## 2 Materials and Methods
### Study Data
#### 2.2.1 Remote Sensing Data  
The surface reflectance data used in this study were sourced from the Landsat surface reflectance dataset provided by the United States Geological Survey (USGS), with a spatial resolution of 30 m. The choice of Landsat data is due to their relatively high spatial resolution, which allows for better capture of fine-scale variations in mountainous regions. Based on the temporal coverage, the dataset includes Landsat 5, Landsat 7, and Landsat 8 data. Cloud-free images with path/row numbers (124, 38), (125, 37), (125, 38), (126, 37), and (126, 38) were selected from 2001 to 2020 ([[https://earthexplorer.usgs.gov/](https://earthexplorer.usgs.gov/)]([https://earthexplorer.usgs.gov/](https://earthexplorer.usgs.gov/)) (accessed on 1 November 2024)). The data were downloaded as surface reflectance data. After the mosaicking and clipping process, a total of 80 scenes were obtained quarterly, covering the whole of northwestern Hubei.  
The Landsat surface reflectance data were processed through band math operations to derive the Landsat NDVI data. The NDVI was calculated as follows:  
\[NDVI=\frac{NIR-Red}{NIR+Red} \tag{1}\]  
\begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Data Category** & **Product/Type** & **Temporal Resolution** & **Spatial Resolution** & **Observation Period** \\ \hline Surface reflectance & Landsat & Quarterly & 30 m & 2001–2020 \\ NDVI & MOD13Q1 & 16 days & 250 m & 2001–2020 \\ \hline \multirow{7}{*}{Climate} & Total precipitation & Daily & 0.5\({}^{\circ}\)\(\times\) 0.5\({}^{\circ}\) & 2001–2020 \\  & Surface net solar & Daily & 0.5\({}^{\circ}\)\(\times\) 0.5\({}^{\circ}\) & 2001–2020 \\ \cline{1-1}  & Clear-sky direct solar & Daily & 0.5\({}^{\circ}\)\(\times\) 0.5\({}^{\circ}\) & 2001–2020 \\ \cline{1-1}  & radiation at surface & Surface solar & Daily & 0.5\({}^{\circ}\)\(\times\) 0.5\({}^{\circ}\) & 2001–2020 \\ \cline{1-1}  & radiation downwards & 2 m temperature & Daily & 0.5\({}^{\circ}\)\(\times\) 0.5\({}^{\circ}\) & 2001–2020 \\ \hline GPP products & GOSIF GPP & 8 days & 0.05\({}^{\circ}\)\(\times\) 0.05\({}^{\circ}\) & 2001–2020 \\ \cline{1-1}  & MODIS GPP & 8 days & 0.05\({}^{\circ}\)\(\times\) 0.05\({}^{\circ}\) & 2001–2020 \\ \hline \hline \end{tabular} Data specifications cover the study period from 2001 to 2020 in northwest Hubei.  
\end{table}
Table 1: Data specifications for the remote sensing, climate, and GPP products used in this study.  
where \(NIR\) represents the near-infrared band, and \(Red\) represents the red band.  
Due to it being difficult to form time series with Landsat data, MODIS NDVI data were also applied and fused with the Landsat data. The selected NDVI product was MOD13Q1 (available at [[https://modis.gsfc.nasa.gov/data/dataprod/mod13.php](https://modis.gsfc.nasa.gov/data/dataprod/mod13.php)]([https://modis.gsfc.nasa.gov/data/dataprod/mod13.php](https://modis.gsfc.nasa.gov/data/dataprod/mod13.php)) (accessed on 1 November 2024)), with a temporal resolution of 16 days and a spatial resolution of 250 m, covering the period from 2001 to 2020. This dataset comprises 460 scenes with tile number h27v05.MODIS data offering a higher temporal resolution (16-day composite) and are relatively less affected by cloud contamination, which makes them well-suited for constructing continuous and consistent time series. After clipping and filtering, the MODIS NDVI data for northwestern Hubei were obtained.