## 3 Results and Discussion
### Satellite Images of Yellow Dust Transport
After that, the PM concentration is lowered, because the amount of air pollutants emitted from the vehicles is decreased, due to the decreased number of vehicles at night after 22:00 LST. Figure 5 shows the hourly distributions of the air temperature (\({}^{\circ}\)C), wind speed (m/s) and relative humidity (%), corresponding to PMs concentrations from 18 to 27 March, 2015 in Gangneung, Korea. It is well known that when yellow dusts are raised up from the dry ground surface of the Gobi Desert, the relative humidity in air near the ground surface is less than 40% and the wind speed is over 10 m/s. A northwesterly wind of more or less 10 m/s transports the yellow dusts toward the downwind regions, such as Gangneung city, Korea. During the dust period in Gangneung city on 21 to 22 March, 2015, the air temperature was high, and visibility was low, but the wind speed was relatively high at about 4 m/s to 6m/s. Namely, as air temperature and wind speed increase, PM\({}_{10}\), PM\({}_{2.5}\) and PM\({}_{1}\) concentrations also increase, concurrently, while relative humidity decreases (Figures 3 and 5). Even though the northwesterly wind over 10 m/s in the source origin of yellow dusts was reduced to 4 m/s to 6 m/s in Gangneung city, still the strong wind could transport the yellow dusts into this city and simultaneously easily raise up dust particles on the road to the low atmosphere of the city. For instance, on 19 March, as the relative humidity at Gangneung city was over 90%, PM\({}_{10}\), PM\({}_{2.5}\) and PM\({}_{1}\) concentrations were very low, showing their minima. On the other hand, when the relative humidity was less than 30% on 21 and 22 March, very high concentrations of PM\({}_{10}\), PM\({}_{2.5}\) and PM\({}_{1}\) were detected with their maxima. Thus, it means that those meteorological variables have strong correlations with the particulate matter concentrations. Correlation Matrix and Predictive Regression Equations among PM\({}_{10}\), PM\({}_{2.5}\) and PM\({}_{1}\) (Gangneung) Associated with PM\({}_{10}\) and PM\({}_{2.5}\) (Beijing)  
In linear regression, there is only one independent and dependent variable involved, but, in the case of multiple regression, there is a set of independent variables \(X_{\rm j}\) to explain  
Figure 5: Hourly distributions of (**a**) air temperature (\({}^{\circ}\)C), (**b**) wind speed (m/s) and (**c**) relative humidity (%) corresponding to PMs concentrations from 18 March to 27, 2015 in Gangneung city, Korea. better or predict the dependent variable, \(Y_{\rm i}\). The applied models for the prediction of values have the forms of a multiple predictive regression equation of each PM\({}_{10}\)(G), PM\({}_{2.5}\)(G) and PM\({}_{1}\)(G) concentration of Gangneung city influenced by the local meteorological parameters and the PM\({}_{10}\)(B) and PM\({}_{2.5}\)(B) concentrations of Beijing city, shown in Table 2.  
\[Y_{1}={\rm a}_{11}X_{1}+{\rm a}_{12}X_{2}+{\rm a}_{13}X_{3}+{\rm a}_{14}X_{4}+{ \rm a}_{15}X_{5}+{\rm a}_{16}X_{6}+{\rm a}_{17}X_{7}+{\rm a}_{18}X_{8}+{\rm b}_{1}\]  
\[Y_{2}={\rm a}_{21}X_{1}+{\rm a}_{22}X_{2}+{\rm a}_{23}X_{3}+{\rm a}_{24}X_{4}+{ \rm a}_{25}X_{5}+{\rm a}_{26}X_{6}+{\rm a}_{27}X_{7}+{\rm a}_{28}X_{8}+{\rm b}_{2}\]  
\[Y_{3}={\rm a}_{31}X_{1}+{\rm a}_{23}X_{2}+{\rm a}_{33}X_{3}+{\rm a}_{43}X_{4}+{ \rm a}_{53}X_{5}+{\rm a}_{63}X_{6}+{\rm a}_{73}X_{7}+{\rm a}_{83}X_{8}+{\rm b}_{3} \tag{1}\]  
or  
\[Y_{\rm i}={\rm a}_{\rm ij}X_{\rm ij}+{\rm b}_{\rm i} \tag{2}\]  
where \({\rm a}_{\rm ij}\) (i = 1 to 3, j = 1 to 8) means the coefficient of matrix (here, \({\rm a}_{11}\), \({\rm a}_{22}\) and \({\rm a}_{33}\) are zero). The observed values of \(X_{\rm i}\) (j = 1 to 8) are PM\({}_{10}\)(G), PM\({}_{2.5}\)(G), PM\({}_{1}\)(G), T(G, air temperature), W(G, wind speed), RH(G, relative humidity), PM\({}_{10}\)(B) and PM\({}_{2.5}\)(B) as independent variables. The predictive values of \(Y_{\rm i}\) (i = 1 to 3) are PM\({}_{10}\)(G), PM\({}_{2.5}\)(G) and PM\({}_{10}\)(G)) as dependent variables.