Appendix S1:Correlation analysis between December-February minimum temperature (WMT) and the chronology generated from different detrending approach.

We reviewed the detrending approach applied for the broadleaf and shrub species at high elevation and at high latitude region, and found that negative exponential function or a straight line of any slope (negative slope) (Barichivich et al. 2009; Hallinger et al. 2010; Li et al. 2013; Liang and Eckstein 2009; Liang et al. 2012) and cubic smoothing spline of 67 % of the series length (Dawadi et al. 2013; Liang et al. 2015; Martin and Pederson 2015; Pederson et al. 2013) are two approaches are widely used. We tried most detrending approaches provide by Arstan program. All the detrended ring-width data averaged into the chronology by computing the bi-weight robust mean, and then correlated with WMT. All the approaches yielded out similar correlation coefficient with same direction (Table 3). This suggests that our results are stable and detrending approach independent. However, the magnitudes of correlation coefficient lowest for cubic smoothing spline of 67 % (32 %) of the series length and highest for negative exponential function or a straight line of any slope. This is because detrending is a process of variance decomposition of ring-width data. Negative exponential function or a straight line of any slope is the conservative detrending approach reserving maximum climate signal for chronology, while the cubic smoothing spline approach can remove some variance that may be produced by climate, so it keepsa relatively low climatic signal for the chronology.

Table S1Detrending methods and its result

Detrending method / Correlation coefficient with December-February minimum temperature (WMT) / P value
Negative exponential function or a straight line of any slope / ‒0.60 / < 0.01
Negative exponential function or a straight line with negative slope or horizontal lines / ‒0.46 / < 0.01
General negative exponential curve / –0.28 / 0.04
General negative exponential curve (any k) / –0.47 / < 0.01
Hugershoff growth curve / ‒0.28 / 0.04
Cubic smoothing spline of 67 % of the series length / ‒0.17 / 0.23
Cubic smoothing spline of 32 % of the series length / –0.24 / 0.08
Negative exponential function or a straight line of any slope plus Cubic smoothing spline of 67 % of the series length / ‒0.17 / 0.23
Regional curve standardization / –0.31 / 0.02

Note: prior to standardization, a data-adaptive power transformation was employed to stabilized the variance in raw ring-width series (Cook and Kairiūkštis 1990; Cook et al. 1994). And to minimize the effect of changing sample size through time, the variance of chronology was also stabilized (Osborn et al. 1997).

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