## Materials and Methods
### Remote Sensing Data
#### 2.5.2 Satellite-Observed Start of Season for JSBACH Model Evaluation  
For the later comparison of satellite observations with modelled start of season, we spatially aggregated the daily time series of FSC and NDWI to a grid resolution of 0.25\({}^{\circ}\) by 0.25\({}^{\circ}\). Because the heterogeneity of land cover is one main factor for discrepancies between satellite-observed phenology and ground observations [67; 68], we focussed on satellite pixels with dominant cover of ENF and DBF according to CORINE Land Cover data of the year 2000 [69] (see also Figure 1b). In the aggregation, the FSC time series were averaged for MODIS pixels with a dominant fraction (\(\geqslant\)70%) of coniferous forest. NDWI time series were averaged for pixels with dominance of deciduous and mixed forest (sum of both vegetation types was \(\geqslant\)70%).  
A sigmoid function was fitted to the FSC time series and ENF_SOSat was detected when the fraction of snow cover decreased from full snow cover, FSC = 1, to FSC = 0.99 as follows:  
\[\mathrm{ENF\_SOSat}=\mathrm{x}_{1}-\ln\left(99\right)\mathrm{x}_{2} \tag{2}\]  
where \(\mathrm{x}_{1}\) is the inflection point (day when FSC reaches 0.5) and \(\mathrm{x}_{2}\) controls the rate of change of the sigmoid function. The full details of the method are given in [PERSON] et al. [33]. The accuracy of ENF_SOSat has been evaluated with ENF_SOSEC at three CO\({}_{2}\) flux measurement sites in Finland. The root mean square error (RMSE) was 5.3 days and the bias 1 day (late) [33]. The quality of the estimate was similar for the southern and the northern boreal sites, but it may be less reliable for the hemiboreal zone in winters with low snow depth [33].  
For the detection of the DBF_SOSat, we followed the method by [PERSON] et al. [27], which is based on the NDWI. This index is useful for the detection of the start of season in boreal areas, because snow melt and greening-up of vegetation can be differentiated from the time series [70], whereas the observed spring increase in the widely applied Normalized Difference Vegetation Index (NDWI) can belargely influenced by reflectance change in the visible range due to the melting of snow, and thus the increase in NDVI corresponds actually to the time of snow melt in boreal areas [71; 72]. The method for determination of DBF_SOSsat from NDWI was first applied in central Siberia [27] and later to boreal Eurasia [73]. DBF_SOSsat is the date when the vegetation within the footprint of the satellite pixel is greening up, which corresponds to the time of NDWI increase after snow melt [27]. Comparison with in situ observations of leaf appearance of birch, larch and aspen in central Siberia with estimates from SPOT-VEGFATION NDWI time series showed an RMSE of 6.7 days and a negligible bias [70].  
In this study, we smoothed averaged daily NDWI time series (spatial resolution 0.25\({}^{\circ}\)) with the adaptive Savitzky-Golay filter [74; 75] that is implemented in the software TimeSat [76]. DBF_SOSsat was then determined from the smoothed time series as the last day when NDWI is lower than the minimum annual NDWI increased by 5% of the NDWI spring amplitude:  
\[\text{DBF\_SOSsat}=\text{arg}\max_{t\in[32,200]}f(t):=\{t\mid\text{NDWI}\,(t)< \text{NDWI}_{\text{min}}+\varepsilon\} \tag{3}\]  
where \(\text{NDWI}_{\text{min}}\) is the minimum NDWI and \(\varepsilon\) equals 5%. The original threshold value \(\varepsilon\) of 20% that accounts for the noise level in the time series [27] was reduced to 5% because of the lower noise level in the averaged and smoothed NDWI time series here.  
Satellite-observed start of season dates were not determined for areas with scarce coverage of the respective vegetation type within a MODIS pixel. Furthermore, long temporal gaps in satellite time series in spring increase the uncertainty in the detection of SOS from satellite observations. Therefore, we excluded grid cells with a temporal gap larger than two weeks around the estimated start of season date for the comparison with JSBACH model results.