## 3 Results  
### Spatiotemporal Pattern of Growth Asymmetric Indices  
#### 3.1.1 Interannual Variability of Vegetation Asymmetries for NEC  
To ascertain the overall status of vegetation asymmetries for NEC, regional average annual asymmetric indices are calculated. Then the corresponding interannual variation was obtained from the time series (Figure 3). The three indices have an evident cycle in their time series, but the periodic phases are variable. To accurately quantify the cycle period, the dominant frequency of vegetation asymmetries is determined from a spectral analysis of the time series (using R package 'forecast') [42]. This procedure revealed that the dominant frequency of AsyV, AsyR is 11 and 10 years, respectively. The periodicity of AsyV and AsyR is statistically significant and is also reflected by obvious periods in the time series plot, such as 1982-1992 and 2003-2013. AsyL has a relatively large interannual fluctuation and does not exhibit a remarkable period, but visually there is a shorter period that is around eight years (not to be identified by spectral analysis). The directions of amplitude in AsyV and AsyR show an opposite pattern, in other words, AsyV decreases with the increasing AsyR. Generally, AsyL keeps a consistent phase with changes in AsyV but with remarkable fluctuation. Prior to 2000, trends and periodic characteristics of the three indices are relatively prominent. During the subsequent time interval, their inter-annual variability increases, and the amplitudes tend to decrease, which may be associated with changing climatic factors such as the global warming slowdown after 1998 [43; 44].  
Across the entire NEC, correlations between the three asymmetric indices (AsyL, AsyV, AsyR) were assessed using Spearman correlation analysis. The results show that AsyR and AsyV have a negative correlation (Spearman r = \(-\)0.67), meaning that if in the trend in AsyR continues to increase (vegetation consistently shows a pattern of slow increase during green up and rapid decrease during senescence), the difference in vegetation activity between the two time periods (AsyV) will decrease. In other words, rapid senescence of vegetation in autumn would result in decreased productivity, thus reducing its impacts on annual productivity as compared to spring productivity. Consistency between AsyV and AsyL indicates that an extension of the senescence window when compared to green up contributes to an increase in autumn vegetation productivity. Due to inherent variability, AsyL is weakly correlated with AsyV (Spearman r = 0.48). AsyR and AsyL show a strongly negative correlation (Spearman r = \(-\)0.81), reflecting that a rapid decrease in vegetation greenness will shorten the duration of senescence.  
Figure 3: Interannual variations in vegetation growth asymmetries for the entire Northeast China (NEC). For better graphical presentation, raw annual time series were normalized.  
Like the temporal distribution, spatial distributions of average annual AsyV and AsyR demonstrate a regular patch pattern that matches vegetation cover types (Figure 4b,c). The map of average AsyL shows a relatively discrete pattern (a weak cluster status) (Figure 4a). Across the NEC, spatially averaged AsyL and AsyR show positive signs, while AsyV has a small negative value (\(-0.01\)). In other words, the late growing period overwhelms the early growing period in controlling total annual growing season length, identified by the positive AsyL occurring in each vegetation type (Figure 4d). Positive AsyL is most statistically significant in grassland and alpine vegetation. At the pixel scale, negative AsyL values can be found in northern and southeastern natural vegetation. AsyV is positive in conifer-leaved forests but is negative in other vegetation types, indicating again that productivity during senescence plays a dominant role in annual productivity for many regions of the NEC (Figure 4e). Grasslands have the most negative values for AsyV, followed by croplands and alpine vegetation.