## 2 Materials and Methods
### Methods
#### 2.3.4 Extraction of PWD  
Based on the spatiotemporal features, we set up a group of restrictions on the spatiotemporal features (Table 2). The single-date NGRDI image could indicate the non-green objects, including wilted pine trees and many other objects with the similar spectral properties. The bi-temporal change detection distinguished between the wilted pine trees and these objects by capturing the temporal behaviors of the wilting process. However, pixels with the certain land (or surface) cover change (e.g., deforestation, falllow) during 2018-2019 could show similar temporal behaviors to tree wilting. As such events were commonly of larger spatial extent and relatively homogeneous \(\Delta NGRDI\) observations, which was different from the wilted pine trees (Figure 4b), spatial analysis was additionally performed to eliminate them.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Category** & **Feature** & **Abbrev** & **Type** & **Criterion** \\ \hline \multirow{2}{*}{Temporal} & NGRDI observation in the first image (22 October 2018) & \(NGRDI_{1}\) & Pixel-wise & \(>\)0 \\  & NGRDI observation in the second image (15 October 2018) & \(NGRDI_{2}\) & Pixel-wise & \(<\)0 \\ \hline \multirow{2}{*}{Spatial} & Output of the spatial convolution on the \(\Delta NGRDI\) & \(Conv\) & Pixel-wise & \(\geq\)\(\alpha\) \\  & Pixel count in a candidate bounding box (BB) & & Object-wise & \(\leq\)\(N\) \\ \hline \end{tabular}
\end{table}
Table 2: The criteria for the spatiotemporal features extracted from image pair to distinguish the pine wilted trees.  
Figure 4: Typical spatial patterns of (**a**) a wilted pine tree on the ground and (**b**) the corresponding \(\Delta NGRDI\) in the satellite image, and (**c**) the proposed kernel matching the spatial pattern of the wilted pine trees. The canopy width is set to twice the pixel size as an example according to the average canopy width acquired from the in situ investigations and spatial resolution of the satellite image used in this study.  
Specifically, a threshold of \(\alpha\) was applied on \(Conv\) to mask the possible witched pine tree pixels (Figure 5a). Then, we converted the pixel-based results into the target-based results, in which the adjacent pixels (including diagonally connected pixels) were reorganized into a target and designated each corresponding rectangular frame as a candidate bounding box (\(BB\), Figure 5b). The number of pixels in each candidate \(BB\) was counted. As the \(BB\)s were approximately squared, the possible pixel count could be inferred in advance. For example, the pixel counts of the candidate \(BB\)s are nine and six in Figure 5b. The upper limit of the pixel count in a candidate \(BB\) was set as \(N\) to avoid false detections of the large-scale land (or surface) cover change.  
In addition, a support vector machine (SVM) classification with the 2019 image was performed as a single-date image classification method to compare with the spatiotemporal change detection method. As there were too few witched pine trees at Sites A and B and Site D was full of pure pine stands, we randomly selected approximately 60% of the samples at Sites C and D to train the classifier. For the key parameters in SVM, kernel type was set as the Radial Basis Function, cost parameter was set as 100, and gamma was set as 0.25 (the reciprocal of the number of bands). For the classification results, only the witched pine tree class was considered, and likewise, the pixel-wise results were also converted to candidate \(BB\)s and screened by \(N\).