## 3 Methodology
### Ecosystem Service Value Assessments
#### 3.1.2 Revision of the ESV  
Considering that an equivalent table is established for the whole China terrestrial ecosystem and only statically reflects the average ESV [27; 58], targeted spatio-temporal revisions are needed when using it.  
By synthesizing comparisons from earlier representative research and considering the TRHR's characteristics, we created the revised indicators of three dimensions--ecological quality, carbon emission and natural landscape aesthetics. Firstly, RSEI is used to reflect the spatial heterogeneity of ecosystems and characterize the influence of ecological quality in TRHR. It can capture the ecological quality rather than primal ESV. Secondly, the CSI is constructed to be relevant to ecosystems' capacities to cope with climate change and carry out carbon modification, which can complement the shortcomings of the primitive ESV. Lastly, most of the previous studies only considered the TRHR's ecological characteristics, ignoring its intangible cultural values. Thus, considering the scientific and cultural characteristics of the TRHR, the LAI is constructed to highlight the value of the TRHR's cultural services. In summary, these criteria represent the manifestation of three major components of the ESV (ecology, carbon emissions, and cultural characteristics).  
(1) Remote Sensing Ecological Index.  
Ecosystem quality is more accurately measured [2] based on the RSEI proposed by [PERSON] [59]. Meanwhile, the relevant literature shows that RSEI demonstrates superior performance in the TRHR [60]. It is calculated as follows:  
\[\text{RSEI}=\text{f}(\text{Greenness},\text{Wettness},\text{Heat},\text{Dryness}) \tag{2}\]  
where the Greenness, Wetness, Heat, Dryness are represented by different components assessed using remote sensing data. The RSEI was obtained by fusing the four major components and extracting the first principal component using Principal Component Analysis [61].  
(2) Carbon Sink Revised Index.  
As a crucial carbon-sensitive area of China's ecosystem, the TRHR has a vital carbon sink function. We qualified the CSI using Net Ecosystem Productivity (NEP) and Vegetation Fraction Coverage (VFC) indicators, which measure the level of carbon balance and can more reasonably highlight the value of carbon sinks provided by the TRHR.  
\[CSI_{i}=\frac{1}{2}\times(\frac{NEP_{i}}{NEP_{mean}}+\frac{VFC_{i}}{VFC_{ mean}}) \tag{3}\]_CSI_ is the carbon sink revised index; \(NEP_{i}\) is the NEP of study unit \(i\)[44]; \(NEP_{mean}\) is the average NEP of the study area; \(VFC_{i}\) is the vegetation cover of study unit \(i\); and \(VFC_{mean}\) is the average vegetation cover of the study area. The explicit illustration of the expression of NEP can be found in [62], and specific descriptions of VFC are based on [52]. The calculation result for NEP is similar to the previous studies.  
(3) Landscape Aesthetics Index.  
A quantitative description of landscape patterns can effectively explore the internal mechanism of ecosystem action to reveal the ESV in the study area better. According to former research [63], [PERSON]'s diversity index (SHDI), the Euclidean distance to places of interest, and naturalness were used to conduct the LAI indicator. The formula is presented below:  
\[LAI_{i}=\frac{1}{3}\times(NT_{i}+NS_{i}+SHDI_{i}) \tag{4}\]  
where \(LAI_{i}\) is the LAI value of grid cell \(i\); \(NT_{i}\) is the naturalness of grid cell \(i\)[64]; \(NS_{i}\) is each grid's Euclidean distance to places of interest in TRHR; and \(SHDI_{i}\) is the normalized SHDI of grid cell \(i\). All three components were normalized to 1-100.