## 3 Methods
### Analysis
#### 3.2.3. Estimation of Correlations between LOS and GSI and Their Trends  
All of the vegetation metrics were detrended to avoid possible spurious regressions of variables with a co-varying trend to allow for focused analysis of correlations in interannual variability. The linear trend derived from the least squares method was removed for both LOS and GSI time series within the  
\begin{table}
\begin{tabular}{c c c c c c c} \hline  & **NH** & \multicolumn{2}{c}{**NA**} & \multicolumn{2}{c}{**EA**} \\ \cline{2-7}  & **n** & **\%** & **n** & **\%** & **n** & **\%** \\ \hline
**Total** & 1,104,980 & & 348,672 & & 756,308 & \\
**(a) \(\mathbf{-1},\mathbf{-1}\)** & 55,999 & 5.07\% & 22,558 & 6.47\% & 33,441 & 4.42\% \\ \(\mathbf{-1},\mathbf{0}\)** & 96,856 & 8.77\% & 36,455 & 10.46\% & 60,401 & 7.99\% \\
**(b) \(\mathbf{-1},\mathbf{+1}\)** & 59,358 & 5.37\% & 35,837 & 10.28\% & 23,521 & 3.11\% \\
**0, \(\mathbf{-1}\)** & 49,435 & 4.47\% & 21,748 & 6.24\% & 27,687 & 3.66\% \\
**0, 0** & 293,989 & 26.61\% & 93,712 & 26.88\% & 200,277 & 26.48\% \\
**0, +1** & 292,000 & 26.43\% & 82,836 & 23.76\% & 209,164 & 27.66\% \\
**(c) +1, \(\mathbf{-1}\)** & 4494 & 0.41\% & 2800 & 0.80\% & 1694 & 0.22\% \\
**+1, 0** & 37,807 & 3.42\% & 10,091 & 2.89\% & 27,716 & 3.66\% \\
**(d) +1, +1** & 215,042 & 19.46\% & 42,635 & 12.23\% & 172,407 & 22.80\% \\
**a + d** & 271,041 & 24.53\% & 65,193 & 18.70\% & 205,848 & 27.22\% \\
**b + c** & 63,852 & 5.78\% & 38,637 & 11.08\% & 25,215 & 3.33\% \\ \hline \end{tabular}
\end{table}
Table 1: Comparison of LOS and GSI time series trends during 1982–2013 (Figure 3) at hemispheric and continental scales. The first mentioned trend represents LOS and the second trend denotes GSI (\(p\) = 0.1). (a): converging trends type 2, (b): diverging trends type 2, (c): diverging trends type 1, (d): converging trends type 1 (a + d: consistent significant positive trends in LOS and GSI, b + c: opposite significant trends in LOS and GSI).  
Figure 3: Comparison of trends in LOS and GSI 1982–2013. \(-1\): denotes significant negative trends, +1: significant positive trends, 0: non-significant trends (\(p\) = 0.1).  
Figure 2: Linear trends in vegetation phenology and growing season integral 1982–2013. (**A**) Linear trends in SOS. (**B**) Linear trends in EOS. (**C**) Linear trends in LOS. (**D**) Linear trends in GSI. Note: positive trends indicate delaying SOS/EOS dates whereas negative trends denote advancing SOS/EOS dates.  
entire research period (1982-2013) and each 16-year window (sub-period analysis described below) [9]. Correlations between LOS and GSI were assessed by means of parametric correlations using the Pearson coefficient for (1) the entire period and (2) for 17 sub-periods calculated from a 16-year window to be able to detect changes on correlation over time. A 16-year period was selected as a compromise between sufficient numbers of years to calculate the correlation on the one hand, and to have enough observations (17) to study changes over time on the other hand. Finally, the trends in the correlations between LOS and GSI were calculated from the 17 time-series correlation maps (for each 16-year window) by linear temporal trend analysis.