## 4 Empirical Analysis
### Data Analysis Design
\[\cos\varphi=\frac{\sin\delta\cos L-\cos\omega\cos\delta\sin L}{\sin\theta} \tag{1}\]  
Here, \(\varphi\): solar azimuth; \(L\): local latitude; \(\delta\): solar declination; \(\theta\): solar azimuth angle; \(\omega\): hour angle. \[\sin\beta=\cos L\cos\delta\cos\omega+\sin L\sin\delta \tag{2}\]  
Here, \(\beta\): solar altitude; \(L\): local latitude; \(\delta\): solar declination; \(\omega\): hour angle. Third, we confirmed the difference in the predictive power of the datasets with the distribution ratio of each PM class in actual air conditions. To minimize the damage to public health caused by air pollution, the Ministry of Environment classifies PM concentrations into four classes (good, moderate, bad, and very bad) for immediate understanding of outdoor activity recommendations and precautions. Based on PM2.5 values, South Korea categorizes the range between 0 and 15 \(\upmu\)g/m\({}^{3}\) as \"good\", between 16 and 35 \(\upmu\)g/m\({}^{3}\) as \"moderate\", between 36 and 75 \(\upmu\)g/m\({}^{3}\) as \"bad\", and higher than 76 \(\upmu\)g/m\({}^{3}\) as \"very bad\". To prevent data bias, this study applied the distribution ratio per PM class in 2021 at the national monitoring station in Juyeop-dong, Goyang-si, Gyeonggi-do, and constructed a dataset that simulates an analysis environment similar to the air condition. The total number of existing datasets is 178,316, with distribution patterns of 54.4% (97,056) in Class 1 (good), 21.0% (37,474) in Class 2 (moderate), 22.6% (40,325) in Class 3 (bad), and 1.94% (3461) in Class 4 (very bad). The total number of actual datasets with the distribution ratio per PM class is 96,500, with distribution patterns of 46.6% (44,969) in Class 1, 38.8% (37,442) in Class 2, 12.7% (12,352) in Class 3, and 1.8% (1737) in Class 4. For reference, the average PM2.5 in 2021 from the Goyang City monitoring station was 21 \(\upmu\)g/m\({}^{3}\), the month with the worst fine dust was March (34 \(\upmu\)g/m\({}^{3}\)), and the month with the best fine dust was September (12 \(\upmu\)g/m\({}^{3}\)) [6]. Fourth, we confirmed the difference in the predictive power of the datasets with outlier removal algorithms. We applied a local outlier removal algorithm based on Median Absolute Deviation (MAD), which removes sudden information in the images (e.g., vehicles and images with poor focus) and noise in each pixel. After selecting \(n\) images at one-second intervals before and after the target image taken at time \(t\), the i-th pixel values (DN) of the n images were divided into outliers and intruders. The values above 3 MADs scaled from the median value are classified as outliers, and the average of the pixel values classified as outliers is calculated and assigned as the new pixel value of the corresponding pixel in the preprocessed images. The calculation method can be found in Equation (3). Additionally,when PM2.5 exceeded PM10, or suddenly high or low observed values (e.g., smoking or street cleaning) were identified as outliers using the sliding window technique. In the above experiments, except for the experimental conditions and variables that change, since all other conditions (e.g., AI model, number of data, and variables) are controlled, the effect of direct predictive power improvement can be confirmed. \[\text{MAD}\,=\,\text{c}\times\text{median}(\text{abs}(\text{DN}-\text{ median}(\text{DN}))) \tag{3}\]  
\[\text{c}\,=\,\frac{1}{\sqrt{(2)}\times\text{erfcinv}(3/2)}\approx 1.4826\]  
Here, median: median value; erfcinv: Inverse Complementary Error Function.