## 1 Introduction
On the other hand, the type of vegetation is also a crucial factor influencing the contribution values of VCI and TCI to VHI. Consequently, VHI calculated using the same weights may not accurately reflect the drought conditions across different vegetation types [6; 28]. The above research shows that the equal weight values of VCI and TCI ignore the differences in climatic conditions and vegetation types in different regions, leading to significant discrepancies in drought monitoring for different regions and various vegetation types [6; 16]. Some scholars have made many efforts in adjusting the contribution of VCI and TCI to VHI. For instance, to analyze the relationship between agricultural drought and grain production in Morocco, [PERSON] et al. optimized the weights of VCI and TCI to VHI by using anomaly data from crop yield and discovered that TCI has a greater weight [29; 30]. [PERSON] et al. discovered that when the weight distribution ratio of VCI to TCI was 7:3, the VHI index effectively combined the strengths of both indices, making it more advantageous for monitoring agricultural drought in the midstream and downstream of the Yangtze River [31]. However, [PERSON] et al. calculated the contributions of VCI and TCI based on the self-calibrating Palmer Drought Severity Index (scPDSI) and discovered that in most parts of the world, assigning a greater weight to TCI than to VCI significantly improved the drought monitoring accuracy of VHI [6; 32]. The multi-scale drought index can be used to evaluate the contribution of VCI and TCI to VHI. SPEI, proposed by [PERSON] et al. in 2010 [33], is a drought indicator that not only considers the combined effects of temperature and precipitation [34] but also incorporates multi-time scale and standardization features [35]. This makes SPEI particularly suitable for drought monitoring in both humid and arid regions [36; 37]. Therefore, SPEI is often employed to calibrate other drought indices [38]. For instance, [PERSON] et al. used the 3-month SPEI during the growing season to calibrate the optimal scale drought condition index (OSDCI) [36]. [PERSON] et al. applied SPEI to calibrate the drought severity index (DSI) [39]. [PERSON] et al. employed SPEI to enhance the comprehensive drought index (CI), resulting in an improved comprehensive drought index that effectively identifies most of the significant historical droughts in Hubei Province [40]. The Yellow River Basin (YRB) is essential for sustaining production and livelihoods in the arid and semi-arid regions of northern China [41; 42; 43]. In recent years, climate change and human activities have intensified drought conditions in the YRB, posing significant challenges to the region's ecological environment, agricultural production, and socioeconomic development [44; 45; 46]. Simple and user-friendly agricultural drought indices such as VHI can be adapted to diverse climatic conditions, facilitating effective drought monitoring across different geographical regions [7; 47; 48]. However, the existing studies primarily utilize the VHI based on empirical weights to assess drought conditions in the YRB, which diminishes the accuracy of the VHI index in monitoring agricultural drought to some extent. Therefore, enhancing the accuracy of agricultural drought monitoring in the YRB is essential. This study seeks to enhance the accuracy of VHI in monitoring agricultural drought by identifying the optimal timescale through maximizing the correlation between SPEI at various timescales and VHI. Using the SPEI at the optimal time scale as a reference, VHIopt is calculated based on the optimal contribution values of VCI and TCI. Based on VHIopt, the trend of agricultural drought development in the YRB from 2021 to 2023 was analyzed.