## 2 Methodology
### Establishment of the Landscape Visual Evaluation Method  
By optimizing the visibility analysis algorithm, this study achieves a transformation from merely making calculations for the visible area to the quantitative evaluation of the quality of visually experiencing the landscape considering parallax. However, comprehensively evaluating the landscape visual effects requires integrating influencing factors. This study selects quantitative indicators (e.g., visible area) and qualitative indicators (e.g., landscape water system distribution, number of landscape resources) closely related to landscape visual satisfaction. Then, by employing the analytic hierarchy process (AHP) to assign weights to these indicators, an integrated landscape visual evaluation method possessing both quantitative computation and qualitative assessment is finally established. This method not only considers the quantified effect but also comprehensively evaluates the qualitative factors affecting the landscape quality, and its scientificity and functionality have been validated in subsequent case studies. (1) Determination of influence indicators  
The Landscape Visual Management System (VMS) developed by the United States Forest Service (USFS) suggests that the spatial relationship between observers and landscapes can affect their visual experience. In 1995, the USFS updated the VMS to the Landscape Management System (SMS), adding terrain features, river systems and cultural features as important indicators affecting the visual quality of the landscape [18]. We select the indicators that affect the landscape visual assessment method based on the SMS in this paper. We can quantitatively analyze the impact of the terrain features on the visual experience within the visible area, which is affected by the vertical angle and relative slope. The landscape water system is divided into river system I, river system II and III river system, according to their river flow and size. The more landscape river systems tourists see and the higher the level, the more comfortable their visual experience will be [19; 20]. The number of landscape resources can reflect the cultural characteristics of different regions, including natural and cultural landscapes. Tourists in areas with rich landscape resources are more likely to resonate with the scenery and history, enhancing their visual experience [21; 22] ([PERSON] 2020; [PERSON] 2010). Overall, we propose a hierarchical landscape evaluation system, shown in Figure 7. The primary indicators include the visible area, landscape resources and landscape water systems, and the secondary indicators are composed of the vertical angle, relative slope, natural landscape, river system I, river system II and river system III. Figure 7: The landscape visual evaluation system. Calculation of the indicator weights  
When determining the weight of each indicator, evaluation using the traditional methods is limited by subjective wishes or qualitative conditions, so the result is not ideal. To solve this problem, [PERSON] et al. [23] proposed consistent matrix discrimination, which compares two factors with each other as much as possible to reduce the difficulty of comparing factors with different properties and improve accuracy. Therefore, in the evaluation process, it is necessary to compare each indicator with each other, and then determine the importance levels based on the importance of each indicator. In this process, \(\text{a}_{ij}\) denotes the results of the comparison of the importance of element \(i\) and element \(j\). Table 1 lists nine importance levels and their assigned values. The matrix formed according to the results of pairwise comparison is called the judgment matrix. The judgment matrix has the following properties:  
\[\text{a}_{ij}=\frac{1}{a_{ji}} \tag{14}\]  
For each obtained weight, a consistency test is required. We use the CR (consistency ratio) to verify the consistency of the weight.