## 2 Materials and Methods
### Vegetation Products and Environmental Land Variables  
The investigated vegetation product datasets, i.e., the FAPAR, the LAI, SIF, and the NDVI, were derived and captured by the PROBA-V, Sentinel-3 (S3), and Sentinel-5P (S5P) satellites. Two years of input data (January 2020-December 2021) was used with 10-day composites. This temporal window was selected because it proved to be the common temporal domain for all datasets whilst still maintaining a relatively short timescale. The LAI, FAPAR, and NDVI products were used from the Global Land Service (CGLS) datasets, originating from PROBA-V and Sentinel-3 OLCI. The CGLS datasets were downloaded from [[https://land.copernicus.eu/global/themes/vegetation](https://land.copernicus.eu/global/themes/vegetation)]([https://land.copernicus.eu/global/themes/vegetation](https://land.copernicus.eu/global/themes/vegetation)) (accessed on 8 August 2023). The retrieval of the FAPAR and LAI involved the application of neural networks on Top-of-Canopy (TOC) input reflectances in red, near-infrared, and shortwave infrared to infer the estimates [46]. The NDVI was calculated using atmospherically and angular corrected Red and NIR TOC reflectances [47]. Amongst many atmospheric satellite missions providing SIF data, SSP TROPOMI (TROPO-spheric Monitoring Instrument) offers the best trade-off between spatial and temporal resolutions [48]. The baseline TROPOMI SIF (TROPOSIF) retrievals are inferred using the 743-758 nm range. Additionally, a secondary SIF dataset obtained from an extended fitting window (735-758 nm window) is incorporated. The SIF data were obtained by directly downloading them from this website: [[http://ftp.sron.nl/open-access-data-2/TROPOMI/tropomi/sif/v2.1/12b/](http://ftp.sron.nl/open-access-data-2/TROPOMI/tropomi/sif/v2.1/12b/)]([http://ftp.sron.nl/open-access-data-2/TROPOMI/tropomi/sif/v2.1/12b/](http://ftp.sron.nl/open-access-data-2/TROPOMI/tropomi/sif/v2.1/12b/)) (accessed on 7 July 2023). The data are provided in the form of ungridded L2B daily data. SIF is derived through a data-driven approach using top-of-atmosphere (TOA) radiance data in the far-red spectral region collected by TROPOMI [49]. The dataset has a spatial resolution of 7 \(\times\) 3.5 km and daily revisit time. Daily SIF data were used to create the 10-day temporal composites. The summarized description of the VPs can be found in Table 1.  
The European Centre for Medium-Range Weather Forecasts (ECMWF) is currently producing an improved global dataset for the land component of the fifth generation of the European ReAnalysis (ERA5). ERA-5-LAND utilizes physical equations and assimilates observations to estimate atmospheric and land-surface variables. The data, available globally, are provided at a horizontal resolution of 0.1\({}^{\circ}\)\(\times\) 0.1\({}^{\circ}\) in hourly, daily, or monthly aggregates [50]. The same temporal window (January 2020-December 2021) was selected for the ELVs. For assessing environmental effects on vegetation mapping, we utilized the daily data that was already available within the GEE platform, and 10-day temporal composites were created. The description [51; 52] of each ELV can be found in Table 2.  
The temporal window for the analysis was 2 years, January 2020-December 2021. This temporal window was selected after conducting Granger analyses with one, two, and three years of data. The goal of this experiment was to derive the shortest timespan while achieving consistent findings. The two-year timespan led to significant improvements as opposed to the one-year window, i.e., the GC \(p\)-value pixels increased nearly two-fold. However, the change was not that significant when comparing the three-year timespan to the two-year timespan, i.e., the GC \(p\)-value pixels only increased approximately 5-10%. Similar increments were observed amongst all ELV\(\rightarrow\)VP cases; exemplary GC \(p\)-value pixel counts are shown in Table 3 for P\(\rightarrow\)LAI.