## 2 Materials and Methods
### Pre-Treatment of the Data  
The spatial resolution of all the data sets in this study needs to be aligned and compatible to be able to produce viable correlations. The spatial scale chosen for this study is 0.05\({}^{\circ}\), and data with a lower resolution thus needs to be converted. This conversion was performed using bilinear interpolation. The spatial resolution (0.05\({}^{\circ}\)), that each pixel covers varies across the study-area, and mainly depends on the latitude. Hence, the pixels in the further north cover a smaller area than in the south. However, this is believed to have a marginal effect on the results, since the GPP products are measured as densities (meaning they are area-independent), rather than quantities.  
The correlations between climate variables were calculated between anomalies (z-scores) relative to the mean of the period 2001-2018. \(z\)-scores were calculated according to Equation (1).  
\[z=\frac{x-\mu}{\sigma} \tag{1}\]  
where \(\mu\) is the seasonal mean of the whole time period per grid-cell and \(\sigma\) is the standard deviation. The raw number \(x\) can thus be more easily interpreted in terms of standard deviations and whether the anomaly is positive or negative compared to the seasonal mean.  
The main approach for assessing legacy affects of spring temperature on plant productivity and their associated drivers was to use [PERSON]'s correlation and partial correlation. This method has often been adopted by previous studies (e.g., [35; 36]) which attempt to identify the dominant drivers for GPP or plant phenology. \(GPP_{summer}\) and \(GPP_{autumn}\) anomalies were the predicted variables, and temperature, soil moisture, VPD, and pre-season GPP anomalies were predictive variables (Table 3). Direct correlations between \(T_{spring}\) anomalies and \(T_{summer}\) anomalies were calculated to gain an overview of the transition patterns for the legacy effects. Possible co-varying effects between environmental variables were accounted for when performing partial correlations. This yields a clear picture of the degree of correlation between any individual environmental variable and summer/autumn GPP. The correlations were based on 18 years of data (2001-2018) per individual grid-cell. The statistical significance was tested based on \(p\)-values, and only correlations with (\(p<0.05\)) were kept. The set of variables was chosen to see how lagged effects from pre-season GPP anomalies correlate to summer/autumn GPP anomalies and how they compare to direct climate effects from soil moisture, air temperature, and VPD anomalies. The dominating variable per grid-cell was determined by selecting the maximum partial correlation value (absolute value) to create a spatial representation of which out of pre-season GPP, soil moisture, air temperature, and VPD that dominates in regulating seasonal plant productivity.  
The \(T_{spring}\) anomalies correlation to \(GPP_{summer}\) and \(GPP_{autumn}\) was further investigated by looking at the transition patterns between summer and autumn. Eight transition patterns were identified: \(+-\), \(-\)+, \(++\), \(--\), \(+\)/, \(-\)/, \(/+\) and \(/-\). The plus, minus, and slash signs denote positive, negative, or non-significant impact, respectively, and the position reveals whether it affects \(GPP_{summer}\) or \(GPP_{autumn}\). Further, the statistical spread of \(T_{spring}\) anomalies correlations was also determined for each biome to assess whether the aggregated overall impact could be considered neutral, positive or negative. The mean value of the correlation coefficients grouped per biome-type was determined as the defining factor of this.