## 2 Data and Methods
### Relevance Evaluation  
As described above, after evaluating all the immediate information during the earthquake, the irrelevant variables and variables with low correlation were filtered out. Finally,  
Figure 1: Sample extraction process.  
seven variables were identified as predictors, and the GAM was utilized to confirm their high correlation.  
1. Magnitude of the earthquake (mag);
2. Depth of the earthquake (depth);
3. The closest distance from the epicenter of the earthquake to the three-level road network (roadDistance);
4. The nearest distance from the epicenter of the earthquake to the surrounding cities (cityDistance);
5. The identification of whether the time of earthquake is day or night (DorN);
6. The population within the earthquake-affected zone (population);
7. The number of human residential points within the earthquake-affected zone (HR-point).  
It was considered that there were multiple predictors, including both natural and anthropic, and the influence of complex environmental factors was taken into account; there may be a nonlinear relationship between them and the light attenuation value. Therefore, a Generalized Additive Model (GAM) was adopted instead of an R-squared test for correlation in this study.  
The Generalized Additive Model (GAM) is a statistical model designed for modeling nonlinear relationships [29]. The fundamental concept involves modeling the relationships of predictor variables as a series of nonlinear functions, and estimating through smoothing methods. Its advantage lies in its flexibility to capture nonlinear relationships without the need for complex data transformations beforehand. Therefore, the GAM is employed to assess the selected sample features deliberately, and prevent the introduction of irrelevant variables.  
In the GAM, the relationship can be accurately modeled by introducing nonlinear functions. There is a corresponding nonlinear function for each predictor variable, allowing for the adaptation of various complex models.  
The basic model of GAM is:  
\[g(E(Y))=\beta_{0}+f_{1}(X_{1})+f_{2}(X_{2})+\cdots+f_{k}(X_{k})\, \tag{1}\]  
where \(f_{i}(\cdot)\) represents the nonlinear smoothing function associated with the predictor variable \(X_{i}\).  
Since the time of earthquake occurrence (day or night) is a Boolean variable, several other predictors are temporarily analyzed. The GAM is flexible to adapt to various data modes; hence, it is needless to normalize the data despite them having a variety of formats and scales. As shown in Figure 2, the relationship between each input feature and target variable is well identified.  
It is obvious that there are varying degrees of partial dependence between each independent variable and response variable. However, the partial dependence value itself does not represent the actual output value. They are the predicted output changes, which result from changes in a single feature when all other features are held constant. As a result, these values are helpful for identifying the high-correlation variables. Other variables in the model are ignored here. For example, it is evident that earthquake magnitude (mag), earthquake depth (depth), population count (population), and distance to the city (cityDistance) have exhibited significant fluctuations, indicating a stronger correlation with the response variable. Additionally, other variables also showed fluctuations at different stages.