## Materials and Methods
### Burned Area Mapping Method
#### 2.3.2 Extraction of Samples Sets  
The empirical formula method [18], multi-threshold method [31; 42; 43; 44; 45] and visual interpretation method [18; 25; 46] were used to extract the sample sets of burned area, vegetation, cloud, bare soil, and cloud shadow. The visual interpretation method is frequently used to visually identify the burned regions on MODIS images while the traditional empirical formula method has proved to be able to detect the burned area based on data analysis, so we utilized these methods to extract the samples of  
Figure 2: The flowchart of the new burned area mapping method. the burned area. Here are the detailed steps. Firstly, two rectangular boxes were used to extract the samples of the burned area and unburned types with ENVI software, as depicted in Figure 3. In the false-color composition RGB image (band 7 at 2.13 \(\upmu\)m as red channel, band 5 at 1.24 \(\upmu\)m as green channel, band 6 at 1.64 \(\upmu\)m as blue channel), the dark purple region in Box 1 of Figure 3 is the burned area of the Range 12 Fire in Washington, according to the independent burned area mapping from the MTBS website. The samples of the burned area and unburned types can be extracted from Box 1, and the samples extracted from Box 2 only belong to the unburned types. Then, the relationship between the reflectance of MODIS band 5 and band 7 can be investigated using the scatter plot with the reflectance of band 7 as the independent variable and the reflectance of band 5 as the dependent variable. Because the unburned types of vegetation and soil have higher reflectance at band 5 (1.24 \(\upmu\)m) than the burned area [18], the samples of unburned types extracted by Box 1 and Box 2 are located in the upper left of the scatter plot while the samples of the burned area extracted by Box 1 are located in the lower right (see Section 3.1 and Figure 5 for details). Finally, the traditional empirical formula method can be established to separate the samples of the burned area and unburned types. The empirical formula can be determined as the following form:  
\[\rho_{5}<\alpha\times\rho_{7}+\beta \tag{1}\]  
where \(\rho_{5}\) and \(\rho_{7}\) are the reflectance of band 5 (1.24 \(\upmu\)m) and band 7 (2.13 \(\upmu\)m) and \(\alpha\) and \(\beta\) are the slope and intercept of the formula line, respectively. The samples satisfying the empirical formula are located below the line, which can be classified as the burned area. The conservative coefficients of the empirical formula can be used to ensure that the samples below the line belong to the burned area type. The samples of the burned area can be extracted using the traditional empirical formula method. The multi-threshold method has been widely used in the detection of land cover types on the satellite images. In order to obtain the samples of unburned types, the multi-threshold method in conjunction with the visual interpretation method was employed to extract the samples of vegetation, cloud and bare soil, while the samples of cloud shadow were selected by photo-interpretation in the true-color RGB images generated from MODIS bands 1, 4 and 3 with ENVI software. The multiple threshold criteria used are shown in Table 3. The vegetation samples were extracted by the Normalized Difference Vegetation Index (NDVI) because NDVI is strongly related to the surface biomass. The cloud samples were obtained based on the cloud detection techniques proposed in the research of [PERSON] et al. [43] and [PERSON] et al. [44]. For the extraction of bare soil samples, the empirical thresholds [45] were applied to NDVI and the normalized reflectance ratio of band 9 and band 7. Also, water pixels  
Figure 3: False-color composition MODIS RGB image (red: 2.13 \(\upmu\)m; green: 1.24 \(\upmu\)m; blue: 1.64 \(\upmu\)m) acquired from Range 12 Fire on 6 August 2016. Box 1 contains samples of burned area and unburned types while Box 2 contains only unburned samples.