## 3 Results
### Model Result from GWR  
Although the OLS regression captured the relationships between RCU and the explanatory variables, nonstationary characteristics in the spatial RCU and the explanatory variables imply that the global model may fail to highlight the spatially variant patterns in the relationship [42]. Therefore, RCU was further analyzed by the GWR model, which is capable of reflecting the nonstationary characteristics in the relationship. Table 4 describes the result from GWR with 58 optimal neighbors suggested by the model. The improved performance, as opposed to that from the OLS model, confirmed that nonstationary patterns do exist among the relationship between RCU and the explanatory variables. For example, the adjusted R\({}^{2}\) had a significant improvement, which was 0.53 from GWR compared to 0.21 in the OLS model. Furthermore, the corrected Akaike's Information Criterion (AICc) is also a useful way to evaluate the performance of a regression model, and lower AICc means model improvement. The decrease of AICc to 951.6, as opposed to 961.7 from the OLS model, confirms that GWR is superior to the OLS model in capturing the variation of the dependent variable. The model residuals from the GWR regression did not show significant bias. In summary, it is evident that GWR improved the model performance compared to that by OLS. The regression coefficient varied over the space, indicating a heterogeneous impact on the reduced carbon uptake (RCU) from each of the variables (Figure 5). The four variables together explain 53% of the variation in RCU (adjusted R\({}^{2}\) = 0.53, Table 4). The model coefficients from the variables differed not only in magnitude but also in directions (positive or negative). The positive coefficients of the grazing intensity in most of the study area, particularly the middle part, confirms that increasing grazing animals would increase RCU, which is a sign of negative impact on vegetation productivity; an opposite impact from grazing animals was identified in the northern and north-eastern part of the area, where \begin{table}
\begin{tabular}{c c c} \hline
**\#ID** & **Statistical Item** & **Value** \\ \hline
0 & Neighbors & 58 \\
1 & Residual squares & 274571.4 \\
2 & Effective number & 15.5 \\
3 & Sigma & 63.3 \\
4 & AICc & 951.6 \\
5 & R-Squired (R\({}^{2}\)) & 0.62 \\
6 & Adjusted R\({}^{2}\) & 0.53 \\
7 & Depend variable & Reduced carbon uptake (RCU) \\  & & Grazing (intensity), \\
8 & Predictors & Road (network density), \\  & & Population (density), \\  & NPP \\ \hline \end{tabular}
\end{table} 
Table 4: Statistics from a geographically weighted model (GWR) for the carbon gap using the explanatory variables. \begin{table}
\begin{tabular}{c c c c} \hline
**Variable** & **Value** & **Probability** & **Value** \\ \hline R\({}^{2}\) & 0.25 & & \\ Adjusted R\({}^{2}\) & 0.21 & & \\ AICc & 961.7 & & \\ Joint F-Statistic & 6.71 & Prob(\(>\)F), (4,79) DF & \(<\)0.01 \\ Joint Wald Statistic & 22.66 & Prob(\(>\)chi-squared), (4) DF & \(<\)0.01 \\ Koenker (BP) Statistic & 9.01 & Prob(\(>\)chi-squared), (4) DF & \(<\)0.01 \\ Jarque-Bera Statistic & 1.17 & Prob(\(>\)chi-squared), (2) DF & 0.56 \\ \hline \end{tabular} DF = degrees of freedom.  
\end{table} 
Table 3: The diagnostics from ordinary least square (OLS) regression. grazing showed an improving effect on vegetation (Figure 5a). The population shows a consistently negative impact on RCU, meaning that a larger population would lead to more RCU (Figure 5b). The impact from road network density shows a complicated pattern over the area (Figure 5c). The coefficient distribution of the road network suggests that the impact of roads on RCU is closely related to vegetation density; the sparsely covered vegetation, which dominates mainly the middle and west part of the study area, is more likely to present RCU.