## 1 Introduction  
Climate change [1, 2, 3, 4] and direct human interference [5, 6, 7, 8] have changed terrestrial vegetation dynamics greatly. Significant efforts have been undertaken to monitor these changes and to understand the mechanisms driving them, so as to better understand and project the Earth system [9]. There have been numerous studies investigating vegetation dynamics and their driving factors at various spatial and temporal scales (e.g., [10, 11, 12, 13, 14]). Among these, the dynamics of vegetation in semi-arid regions are of particular interest [15, 16, 17], for several reasons. First, ecosystems of semi-arid regions are easily affected by climate change and human interference [18, 19, 20, 21, 22, 23]. Second, because vegetation in semi-arid landscapes has large interannual variability compared to in other systems, it is especially important to understand these dynamics in order to clarify their roles in the global carbon cycle [24, 25]. Third, the dynamics of vegetation in semi-arid regions affect the availability of water resources [26, 27]. Fourth, variations of vegetation in semi-arid regions have the potential to cause feedback to climate warming through changes in albedo and evapotranspiration [28, 29, 30, 31, 32]. Northwest China is one of the largest semi-arid regions in the world [33], with an area of 790,000 km\({}^{2}\), about 8% of the land area of China. Multiple ecological engineering projects are carried out here, such as the Three-North Shelter Forest program [34] and the Grain for Green project [35]. How the vegetation evolves in this semi-arid region not only affects the local environment and socio-economic development, but also has implications for the carbon cycle [6, 24], water cycle [27, 36], and energy exchange [29], at the local, regional, and global scales. Thus, it is informative to investigate the vegetation dynamics in semi-arid regions of Northwest China, their drivers, and their environmental consequences. [PERSON] et al. [8] assessed the global interannual dynamics of leaf area index for the period from 2000 to 2017, claiming that China and India lead in the greening of the world through land-use management. [PERSON] et al. [28] suggested a weakening relationship between interannual temperature variability and northern vegetation activity. The research was based on satellite remote sensing and reanalysis meteorological data from the Climate Research Unit, University of East Anglia [37]. The spatial resolution of this investigation was 0.5\({}^{\circ}\)\(\times\) 0.5\({}^{\circ}\), which is very coarse for the highly heterogeneous landscapes of Northwest China. As a consequence, in that study, some insights about the relationship between vegetation and temperature might have been missed. [PERSON] et al. [2] suggested that increased vapor pressure deficit reduces global vegetation growth, while [PERSON] et al. [38] suggested that soil moisture dominated water stress on ecosystem production. As for the methods for deriving the trends of vegetation greenness, the ordinary least squares method and [PERSON]'s method [39] have usually been applied. There are some gaps in the previous literature. First, vegetation dynamics have not been assessed by land cover types in the semi-arid regions of Northwest China. Vegetation dynamics differ by land cover type, and an analysis of the differences could lead to a better understanding of the nature of these vegetation changes. Second, a detailed analysis of the relationship between interannual vegetation change and air temperature, using satellite remote sensing as well as direct measurements from meteorological stations, is missing. Third, limited work has been done to compare the effects of precipitation and atmospheric vapor pressure deficit (VPD) on the interannual dynamics of vegetation, specifically in semi-arid regions. Air temperature and vapor pressure deficit impact the vegetation photosynthesis rate through their respective mechanisms.