## 2 Materials and Methods
### Data Acquisition and Preprocessing  
Daily precipitation, temperature, downward shortwave radiation, wind speed, specific humidity, and pressure data from 2001 to 2018 were obtained from the China Meteorological Forcing Dataset (CMFD, [[http://data.tpdc.ac.cn](http://data.tpdc.ac.cn)]([http://data.tpdc.ac.cn](http://data.tpdc.ac.cn)), accessed on 29 October 2022), with a spatial resolution of 0.1\({}^{\circ}\)\(\times\) 0.1\({}^{\circ}\)[32]. Temperature data with 3 h resolution were also used. CMFD has been widely used in recent research for its higher accuracy [33; 34; 35]. Downward shortwave radiation has been used in this investigation to approximate solar radiation [36]. Weather stations in the MHRB are sparse, which can affect the accuracy of data analysis. CMFD has 1962 grid points in the MHRB, which is dense and beneficial to improve the accuracy of interpolation. Since CMFD is not available after 2018, our study was also up to 2018.  
LAI (MOD15A2H, temporal resolution of 8 days) and yearly GPP (MOD17A3 HGF) data from 2001 to 2018 were downloaded from USGS ([https://e4 ftl01.cr.usgs.gov/](https://e4 ftl01.cr.usgs.gov/), accessed on 20 September 2022), with a spatial resolution of 500 m. Savitzky-Golay filtering method was applied to smooth the original LAI data to reduce invalid values. The LAI data were synthesized to the monthly scale by the maximum synthesis method, and the annual LAI was the average of all the monthly data within the year.  
The DEM data (ASTER GDEM V3, spatial resolution of 30 m) were obtained from the National Aeronautics and Space Administration ([[https://cmr.earthdata.nasa.gov/](https://cmr.earthdata.nasa.gov/)]([https://cmr.earthdata.nasa.gov/](https://cmr.earthdata.nasa.gov/)), accessed on 20 June 2020). The landform data with a spatial resolution of 1000 m were acquired from the Resource and Environment Science and Data Center ([[https://www.resdc.cn/](https://www.resdc.cn/)]([https://www.resdc.cn/](https://www.resdc.cn/)), accessed on 9 October 2021). The China land cover dataset (CLCD, [[https://doi.org/10.5281/zenodo.5816591](https://doi.org/10.5281/zenodo.5816591)]([https://doi.org/10.5281/zenodo.5816591](https://doi.org/10.5281/zenodo.5816591)), accessed on 9 September 2022) was employed to analyze the land use change from 2001 to 2018, whose accuracy is comparatively good in China [37]. The original statistics in the MHRB primarily consist of eight land use types. Due to the small areas of shrub and wetland, they were merged with forest and water, respectively. Ultimately, land use consisted of six categories: cropland, grassland, forest, water, barren, and impervious. In order to reduce the impact of land use changes, unchanged land use data from 2001 to 2018 were utilized for the geographical detector model. Table 1 lists the four kinds of driving factors that were taken into consideration, including climate, topography, land use, and geomorphology. Climate factors include temperature (X1), precipitation (X2), humidity index (X3), VPD (X4), reference evapotranspiration (ETo, X5), and solar radiation (X6). The topography factors include elevation (X7), slope (X8), and aspect (X9).