## 1 Introduction
However, these modeling approaches usually lack attention to ecological and environmental factors, and the simulated urban spatial patterns are not conducive to sustainable ecological, social, and economic development. The third type of method is a combination of the first two methods, which not only considers the development needs of the urban space but also focuses on the requirements for the protection of the ecological environment; considers the requirements for economic, social, and ecological development; and is conducive to guiding the smart growth of urban land [22; 23; 24; 25]. The ecologically oriented method involves more ecological factors, but the factor weight setting is more subjective, and there is no unified standard, which is not conducive to objectively reflecting the actual situation of the regional ecological environment. The remote sensing ecological index (RSEI) is entirely based on the use of remote sensing technology to extract the ecological factors, so it can be used to monitor the regional ecology and quickly identify ecologically sensitive areas. It has the advantages of easy access, timeliness, and avoidance of the uncertainty caused by human intervention [26], and it has been successfully applied. Regarding the urban growth simulation models, the CA-Markov model lacks consideration of the spatial distribution changes. The CLUE-S model calculates the influences of the driving factors on land-use changes using the logistic regression method, which only takes into account the linear relationships between the individual variables [27]. The FLUS model adds adaptive inertia coefficients and a competition mechanism, so it can simulate land-use changes more realistically; however, it has the disadvantage that it is only trained based on the land class samples from the first-phase land use data and lacks analysis of historical land-use changes [28]. The patch-generating land use simulation (PLUS) model overcomes the shortcomings of the FLUS model and provides a better explanation of the land-use change mechanism through the use of two-phase land-use data. In addition, the PLUS model combined with the CA model and the patch-generating simulation strategy is more effective in simulating complex changes in multi-type land classes [29]. Therefore, this study proposes a RSEI-PLUS-based method to delineate the UGB. Previous studies have focused on less urban tropical island regions, which contain many important natural resources and are indispensable to the sustainability of global ecosystems. In addition, due to the closed nature of islands and their limited resources and environmental carrying capacity, the ecology of islands faces great challenges in the context of rapid urbanization and population growth. Sanya is a famous international tropical coastal tourist city located on the southernmost tip of Hainan Island, China. Driven by the development of tourism, Sanya has experienced rapid urban expansion and population growth in recent decades. In the process of urban development, a series of ecological and environmental problems have emerged, such as damage to or destruction of precious tropical rain forests, fragile mountains, key ecologically fragile areas in the coastal zone (coral reefs), and rare freshwater ecosystems. Moreover, the ecological security and resource carrying capacity have declined, threatening the sustainable development of the city's ecology, society, and economy [30]. Therefore, how to ensure the ecological safety of this region during the process of urban development is a problem that urgently needs to be solved. There is an immediate need to coordinate the contradiction between ecological protection and urban spatial growth, and ensure the region's ecological safety and the sustainable development of cities. Delineation of UGB scientifically and reasonable, is one of ways to solve the problem, and it is also the focus of current territorial space planning in China.