## 3 Results and Discussion
### Test of Three Methods for Estimating the Fraction of Sunlit Leaves
As in model II, fThis further indicated that the penumbra region was better represented by sunlit leaf conditions under light stress, and model I had a higher accuracy. As the ray tracing treatment of GOST was computationally demanding, model III was more computationally intensive than the other two models by several orders of magnitude to simulate \(P_{T}\) and \(P_{S}\). Therefore, only data acquired in April were processed using model III to compare its accuracy with those of the other two models. Figure 3 showed differences between the frequencies of the three models in April. The accuracy of model III was higher than the other two models under most significant levels. However, its leading position faded away with increases of significance level from 0.05 to 0.001. Its accuracy was lower than that of model I at significance level of 0.0001. The mean residuals (multiplied by 1000) of PRI\({}_{\text{inv}}\) of model III were larger than residuals of model I but smaller than those of model II. Figure 2: The data fraction, expressed as percent frequency, that reaches a level of significance (\(p<0.05\)) in the correlation between observed and retrieved photochemical reflectance index (PRI) values using model I and model II within every 15-min interval during the study period from April to September. The solid lines represent the mean residuals (multiplied by 100) of retrieved PRI in each month. The enumbra region occupied a substantial portion of the conifer forest canopy. To accurately estimate the fraction of sunlit leaves in the canopy, the way to treat penumbra region was vital for the estimation accuracy (T  
which was of low PRI values, was observed due to the sun-viewer geometry, so that the value of PRI\({}_{\text{b}}\) was as low as that around noon and had marginal diurnal variation. PRI\({}_{\text{t}}\) reduced effect of sun-viewer geometry and had similar diurnal variation with LUE. Seasonal variations of daily PRI\({}_{\text{b}}\), PRI\({}_{\text{t}}\), LUE and APAR averaged from half-hourly data from 10:00 to 15:30 per day were shown in Figure 5. LUE and APAR exhibited quite inversely similar seasonal trends. During the period from day 218 to 225, when a long-term heat wave with high values of APAR occurred [78], both PRI\({}_{\text{b}}\), PRI\({}_{\text{t}}\) and LUE decreased, whereas PRI\({}_{\text{b}}\) seriously declined but the relationship between PRI\({}_{\text{t}}\) and LUE also broken down under severe heat wave [73]. As the study period was the growing season of this confer forest while the chlorophyll content and LAI changed marginally [73], there was no obvious seasonal variations of these four terms were observed. Figure 4: Diurnal variations of half-hourly PRI\({}_{\text{b}}\), PRI\({}_{\text{t}}\), light use efficiency (LUE) and absorbed photosynthetically active radiation (APAR) from 8:00 to 17:00. The coefficients of determination (\(R^{2}\)) of LUE and APAR with PRI\({}_{\text{b}}\) and PRI\({}_{\text{t}}\) were also calculated. The grey areas denote the standard deviations of each of the four terms. Figure 5: Seasonal variations of daily PRI\({}_{\text{b}}\), PRI\({}_{\text{t}}\), LUE and APAR averaged from half-hourly data from 10:00 to 15:30 per day. The solid line indicates the moving averages of the five samples. Figure 6 showed the number of days on which the correlation coefficients (\(R\)) were significant at different levels (\(p\)). The \(R\) between half-hourly \(\mathrm{PRI_{b}}\) or \(\mathrm{PRI_{t}}\) and LUE (Figure 4a) or APAR (Figure 6b) on individual days were calculated with more than five good-quality observations from 7:00 to 17:30, when the solar zenith angle was less than 75\({}^{\circ}\). As PRI was known to be positively correlated with LUE during the growing season, the numbers of days that \(\mathrm{PRI_{t}}\) was positively correlated to LUE at the significance levels of 0.01 and 0.001 are almost double those of \(\mathrm{PRI_{b}}\) (Figure 6a).