## 3 Results  
### Altitudinal Patterns of \(SIF_{yield}\) Changes  
#### 3.1.1 Altitudinal Variation in \(SIF_{yield}\)  
The \(SIF_{yield}\) changes along the elevation gradient shows an increase in values at higher elevation on summer days in the Tibetan Plateau. From DOY 173 (21 or 22 June) to DOY 245 (1 or 2 September), 8 out of 10 records (with 8-day intervals) support the increase in \(SIF_{yield}\) at high altitudes in summer, and the increase trend is particularly apparent on DOYs 197, 205, 213, and 221. On DOY 197 (14 or 15 July, in summer), \(SIF_{yield}\) increases along the altitude gradient, while the ambient temperature decreases simultaneously, as shown in Figure 1a. The coefficient of determination of the linear regression between \(SIF_{yield}\) and altitude is fairly high (R\({}^{2}\) = 0.91) on DOY 197 for the 12-year averaged observations (Figure 1a). This high R\({}^{2}\) value demonstrates that the elevation itself can explain nearly 91% of variations in \(SIF_{yield}\) in general, while the much weaker correlation (Figure 1b) shows that the discrepancy of \(SIF_{yield}\) in different years still exists, probably due to the impacts of other factors. The increased \(SIF_{yield}\) (Figure 1a) passed the Mann-Kendall trend test with \(p<0.05\), which confirms the significance of the trend. The trends of \(SIF_{yield}\) generally increase in high-altitude regions each year, as shown in Figure 1b. Both results displayed in Figure 1a,b confirm an increasing trend of \(SIF_{yield}\) along the elevation gradient, but the coefficient of determination of the linear regression in Figure 1b is much lower than that in Figure 1a. This might be explained by the stochastic field theory. If the distribution of \(SIF\) yield is considered as a stochastic field, the values of \(SIF\) yield taken at different elevations will be stochastic variables taken with a certain probability, thus the averaging process can bring down the uncertainties as listed in Figure 1a. Although \(SIF_{yield}\) varies in different years, there are apparent increasing trends of \(SIF_{yield}\) along the elevation gradient for most of the years (9 out of 12 in Figure 1b). This phenomenon suggests that the average pattern of higher \(SIF_{yield}\) along the altitude in summer (Figure 1a) is not the result of high-value anomalies in particular years (such as relatively high \(SIF_{yield}\) at high altitudes in 2018, Figure 1b). Figure 2 shows observations from 12 years and compares the altitudinal \(SIF_{yield}\) changes in each year on DOY 197 and 149, and the results confirm that there are indeed occasions when \(SIF_{yield}\) increases as the elevation goes up, but it is not always correct. In Figure 2a, 10 out of 12 years (except 2009, 2012) follow the rule demonstrated in Figure 1a (DOY 197, in summer), while only 2 year (2010, 2015) in Figure 2b (DOY 149) obey the rule. Despite large interannual variations in \(SIF_{yield}\) (and there also seems to be atypical values associated with 2018 compared to other years), an increasing trend of \(SIF_{yield}\) along the altitude gradient can still be found for each year in summer (Figure 2a). Therefore, it seems that the interannual variation in \(SIF_{yield}\) mainly causes the systematic differences in absolute \(SIF_{yield}\) values among years, but it does not change the relative relationship among \(SIF_{yield}\) at different altitudes in each year. Interestingly, although the \(SIF_{yield}\) is usually larger at higher elevation in summer, there are still exceptional cases (for example, 2009 in Figure 2a, when \(SIF_{yield}\) at high altitudes is lower than in low altitudes). This phenomenon may be caused by phenological changes in different years, but other possibilities cannot be excluded based on the limited knowledge in this research. Figure 1: Variations in \(SIF_{yield}\) along altitudinal gradient.