## 2 Data and Methodology
### Research Methodology  
#### 2.3.1 Drought Event Recognition and Multidimensional Feature Extraction  
An integrated drought identification framework was developed by combining the Standardized Precipitation Evapotranspiration Index (SPEI) ([PERSON] et al., 2019) with a three-dimensional spatiotemporal clustering algorithm, enabling systematic detection and quantification of drought events ([PERSON] et al., 2019). The drought identification process began by detecting drought seed points, defined as grid cells with SPEI values \(<-1\). Spatially connected drought patches were then constructed using the Moore neighborhood 8-direction search algorithm implemented in two stages. First, within each monthly timestep, contiguous grid cells meeting SPEI \(<-1\) were clustered into spatial drought patches through 8-directional connectivity. Then, across consecutive months, drought patches were linked into unified events when exhibiting spatial overlap exceeding the predefined area threshold. During which a double filtering mechanism was applied to enhance spatial clustering accuracy. Finally, drought events were identified by applying spatiotemporal continuity constraints to link clusters across consecutive time steps. Small isolated drought patches covering less than 1.6% of the study area were excluded ([PERSON] et al., 2019) following noise suppression principles ([PERSON] et al., 2019; [PERSON] et al., 2020). To ensure physical coherence in spatiotemporal evolution, drought events were retained only when exhibiting overlap areas exceeding 6400 km\({}^{2}\) for two consecutive months, which was an empirical parameter from 3D clustering methods. Studies have demonstrated this threshold's effectiveness in identifying spatiotemporal continuity of drought events; thus, this study adopts the established empirical value, as determined by the overlap area threshold method ([PERSON] et al., 2019; [PERSON] et al., 2020). The construction of the characterization index system contains four core parameters: drought duration (DD), drought severity (DS, km\({}^{2}\)-month), drought-affected area (DA) [40], and drought migration path length (DL) [28; 44]. DD characterizes drought event duration. DS quantifies drought intensity and spatial cumulative effect. DA reflects maximum spatial coverage. DL portrays drought dynamic propagation characteristics through center-of-mass migration trajectory. Building upon these four indicators established in prior studies, this study introduced a weighting scheme to integrate them and proposed the comprehensive drought index (DI) for a more holistic characterization of drought intensity. To ensure objectivity and avoid subjective bias in weight assignment, the weights of each index were determined (DD: 0.22, DA: 0.17, DS: 0.24, DL: 0.28) using the entropy weighting method. This approach leverages information entropy--a measure of system disorder that quantifies useful information in data. Indicators exhibiting significant value variations yield low entropy, indicating high information content and thus warranting greater weights. Conversely, minimal variations correspond to high entropy and lower weights. The weight coefficients were derived automatically based on the information entropy of raw data [45]. This process involved solely the integration and weighting of existing indicators without defining new variables. The comprehensive drought index (DI) was constructed to realize the multidimensional feature coupling:  
\[\text{DI}=0.22\text{DD}+0.17\text{DA}+0.24\text{DS}+0.28\text{DL} \tag{1}\]  
While inherent drought characteristics lead to some linear correlation among DD, DS, DA, and other indicators, these variables capture distinct physical aspects and thus provide complementary information within the comprehensive model. Crucially, the entropy weighting method, being information-based, is unaffected by multicollinearity issues common in linear models. It effectively reduced the influence of inter-correlated variables and enhanced the discriminative power of DI.