## Materials and Methods
### Accuracy Assessment  
To validate the effectiveness and applicability of our method, accuracy assessment was applied to the extracted training sample sets and the final burned area map. Since the performance of the proposed method depends on the accuracy of the training sample sets, it is necessary to assess their accuracy first.  
Figure 4: Framework of the back-propagation neural network (BPNN) in our method.  
We applied the 10-fold cross validation method to access the accuracy of the training sample sets used by the BPNN. The sample sets were divided into 10 groups, nine groups of which were employed as the training samples, and the remaining group was used as the test sample. The validation process can take all the samples as training sets and test sets, and each sample can be validated once. The evaluation metrics of overall accuracy (OA), omission error (OE), commission error (CE), and Kappa coefficient (K) were measured to quantificationally assess the accuracy. These evaluation metrics are defined as follows:  
\[\text{OA}=\frac{N_{c}}{N_{total}} \tag{7}\]  
\[\text{OE}_{m}=\frac{N_{miss,m}}{N_{actual,m}} \tag{8}\]  
\[\text{CE}_{m}=\frac{N_{false,m}}{N_{predict,m}} \tag{9}\]  
\[\text{K}=\frac{\text{OA}-y}{1-y}\text{ where }y=\frac{\sum\limits_{m=1}^{m} \left(N_{actual,m}\times N_{predict,m}\right)}{{N_{total}}^{2}} \tag{10}\]  
In these formulas, \(m\) represents a certain type, \(n\) refers to the number of types, \(N_{c}\) is the number of samples correctly classified, \(N_{total}\) is the total number of the samples of all types, \(N_{miss,m}\) is the number of miss-classified samples of type \(m\), \(N_{actual,m}\) is the actual number of type \(m\), \(N_{false,m}\) is the number of false-classified samples of type \(m\), and \(N_{predict,m}\) is the predicted number of type \(m\).  
Also, accuracy assessment for the burned area map was carried out to demonstrate the applicability of the proposed method. We assessed the accuracy of the burned area maps derived from our method using the reference data compiled by remote sensing data of finer resolution [9; 16]. In this study, Landsat 8 OLI Collection 1 L1 TP products were processed to generate the reference burned area map as ground truth. The OLI products have already been radiometrically calibrated and orthorectified using ground control points and digital elevation model (DEM) data to correct for relief displacement [5]. Here are the processing steps of Landsat-8 OLI data with ENVI software: Firstly, the L1 TP products were atmospherically corrected to obtain surface reflectance free from the influence of atmosphere, solar illumination and similar interferences [27; 47]. Then, two adjacent atmospherically-corrected images in the pre-fire or post-fire period were processed by image mosaic to a wide and seamless image. Thirdly, the mosaic images were cropped to the study area according to the longitude and latitude of the wildfires. Then the OLI spectral bands at finer spatial resolution (30-m) were then spatially down-sampled to the 1-km resolution for comparison with the MODIS-based burned area results. Afterward, the Normalized Burn Ratio (NBR) images in the pre-fire and post-fire period were obtained. The post-fire NBR image was subtracted from the pre-fire NBR image to get the differenced NBR (dNBR) according to the formula below [62]:  
\[\text{dNBR}=\text{NBR}_{pre-fire}-\text{NBR}_{post-fire} \tag{11}\]  
Finally, the dNBR in conjunction with the post-fire NDVI and post-fire NDWI were used with empirical thresholds to remove noisy pixels [33; 63]:  
\[\left(\text{NDVI}_{post-fire}<0.2\right)\text{ and }\left(\text{NDWI}_{ post-fire}<0\right) \tag{12}\]  
Both the MODIS and OLI data used the map projection of transverse Mercator. In the comparison between the MODIS-based and OLI-based burned area maps, a pixel-wise accuracy assessment was performed to evaluate the proposed method. The commission error (CE) and omission error (OE) of the burned area detection have been analyzed to represent the accuracy of the MODIS-based burned area map.