## 3 Results  
### Spatial and Temporal Characteristics of Extreme Drought Events  
Based on the 3D clustering algorithm, 101 drought events were identified in the Yellow River Basin from 2000 to 2020, in which there were 42 composite drought events with durations longer than 2 months. The eight typical events were identified with the DI of more than 0.55 (Table 3). The drought duration exhibited a distinct bimodal distribution, with 28% of events persisting for 3-5 months and only seven events lasting beyond 5 months. The most prolonged event occurred from August 2002 to February 2003, maintaining drought conditions continuously for seven months. Spatially, DA of 8.9% of the events were more than 5 \(\times\) 10\({}^{5}\) km\({}^{2}\), with the March-July 2000 event covering the largest area of 7.11 \(\times\) 10\({}^{5}\) km\({}^{2}\). The high DS events exceeding 8 \(\times\) 10\({}^{5}\) km\({}^{2}\)-h were predominantly concentrated in the central Loess Plateau (107-112\({}^{\circ}\)E, 34-37\({}^{\circ}\)N), where the sparse surface cover and strong evapotranspiration synergistically amplified the cumulative drought effect. The March-July 2000 drought events demonstrated peak values in both integrated intensity and drought severity, reaching 0.919 and 946.3 \(\times\) 10\({}^{3}\) km\({}^{2}\)-h, respectively. This severity magnitude exceeded the mean event severity of 108.2 \(\times\) 10\({}^{3}\) km\({}^{2}\)-h by a factor of 8.7.  
Drought event centroids predominantly cluster within the midstream topographic transition zone (107-112\({}^{\circ}\)E, 34-38\({}^{\circ}\)N) (Figure 2a), displaying two distinct migration patterns. Local retention events, typified by the 2013 case, maintained stable centers near the Gansu-Ningxia border with <400 km displacement. Conversely, inter-regional propagation events like the 2000 case showed substantial centroid movement from southwestern Shanxi to Lanzhou's periphery in Gansu Province, traversing 1442.48 km (Figure 2b).  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Sight** & **Precipitation** & **Temperature** & **NDVI** & **PAR** \\ \hline S1 & \(\bullet\) & \(\bullet\) & \(\bullet\) & \(\bullet\) \\ S2 & \(\bigcirc\) & \(\bigcirc\) & \(\bullet\) & \(\bullet\) \\ S3 & \(\bullet\) & \(\bullet\) & \(\bigcirc\) & \(\bullet\) \\ S4 & \(\bigcirc\) & \(\bigcirc\) & \(\bigcirc\) & \(\bullet\) \\ \hline \end{tabular} \(\bullet\): Real observed value \(\bigcirc\): Experimental simulated value.  
\end{table}
Table 2: Comparison of S1–S4 scenario inputs.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Event ID**} & \multirow{2}{*}{**Time Period**} & \multirow{2}{*}{**DD (Months)**} & \multicolumn{2}{c}{**DA**} & \multicolumn{2}{c}{**DS**} & \multirow{2}{*}{**DL (km)**} & \multirow{2}{*}{**DI**} \\  & & & **(\(\times\)10\({}^{3}\) km\({}^{2}\))** & & **(\(\times\)10\({}^{3}\) km\({}^{2}\).h)** & & \\ \hline DEa & March, 2000–July, 2000 & 5 & 710.65 & 946.30 & 1442.48 & 0.919 \\ DEb & May, 2001–September, 2001 & 5 & 702.86 & 930.11 & 1204.55 & 0.861 \\ DEc & July, 2015–December, 2015 & 6 & 579.54 & 567.59 & 1348.88 & 0.800 \\ DEd & August, 2002–February, 2003 & 7 & 537.02 & 928.34 & 714.93 & 0.794 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Eight typical drought events and their characteristic variables in the Yellow River Basin, 2000–2020.  
Figure 2: Spatial distribution of the center of mass of drought events in the Yellow River Basin from 2000 to 2020 (**a**) and spatial migration paths of the center of mass of eight typical drought events (**b**).