## 4 Discussion
### Uncertainty of the Developed Methods  
Credible theoretical frameworks and external environmental variables were introduced to the developed methods to meet the challenges of modeling T by SIF. The WUE method links SIF and T from the carbon-water economy perspective, in which WUE is treated as a function of VPD. The conductance method clarifies how the information about J contained in SIF can be used to estimate gs, and the Penman-Monteith based on energy balance further combines the gs with other meteorological variables. The conductance method has a clearer physical meaning, which better describes the linkage between SIF and T. However, assumptions of optimal carbon-water coupling relationship, the uncertainty of input data, and the experimental design may also undermine the performance of the developed methods. Compared with the simple linear regression method, though the influence of VPD on WUE is included in the WUE method, soil moisture, hydraulic conductance, and other environmental variables could also influence the WUE independently [15; 59; 60]. It would be helpful to incorporate the effects of these factors on WUE. For the conductance  
Figure 4: Scatterplot between sun-induced chlorophyll fluorescence (SIF) and T\({}_{\text{WUE}}\) for the four study sites. Subfigures (**a–d**) for hourly scale; (**e–h**) for daily scale. method, plants under stress or competition cannot keep the optimal stomatal conductance behavior [61; 62]. The carbon-water economy is also influenced by traits of plants and environmental variables [63]. A more physiologically based water-carbon coupling framework will improve the models from the bottom up. Uncertainty of the input data might also introduce uncertainty to the results. First, VPD of air above the canopy was used to assess the aridity stress by assuming the canopy and the atmosphere were fully coupled. Ecosystems with a dense closed-canopy tend to decouple from the air [64; 65]. As both the WUE method and the conductance method show great sensitivity to VPD, using VPD at the leaf scale could help to improve the performance of the SIF-T relationship. Second, SIF data from four sites were measured by different instruments and derived by different methods as above-mentioned. Moreover, the field of view (FOV) and heights of the observation systems vary among different sites. The emergence of remotely sensed SIF will fill the gap in the difference in the observation data. The data during the period of cooling of Niwot Ridge were used in our research. However, during winter, water transport of the trees was blocked due to frozen bole [19]. Most stomata were closed and there was almost no transpiration and, to our knowledge, the carbon-water coupling relationship under physiological stress remains unclear. Moreover, the site was covered by snow during the winter, but the sublimation and melting process were not included in the evaporation model due to a lack in parameters about the snowpack, which might undermine the results of the NR site. Last but not least, the canopy-scale SIF was directly used to model T due to data restriction. Nevertheless, recent works indicated that the relationship between SIF and GPP is strongly affected by the structure of the canopy [66; 67]. We suggest that downscaling SIF from the canopy scale to the photosystem scale may improve the performance of the developed methods. Due to the absence of direct measurements of T during the study period, three models were calibrated by ET observed from EC. Net radiation is separated into energy intercepted by canopy and soil available energy by one dimensional Beer's law. The simple structure of Beer's law could introduce great uncertainty to energy partition, especially for heterogeneity canopy and plants with highly anisotropic leaves in the azimuthal direction [68], for example, maize at the early growing season at DM and HL sites. Canopy available energy was also used to estimate T in the two-layer Penman-Monteith model in the conductance method.