## 2 Materials and Methods
### Data  
We selected remotely sensed normalized difference vegetation index (NDVI) data from Vegetation Index and Phenology (VIP) dataset during 1981-2014 ([[https://cmr.earthdata.nasa.gov/search/concepts/C1328419482-LPDAAC_ECS.html](https://cmr.earthdata.nasa.gov/search/concepts/C1328419482-LPDAAC_ECS.html)]([https://cmr.earthdata.nasa.gov/search/concepts/C1328419482-LPDAAC_ECS.html](https://cmr.earthdata.nasa.gov/search/concepts/C1328419482-LPDAAC_ECS.html)), accessed 1 March 2019) to calculate FPAR, which has a temporal resolution of monthly interval and a spatial resolution of 5600 m \(\times\) 5600 m [31]. The dataset is created using multisource remotely sensed surface reflectance data, including Advanced Very High Resolution Radiometer (AVHRR) (during 1981-1999) and MODIS (during 2000-2014) datasets, and was updated to 2014, when we ran our model.  
Land-cover data in 2010 from the Data Center of Resources and Environmental Sciences, Chinese Academy of Sciences with a spatial resolution of 1000 m \(\times\) 1000 m were used to define the baseline cropland map. These data were resampled to a spatial resolution of 5600 m \(\times\) 5600 m to match the NDVI data. These data are generated by supervised classification and manual correction of Landsat TM/ETM+ images [32].  
Following previous studies [33; 34], we defined areas above 1000 m above sea level (ASL) as alpine region. Digital elevation data with a spatial resolution of 90 m \(\times\) 90 m from Shuttle Radar Topography Mission (SRTM) were resampled to a spatial resolution of 5600 m \(\times\) 5600 m to define the alpine region and an elevational gradient with an elevation interval of 100 m. To avoid statistical anomalous fluctuations caused by inadequate pixels at a given elevation bin, elevation bins with pixel amounts less than 100 were excluded, which resulted in inclusion of elevation bins from 1000 m ASL to 4500 m ASL in the study.  
Monthly meteorological records were derived from China Meteorological Data Service Center of the China Meteorological Administration ([[http://data.cma.cn/](http://data.cma.cn/)]([http://data.cma.cn/](http://data.cma.cn/)), accessed 1 March 2019), which has 92 field stations across the study area. The meteorological records were interpolated to spatially continuous datasets with a temporal resolution of monthly interval and a spatial resolution of 5600 m \(\times\) 5600 m by ANUSpin software. The ANUSpin software incorporates a covariate of elevation with the independent spline variables in partial thin plate spline method and, consequently, has a higher accuracy than other interpolation methods in obtaining spatially continuous meteorological data for alpine region [35]. Based on results of previous studies about climate driving effects on cropland ecosystem NPP [29; 36; 37], we selected three factors in the study, i.e., temperature, precipitation, and solar radiation.  
The model simulated NPP results were validated by field survey data before we began analyses. The field survey was conducted in September to October during 2012-2014. Thirty-two sites were surveyed. In each site, five 1 m \(\times\) 1 m quadrats were laid out  
Figure 1: Spatial patterns of elevation (**a**), cropland distribution (**b**), annual mean temperature (**c**), and annual total precipitation (**d**) in the alpine region of the southwest China. (**b**) Alpine cropland distributed above 1000 m ASL and locations of field survey sites. Details of survey methods can be found in Section 2.2.  
randomly, and all crop components were collected. The collected crop was oven-dried at 65 \({}^{\circ}\)C for 72 h, and then, its carbon content was measured. The carbon content of each site was the average value of the five 1 m \(\times\) 1 m quadrats.