## 1 Introduction  
Vegetation plays a significant role in the terrestrial-atmospheric water cycle by transpiring and has a considerable impact on energy flow and carbon cycles in the Earth's system [1]. The Leaf Area Index (LAI) is a crucial biophysical parameter of vegetation [2]. It is an essential input parameter for vegetation dynamics, phenology monitoring, crop yield estimation, and climate model [3, 4, 5, 6], and LAI can also detect changes in climate and land use/cover [6, 7]. In recent decades, numerous studies have been conducted using satellite LAI to examine vegetation's response to climate change [8; 9]. Studies by [PERSON] et al. [10] and [PERSON] et al. [11] confirmed that CO\({}_{2}\) primarily affects vegetation by modifying its stomatal resistance, resulting in fertilization effects and increased evaporation. [PERSON] et al. [12] and [PERSON] et al. [13] studied vegetation dynamics (recovery, migration, and extinction) under drought and varying climatic conditions, rainfall, and altitude. Simultaneously, these studies identified that these drivers have diverse effects on vegetation dynamics at the regional scale. [PERSON] et al. [14] and [PERSON] et al. [15] studied the distinct effects of drought on species composition and carbon sink storage in the central and western Amazon forests, revealing that deep rooting is a leading cause of greening during severe drought. [PERSON] et al. [16] and [PERSON] et al. [17] identified different driving patterns of vegetation climate under various altitude gradients of the Qinghai-Tibet Plateau, and vegetation growth in relatively high-altitude areas is determined by growing season precipitation and atmospheric CO\({}_{2}\) concentrations, while relatively low altitudes are dominated by growing precipitation. Climate change has a profound impact on vegetation dynamics, hydrological cycles, and ecosystem productivity globally [18; 19]. Consequently, changes in vegetation dynamics have a biophysical effect on the local and even global climate, resulting in positive or negative feedback on the climate system [20]. An increase in vegetation LAI has the potential to affect soil moisture, precipitation, and increase global terrestrial carbon sinks [21; 22]. Furthermore, it can alter surface albedo and evapotranspiration, leading to increased warming in northern regions and slowed warming in local tropical regions [23; 24]. Numerous studies have reported a nearly 50% increase in greening trends for global vegetation since the 1980s [25; 26; 27]. Moreover, the greening differences among various vegetation species have been widely studied. [PERSON] et al. [28] and [PERSON] et al. [29] found that forests, which have access to deeper aquifers and dominate over grasslands in bare landscaping, exhibit the main climatic factor in mixed forests, evergreen needle-leaf forests, and deciduous broadleaf forests as temperature, while grasslands are more impacted by precipitation, temperature, and solar radiation [30]. The differences between grasslands and forests in mountainous or polar regions have also received attention in recent greening [2; 31]. Shrublands and tundra at high latitudes have been prioritized over forest greening [32] in which the annual carbon increase in tundra greening is associated with water loss at the weakest, yet, it has produced positive feedback on Arctic warming [33; 34]. Most vegetation-to-vegetation difference studies rely on land cover maps [30; 32; 35]. The main land cover products to date have used random forests, decision trees, and some machine learning methods to achieve high classification accuracy and efficiency [36; 37; 38; 39]. They usually distinguish only vegetation types or provide the proportion of major vegetation types [40; 41]. However, there is a lack of research on the differences between vegetation in the corresponding vegetation functional areas.