## 1 Introduction  
Drought is a phenomenon manifested by insufficient water resources that fail to meet the growth requirements of both humans and plants [1, 2]. It is a severe natural disaster impacting agricultural production in China [3]. The mechanisms underlying this natural disaster are complex, and its effects are far-reaching [4]. Drought is commonly categorized into four specific types: meteorological, agricultural, hydrological, and socioeconomic drought [5]. Agricultural drought develops when soil moisture is insufficient to sustain plant growth [6], which can be reflected by soil moisture content and the condition of plant growth [7]. Given the strong correlation between agricultural drought and crop production, improving the accuracy of agricultural drought monitoring is essential [8]. Agricultural drought directly influences crop development, resulting in decreased crop yields, substantial agricultural losses, and heightened threats to food security [9, 10, 11]. To monitor agricultural droughts more accurately and mitigate the substantial losses in agriculture caused by frequent droughts, Kogan developed a new drought index known as the vegetation health index (VHI), which combines two key components: the vegetation condition index (VCI) and the temperature condition index (TCI) [12]. Utilizing satellite remote sensing data, the VHI was designed to sensitively reflect the health of vegetation under drought [13; 14]. The VHI not only reflects the drought status of vegetation in a specific region but also indirectly indicates the overall health of vegetation [15]. By integrating various factors such as regional soil characteristics, biological conditions, topography, and climate, the VHI offers a comprehensive approach to drought assessment. For instance, [PERSON] et al. employed this index to characterize drought conditions in the North China Plain [16]. [PERSON] et al. [17] applied the VHI to monitor several severe drought events in global arid regions, with results showing that VHI performs excellently well in monitoring terrestrial systems. [PERSON] et al. compared the standardized precipitation index (SPI) and the VHI, revealing that the VHI effectively captures changes in soil relative humidity and could accurately identify the occurrence of drought [18]. [PERSON] et al. [19] utilized the VHI to monitor agricultural drought in the United States, Mexico, Brazil and China and expanded the application scope of the VHI in agricultural drought monitoring from regional to global [19; 20]. Therefore, the VHI has been widely used in the field of vegetation drought monitoring, providing valuable insights into the temporal and spatial distribution of drought across various regions [6]. VHI is primarily based on two key assumptions: (1) low normalized difference vegetation index (NDVI) and high land surface temperature (LST) indicate poor vegetation health, while high NDVI and low LST signify good vegetation health. (2) VCI and TCI are assumed to contribute equally to VHI based on empirical weights [6; 12; 21; 22]. Many studies have assumed that VCI and TCI each contribute equally (0.5) to VHI for drought monitoring [21; 22; 23]. However, this assumption has significant limitations in practical applications and may increase errors in drought assessments, thereby affecting the accuracy of the VHI in drought monitoring [24]. In reality, the contribution value of VCI and TCI to VHI is greatly influenced by regional location, climate conditions, and vegetation types [16; 17; 25]. On one hand, VCI has a more significant impact on VHI in arid regions, where water availability is a primary constraint. Conversely, TCI exerts a greater influence in areas where temperature is the main limiting factor [22; 26]. However, [PERSON] et al. discovered the LST dataset that was developed at Princeton University cannot be updated regularly, which may lead to deviation in monitoring results for specific areas [27].