## 2 Materials and Methods
### Model and Method  
#### 2.3.1 NEP Estimation Model  
Net primary productivity (NPP) is the portion of photosynthetic products fixed by plant photosynthesis minus the portion consumed by the plant's own respiration. While the ecosystem carbon sink also includes the respiration of soil organic matter, the net ecosystem productivity (NEP) is the net carbon produced by terrestrial ecosystems, which serves as an important indicator of the terrestrial ecosystem carbon sink. When the influence of various disturbance factors is ignored, NEP is used as the net carbon amount of the terrestrial ecosystem to characterise a carbon sink. Its calculation formula is as follows:  
\[NEP(x,t)=NPP(x,t)-R_{h}(x,t) \tag{1}\]  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Data Types** & **NPP** & **Meteorological Data** & **Topographic Data** & **Land Use Data** \\ \hline \multirow{8}{*}{Data Sources} & & Temperature and & Digital Elevation & Derived from three \\  & & precipitation data & Model (DEM) data & phases of land use data \\  & & from the National & from NASA’s SRTM & for 2000, 2010 and 2020 \\  & MODIS Terra NPP & Earth System Science & with a spatial & at a resolution of 1 km \\  & data from the NASA & Data Centre\({}^{2}\), with a & resolution of 30 m; & from the Centre for \\  & Data Centre\({}^{1}\) & temporal resolution & slope gradient and & Resource and \\  & (MOD17A3 HGF) & of 1 m and a spatial & slope aspect data & Environmental Science \\  & & resolution of 1 km, & calculated based on & and Data of the Chinese \\  & & both spanning the & the elevation data. & Academy of Sciences. \\ \cline{1-1}  & & period 2000–2021. & & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Research data and sources.  
Figure 2: Location and main vegetation types of the study area.  
where \(NEP\) denotes the net ecosystem productivity of vegetation, \(x\) denotes the picture element, \(t\) denotes time, and \(t\) is measured in years. Similarly, \(NPP(x,t)\) represents the net primary productivity of vegetation in picture element \(x\) in year \(t\). When NEP(x,t) > 0, it means that the carbon fixed by vegetation is greater than the carbon emitted by soil microbial respiration, which manifests as a carbon sink, and vice versa. Soil microbial respiration estimation models have been widely used in the calculation of regional vegetation carbon sinks. \(R_{h}\) indicates the consumption of microbial respiration in soil. Therefore, the estimation model of soil microbial respiration was also used in this study with the following formula:  
\[R_{h}(x,t)=0.22(Exp(0.0913T(x,t))+\ln(0.3145R(x,t)+1))\times 30\times 0.465 \tag{2}\]  
where \(T(x,t)\) and \(R(x,t)\), respectively, represent the average temperature and precipitation of picture element \(x\) in year \(t\).  
Through comparative analysis with similar studies on carbon sinks in the Taihang Mountains, the NPP data used in this paper based on the MODIS Terra NPP data (MOD17A3 HGF) provided by the NASA Data Center are in the same range as some other scholars' estimated NPP data. In addition, the spatial distribution of vegetation carbon sinks in the Taihang Mountains estimated by many scholars using the same model is high in the middle west and low in the southeast, and the decreasing trend from west to east is basically the same as the results obtained from the analysis of MODIS data. Therefore, the data used in this paper for the study of vegetation carbon sinks in the Taihang Mountains have high credibility.