## 2 Materials and Methods
### Active Fluorometry in the Field  
Fluorescence parameters and incident PAR at the leaf level were obtained with a PAM-2000 (Heinz Walz Gmbh, Eichenring, Effeltrich, Germany) equipped with a leaf clip holder. Fluorescence emission was filtered before detection with a RG9 long-pass filter (Schott, Germany, cut-off wavelength 700 nm) and a heat protection filter. The RG9 filter prevents from detecting excitation light (650 nm) and defines a spectral detection band in the far red, without any sensitivity to the red peak. PAM-2000 measurements were taken at 8:30, 12:00, and 16:00 (Coordinated universal time, UTC). At each measurement time, around 20 positions on different leaves in the canopy were randomly selected, and the following measurements were performed at each position \(p_{i}\): (i) incident PAR on the leaf (\(PAR_{i}\)); (ii) steady state fluorescence under ambient light (\(Fs_{i}\)); and (iii) maximum fluorescence level under a saturating light pulse (\(F^{\prime}m_{i}\)). Care was taken to avoid changing the leaf orientation by the measuring process. From these measurements, the photochemical yield (\(\Phi_{i}\)) of photosystem II (PSII) was derived according to [44]:  
\[\Phi_{P_{i}}=\frac{F^{\prime}m_{i}-Fs_{i}}{F^{\prime}m_{i}}=\frac{\Delta F_{i }}{F^{\prime}m_{i}} \tag{8}\]  
Leaf measurements taken at a given time were averaged using \(PAR_{i}\) as weight coefficients. As the intensity of the pulsed excitation and the configuration of the leaf clip remained constant, \(Fs_{i}\) can be considered as a relative measurement of the apparent fluorescence yield at position \(p_{i}\), which is defined as the ratio between emitted fluorescence and incident light. Under natural sunlight, fluorescence flux emitted by each leaf area at position \(p_{i}\) can be approximated by \(PAR_{i}*Fs_{i}\), if we neglect variations of apparent yield caused by chlorophyll content and excitation wavelength. This approximation can be justified by the fact that leaf chlorophyll content is high (i.e., >40 \(\upmu\cdot\text{cm}^{-2}\)) and that incident radiation is almost totally absorbed. The fluorescence flux at each individual position sums up to produce the total fluorescence flux emitted by the whole leaf area of the canopy. Hence, we can define the mean apparent fluorescence yield of the total leaf area as:  
\[\overline{F}_{s}=\frac{\sum_{i}PAR_{i}\times Fs_{i}}{\sum_{i}PAR_{i}} \tag{9}\]  
Ideally, the whole set of individual measurements should cover exactly the total leaf area of the canopy. Practically, we only have a subsample of it. However, we assume that the resulting weighted mean is still an approximation of the true value within the experimental error caused by imperfect sampling.  
Similarly, electrons flux--which varies as the product of \(\Phi_{P}\) and PAR--sums up on the total leaf area of the canopy, and we can define the mean photochemical yield (\(\overline{\Phi}_{P}\)) as:  
\[\overline{\Phi}_{P}=\frac{\sum_{i}PAR_{i}\times\Phi_{P_{i}}}{\sum_{i}PAR_{i}} \tag{10}\]  
Here we again assume (as above) that \(\overline{\Phi}_{P}\) can be considered as an approximation of the true canopy photochemical yield, despite the error introduced by under-sampling.