## 2 Materials and Methods
### Dataset and Data Processing  
#### 2.2.1 Annual Net Primary Productivity (NPP)  
NPP derived from MODIS from 2001-2014 in China were used (MOD17A3, 1 km), which have been further used as an important data source for plant productivity monitoring and assessment [35]. The MODIS annual NPP algorithm relies on the summation of the daily estimation of Gross Primary Productivity (GPP) computed globally minus growth and maintenance respiration [14]. To estimate annual NPP, first, the daily estimates of maintenance respiration for leaves and fine roots are subtracted from the daily GPP values. These daily reduced GPP estimates are then summed for each year, and estimates for annual maintenance respiration of living wood tissue and annual total growth respiration are subsequently subtracted, resulting in annual NPP estimates. Full details of the algorithm in MODIS derived NPP can be found in Reference [14]. However, due to the deficiencies and uncertainty of MODIS derived NPP as above-mentioned, the Miami model and Thornthwaite Memorial model were applied in this study, as they are simple to operate with only a few parameters that were easy to obtain, and have a higher spatial and temporal resolution of climate data in China. Additionally, they have previously been applied in China [11; 13]. The Miami model is calculated as follows (Equations (1)-(3)):  
\[NPP_{T,P}=\ \min\{f_{1}(T),\ f_{2}(P)\} \tag{1}\]  
\[f_{1}(T)\ =\frac{k_{1}}{1\ +\ e^{k_{2}\ -\ k_{3}\ \times\ T}} \tag{2}\]  
\[f_{1}(P)\ =k_{4}\ \times\ \left(1-e^{-k_{5}\ \times\ P}\right) \tag{3}\]  
where \(K_{1}\), \(K_{2}\) and \(K_{3}\) in Equation (2) are the temperature response parameters with values of 3000, 1.315 and 0.119, respectively and \(T\) is the annual average temperature (\({}^{\circ}\)C); \(K_{4}\) and \(K_{5}\) in Equation (3) are the precipitation response parameters with values of 3000 and 0.000664, respectively, and \(P\) is the annual average precipitation (mm). The parameters of \(K_{i}\) (\(i\) = 1, 2, \(\ldots\), 5) were calculated using the least squares method based on the field testing of NPP, and the relative temperature and precipitation collected at 50 locations scattered across five continents [36]. The Thornthwaite Memorial model is expressed as follows (Equations (4)-(6)):  
\[NPP\ =\ 3000\ \times\ \left(1\ -\ e^{-0.0009695\ \times\ \left|v\right.-20 \right|}\right) \tag{4}\]  
\[v\ =\ \frac{1.05\ \times\ R}{\sqrt{1\ +\ \left(1\ +\ 1.05\frac{R}{L}\right)^{2}}} \tag{5}\]  
\[L\ =\ 3000\ +\ 25\ \times\ T\ +\ 25T^{3} \tag{6}\]where \(v\) represents the mean annual actual evapotranspiration (mm); \(L\) represents the mean annual evapotranspiration (mm); and \(T\) and \(R\) represent the mean annual temperature and mean annual precipitation, respectively. Due to the different inputs and parameters in the three models, all the estimated NPP results were compared with the field observed NPP (Table S1), which was calculated from flux tower data based on the eddy covariance method, a micrometeorological method with high-frequency data collection. This method provides direct measures of net carbon fluxes between vegetated canopies and the atmosphere over short and long timescales with minimal disturbance to the underlying vegetation. The observation data were collected from ChinaFLUX sites [37] directly and indirectly from the literature. High-precision CO\({}_{2}\) concentration measurements and surface carbon flux measures, made at eddy covariance measurement sites, can be used to improve and validate the algorithms being used by remote sensing and ecosystem models [38]. The observations almost covered the typical ecosystem types in China. Therefore, observations from carbon flux data were applied as a reference to compare the results from the three models. Sites only having one year, the corresponding yearly data for observations, and three simulated values were used directly; and for sites longer than one year, the corresponding multi-year averaged data were applied.