## 2 Materials and Methods  
### Rationale and Hypothesis  
To date, several studies have suggested a near-linear proportional relationship between GPP and SIF over temporal scales larger than daily [48; 58; 59]. Since stomatal opening regulates both the CO\({}_{2}\) uptake and vapour loss through transpiration, SIF may also be of use to diagnose transpiration [42; 44; 60].  
From that rationale, it follows that transpiration (T) and SIF hold a proportional relationship that is mediated by the ecosystem water-use efficiency (WUE):  
\[\mathrm{T}\propto\mathrm{SIF}\times\mathrm{WUE} \tag{1}\]  
where WUE reflects the ratio of GPP to T. While in nature WUE depends on a plethora of factors, it is widely acknowledged that the atmospheric demand for water explains a large fraction of its variability at ecosystem scale (44; 61): under conditions of high potential evaporation (E\({}_{\mathrm{P}}\)), the water loss per unit gain of carbon increases. As such, here we explore whether the fraction of E\({}_{\mathrm{P}}\) that is transpired (hereafter referred to as 'transpiration efficiency', \(\tau\)) holds a proportional relationship to the fraction of photosynthetically active radiation (PAR) that is emitted as SIF:  
\[\tau=\frac{\mathrm{T}}{\mathrm{E}_{\mathrm{P}}}\propto\frac{\mathrm{SIF}}{ \mathrm{PAR}} \tag{2}\]  
The normalization of SIF (mW/m\({}^{2}\)/sr/nm) by PAR (W/m\({}^{2}\)) allows the correction of incoming radiation changes--independent of phenological variability or physiological stress (62)--in an analogous way that the normalization of T by E\({}_{\mathrm{P}}\) buffers the effect of short-term changes in available energy. Moreover, normalizing by PAR intentionally retains the variability in SIF associated with changes in the fraction of absorbed PAR (i.e., fPAR), which allows us to employ an analogous E\({}_{\mathrm{P}}\) calculation that is merely atmospheric, so that \(\tau\) reflects the limitations of the actual ecosystem in response to the atmospheric demand for water (whether that ecosystem limitation has a structural or physiological origin). Following the findings in [PERSON] et al. (2016), in which multiple E\({}_{\mathrm{P}}\) equations were evaluated, E\({}_{\mathrm{P}}\) (W/m\({}^{2}\)) is calculated here based on the simple radiation-based formulation by [PERSON] and [PERSON] (2010):  
\[\mathrm{E}_{\mathrm{P}}=\alpha(\mathrm{R}_{\mathrm{n}}-\mathrm{G}) \tag{3}\]  
where \(\alpha\) is a constant unitless parameter (similar to \(\alpha\) in the Priestley and [PERSON] equation), R\({}_{\mathrm{n}}\) (W/m\({}^{2}\)) is the surface net radiation and G (W/m\({}^{2}\)) is the ground heat flux. [PERSON] et al. (2016) recommended using a biome-specific parameterization of \(\alpha\) rather than the universal value of \(\alpha\) = 0.8 proposed by [PERSON] and [PERSON] (2010)--see Table S1 for specific values of \(\alpha\) per biome type.  
The rationale behind the hypothesis confined in Equation (2) is illustrated in Figure 1. Given a certain amount of R\({}_{\mathrm{n}}\) and PAR, under low stress conditions (and/or high leaf area), we expect higher levels of transpiration (i.e., \(\lambda\)E), GPP and SIF than under high stress conditions (and/or low leaf area) given the same R\({}_{\mathrm{n}}\) and PAR. For the latter, we expect more sensible heat flux (H), non-radiative decay and non-photochemical quenching (Q). This hypothesis is further sustained by the results from [PERSON] et al. (2016), which, by employing an advanced radiative transfer model, showed that most of the variance in T that is left unexplained by SIF variability can be explained by changes in the atmospheric potential to evaporate water.