## 2 Methods and Data Sources
### Methods for Estimating Carbon Sinks in Semic Areas
#### 2.2.2 Calculation Method  
Estimation of national scenic area vegetation carbon sinks needs to be limited to the scope of natural scenic areas. Therefore, this study first uses ArcGIS 10.2 to conduct  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**PUOT** & **Sightsee** & **Lei Vac** & **BT** & **VRF** & **Others** \\ \hline CAEF (g/per) & 417 & 1670 & 591 & 786 & 172 \\ \hline \hline \end{tabular} Note: The calculation parameters for carbon emissions of different tourism purposes are derived from existing literature studies [11; 12; 13; 14; 15; 16], and the number of domestic and international tourists in each province is obtained from the Statistical Yearbooks of respective provinces for the years 2020-2021. PUOT (Purpose of the tour); Sightseeing); Leis Vac (leisure vacation); BT (Business travel); VRF (visiting relatives and friends).  
\end{table}
Table 3: Calculation parameters of carbon emissions for different tourism purposes.  
kernel density analysis on the distribution of natural scenic areas nationwide. Based on the density classification, the distribution of scenic areas is divided into \"clustered areas\" and \"non-clustered areas,\" and the scope of the \"clustered areas\" is extracted. Kernel density analysis calculates the density distribution of point elements within a specified radius from each grid center, resulting in a density distribution map of features within the region.  
The specific formula is as follows:  
\[f(x)=\frac{1}{nh^{2}}{\sum_{i=1}^{n}{K\left(\frac{x-x_{i}}{h}\right)}} \tag{5}\]  
In this equation, _f(x)_ represents the kernel density equation, where h is the radius of the search window; \(n\) is the number of points falling within the threshold range, and \(K\) is the weight function. When the bandwidth is determined, the closer the distance to the core, the higher the weight value.  
The vegetation carbon sink value in national scenic areas is calculated as the difference between net primary productivity (NPP) and soil microbial respiration (\(R_{H}\)). Considering that MODIS NPP data are already calculated based on the light use efficiency model, this study directly uses MODIS NPP data without further calculation. By subtracting NPP data from \(R_{H}\), the net ecosystem productivity (NEP) is obtained as an indicator of vegetation carbon sinks.  
The formula for calculating the vegetation carbon sink value is as follows:  
\[NEP=NPP-R_{H} \tag{6}\]  
In this equation, \(R_{H}\) represents soil microbial respiration, which is related to the types and quantities of microorganisms in the soil, as well as plant root exudates [36]. External climate conditions also have an impact on soil microbial respiration. This study adopts the research findings of [PERSON] [37] and others, who established a regression model between temperature, precipitation, and carbon emissions to estimate the distribution of soil microbial respiration.  
The formula for calculating soil microbial respiration is as follows:  
\[R_{H}=0.22\times(Exp(0.0913T)+Ln(0.314R+1)\times 30\times 46.5\%) \tag{7}\]  
where \(T\) represents temperature (\({}^{\circ}\)C) and \(R\) represents precipitation (mm).