## 1 Introduction  
With the rapid growth of tourism in China, the visual experiences of visitors at tourist sites significantly impact the overall quality of these sites [1]. We can thus utilize approaches to landscape visual assessment, using comprehensive analysis of the visible area, landscape water system distribution and number of landscape resources, to evaluate aesthetic qualities and provide scientific grounds for planning and the protection of landscapes. In the domain of analytical systems for landscape visibility, abundant research has been conducted by scholars in China and abroad. For instance, [PERSON] et al. [2] applied the analytic hierarchy process (AHP) to assessing the quality of the landscape in five housing quarters in Yangling, China, considering functionality, eco-friendliness and attractiveness. Meanwhile, [PERSON] et al. [3] devised questionnaires using the Semantic Differential (SD) method, evaluated the visual qualities of historical building blocks and constructed an assessment structure using the Factor Analysis (FA) method. [PERSON] [4] presents a methodology for assessing the visual aesthetic value of landscapes, which is analyzed with respect to a highly environmentally diverse fragment of the Malopolska Upland (central Poland). This methodology provides a versatile platform for evaluating nature and landscapes, as well as for practical applications such as nature preservation, tourism development and spatial planning. However, by relying primarily on expert surveys, these methods lack objectivity and rigor. The imperative task of transforming subjective visual perceptions into computable data is essential to enabling quantitative evaluation of the landscape visibility and enhancing enjoyment for tourists.  
Visibility is a prerequisite for judging whether a view of the landscape exists or not [5], which can be calculated using visibility analysis algorithms. Traditional algorithms like R3, R2 and XDraw have their respective strengths and weaknesses--R3 features high precision yet a lengthy computation time, while R2 and XDraw are more efficient but less accurate [6]. In recent years, visibility analysis has been widely applied across various domains, including travel route planning [7; 8], scenic resource allocation and conservation [9; 10; 11; 12] and site selection for fire lookout towers [13; 14]. Different contexts require tailored optimization strategies. The existing improvements have centralized around speed and precision, as exemplified by [PERSON] et al. [15], who combined parallel computing with visibility algorithms for geographic data processing, and [PERSON] et al. [6], who proposed the PDERL (Proximity-Direction-Elevation Reference Line) algorithm by establishing visibility algorithms in partial differential equation spaces, achieving precision close to R3 and efficiency comparable to XDraw. However, from tourists' perspective, the current algorithms can only determine whether landscape features are visible, without quantitatively assessing their viewing experiences. Prior studies like that undertaken by [PERSON] and [PERSON] [16] defined distance zones to indicate decaying clarity, and [PERSON] [17] adopted fuzzy set theories to model atmospheric impacts across distances. Yet, vertical influences on viewing experiences remain insufficiently addressed.  
This study aims to quantify tourists' landscape viewing experiences and construct an objective assessment framework for scenic visibility. To achieve this goal, the parameters in the visibility analysis are optimized from horizontal and vertical perspectives, incorporated with influential factors like aqueous distributions and the available resources. An enhanced approach is thereby established, integrating optimized visibility algorithms and the analytic hierarchy process (AHP) for the quantitative evaluation of landscape visibility. Its validity and accuracy will be evidenced using the case study of Fenghuang Town, Shaanxi Province, China, whereby sightseeing tower sites are selected based on the proposed method.