## 1 Introduction  
In the current narrative of global climate change, ecosystems are increasingly vulnerable to various challenges. Foremost among these is drought, a critical natural phenomenon projected to escalate in frequency, duration, and intensity in the upcoming years [1]. The impacts of drought extend beyond the mere reduction of water resources, which significantly influences terrestrial ecosystems, particularly affecting vegetation growth and the stability of plant community. While a universal definition of drought remains elusive, it is typically classified into four categories: meteorological, agricultural (soil moisture), hydrological, and socio-economic droughs [2, 3]. Each category interacts with vegetation uniquely. For instance, decreased soil moisture directly hinders plant growth, whereas meteorological drought indirectly affects vegetation by altering the climatic conditions [4, 5]. The growth stage of vegetation has a significant impact on the response of NDVI. In the early growth stage, there is less vegetation coverage and lower NDVI values; As vegetation growth and coverage increase, NDVI values increase. In the mature stage, NDVI values may reach high values, reflecting high vegetation density and health status. In the middle and later stages of the lifecycle, although vegetation begins to decline, the sensitivity of NDVI values decreases due to the high vegetation coverage, making it difficult to capture vegetation growth dynamics in a timely manner. kNDVI provides improved sensitivity for capturing changes in vegetation growth stages, especially in the mid to late stages of vegetation growth. Due to its data processing method, kNDVI can more accurately reflect minor changes in vegetation growth and aging processes. Satellite remote sensing technology has become indispensable for monitoring and assessing the impact of drought on ecosystems [6]. The Normalized Difference Vegetation Index (NDVI) has been the predominant proxy index for vegetation monitoring, which leverages the spectral characteristics of vegetation in the near-infrared and red bands to detect photosynthetically active substances [7; 8]. However, NDVI may experience saturation in regions of dense vegetation or during seasonal peaks [9]. The kernel Normalized Difference Vegetation Index (kNDVI) offers a non-linear enhancement of NDVI, capturing a broader range of differences between the near-infrared and red bands [10]. This makes kNDVI more adept at estimating key vegetation physiological parameters, such as Leaf Area Index (LAI), Gross Primary Productivity (GPP), leaf and canopy chlorophyll content, and vegetation light use efficiency, as well as in applications like flux tower-level latent heat measurements [11]. Solar-Induced Chlorophyll Fluorescence (SIF) provides insights into the dynamic shifts in plant photosynthesis. Unlike indices based on vegetation reflectance, SIF directly tracks the efficiency of vegetation photosynthesis [12; 13]. However, the effectiveness of SIF varies across different ecosystems and climatic conditions. For example, its sensitivity to meteorological drought is especially pronounced in arid areas characterized by high temperatures during the growing season and low vegetation productivity [14]. While comparisons between SIF and traditional vegetation indices in drought monitoring have been conducted, the performance of kNDVI in such comparisons has been limited [15]. Thus, this study aims to address this gap by evaluating the responsiveness of SIF, NDVI and kNDVI in tracking changes in soil moisture and vapor pressure deficit, and further enhances our understanding of vegetation physiological status under water stress conditions. Statistical techniques (e.g., correlation and regression analyses) [16; 17; 18] and ecosystem simulation models [19] are commonly employed to assess vegetation response to water stress. Traditional statistical methods, however, mainly focused on linear relationships between vegetation changes and their drivers, and correlation does not necessarily denote causation [17].