## 5 Variability of the \(Q_{p}/R_{s}\) Ratio with the CIE Standard Sky Types  
Figure 11 shows the average photosynthetic photon flux density to broadband solar irradiance, \(Q_{p}/R_{s}\), ratio, calculated on a ten minutes basis, for each CIE standard sky type. Clear sky types 12, 13, 14, and 15 showed smaller standard deviations (from 0.06 to 0.11 \(\upmu\)mol\(\cdot\)J\({}^{-1}\)) and a smaller interquartile range (from 0.05 to 0.09 \(\upmu\)mol\(\cdot\)J\({}^{-1}\)). However, the numbers of outliers were important for all these categories. The dispersion of the data within the categories corresponding to overcast and partial overcast skies was similar, with standard deviations between 0.15 \(\upmu\)mol\(\cdot\)J\({}^{-1}\) (sky type 4) and 0.21 \(\upmu\)mol\(\cdot\)J\({}^{-1}\) (sky type 9) and an interquartile range between 0.16 \(\upmu\)mol\(\cdot\)J\({}^{-1}\) (sky types 3 and 4) and 0.21 \(\upmu\)mol\(\cdot\)J\({}^{-1}\) (sky types 8 and 9). The highest values of the \(Q_{p}/R_{s}\) ratio were under CIE standard sky types 1, 2, 3, and 4; all categories of overcast sky conditions. The categories of clear skies (CIE standard sky types from 11 to 15) showed the smallest values of the ratio. Sky types 5 and 9 presented an anomalous behavior. They are categorized as overcast and partial overcast categories, but the average values of the \(Q_{p}/R_{s}\) ratios for both sky types were closer to the values of clear sky categories. Furthermore, sky type 9 showed the smallest average value: \(1.89\pm 0.21\)\(\upmu\)mol\(\cdot\)J\({}^{-1}\). The FOCs of both sky types, 5 and 9, were very scarce in the measurement campaign: 1.65% and 0.64%, respectively. CIE standard sky type 5, described as \"overcast, foggy or cloudy, with overall uniformity\", presented high uniformity in terms of illuminance and broadband solar irradiance, as well sky type 9, described as \"partly cloudy with a shaded sun position\". When the 15 CIE standard sky types were reduced to three, (overcast, from sky types 1 to 5, partial, from sky type 6 to 10, and clear sky, from sky types 11 to 15), the average photosynthetic photon flux density to broadband solar irradiance ratio, \(Q_{p}/R_{s}\), increased when sky cloudiness increased, as shown in Figure 12.  
Figure 11: Box-plot ratio of photosynthetic photon flux density to broadband solar irradiance, \(Q_{p}/R_{s}\), for each CIE standard sky type. Figure 12: Box-plot of the ratio of photosynthetic photon flux density to broadband solar irradiance, \(Q_{p}/R_{s}\), by CIE cloudiness sky classifications. The average \(Q_{p}/R_{s}\) ratio for clear skies and for overcast skies was \(1.90\pm 0.11\) umolJ\({}^{-1}\) and \(1.98\pm 0.16\) umolJ\({}^{-1}\), respectively. Partial cloudy skies showed the highest dispersion of the data, with standard deviation and interquartile range values of 0.17 and 0.19 umolJ\({}^{-1}\), respectively. However, the clear skies dataset had the largest number of outliers. The Spearman correlation coefficient is a non-parametric measure of rank correlation, to determine the strength and direction of the relationship between two variables. If two datasets X and X' are strongly correlated, then the Spearman coefficient will be 1 (direct correlation) or if otherwise -1 (inverse correlation). Although \(r(Q_{P},CIE)=0.56\) (\(p\)-value \(<0.001\)) and \(r(R_{s},CIE)=0.57\) (\(p\)-value \(<0.001\)) both imply a moderate correlation, \((Q_{P}/R_{s},CIE)=-0.23\) (\(p\)-value \(<0.001\)). The \(p\)-value determine the significance of the results in relation to the null hypothesis (the results are due to random chance). The lower the p-value, the greater the statistical significance of the test and greater the confirmation of the hypothesis [50]. As the \(p\)-value was lower than 0.05 in all the tests, there was a statistically significant difference between the average \(Q_{p}/R_{s}\) ratios for each type of CIE sky, at a significance level of 5%.