## 2 Study Area, Methods, and Data Sources
### Methodology
#### 2.3.1 Reduced Carbon Uptake by Neighborhood Analysis  
Factors affecting carbon sequestration from vegetation are grouped into the following: (1) climatic factors (e.g., precipitation and temperature), (2) non-climatic natural conditions, such as the provision of nutrients from soil, topography, and vegetation types, and (3) human-related factors ranging from vegetation disturbances to grassland management such as enclosure fencing, fertilizing, and irrigation [18]. After deducting the impact on carbon sequestration from climatic and non-climatic factors, the spatial variation in the carbon sequestration will be attributed to human-related factors only. Accordingly, the flowchart for assessing RCU is designed as shown in Figure 2a. First, the study area is segmented into areal patches considering soil (S), topography (T), and vegetation (V), so that each S-V-T patch has no internal variations in terms of soil, terrain, and vegetation types; thus, there is no significant difference in the impact on RCU from the natural conditions. Second, the impact from the climatic factors (monthly precipitation and temperature) is rectified among the locations (pixels) in each S-V-T patch using potential NPP (PNPP) from the Miami model, which is a widely applied empirical NPP model driven by climate data [29]. The PNPP reflects the impact from the climatic variables only, and the relative magnitude in PNPP reflects the contribution of the climatic factors on NPP. By analyzing the spatial variation of PNPP in the S-V-T patch, the climate-rectified NPP (NPP\({}_{\text{CR}}\)was derived from the observed NPP and PNPP. The variation of NPPCR within each S-V-T patch is attributed solely to human impact. Lastly, the within-patch variation of NPPCR is analyzed using zonal statistics to derive RCU and to locate the optimal grassland management practices (OGMPs) within each S-T-V patch. The Miami NPP model, which is widely recognized as a benchmark for NPP models, is applied to map grassland PNPP [29; 30], in the form of,  
\[\text{PNPP}=0.45\times\min\{\frac{3000}{1+e^{1.315-0.119t}},3000\times\left(1- e^{-0.000664r}\right)\} \tag{1}\]  
where \(t\) is the annual average temperature (\({}^{\circ}\)C), \(r\) is the annual precipitation (mm), and the coefficient 0.45 converts the PNPP to a carbon unit (gC m\({}^{-2}\) yr\({}^{-1}\)) from dry matter. The PNPP for arid regions increases by 1.0 gC/m\({}^{2}\) for every mm of precipitation, and productivity doubles every 10 \({}^{\circ}\)C between \(-\)10 and 20 \({}^{\circ}\)C [31]. Then, given an S-T-V patch \(g\), which contains a set of \(k\) pixels (locations) homogeneous in soil, topography, and vegetation cover type, a relative contribution (RC) index at location \(i\) reflecting the differed impact from the climatic factors is written as  
\[\text{RC}(i,g)=\text{PNPP}(i,g)-\text{PNPP}_{\text{Mean}}(g) \tag{2}\]  
where PNPPMean(g) is the averaged PNPP in \(g\), PNPP(\(i,g\)) is the PNPP at location \(i\) in \(g\), and RC(\(i,g\)) is the deviated PNPP at location \(i\) from the mean PNPP (PNPPMean(g)). A relatively more favorable climatic condition (e.g., more precipitation or temperate temperature) will promote PNPP (higher  
Figure 2: Flowchart of the study. PNPP), resulting a positive RC(_i,g_) at location \(i\) in \(g\). Conversely, less favorable climate (shortage of precipitation or high temperature) results in a negative RC(_i,g_). Clearly, the total RC(_i,g_) for all \(i\) (_i_ = 1, 2,..., _k_) makes 0--that is, \(\sum_{i=1}^{k}RC(i,g)=0\) in \(g\). To level off the difference of climatic impact within an S-T-V patch \(g\), climate-rectified NPP, or termed as NPP\({}_{\text{CR}}\), at location \(i\) in \(g\) is computed as  
\[\text{NPP}_{\text{CR}}(i,g)=\text{NPP}(i,g)-\text{RC}(i,g). \tag{3}\]  
The internal variation of NPP\({}_{\text{CR}}\)(_i,g_) in an S-T-V patch \(g\) will be attributed to human-related impact only.