## 3 Methods
### Machine Learning Modeling  
An ensemble model was proposed in this study, combining two machine learning models with different input variables. The reason for adopting the ensemble approach is to complement the different characteristics of two types of input variables: static variables and dynamic weather variables. As forest fires generally occur due to anthropogenic factors in South Korea, static input variables such as Popdens and Roaddens often have a relatively higher influence on the model than other dynamic variables (Supplementary Figure S2), which tends to result in high risk around urban areas all the time in the model results when using all variables (hereinafter, the integrated model). To mitigate the problem, the meteorological model based only on weather input variables was developed to show the seasonal and diurnal changes of forest fire risk. These two models were linearly combined through the weighted averaging approach to produce the final HFRI. The empirically determined optimum weighting ratio was 8:2 (i.e., integrated model: meteorological model). The pixels of in-situ forest fire observations within the fire duration up to eight hours were assigned with a value of \"1\" showing the highest fire risk. Most forest fires occurred in the study \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Monthly Forest Fire Density Percentile** & **0 \(\leq\) X \(<\) 25** & **25 \(\leq\) X \(<\) 50** & **50 \(\leq\) X \(<\) 75** & **75 \(\leq\) X** \\ \hline \multirow{2}{*}{Assigned values} & Fire & & 1 & & \\ \cline{2-6}  & Non-fire & 0 & 0.1 & 0.2 & - \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Assigned values for fire and non-fire samples, representing very high and low fire risk respectively, based on the monthly forest fire density. X denotes the monthly forest fire density percentile value for each pixel. area were extinguished within 8 h, except for a few very large (more than 100 ha damaged area) fires. In addition, even if a forest fire has continued over 8 h, it is difficult to determine whether the situation at that time is really a high forest fire risk. It should be noted that the model was targeting forest fire risk, not fire itself. Therefore, we used eight hours as a threshold when selecting training samples to avoid any impact from fire extinguishing work. Non-fire samples representing low fire risk were randomly extracted only at the time that forest fires have occurred in the forest areas except those within 5 km from forest fire locations for the integrated model. The buffer of 5 km was empirically determined with the assumption of relatively high fire risk within the buffer. Stratified sampling by the monthly forest fire density was used to collect non-fire samples. Since non-fire samples were taken only at the same time as forest fires, the integrated model can distinguish between high and low forest fire risk depending on the location. On the other hand, non-fire samples for the meteorological model were additionally collected covering all seasons and time with the same stratified random sampling approach. That way, differences in variables according to the temporal change were well reflected in the meteorological model to distinguish high and low forest fire risk. As a result, non-fire samples for the integrated model were extracted almost the same rate as the number of forest fires, while non-fire samples for the meteorological model were not to be biased in season and time by extracting non-fire samples in time when forest fires did not occur, which resulted in the non-fire sample size three times more than those for the integrated model. Different sampling strategies for two models were to intentionally emphasize the spatial characteristics of forest fires for the integrated model, while the temporal characteristics for the meteorological model. The training sample sizes used for the two machine learning models are summarized in Table 3.  
Both the integrated and meteorological models were developed using Catboost.