## 1 Introduction  
Veggetation is an important link connecting the relationship between atmosphere, water, and soil at the micro level, and vegetation coverage is an important indicator for measuring the ecological environment at the macro level [1, 2]. Vegetation, as an important ecological barrier in a region, plays an irreplaceable role in regional ecological security and sustainable development. As an important ecological climate parameter, the extraction and change analysis of regional surface vegetation coverage is of great significance for revealing changes in the ecosystem environment, vegetation restoration, and reconstruction layout [3]. Especially with the support of timely satellite remote sensing data, large-scale monitoring of ecosystem and regional vegetation changes has been achieved [4, 5]. Land-use and land cover (LULC) changes reveal the spatiotemporal dynamics of surface landscapes and can also reflect the degree of disturbance to ecosystems caused by human activities [6, 7, 8]. Coastal regions are one of the most concentrated areas for human activities, with mostly favorable natural environments, abundant marine resources, convenient land-sea transportation, and a long history of development [9, 10]. At the same time, they are also places with rapid urbanization and enormous economic and environmental pressures, posing serious challenges to coastal management and sustainable development [11; 12; 13]. However, compared to other regions, coastal areas are more risk-prone in terms of floods [14], droughts [15], and sea level rise [16], thus they require sufficient attention. There is a certain interplay between vegetation coverage change and LULC changes [17; 18]. Analyzing the response of vegetation coverage change to LULC changes can help deepen the understanding of the impact of human activities on vegetation coverage change, guiding humans to achieve sustainable cities and communities through harmonious coexistence with nature. Vegetation coverage is usually expressed using the Normalized Difference Vegetation Index (NDVI) and Enhanced Vegetation Index (EVI) [19; 20], as well as the newly proposed nonlinear Vegetation Index (kNDVI) [21]. The NDVI has been used to describe vegetation cover for a long time [22; 23], as well as geographical phenomena such as aridification [24]. The NDVI quantifies the growth status of vegetation by calculating the difference between near-infrared and red bands, which can reflect the health and growth of vegetation and allow for widespread used in fields such as agriculture, forestry, and ecological environments [25; 26; 27]. The NDVI is based on the effectiveness in capturing vegetation and land-use dynamics under urban pressure, which would better support the choice of methodology. An important research perspective is that trend analysis, stability analysis, Hurst exponent analysis, and partial correlation analysis have been widely used to explore the spatiotemporal characteristics of continuous changes in vegetation cover. Research has shown that the vegetation change trends in northwest and northern China are not consistent, with the NDVI decreasing from 2000 to 2012, increasing from 2013 to 2018, decreasing in the northwest, and increasing in the east of northern China [28]. More studies have shown an increasing trend in NDVI change. The NDVI of the Shiyang River Basin in the arid northwest region shows an increasing trend of 0.034/10a in interannual variation [29]. The vegetation NDVI in Ordos City, a semi-arid region in the north, shows a clear growth trend, with 0.0075/a of the interannual growth rate [30]. The NDVI of the Shanxi section of the Yellow River Basin shows an overall increasing trend, with an annual growth rate of 1.82% [31]. Between 2000 and 2022, the vegetation coverage on the Loess Plateau increased by an average of 0.86% per year [32]. During the same period, it was also found that 73.69% and 73.86% of the vegetation conditions in the Luohe River Basin and Shaanxi Province had been improved, respectively [33; 34].