## 2 Materials and Methods
### Statistical Analysis  
According to previous studies, _SIF_ can be expressed as the product of _APAR_ and _SIF\({}_{yield}\)_[26; 59]. Therefore, _SIF\({}_{yield}\)_ is represented by the following formulation:  
\[SIF_{yield}=\ \frac{SIF}{APAR}=\ \frac{SIF}{PAR\times fPAR} \tag{1}\]  
_SIF\({}_{yield}\)_ can be treated as normalized _SIF_, getting rid of the impact of incident light intensity. Thus, it can indicate the _SIF_ emission capacity of plants. Instantaneous _SIF\({}_{yield}\)_ (at about 09:30) was analyzed in this study to discuss the uncertainty caused by varying light conditions. Calculating instantaneous _SIF\({}_{yield}\)_ requires converting daily _SIF_ data, provided by [PERSON], to instantaneous _SIF_ at about 09:30. The conversion method is based on the cosine of SZA and is similar to the instantaneous _PAR_ conversion inside the time zone, as mentioned above. In our analysis, _SIF\({}_{yield}\)_ observations from 2007-2018 were aggregated to a temporal interval of 8 days or 1 month, in order to support the investigation of _SIF\({}_{yield}\)_ changes along the elevation gradient. According to the time resolution of the _SIF_ observations, a total of 46 altitudinal _SIF\({}_{yield}\)_ variations for 8-day _SIF_ and 12 for monthly _SIF_ were obtained. Altitudinal variations in _SIF\({}_{yield}\)_ were observed first, then the seasonal and interannual changes of the variation patterns were analyzed. Seasonal changes of _SIF\({}_{yield}\)_ were investigated based on the multi-year average, and the relationship between _SIF\({}_{yield}\)_ and ambient temperature was explored. Considering the possible altitude-specific patterns, we also employed the observations at different altitudes to find out whether there were differences in the _SIF\({}_{yield}\)_-temperature relationships. For analysis at the interannual scale, relationships between _SIF\({}_{yield}\)_ and ambient temperature or _PAR_ were investigated at different days of the year (DOYs), and the results obtained during the peak growth period are discussed. We also analyzed the altitudinal variations in _SIF\({}_{yield}\)_ temperature sensitivity at seasonal and interannual scales. Sensitivity of _SIF\({}_{yield}\)_ to ambient temperature changes is defined as the slope of the linear model between _SIF\({}_{yield}\)_ and temperature in this study (the relationship can be expressed as a linear function only when the temperature reaches 275 K, a relatively mild temperature condition for alpine vegetation), thus it is also the indicator of the relationship between _SIF\({}_{yield}\)_ and temperature. Linear regressions on the relationship between _SIF\({}_{yield}\)_ and temperature were employed for the calculation of temperature sensitivity at both seasonal and interannual scales; in addition, the relationship between the altitudes and temperature sensitivity (the slopes of these linear regressions above) is also investigated by regression analysis. To identify areas sensitive to climate change, we took the seasonal temperature sensitivity at each altitude as the reference and then compared the interannual results with it. In order to visualize the spatial distribution of temperature sensitivity, linear regression analysis was conducted pixel by pixel, and the statistical significance of regression was also investigated here. As a nonparametric test without requiring normal distribution [60], the Mann-Kendall trend test was employed to judge the monotonic trend of \(SIF_{yield}\) and temperature sensitivity series and indicate whether they were significant by inspecting the value of tau statistics. In addition, the Mann-Kendall test can also tell us whether there is an abrupt change in data series [61]. By observing the intersection point of the UF and UB statistics, we can locate the abruption. If there is only one intersection point and it falls into the confidence interval (usually defined as between +1.96 and \(-1.96\)), it indicates that there is an abrupt change in the series and it is significant at the given level.