## 2 Study Area, Data Sources, and Methodology
### Methodology
#### 2.3.1 Mapping NPP to Indicate Carbon Uptake from Urban Vegetation  
In the first phase, net primary productivity (NPP) was most commonly taken as the proxy for vegetation carbon capture. Development in remote sensing technology combined by ecological models has allowed timely NPP mapping over a large region. This study integrated two models to map NPP in GGA: the Carnegie-Ames-Stanford Approach (CASA) for croplands, settlements, and rangelands, and 3-PGS (Physiological Principles Predicting Growth with Satellite Data) for forests. First, the CASA model is one of the NPP models that have been widely applied to map large-scale NPP with only a few land cover and climate variables inverted by remote sensing imagery. NPP reflects the absorbed photosynthesis active radiation (APAR) and light use efficiency in turning energy into biomass from vegetation, in the form of:  
\[NPP(x,t)=APAR(x,t)\times\epsilon(x,t) \tag{1}\]  
and  
\[APAR(x,t)=SOL(x,t)\times FPAR(x,t)\times r \tag{2}\]  
where \(\epsilon(x,t)\) is light utilization; \(x\) represents the location; and \(t\) denotes the month for the model. \(SOL\) (\(x\),\(t\)) is solar radiation location \(x\) and month \(t\)) of each year. \(FPAR(x,t)\) is the fraction of incoming photosynthetically active radiation by the vegetation cover. \(R\) is the proportion of total solar radiation and assigned to be 0.5 as recommended by previous study [52]. \[FPAR(x,t)=\frac{(NDVI(x,t)-NDVI_{i,\min})}{(NDVI_{i,\max}-NDVI_{i,\min})}\times (FPAR_{\max}-FPAR_{\min})+FPAR_{\min} \tag{3}\]  
where \(NDVI_{i,\max}\) and \(NDVI_{i,\min}\) are the maximum and minimum \(NDVI\), respectively, for the \(i\)th (I = #2, #5, #7, and #11, Table 1) vegetation cover class; \(FPAR_{\max}\) and \(FPAR_{\min}\) are the maximum and minimum proportion of incoming photosynthetically active radiation absorbed which are set to be 0.950 and 0.001, respectively. Computation of light use rate \(\epsilon(x,t)\) is detailed in the literature [52]. As CASA outputs monthly NPP, the NPP at the monthly scale output is then summed up to derive yearly NPP. In addition to CASA, the 3-PGS model was applied for NPP in vegetation productivity in forests. 3-PGS is a modified version of 3-PG (Physiological Processes Predicting Growth), a well-known process-based carbon balance model designed to predict the growth, diameter distribution, and annual mortality for forest stands [53]. The 3-PGS model takes the use of satellite data in the model framework to assess productivity at a range of forest sites [54; 55; 56]. The 3-PGS model has been applied to several projects; its performance was reported to be extremely encouraging (r\({}^{2}\) = 0.93, in comparison to field measurement) for forest ecosystem [54]. NPP computation takes the form of:  
\[NPP(x,t)=C_{pp}\cdot GPP(x,t)=C_{pp}\cdot APAR(x,t)\cdot\epsilon_{\max}\cdot f _{x,t} \tag{4}\]  
where \(x\) and \(t\) indicate the location and month of a year, \(GPP(x,t)\) is the gross primary productivity for location x and time t. \(C_{pp}\), a conversion coefficient for forests from GPP to NPP and without calibration data, is assigned to be 0.47. \(\epsilon_{\max}\) is the max conversion rate from light energy to biomass, which is 1.80 gC\(\cdot\)MJ\({}^{-1}\). \(f_{x,t}\) is the coefficient of the overall environmental constraints. \(APAR(x,t)\) is the absorbed photosynthetically active radiation in forest vegetation which is modeled using:  
\[APAR(x,t)=PAR(x,t)\times FPAR(x,t)=PAR(x,t)\times(\mathbf{a}\times NDVI(x,t)+b \tag{5}\]where \(PAR\) is effective photosynthetically active radiation; \(FPAR\) is the fraction absorbed from PAR; \(NDVI\) reflects vegetation greenness and is positively related to FPAR; and \(a\) and \(b\) are coefficients which are empirically set to be 1.24 and \(-0.168\). The complete protocol and processes for the 3-PGS model are detailed in the literature [54; 55; 56].