## Materials and Methods
### Burned Area Mapping Method
#### 2.3.4 Back-Propagation Neural Network
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Spectral Index** & **Formula** & **Reference** \\ \hline Burned Area Index & \(\text{BAI}=1/((0.1-\rho_{1})^{2}+(0.06-\rho_{2})^{2})\) & [50] \\ Char Soil Index & \(\text{CSI}=\rho_{2}/\rho_{6}\) & [51] \\ Mid Infrared Burn Index & \(\text{MIBRI}=10\rho_{7}-9.5\rho_{6}+2\) & [52] \\ Normalized Burn Ratio & \(\text{NBR}=(\rho_{2}-\rho_{7})/(\rho_{2}+\rho_{7})\) & [53] \\ Normalized Difference Vegetation Index & \(\text{NDVI}=(\rho_{2}-\rho_{1})/(\rho_{2}+\rho_{1})\) & [54] \\ Enhanced Vegetation Index & \(\text{EVI}=\text{G}\times(\rho_{2}-\rho_{1})/(\rho_{2}+6\rho_{1}-7.5\rho_{3}+1)\) & [55] \\ Global Environment Monitoring Index & \(\text{GEMI}=\eta(1-0.25\rho_{7})\times(\rho_{5}-0.125)/(1-\rho_{5})\) with & [56] \\  & \(\eta=(2(\rho_{2}-\rho_{5})^{2}+1.5\rho_{5}+0.5\rho_{5})/(\rho_{7}+\rho_{5}+0.5)\) & [57] \\ Soil Adjusted Vegetation Index & \(\text{SAVI}=1.5(\rho_{2}-\rho_{1})/(\rho_{2}+\rho_{1}+0.5)\) & [57] \\ burn-sensitive Vegetation Index & \(\text{bsVI}=(\rho_{5}-\rho_{7})/(\rho_{5}+\rho_{7})\) & [16] \\ NIR-SWIR-emissivity Version 1 & \(\text{NSEv1}=(\rho_{2}-\rho_{7})\times\text{E}/(\rho_{2}+\rho_{7})\) & \\ NIR-SWIR-emissivity Version 2 & \(\text{NSEv2}=(\rho_{2}-(\rho_{7}+\text{E}))/(\rho_{2}+\rho_{7}+\text{E})\) & [22] \\ NIR-SWIR-Ts Version 1 & \(\text{NSV1}=(\rho_{2}-\rho_{7})\times T_{S}/(\rho_{2}+\rho_{7})\) & \\ NIR-SWIR-Ts Version 2 & \(\text{NSV1}=(\rho_{2}-(\rho_{7}+T_{S}))/(\rho_{2}+\rho_{7}+T_{S})\) & \\ \hline \hline \end{tabular} The subscript of each spectral index corresponds to the spectral band of MODIS sensor. \(\rho_{i}\) represents the reflectance of band \(i\), \(E\) represents the emissivity, \(T_{s}\) refers to the land surface temperature.  
\end{table} 
Table 4: Formula of the spectral indices used and corresponding reference. outputs of the network are maximized to approximate the target outputs. The formula of the error function is shown below:  
\[E_{r}=\frac{1}{s_{2}}\sum_{k=1}^{s_{2}}\left(t_{k}-a_{2k}\right)^{2} \tag{6}\]  
where \(E_{r}\) stands for the error function; \(k\) and \(s_{2}\) represent the output layer neurons and the number of them, respectively; \(a_{2k}\) is the actual output of neuron \(k\) in the output layer; and \(t_{k}\) is the target output of neuron \(k\). The nonlinear optimization method used in the network is the gradient descent with momentum and adaptive learning rate method, which is used to update the weights and biases. In order to apply the proposed method to a variety of wildfire cases, the local minima that approximate the global minimum are generally acceptable. The additional momentum of the gradient descent method was utilized to reduce the error and achieve the local minimum. The learning rate adjusts based on the performance of the network toward the goal in each training epoch. The learning rate will increase if the weights of the network make the value of error function decrease while it will decrease if the error increases [61]. In practice, the gradient descent with momentum and adaptive learning rate back-propagation method outperforms other optimization methods in training experiments, and it exhibits a superior convergence speed. Training of the BPNN was implemented using MATLAB. The training sample sets of the indicators on behalf of the five typical types were used to train the BPNN until it reached the optimal performance with a low mean squared error. Finally, the trained network was applied to several wildfire cases to generate burned area maps. We adopted a threshold T for the final outputs of the output layer. The output layer pixels with output values greater than T were identified as burned pixels, whereas the pixels with output values lower than T were regarded as unburned pixels. The omission error and commission error of the final burned area map will change as the threshold T changes. If the T value is set relatively high, that is a conservative threshold, and the omission error will increase while the commission error will decrease.