## 3 Results and Discussion  
### Test of Three Methods for Estimating the Fraction of Sunlit Leaves  
With the three models, three sets of \(P_{T}\) were derived from multi-angle datasets. Figure 1 showed the variations of three sets of \(P_{T}\) with different view angles within an observation cycle from 10:45 to 11:00 on April 11. \(P_{T}\) from model I and model II showed quite similar trends but totally different values. Considering the penumbra effect, a substantial portion of penumbra was considered as shaded leaves in model II, leading to the much lower values of \(P_{T,II}\) than that of \(P_{T,I}\). \(P_{T}\) from model III exhibited a larger variation range than the other two models, with a slightly different variation trend. High values of \(P_{T,III}\) matched those of \(P_{T,I}\) well, while low values were close to those of \(P_{T,II}\). High values of \(P_{T}\) were observed from backward looking (sensor pointing north) and low values were observed from forward looking (sensor pointing south). At the same view azimuth angle, larger view zenith angle had bigger values of \(P_{T}\). \(P_{T,III}\) from forward looking had low values with changing view zenith angle. Model III assumed a uniform canopy and used statistical methods to simulate \(P_{T}\)[70; 79], which meant that it needed a large sample for satisfying this assumption. This indicated that model III cannot capture small structural changes from the real canopy, which was heterogeneous, so that the variation of \(P_{T,III}\) was different from the other two. Figure 1: \(P_{T}\) estimated from three models. Data observed from 10:45 to 11:00 on April 11, 2013 were displayed here. The view zenith angle was the same as solar zenith angle (triangles) to finish a horizontal cycle at the beginning of the observation cycle, and then changed to (42\({}^{\circ}\), 52\({}^{\circ}\), 62\({}^{\circ}\)) for each view azimuth angle (backward and forward looking changing alternatively, defined from geodetic north). Different symbols represent different view zenith angles. The correlations between observed PRI (PRI\({}_{\text{obs}}\)) and inversely retrieved PRI (PRI\({}_{\text{inv}}\)) from estimated \(P_{T}\) were used to evaluate the accuracy of three models. The frequency of the correlations at different significance levels was a proxy for accuracy. Figure 2 showed variations of the frequencies of the models I and II over the study period (number of measurements = 5700). PRI\({}_{\text{inv}}\) from both models matched observed PRI well (\(>\)70% samples) with a significance level of 95% over the entire period. Model I performed marginally better than model II either in each month or over the entire period. The solid lines in Figure 2 showed variations of the mean residuals (multiplied by 100) throughout the six months, which include estimation errors and PRI of sunlit background (shaded background was approximately 0), as PRI of background was presumed to be constant and not taken into account. Residuals in model I were considerably smaller than those in model II, indicating model I was better than model II. Moreover, the difference of PRI between sunlit and shaded background in the dry season (from July to September) [78] was theoretically higher than that of wet background in the rainy season (from April to June), indicating that residuals should be large in the dry season [73]. In model I, mean residuals in July and August were larger than other months. The mean residual in September was small probably due to large solar zenith angle and more litter cover on the ground. However, in model II, a big part of the penumbra region was treated as shaded leaves, so that the fraction of leaves exposed to diffuse radiation contributed to \(P_{S}\). Residuals in model II varied in a large range and were much larger in the rainy season than in the dry season, proving that model II was of lower accuracy due to underestimated \(P_{T}\) especially in the rainy season when the fraction of diffuse radiation was high.