## 2 Materials and Methods
### Wind Plots  
For a better comprehension of BC data, it is necessary to determine wind drifts. BC in the air is a practice that varies in time and space according to how it moves, spreads, and is removed. As a result, knowledge of the procedure in various scales based on meteorological characteristics is required. The wind rose diagram provides a brief view of wind speed and path distribution at a specified location. Wind path is the representation of wind frequency using color bands interpreting wind speed ranges through a gridding polar coordinate system. Wind rose diagrams are developed to represent the wind blowing frequency from specific directions over a particular stage for three study sites (i.e., Hindukush, Karakoram, and Himalaya) for the sampling period (i.e., June 2017 to May 2018). Data for wind rose plots have been acquired from [[https://worldweatheronline.com](https://worldweatheronline.com)]([https://worldweatheronline.com](https://worldweatheronline.com)), accessed on 5 August 2020 [28]. Sixteen cordial directions have been used in wind roses such as north, north east, etc., even though they have thirty-two direction sub-divisions. As per measurement of angles (in degree), north, east, south and west correspond to \(0^{\circ}/360^{\circ}\), \(90^{\circ}\), \(180^{\circ}\) and \(270^{\circ}\) respectively. Wind rose diagrams have been developed in WR plot view software. The distance end to end of every \"spoke\" about the loop is directly related to the frequency of wind blow from a specific direction per unit time. Every concentric circle signifies a dissimilar frequency, originating from zero at the middle to growing at the outer. Data to generate wind-rose plots have been summarized in Table 2. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Hindukush** & **Karakoram** & **Himalaya** & **Cumulative** \\
**(R\({}^{2}\))** & **(R\({}^{2}\))** & **(R\({}^{2}\))** & **(R\({}^{2}\))** \\ \hline
0.5904 & 0.0082 & 0.5135 & 0.1575 \\ \hline \end{tabular}
\end{table} 
Table 1: Coefficient of determination values for three mountain ranges. A following wind rose represents the wind blowing frequency from specific directions over a particular stage for three study sites during the sampling period (Figure 4). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Hindukush**} & \multicolumn{2}{c}{**Karakoram**} & \multicolumn{2}{c}{**Himalaya**} \\
**Year** & \multicolumn{2}{c}{**(Mergagram)**} & \multicolumn{2}{c}{**(Passu)**} & \multicolumn{2}{c}{**(Raikot)**} \\ \cline{2-7}  & **Wind Speed** & **Wind** & **Wind Speed** & **Wind** & **Wind Speed** & **Wind** \\  & **(m/s)** & **Direction** & **(m/s)** & **Direction** & **(m/s)** & **Direction** \\ \hline Jun-17 & 2.50 & NNW & 1.39 & NNW & 3.33 & ENE \\ Jul-17 & 1.66 & WNW & \(1.11\) & NW & 5.00 & ENE \\ Aug-17 & 2.50 & NNW & 1.39 & NE & 3.05 & NE \\ Sep-17 & 2.22 & NNE & 2.22 & ENE & 3.89 & NE \\ Oct-17 & 3.89 & SE & 4.17 & SSW & 3.89 & NE \\ Nov-17 & 1.94 & NNE & 3.33 & SSW & 3.89 & ENE \\ Dec-17 & 2.78 & SSE & 5.83 & SSW & 3.61 & NE \\ Jan-18 & 3.61 & SSE & 9.73 & WSW & 3.61 & SW \\ Feb-18 & 2.22 & ENE & 3.61 & SSW & 4.17 & SSW \\ Mar-18 & 3.33 & NNE & 3.05 & SSW & 5.00 & SW \\ Apr-18 & 3.05 & N & 2.78 & WSW & 3.89 & SW \\ May-18 & 1.39 & NNE & 2.78 & SW & 3.89 & SW \\ \hline \hline \end{tabular} Note: The directions of wind N (North), E (East), S (South), and W (West).  
\end{table} 
Table 2: Wind direction at study sites. Figure 4: Wind trajectories of Karakoram (**a**), Himalaya (**b**), and (**c**) Hindukush. In the Karakoram, the meteorological conditions were quiet to calm, and at other times the wind velocity was usually greater than 2 m/s. As the annual wind rose shows (Figure 4a), most winds occurred southwards and southwestwards. Furthermore, between sampling duration, the wind was characterized by south-west to southwards directions with average speed remains more than 2 m/s. In the Himalayas, meteorological conditions were also quiet, and at other times the wind velocity was also more than 2 m/s.