## 1 Introduction  
At present, global climate change is posing unprecedented challenges. As global climate change intensifies, drought, a significant natural disaster, has garnered considerable attention from experts both domestically and internationally [1,2]. Drought not only has a significant impact on agricultural production, but also may lead to ecological degradation, water shortages, and a series of environmental and social problems. Generally, drought can be divided into meteorological drought, agricultural drought, hydrological drought, socioeconomic drought, and other types according to their characteristics and impacts [3]. Among them, ecological drought is an emerging research hotspot. By examining the spatiotemporal characteristics of ecological drought and the transition mechanisms from meteorological to ecological drought, we can more effectively delineate and describe the regional vegetation growth patterns and the overall status of drought in the area. Meteorological drought is the basis for the formation and development of other drought types [4]. It explains the formation of drought from a macro perspective, often focusing on the meteorological drought caused by global warming [5], abnormal atmospheric circulation [6], thermal anomalies [7], and aerosols [8]. Meteorological drought is defined by the meteorological drought index, which typically comprises single-factor and multi-factor assessments, with precipitation being the primary determinant influencing drought conditions. The single-factor drought index only considers precipitation, such as the Munger drought index [9], Standardized Precipitation Index (SPI) [10,11], positive and negative anomaly drought index [12], etc. These single-factor indices are relatively easy to calculate. However, meteorological drought indices that only consider a single factor have many limitations in the practical application processes. The multi-factor meteorological drought index accounts for the primary determinant of drought (precipitation) as well as the effects of additional variables including temperature, evaporation, and antecedent precipitation. This category includes the Palmer Drought Severity Index (PDSI) [13], Meteorological Comprehensive Drought Index (MCI) [14], and Standardized Precipitation Evapotranspiration Index (SPEI) [15]. Among them, the Standardized Precipitation Evapotranspiration Index (SPEI) is the most widely used [16]. Researchers have fully studied the spatiotemporal evolution characteristics of drought by using different meteorological drought indices, and many studies have revealed the changing trend of drought in the Yellow River Basin, providing certain references for drought prevention and control in the area [17, 18, 19]. Nonetheless, the meteorological drought index's response to vegetation drought conditions is slow, failing to accurately represent the internal mechanisms of drought. Additionally, its depiction of precipitation changes is limited, as it does not adequately consider evaporation and underlying surface conditions. The use of the meteorological drought index alone is not enough to fully explain the regional drought situation. Ecological drought was first proposed by the Ecological Drought Working Group, which was established by the American People and Nature Cooperation Organization (NAPP). It is defined as \"the development and change of hydrometeorological conditions caused by the periodic water supply shortage caused by natural or human management, so that the vegetation under water stress constitutes a xerophytic environment in the soil environment in which it lives\". It is a complex process that feeds back into other systems [20]. Abnormal air circulation and water vapor transfer can result in significantly less precipitation in a certain region, potentially leading to meteorological drought. Meteorological drought spreads down the disaster chain.