## 1 Introduction
The understanding of global vegetation anomalies lies within unraveling its causal dependencies from abiotic factors, such as fluctuations in soil moisture content and precipitation (i.e., water availability), as well as changes in air temperature and solar radiation (i.e., energy availability). Further, the water availability to plants drives changes in stomatal guard cell turgor pressure, which actively regulates the stomatal opening. Thus, greater supplies of water will increase stomatal opening, leading to augmented rates of CO2 uptake for photosynthetic activity [23; 24]. The causality analysis of VPs to precipitation (P) and soil moisture (SM) may possibly explain anomalies in vegetation dynamics associated with water limitation. Additionally, the health of vegetation across the Earth's surface hinges on the environmental temperature and its fluctuations. Terrestrial vegetation undergoes growth, reproduction, and productivity patterns related, among others, to environmental temperature [25]. Moreover, through various factors including the amount of total energy, photons, spectral characteristics, duration, and photoperiod, light also governs numerous aspects of plant development [26]. Therefore, apart from water, plants' responses to air temperature (T) and solar radiation (R) also play a crucial role in photosynthetic activity [27]. The spatial patterns of vegetation type and function vary in connection with the existing environmental circumstances. Climatic and soil-related conditions are known to directly influence different plant species distributions. To model vegetation anomalies to environmental stress (e.g., water and energy availability), the analysis needs to be adapted to account for the role of dominant biomes in determining how vegetation responds to environmental drivers and disturbances [28]. Vegetation anomalies and responses to multiple ELVs have previously been monitored with multi-decadal data (e.g., [29; 30; 31]). A variety of approaches have previously been applied to investigate vegetation-environment interconnections. For instance, [PERSON] et al. [29] used deep learning methods to simulate the long-term vegetation greenness dynamics and assess their sensitivity, whilst [PERSON] et al. [31] implemented the Fisher-Shannon statistical algorithm to assess the complexity and non-stationarity of non-linear time series. [PERSON] et al. [30] used regression analysis on long-term NDVI data to assess the correlation between vegetation and environment. Yet, there is a lack of shorter-term sensitivity analysis to assess the environmental stress on ecosystem integrity. Although efforts have been presented to apply analysis to shorter timescales [32; 33], these studies usually focused on a regional scale and not the globe as a whole. For example, [PERSON] and [PERSON] [32] investigated the response of the NDVI to the preceding 10 to 40 day temperature anomalies over Canada, while [PERSON] et al. [33] applied monthly relative anomalies to correlate the temporal dynamics of Gross Primary Production (GPP), SIF, and absorbed photosynthetically active radiation (APAR) to investigate the vegetation's response to droughts in Victoria, Australia. While the usage of simple correlation and multi-linear regression analyses have significantly contributed to the comprehension of the interconnections between climate and vegetation, these are generally inadequate to reveal causalities [34]. Therefore, an important step towards understanding the stress-response relationship between environment and vegetation is the exploration of causal relationships, such as the Granger Causality (GC) [35]. The GC is a statistical concept used to assess whether one time series can be considered a predictor for another time series. If past values of one time series provide information that helps predict the second time series, then the first time series is causal to the second one [36].