## 3 Results
### Trends in NPP  
NPP has an increasing temporal trend as seen in Figure 1(c). We will denote the correlation coefficient as \"r\" and the coefficient of determination which is the fraction of variability explained by a linear regression model as \"R\({}^{2}\)\". The total NPP over the country increased from0.78 PgC\(\cdot\)y\({}^{-1}\) in 1982 to 0.86 PgC\(\cdot\)y\({}^{-1}\) in 2006. The increase is consistent with the spatial pattern presented in [8], which  
Figure 1: Spatial pattern of (**a**) annual mean, (**b**) standard deviation, (**c**) temporal evolution of domain-mean NPP, (**d**) coefficient of variation of NPP, (**e**) spatial pattern of the annual NPP trends, and (**f**) percentage decadal trends of NPP from 1982 to 2006.  
shows an increase in NPP from 1982 to 1999. The linear growth rate estimate suggests a positive trend of 0.39% per year during the analysis period (r = 0.78, R\({}^{2}\) = 0.61) or 3.9% per decade, which is in close agreement with the positive trend of 3.5% per decade obtained from a different dataset [18]. Linear regression was performed for every grid point to obtain the spatial pattern of linear trends (Figure 1(e-f)). Positive trends are observed over the Western Ghats, Himalayan forests in the north, parts of northeast India, central and eastern India. Near-zero or slightly negative trends are observed over parts of the northwest and northernmost parts of India. To examine the role of temperature, precipitation, atmospheric CO\({}_{2}\), soil water in the top 3.4 m and downward surface solar radiation on the evolution of NPP, we used single and multivariate analysis:  
\[\text{NPP}=\text{C}_{0}+\text{C}_{1}\text{X}_{1}+\text{C}_{2}\text{X}_{2}+ \text{C}_{3}\text{X}_{3}...+\text{C}_{\text{N}}\text{X}_{\text{N}}+\text{R} \tag{1}\]  
where X\({}_{1}\), X\({}_{2}\), X\({}_{3}\),...X\({}_{\text{N}}\) are the independent variables such as temperature, precipitation, soil water, downward solar radiation at the surface and global-mean atmospheric CO\({}_{2}\), and C\({}_{0}\), C\({}_{1}\), C\({}_{2}\),...C\({}_{\text{N}}\) are constants, and R is the residue which represents the nonlinear terms. N = 1 for single variable analysis. We have used at most N = 5 in this paper. It should be noted that the variables such as temperature and solar radiation, and precipitation and soil water are not truly independent of each other. The NPP time series developed using Equation (1) will be called multivariate NPP and we will be mostly interested in the correlation (r) between observed NPP and the multivariate NPP and the R\({}^{2}\) values to infer the influence of a single, or a combination of, variables on NPP. Figure 2(a-i) shows the time evolution of spatially averaged NPP, precipitation, temperature, CO\({}_{2}\), surface solar radiation and soil water in the top 3.4 m in India. The correlation between domain-mean NPP _versus_ precipitation, temperature, CO\({}_{2}\), solar radiation and soil moisture are 0.18, 0.42, 0.76, \(-\)0.72, and \(-\)0.61, respectively (Figure 2, Table 1).The corresponding R\({}^{2}\) values are 0.03, 0.18, 0.58, 0.51 and 0.37, respectively (Figure 3, Table 1). This implies that NPP increase is primarily associated with an increase in global mean CO\({}_{2}\). The correlations are negative with soil water and solar radiation because these variables have a declining trend while NPP has a positive trend (Figure 2).