## 2 Data and Methodology
### Methodology
#### 2.2.2 Elucidation of Flash Drought Phenomena and Their Commencement Phases  
This investigation delineates flash drought occurrences through a dual-lensed perspective, focusing on the temporal evolution of soil moisture content alongside the duration of aridity episodes. Drawing upon precedents set by [PERSON] et al. [2], this study synthesizes criteria encompassing both the precipitous decline in soil hydration levels and the sustained period of drought to characterize flash drought events. A soil moisture percentile below 40% signals the initial phase of departure from normative hydration states, serving as the preliminary demarcation of the flash drought sequence; when the soil moisture percentile descends beneath the 20% mark, it signifies substantial ecological distress. This latter threshold, endorsed by the U.S. Drought Monitor as indicative of \"Moderate Drought--D1\" conditions, underscores a critical juncture at which vegetative systems may exhibit signs of compromised water transport mechanisms [33].  
Hence, the 20% threshold is adopted as the critical lower limit for identifying the progression into a drought condition. Leveraging the methodology of [PERSON] et al. [2], our analysis not only captures the onset and cessation of flash droughts but also emphasizestheir swift escalation and duration as definitional hallmarks. Specifically, a flash drought is recognized by a swift reduction in the average soil moisture percentile from above 40% to below 20%, at a decline rate exceeding 5%, persisting for a minimum of 15 days (Figure 2). The termination of a flash drought is marked by the recovery of soil moisture percentile levels above 20% [10]. The criteria for determining such events are as follows: (1) for an event to qualify as a flash drought, the soil moisture percentile must not exceed 40% at any point, with at least 15 consecutive days where the soil moisture remains at or below the 20% threshold; (2) the temporal span from the onset to the conclusion of a flash drought is categorized based on calendar duration, with the inception defined by the last instance above the 40% percentile and cessation as the final occurrence below the 20% threshold; and (3) the initiation phase of a flash drought necessitates a rapid fall to the 20% percentile within 20 days or fewer, characterized by an average decrement rate surpassing 5%.  
\[Intensification\ rate:\left\{\begin{array}{l}\frac{\text{SM}(t_{i+1})-\text{SM}(t _{i})}{t_{i+1}-t_{i}}\geq 5\text{ th percentile}\\ 0<t_{\text{e}}-t_{\text{o}}\leq 5\end{array}\right. \tag{1}\]  
\[Drought\ condition:\left\{\begin{array}{l}\text{SM}(t_{\text{o}})\geq 40 \text{ th percentile}\\ \text{SM}(t_{\text{e}})\leq 20\text{ th percentile}\\ t_{\text{p}}-t_{\text{e}}\geq 3\end{array}\right. \tag{2}\]  
Unlike the broader process of drought identification, the incipience of a flash drought is demarcated by the initial 20 instances wherein the soil moisture percentile first descends to the 20% threshold, marking the preliminary phase of the drought's duration. Consequently, recognizing the onset of a flash drought acts as a harbinger for discerning its persistence phase. To circumvent scenarios of extreme percentile fluctuations or the sustained presence of drought conditions within the 30-40% percentile range, the criterion for initiating the flash drought identification employs the last occurrence among three successive instances where soil moisture percentiles exceed 40%, within the first 22 days of the persistence phase.