## Appendix B Two-Leaf Algorithm for LUE Calculation  
This algorithm differentiates the transfers of diffuse and direct radiation within a canopy and separates leaves into sunlit and shaded portions. The total LAI can be separated into sunlit LAI (\(L_{sun}\)) and shaded LAI (\(L_{sh}\)). Sunlit leaves can absorb both direct and diffuse radiation, while shaded leaves can only absorb diffuse radiation. The APAR on per unit leaf area was calculated separately for sunlit (APAR\({}_{\text{sun}}\)) and shaded leaves (APAR\({}_{\text{sh}}\)) [21, 59, 60, 61], and the total canopy APAR calculated using this algorithm was termed as TL\({}_{-}\)APAR:  
\[\text{TL\_APAR}\ =\ \text{APAR}_{\text{sun}}\times L_{sun}\ +\ \text{APAR}_{\text{ sh}}\times L_{sh} \tag{1}\]  
APAR on the per unit leaf area was calculated separately for sunlit (APAR\({}_{\text{sun}}\)) and shaded leaves (APAR\({}_{\text{sh}}\)), and sunlit LAI (\(L_{sun}\)) and shaded LAI (\(L_{sh}\)) were calculated as [21, 59, 60, 61]:  
\[L_{sun}\ =\ 2\cos(1-\text{e}^{-0.5\Omega\times\text{LAI}/\cos\theta}) \tag{2}\]  
\[L_{sh}\ =\ \text{LAI}-L_{sun} \tag{3}\]  
\[\text{APAR}_{\text{sun}}\ =\ (1-\alpha)\times(\text{PAR}_{\text{dir}}\times \cos\beta/\cos\theta\ +\ \text{APAR}_{\text{sh}}) \tag{4}\]  
\[\text{APAR}_{\text{sh}}\ =\ (1-\alpha)\times(1-\delta)\times((\text{PAR}_{ \text{dir}}-\text{PAR}_{\text{diff},\text{a}})/\text{LAI}\ +\ C) \tag{5}\]  
\[\ C\ =\ 0.07\Omega\times\text{PAR}_{\text{dir}}\times(1.1-0.1\text{LAI})\text {e}^{-\cos\theta}\ (\text{A5}) \tag{6}\]  
\[\text{PAR}_{\text{diff},\text{u}}\ =\ \text{PAR}_{\text{diff}}\times\text{e}^{-0.5 \Omega\times\text{LAI}/(0.537\ +\ 0.025\text{LAI})} \tag{7}\]  
\[\delta\ =\ 0.2(1-\text{e}^{-0.5\Omega\times\text{LAI}/(0.537\ +\ 0.025\text{LAI})}) \tag{8}\]  
where \(\alpha\) is the albedo related to vegetation types set as 0.15 for coniferous forest; PAR\({}_{\text{diff}}\) and PAR\({}_{\text{dir}}\) are the diffuse and direct components of incoming PAR, respectively, and they are calculated using equation 9; PAR\({}_{\text{diff},\text{u}}\) is the diffuse PAR under the canopy; (PAR\({}_{\text{diff}}-\text{PAR}_{\text{diff},\text{u}}\))/LAI represents the diffuse PAR on per unit leaf area within the canopy; C quantifies the contribution of multiple scattering of the total PAR to the diffuse irradiance per unit leaf area within the canopy; \(\beta\) is the mean leaf-sun angle and is set as \(60^{\circ}\) for a canopy with spherical leaf angle distribution; \(\delta\) is a correction for the nonlinear response of leaf photosynthesis to the vertical variation of diffuse radiation within the canopy; and \(\theta\) is the solar zenith angle. Figure 10: Picture of outdoor part of iAMSPEC II on the tower. Diffuse and direct PAR were partitioned [21, 59, 60] with parameters calibrated using the daily clearness index (CI) and total incoming radiation as:  
\[\mathrm{PAR_{diff}}\,=\,\mathrm{PAR}\times(0.7702\,+\,3.6895\mathrm{CI}-15.452 \mathrm{CI}^{2}\,+\,16.9828\mathrm{CI}^{3}-5.7773\mathrm{CI}^{4})\] (A9)  
Half-hourly \(\mathrm{LUE_{c}}\) was calculated as:  
\[L_{sun}\ =\ 2\cos(1-\text{e}^{-0.5\Omega\times\text{LAI}/\cos\theta}) \tag{2}\]0 (A10)  
_Appendix C. Performance of LUEc Calculated Using Two-Leaf Algorithm_  
Considering the impact of varying irradiance and shadow fraction of canopy on temporal variation of LUE, we re-calculated canopy \(\mathrm{LUE}\) (\(\mathrm{LUE_{c}}\)) on the basis of a two-leaf model, and Figure 11 showed the results. Figure 11 illustrated the difference between APAR calculated with FPAR and two-leaf APAR (TL_APAR) calculated using the two-leaf LUE model. APAR was totally higher than TL_APAR, which indicated that the FPAR algorithm might overestimate the part of absorbed PAR intercepted by non-photosynthetic parts of the canopy, especially when incident radiation was low (with more diffuse irradiance). The correlations between PRI and \(\mathrm{LUE_{c}}\) (Figure 11 and C1 Apr.-Sep.) were slightly stronger compared with the results shown before (Figures 5 and 6).