## 3 Results
### Relationship between SIF and PAR  
Similar to light response curves used in photosynthesis research [32], the SIF-PAR curves were fitted with the Michaelis-Menten function (Equation (7)), in which the parameters \(\mathrm{SIF_{max}}\) and \(\mathrm{Km}\) are fitting parameters. This equation suggests that an increase in PAR leads to an increase in SIF emission, up until a certain degree of saturation. The \(\epsilon_{760}\)-PAR curve was fitted using a second order polynomial function with the mustard reaching its maximum at PAR = 90 W/m\({}^{2}\) and lettuce reaching its maximum at PAR = 97 W/m\({}^{2}\). The lettuce \(\epsilon_{760}\)-PAR plot is more curved compared to its mustard counterpart (Figure 7). The SIFA-PAR curve for the lettuce shows a lot more scatter compared to its counterpart over the mustard canopy. The SIFB-PAR plots show a near-linear relationship. There is little difference in the SIFB-PAR plots between the two crops. The lower R\({}^{2}\) values for the SIFA-PAR compared to the SIFB-PAR plots suggest that there is more non-PAR related information in the SIFA compared to the SIFB.  
\[\mathrm{SIF}=\frac{\mathrm{SIF_{max}}\cdot\mathrm{PAR}}{\mathrm{Km}+\mathrm{ PAR}} \tag{7}\]  
Figure 6: Evolution of SIFA, SIFB, \(\epsilon_{760}\), FCVI, PRI for the lettuce campaign. The drought conditions are given by the VPD, PAR, soil water potential and soil moisture.  
Response of \(\epsilon_{760}\) and SIFBY to Different Light Intensities under Light and Water Limitation  
Figure 8 shows the daily correlation coefficient between PAR and two SIF related variables: \(\epsilon_{760}\) and SIFBY for both the lettuce and mustard datasets. They each show a different behaviour. The daily \(\rho\) between \(\epsilon_{760}\) and PAR show a high, positive \(\rho\) on days with clear light-limitation values (e.g., between DOY 196 or DOY 245). This correlation switches to an anti-correlation in the case of water limitation, as seen between DOY 198 and DOY 205 for the mustard dataset and between DOY 246 and DOY 251 for the lettuce dataset. This negative \(\rho\) is quick to switch to a positive \(\rho\) on days with a lower VPD, or on days with a lower pF value. Examples are the increased \(\rho\) between DOY 206 and DOY 215 for the mustard dataset and between DOY 252 and DOY 260 for the lettuce dataset. The correlation between SIFBY and PAR remained between 0.5 and 1 for almost the entire growing season for both crops. A decrease in the SIFBY-PAR correlation is found between DOY 199 and DOY 205 for the mustard dataset, which corresponds to days with intense water limitation. The period between DOY 205 and DOY 209 still has a low soil water availability, but the period is cloudier, lowering the PAR and therefore putting the plant in a light-limited regime for large parts of the day. The anticorrelation between PAR and \(\epsilon_{760}\) is the most expressed on DOY 203 and DOY 204, corresponding to the days with the highest pF values. Similarly, a drop in the \(\rho\) between SIFBY and PAR is found on DOY 250 and DOY 251 for the lettuce dataset, corresponding to two days with clear water limitation.  
Figure 7: Fitted (black lines) and observed (red dots) values of SIFA, SIFB and \(\epsilon_{760}\) in function of PAR.