## 2 Study Area, Methods, and Data Sources
### Methodology
#### 2.3.1 Reduced Carbon Uptake by Neighborhood Analysis
Locations presenting the highest (target) NPP\({}_{\text{CR}}\) in the S-T-V patch are under optimal grassland management practices (OGMPs); conversely, locations showing relatively lower NPP\({}_{\text{CR}}\) in the S-T-V patch suggest that they experience RCU. By copying the OGMPs to locations presenting low NPP\({}_{\text{CR}}\), it is expected that NPP\({}_{\text{CR}}\) can also be promoted to the target level given that all the locations in an S-T-V patch have similar natural (or non-climatic) environments. Here, the target level of NPP\({}_{\text{CR}}\) for each S-T-V patch is computed by neighborhood analysis [32], which is a spatial analytical routine finding a zonal statistic (e.g., maximum value) from a set of NPP\({}_{\text{CR}}\) inputs for locations within a neighborhood, i.e., the S-T-V patch. Rather than computing a statistic of the maximum value from the input data, we decided on a zonal statistic of 95% percentile (95%PCT), which may provide a more robust estimation of the target NPP level within each S-T-V patch considering possible noise in the patch segmentation [18]. Here, 95%PCT corresponds to an NPP\({}_{\text{CR}}\) value such that NPP\({}_{\text{CR}}\) out of 95% cases is below the value, while 5% of the cases are above it. Therefore, by referencing 95%PCT as the target NPP\({}_{\text{CR}}\) level, the RCU at any location \(i\) in an S-T-V patch \(g\) can be computed as,  
\[\text{RCU}_{95\%PCT}(i,g)=\text{{{{{\text{{{{{{{{\text{{\  
indicates there are underlying mechanisms explaining RCU clustering. Analytical models can be applied to understand the impact from the selected explanatory variables on RCU. Ordinary least square (OLS), or a global regression model, was adopted first to reveal the relationship between RCU and the selected variables without reflecting the possibly spatial varied patterns in the relationships by the function,  
\[y=\beta_{0}+\sum\
olimits_{k=1}^{p}\beta_{k}\cdot x_{k}+\varepsilon \tag{5}\]  
where \(y\) is the observed outcome, \(\beta_{0}\), \(\beta_{1}\),..., \(\beta_{\text{P}}\) are the fit model coefficients, \(x_{k}\) are explanatory variables \(k\) (\(k\) = 1, 2,..., \(p\), where \(p\) is the number of explanatory variables), and \(\varepsilon\) is the residual with zero mean and homogenous variance \(\sigma^{2}\). Geographically weighted regression (GWR) is a local regression model that can estimate parameters to vary across regions to accommodate potential spatial dependencies [38]. A GWR model takes the form of,  
\[y_{s}=\beta_{0}(s)+\sum\
olimits_{k=1}^{p}\beta_{k}(s)\cdot x_{k,\ s}+ \varepsilon_{s} \tag{6}\]  
where \(y_{s}\) is the response variable (RCU) at location \(s\), \(x_{k,s}\) and \(\beta_{k}(s)\) (\(k\) = 0, 1, 2,..., \(p\), and \(p\) is the number of variables) are the observed value and spatially varied coefficient for the \(k^{\text{th}}\) variable at \(s\), respectively, and \(\varepsilon_{s}\) is a random error at location \(s\). Compared to the global OLS, all the parameters (coefficients) and the error term (\(\varepsilon\)) in the local regression model (GWR) are location dependent and vary at different locations. Gaussian kernel using corrected Akaike Information Criterion (AICc) to determine the optimal number of neighbors was specified for the model. Global Moran's \(I\) on the regression residuals was applied to test if they are spatially clustered or random, which is a necessary step to verify that the GWR model is correctly specified. Multicollinearity or strong correlation among the input variables should be avoided in either OLS or a local model. The variance inflation factor (VIF) and condition number (CN) are indicators for checking global multicollinearity and local multicollinearity, where a VIF greater than 7.5 in OLS or CN greater than 30 indicates multicollinearity [39; 40]. An adjusted coefficient of determination (adjusted R\({}^{2}\)) and AICc can be taken to decide whether the global or local model interprets the data better.