## 4 Results and Discussion
### Vegetation Type Productivity Response to the Potential Environmental Variables  
To better understand the potential drivers of the interannual variability in productivity among vegetation communities in the study area, the interannual variability of productivity was modeled as a function of the same potential drivers. Tables 3-5 illustrate the results for the three dominant vegetation communities in the study area: grasslands, shrublands, and needleleaf forest. The extent of variability in vegetation productivity explained by the potential explanatory variables varies from one vegetation type to another. The percent of the explanatory variables involved in each regression model also varies from one vegetation community to another. The interannual variability in vegetation productivity among grasslands explained by the explanatory variables was around 23%. The contribution of the explanatory variables in the regression model for grasslands was 30% (3 out of 12 explanatory variables show a significant relationship at the 95% confidence level). One topography driver, aspect, was included in the model and shows a positive relationship with the interannual variability in grassland productivity. Spring temperature and fall precipitation shows a negative coefficient in the regression model, suggesting that grassland productivity decreases with spring temperature and fall precipitation, while the aspect shows opposite correlation. This is consistent with the behavior of plants based on their root depth (grass versus large trees) and water availability [38]. The regression model for shrublands (see Table 4) resulted in an adjusted R-square of 0.31. Climate and topography drivers were significantly correlated with the interannual variability in shrubland productivity. Winter and spring precipitation and fall temperature exert stronger controls over interannual variability of vegetation productivity. However, winter temperature, summer and fall precipitation, as well as topographic drivers showed a significant but negative relationship. These results suggest that the interseasonal temperature plays an important role in the interannual variability in shrubland productivity. Figure 8: Spatial distribution of residuals resulting from the multiple regression model of vegetation productivity. The regression model between the interannual variability in productivity for forest area (pinyon-juniper woodlands) and the considered explanatory variables shows very low correlation. Table 5 shows the results for the model. The aspect has a strong impact on forest productivity, and is related to variation in sunlight and moisture availability in these areas. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Variables** & **Estimated Coefficient** & **Standard Errors** & \(p\)**-Value** \\ \hline Fall precipitation & \(-0.22\) & \(0.02\) & \(6.25\times 10^{-27}\) \\ \hline Fall temperature & \(1.07\) & \(0.19\) & \(2.16\times 10^{-8}\) \\ \hline Spring precipitation & \(0.16\) & \(0.02\) & \(8.22\times 10^{-14}\) \\ \hline Summer precipitation & \(-0.18\) & \(0.02\) & \(1.47\times 10^{-23}\) \\ \hline Winter precipitation & \(0.05\) & \(0.02\) & \(0.0016\) \\ \hline Winter temperature & \(-0.72\) & \(0.09\) & \(4.48\times 10^{-14}\) \\ \hline Aspect & \(-1.21\times 10^{-4}\) & \(1.02\times 10^{-5}\) & \(2.07\times 10^{-31}\) \\ \hline Elevation & \(-8.68\times 10^{-5}\) & \(6.05\times 10^{-6}\) & \(1.30\times 10^{-44}\) \\ \hline \multirow{4}{*}{_Whole model_} & \multicolumn{3}{c}{_Intercept = 0.37_} \\  & \multicolumn{3}{c}{_RMSE = 0.04_} \\ \cline{1-1}  & \multicolumn{3}{c}{_Adjusted R-Square = 0.31_} \\ \cline{1-1}  & \multicolumn{3}{c}{_p-value = 1.06 \(\times\) 10\({}^{-158}\)_} \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Statistical results of the stepwise regression model for the response variable (vegetation productivity for shrublands) showing the estimated error, standard error, and \(p\)-value for only significant explanatory variables as well as for the whole model.