## 2 Data and Methods
### Satellite Data  
In this study, we used \(NDVI\) from Landsat and MODIS datasets to drive the revised EC-LUE model. \(NDVI\) was calculated from the spectral reflectance at the red and near infrared wavelengths, using the following expression.  
\[NDVI=\frac{R_{nir}-R_{red}}{R_{nir}-R_{red}} \tag{8}\]  
where \(R_{nir}\) is the surface reflectance in the near infrared wave band, and \(R_{red}\) is the surface reflectance in the red wave band.  
In this study, Landsat data (red and near infrared bands) with 30 m resolution were used to calculate NDVI from sensors of Landsat-5 TM, Landsat-7 ETM+, and Landsat-8 OLI, respectively, through the Google Earth Engine (GEE) platform. Then, the maximum composited NDVI with 16-day time step was obtained. First, the 16-day maximum composited NDVI data were extracted at the 3 km \(\times\) 3 km window surrounding each site to fully cover the footprint source. Second, the Landsat NDVI data that corresponded to the pixels of the spatial variation of footprint at each site with 16-day intervals were averaged to generate Landsat-footprint-NDVI. Landsat pixels with clouds were not used in NDVI computations or in model parameterization or evaluation.  
For each site, MODIS-derived surface reflectance products from the red and near infrared bands were obtained from Oak Ridge National Laboratory's Distributed Active Archive Center (ORNL DAAC) with 8-day and 500 m resolution. These products were used to calculate NDVI, which was then averaged into 16-day time steps to match the time step of the Landsat NDVI. The MODIS surface reflectance products were extracted within the 1 km \(\times\) 1 km (2 pixels \(\times\) 2 pixels) window, centered on the flux tower, and used to calculate MODIS-footprint-NDVI at the croplands and savannas sites, which had small footprints with elliptic curves below a 500 m radius. For the forest sites, MODIS surface reflectance products were extracted within the 3 km \(\times\) 3 km (6 pixels \(\times\) 6 pixels) window surrounding to calculate MODIS-footprint-NDVI, fully covering the footprint. The footprints at forest sites had a relatively wide radius (larger than 1.5 km) due to the canopy and measurement heights. For all sites, site-based meteorological data (temperature, atmospheric vapor pressure deficit, atmospheric pressure, and CO\({}_{2}\) concentration) were averaged to 16-day intervals to match the time step of the MODIS NDVI and Landsat NDVI data. The meteorological data, MODIS NDVI, and Landsat NDVI were then used to drive the revised EC-LUE model at 16-day intervals.  
We adopted the weighted Whittaker with dynamic \(\lambda\) (wWHd) method to reconstruct the Landsat NDVI and MODIS NDVI to eliminate the effect of the poor quality NDVI data. Whittaker smoothing is a well-known reconstruction approach and has been widely used for vegetation index time series reconstruction [29; 30; 31]. The original Whittaker method has only a single parameter (\(\lambda\)) for penalizing and smoothing the data [32]. The greater the value of \(\lambda\), the stronger the smoothing, and so the larger value of \(\lambda\) is required when the vegetation index is heavily contaminated or fluctuated sharply. Ref. [33] introduced weights (W) into the Whittaker method and called it weighted Whittaker with dynamic \(\lambda\). The value of weight depended on the quality of the corresponding point. The maximum weight, W = 1, represented a good point, and W decreased to a minimum of 0.2 for points with poor quality data. More detailed information about reconstruction is available in [33].