## 3 Results  
### Global GC Maps  
The 2-year temporal series of both ELV and VP pixels was analyzed by the GC significance test, yielding a value between 0 and 1. The resulting values were mapped and a causal/non-causal representation was obtained for each ELV\(\rightarrow\)VP case. Figure 2 shows an example of a global map depicting G-Caused and Non-G-Caused pixels where the LAI is investigated on causality by soil moisture. Note that in order to ascertain whether one variable is causal to another, the GC significance test should yield a \(p\)-value lower than 0.05 (see also Section 2.1). Red pixels indicate causation, or \(p\)-values of less than or equal to 0.05, whilst blue areas show non-causation, or \(p\)-values of greater than 0.05. Note that the  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Time Window** & **1 Year** & **2 Year** & **3 Year** \\ \hline GC significant & & & \\ \(p\)-value pixels & & & \\ \hline Increment compared & & & \\ to previous year & & & \\ \hline \hline \end{tabular}
\end{table}
Table 3: Exemplary GC \(p\)-value pixels that explicitly show causality. P\(\rightarrow\)LAI.  
fluctuations in soil moisture cause delayed increments in the LAI, as seen on the bottom left temporal profiles in Figure 2. Similar ELV/VP dynamics were observed over dry, arid areas where it was clearly visible that the given ELV was the causal factor for the investigated VP. Conversely, the other time series pair on the bottom right depicts a case where the dynamics of soil moisture have no influence on the time series of LAI. This does not mean that an ELV has no effect on VP, but, under the investigated circumstances, the ELV poses no direct, explicit causal effect on the vegetation dynamics. The non-causal relationship displayed in Figure 2 depicts that the temporal variations in the LAI show no major changes to the fluctuations in SM availability. Inspecting the two temporal profiles, for causal and non-causal, it can be observed that the LAI varies with a greater amplitude for non-causal, as opposed to causal, but without the direct causal link from SM, as SM stays constantly low throughout the investigated timeframe. Conversely, for the causal time series, the LAI stays low all year round, with the only variations directly related to the increments in SM. The non-causal time series did not improve when adding an additional year to the investigated timeframe. Furthermore, the GC statistics were calculated by the normalized values of these time series, as the ones depicted in Figure 2 stand for a visual representation.  
Since the \(p\)-value represents a Boolean, True-or-False, approach to causality, the F test was used to further quantify and investigate causality, and the F statistics for GC pixels were calculated as shown in Figure 3.  
As can be derived from Figure 3, water availability (SM and P) proved to be an outstanding causal factor in arid biomes for all variables, with higher F statistics (>6 F stat). The most noticeable regions of strong water dependency are present over the African Savannas and Northern Australia. Inspecting Figure 3 more closely, especially the SM \(\rightarrow\) LAI and P\(\rightarrow\)LAI F statistic maps, one can observe the hot spots over the Great Plains in Northern America, too. Furthermore, P also causes areas over the Iberian Peninsula and arid regions near the Thar Desert. Soil moisture causality plays a prominent role in Northern Russia on polar biomes. The most significant effect of SM is observed for the LAI, over the Northernmost latitudes both for the Asian and American continents.  
Figure 2: Two exemplary pairs of time series showing causal/non-causal cases of GC: SM\(\rightarrow\)LAI, G-Caused \(p\)-values.  
Areas that are driven by R are also distributed over Scandinavia and Northern Russia with minor spots in Southern Africa. Temperature limitation does not show any well-defined spatial pattern for any biomes or ELV\(\rightarrow\)VP links but presents an even distribution along the globe across all climate zones.