# Event Detection and Spatio-temporal Analysis of Low-Altitude Unstable Approach
## 3 Results and Discussion
### Correlation Analysis between Influential Factors
#### 3.3.2 Geographically-weighted Correlation Coefficient  
The geographically-weighted correlation coefficient (GWCC) [24; 25; 26] is an indicator used to explore the spatial heterogeneity of correlations between variables. The GWCC is calculated using the following formula:  
\[\rho_{(x,y)}(u_{i},v_{i})=\frac{Cov_{(x,y)}(u_{i},v_{i})}{SD_{x}(u_{i},v_{i})SD _{y}(u_{i},v_{i})}, \tag{7}\]  
where \((u_{i},v_{i})\) is the spatial coordinate, and \(SD_{x}(u_{i},v_{i})\) and \(Cov_{(x,y)}(u_{i},v_{i})\) are the geographically-weighted standard deviation and covariance, respectively. \(Cov_{(x,y)}(u_{i},v_{i})\) is calculated using the following equation:  
\[Cov(x_{i},y_{i})=\frac{\sum_{j=1}^{n}x_{ij}\big{(}(x_{j}\!-\!\mu(x_{i}))\big{(} y_{j}\!-\!\mu(y_{i})\big{)}\big{)}}{\sum_{j=1}^{n}w_{ij}}, \tag{8}\]  
where \(w_{ij}\) is the weighting factor of observation point \(j\) at calculation point \(i\) and can be calculated using the kernel function. In Table 3, we present four common kernel functions. Figure 4: Schematic representation of factor correlation. “***” means the corresponding correlation coefficient is significant at a level close to 0. In Equations (9-12), \(d_{ij}\) is the distance between the location points \(i\) and \(j\), and \(b\) is the bandwidth, which can be either fixed-type or adaptive-type. Fixed bandwidth takes a constant value as the distance threshold, while the adaptive bandwidth takes an integer \(N\), and uses the distance value to the \(N\)-\(th\) nearest neighbor as the specific bandwidth value for each location-wise solution. In this work, the Gaussian kernel function and adaptive bandwidth were used to calculate the GWCC. Choosing the appropriate bandwidth is very important for GWCC calculation, as the size of the bandwidth will determine the spatial variation scale of the coefficient, which can be optimized using the cross-validation (CV) method. The local correlations between UA events and meteorological and topographical factors were analyzed with GWCCs, which embody typical regional differences, especially for factors such as wind level and weather parameters. Pearson's correlation coefficient was firstly calculated by analyzing the correlation between the number of days corresponding to the wind level at each airport in January and the triggering frequency of UA during the same period, as shown in Table 4. The correlation coefficients reveal that the triggering frequency of the UA of the aircraft and the number of days of each wind level have a relatively positive correlation, especially for wind of levels 4-5. The correlations between the number of days of bad weather conditions (rain, clouds, and snow) and the triggering frequency of corresponding UA events in January were also analyzed. The results are exhibited in Table 4, where a positive correlation was also found between the triggering frequency of UA events and bad weather. Observe that the strongest correlation appears for wind of levels 4-5, instead of levels 5-6 as anticipated empirically. We presume that a very bad weather condition (meaning strong winds of levels 5-6 or even higher) might lead to strict air traffic control or even cancellation. The correlation coefficient between UA triggering frequency and wind of levels 4-5 up to 0.69 is sufficient to demonstrate that windy weather plays a vital role in UA risks. In addition, digital elevation model (DEM) data were used to analyze the correlation between the triggering frequency of UA and the elevations of the corresponding airports. As shown in Figure 5, Boeing aircraft were found to exhibit an insignificant anomalous negative correlation. This is mainly attributable to the performance of Boeing aircraft and the limitation of the oxygen supply, and the fact that a very small number of Boeing aircraft are employed to execute flights in high-altitude areas, like the western part of China. In this sense, this insignificant finding here does not necessarily mean