## 2 Data and Methodology
### Methodology
#### 2.2.4 Ecological Impacts of Flash Drought Episodes  
GPP constitutes the foundational element for global vegetative growth and alimentary production, occupying a pivotal role in the modulation of atmospheric carbon dioxide levels through its influence on the carbon balance within ecosystems [15]. Drought emerges as the most prevalent agent impinging upon GPP, markedly affecting it by modulating ecosystem respiration and plant photosynthetic processes, thereby injecting considerable uncertainty into forecasts of future terrestrial carbon sequestration capacities [36; 37]. GPP encapsulates the aggregate volume of photosynthetic carbon dioxide fixation at the ecosystem scale, impacting all variables within the carbon cycle [38; 39; 40]. The process of photosynthetic carbon dioxide assimilation is modulated by factors such as the leaf area index, Rubisco enzyme activity, and stomatal conductance [41]. From an ecological standpoint, a negative deviation in GPP signals the initiation of an ecological response, with standardized anomalies being computed as follows [42; 43]:  
\[GPPSA=(GPP-\mu_{GPP})/\sigma_{GPP} \tag{3}\]  
where \(GPPSA\) represents the standardized anomalies of \(GPP\), with \(\mu_{GPP}\) and \(\sigma_{GPP}\) denoting the standard deviation and mean of the GPP time series, respectively. This investigation utilizes response time indices and frequency metrics to probe the interplay between ecological responses and flash drought events. The response rates for each grid are ascertained by the ratio of flash drought occurrences with negative GPPSA to the aggregate count of flash droughs. A diminished response frequency suggests a reduced ecological risk, and conversely, a higher frequency indicates elevated vulnerability. The response time is delineated as the sequence of positive standardized anomalies during a flash drought until the emergence of the initial negative anomaly. The calculation equation for the response rates (Rate) is as follows:  
\[Rate=\frac{n_{GPPSA_{negative}}}{N} \tag{4}\]  
where \(n_{GPPSA_{negative}}\) refers to the number of flash droughs with negative \(GPPSA\); \(N\) shows the aggregate count of flash droughs.  
The carbon and water cycles are intricately interconnected via stomatal pathways, with vegetation adopting mitigative strategies to counteract drought stress, such as enhancing water use efficiency (WUE, defined as GPP/ET) [44; 45]. Beyond drought, WUE is also influenced by Vapor Pressure Deficit (VPD). Hence, this study employs the underlying water use efficiency (uWUE) concept introduced by [PERSON] et al. (2020) to examine the sensitivity of the ecosystem's WUE to VPD fluctuations [46]. uWUE, computed as the ratio of (GPP \(\times\)\(\sqrt{GPP}\)) to ET, accounts for the effects of VPD and offers a more accurate depiction of plant biochemical functions compared to traditional WUE metrics. It is computed as the ratio of GPP to potential evapotranspiration (PED), capturing the nonlinear dynamics between PED, VPD, and GPP. Variations in uWUE are closely aligned with drought conditions, with more severe droughts eliciting pronounced, positive anomalies in uWUE metrics. Consequently, deviations in uWUE are positively correlated with the intensity of the drought, underscoring the magnitude of potential positive anomalies in uWUE in response to severe drought conditions [15; 43; 47].  
This study calculates annual averages of WUE and uWUE based on daily values, with standardized anomalies for WUE and uWUE determined in a manner akin to the equation, facilitating the assessment of anomaly impacts. This research examined the response of GPP to flash drought events spanning from 2002 to 2018. Given the disparity in time resolution between GPP and flash droughts, 8-day GPP was linearly transformed into 5-day GPP using linear interpolation for a more precise correspondence analysis of GPP's response to flash droughts.