s}\) is the concentration of the constant gas source, erf is the error function, and \(D\) is the measured DC. [PERSON] et al. [8] reported calculated values (corrected for porosity and tortuosity) of the DC of CO\({}_{2}\) in snow in the range of 8.1-9.9 mm\({}^{2}\cdot\)s\({}^{-1}\). In another study, the authors attempted to estimate DCs from measured fluxes and concentration profiles measured during winter using the first Fick's law and obtained values in the range of 2-50 mm\({}^{2}\cdot\)s\({}^{-1}\), with values exceeding the DC of CO\({}_{2}\) in air attributed to the effect of convection [8]. [PERSON] et al. [14] conducted a study on the diffusion of respiratory gases, O\({}_{2}\) and CO\({}_{2}\), to determine the age differences between ice and gases in their air pockets. The cylindrical firn samples used in the study were placed between two stainless steel adapters, sealed in a rubber tube, and then analyzed for their DCs of CO\({}_{2}\) and O\({}_{2}\) using a thermal conductivity detector. The firn had a porosity ranging from 0.13 to 0.5. The DC was discovered to have a near-linear dependence on the porosity, with DCs ranging from 0 to 10 mm\({}^{2}\cdot\)s\({}^{-1}\). In an effort to investigate the gas exchange of an individual buried in avalanche snow, [PERSON] et al. [15] conducted a study to identify materials that could simulate snow.