## 2 Study Area and Methodology
### Materials and Methods  
Presently, CALIPSO is used to obtain high-resolution and vertically-resolved global aerosol vertical distribution data [48] that counter the lack of or low frequency of aviation flight measurements or airborne radar detection. Furthermore, CALIPSO helps establish the basis for analyzing the spatiotemporal variations of aerosols and the physical mechanisms involved in the occurrence of pollution events. CALIPSO is an Earth-observing satellite project initiated and executed by NASA's Langley Research Center (LARC) and the National Space Research Center of France in 2006. It orbits the Earth at 705 km altitude, 1.55\({}^{\circ}\), and 96 min orbital parameters, respectively, for 16 days to retrieve data on a three-dimensional distribution of the cloud and aerosol layers around the globe [49]. The CALIOP lidar is a key instrument of the CALIPSO satellite as it provides polarization backscattering vertical profile data for clouds and aerosols between south and north latitude 82\({}^{\circ}\) on a 532 nm channel and attenuation scattering vertical profile data on a 1064 nm channel [30,31]. CALIOP can be used to accurately reconstruct the vertical distribution of clouds and aerosols as well as to quantify their size, irregularity, and type of aerosol particles, by considering vertically resolved backscattering coefficients with high resolution. Notably, CALIOP is free from surface interference and it is used to measure both during daytime and nighttime [20,50,51]. CALIOP's data quality is limited by its signal-to-noise ratio (SNR). At night, the SNR is high and the data quality is good, while during the day, the interference from solar radiation reduces the SNR and causes the data quality to be slightly poor [52,53]. Overall, CALIPSO measurements are advantageous for studying the vertical profiling and transport mechanisms of aerosols. CALIOP data is made available on multiple levels (Level 4, Level 3, Level 2, Level 1B, Level 1A, and Level 0). We used Level 2 data products in this study. Level 2 data products provide stratigraphic, profiling, vertical characteristic, and layer distribution characteristic information on aerosols and clouds. For analysis of the vertical optical and physical properties of the aerosol layer, the variability of a few aerosol characteristics was analyzed. The sum of the AOD derived from all aerosol layers (AOD\({}_{\text{s}}\), Equation (1)), AOD of the lowest aerosol layer (AOD\({}_{\text{1}}\), N = 1 in Equation (2), \(\delta\) is the value of AOD of different heights), the top height of the lowest aerosol layer (HT\({}_{\text{1}}\)), the base height of the lowest aerosol layer (HB\({}_{\text{1}}\)), top altitude of the highest aerosol layer (TAH), number of  
Figure 1: The geographic location of Saudi Arabia. The color variations represent the topography. aerosol feature layers (N), AOD proportion of the lowest aerosol layer (PAOD\({}_{1}\)), volume depolarization ratio of the lowest aerosol layer (VDR\({}_{1}\)), and the color ratio of the lowest aerosol layer (CR\({}_{1}\)) were analyzed. \[\text{AOD}_{\text{S}}=\sum_{1}^{\text{N}}\text{AOD}_{\text{N}};\ \text{N}=1,2, \cdots,7,8 \tag{1}\]  
\[\text{AOD}_{\text{N}}=\int\limits_{\text{HB}_{\text{N}}}^{\text{HT}_{\text{N}} }\delta(z)dz;\ \text{N}=1,2,\cdots,7,8 \tag{2}\]  
The HTH\({}_{1}\) indicates the thickness of the lowest aerosol layer, which is determined by the top height of the lowest aerosol layer (HT\({}_{1}\)) and the base height of the lowest aerosol layer (HB\({}_{1}\)). The abbreviations of aerosol optical physical parameters in this paper are shown in Table 1.  
According to the location of the various regions of Saudi Arabia, the 13 provinces were divided from west to east into three regions in this study. Figure 1 illustrates the distribution of the study area. Region I comprises six provinces such as Tabuk, Makkah, Al Madinah, Asir, Al Bahah, Jizan, Riyadh, Mecca, Medina, the eastern region, Kassim, Hale, Asir, Baha, Tabuk, the northern border region, Jizan, Najilan, and Jufu.