# How Environmental Factors Affect Forest Fire Occurrence in Yunnan Forest Region
## 2 Materials and Methods
### Research Method  
Estimating the probability of wildfire from only existing data requires random non-fire points and fire points for the sample data. As per previous studies [37; 38; 39], the ratio of fire points to non-fire points was adjusted to 1:1.5. To do this, we added 6974 random non-fire points randomly generated in ArcGIS 10.7, and the dates of these non-fire points were randomly assigned using Excel to ensure that all points were unique in terms of time and location. The environmental factor was then extracted in the same way as the fire point samples. The logistic regression (LR) model reveals the relationship between wildfire ignition and environmental factor, and it has been widely applied to study wildfires [40; 41]. Although researchers have used various methods to study forest fire probability ignition [42; 43], the LR model has been used more often in empirical studies because of its simplicity and its reliable results. Most importantly, the LR model can be used to establish, based on the data, mathematical equations for the forest fire probabilities and other environmental variables \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Variable Type** & **Variable Factor** & **Data Sources** & **Unit** \\ \hline \multirow{6}{*}{Meteorological} & Precipitation & & mm \\  & Maximum temperature & & \({}^{\circ}\)C \\  & Minimum relative humidity & China National Meteorological & Relative humidity \\  & relative humidity & Information Center & (RH\%) \\  & Maximum wind speed & & m/s \\  & Sunshine duration & & h \\  & Altitude & & m \\  & Slope & Digital elevation & \({}^{\circ}\) \\  & NS-Aspect & & \({}^{\circ}\) \\  & EW-Aspect & & \({}^{\circ}\) \\  & Combustible substance & GPP & NASA & kg C \\  & Distance from & 1:250,000 National & \\ \multirow{2}{*}{Human activity} & Distance from & Basic Geographic & m \\  & residence & Information Database & \\  & Distance from road & & m \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Data source. and then to determine the threshold values of the corresponding variables for 50% forest fire probability and the partial derivatives when the forest fire probability is 50%. Therefore, an LR model with 12 environmental variables was established to clarify the relationship between each environmental variable and forest fire probability [44]:  
\[\ln(\frac{P}{1-P})=\beta_{0}+\sum_{j=1}^{n}\beta_{j}x_{j} \tag{1}\]  
where \(P\) is the forest fire probability and \(1-P\) is the probability of no forest fire, \(\beta_{j}\) is the regression coefficient of environment variable \(j\), \(x_{j}\) is environment variable \(j\), and \(n\) is the total number of environment variables. The receiver-operator characteristic curve is often used to evaluate the accuracy of the classification model and to calculate the optimized threshold [45]. It uses a horizontal coordinate of specificity (a positive class misclassified as a negative class) and a vertical coordinate of sensitivity (a positive class judged as a positive class), and the area under the curve (AUC) of the receiver-operator characteristic curve serves to evaluate the accuracy of the model. The range of AUC is 0-1, and the model has good predictive ability when AUC \(>\) 0.8 [46; 47; 48]. Given the possible collinearity problem between environmental variables, which decreases the accuracy of the model, we apply a multiple collinearity diagnosis to eliminate the relevant variables. The random forest algorithm serves to rank the importance of the environmental variables filtered by the model. The importance of each explained variable is expressed in terms of the decrease in the AUC when the variables are randomized 500 times [49; 50]. The mathematical interpretation of the LR model leads to two important features of the derived mathematical equation, which should be further analyzed. The first important feature is the marginal threshold of each environmental variable when the forest fire probability is 50%, which can be calculated in the reverse direction by using mathematical equation.