# Evaluation of Clumping Effects on the Estimation of Global Terrestrial Evapotranspiration
## 5 Results
### Leaf Clumping Effects on ET Estimation and Its Components for Various PFTs
Figure 10: Variations of (**a**) PPFD, (**b**) R\({}_{n}\), (**d**) gsw, (**e**) the leaf-level transpiration rate (T) for a representative sunlit and a representative shaded leaf in the overstory and understory canopies; (**c**) LAI and (**f**) canopy-scale transpiration rates (T) for overstory and understory canopies with \(\Omega\), when true LAI is used ignoring clumping (Case II). Overstory and understory LAI are set as 4.0 and 0.4, respectively, which are common in a typical conifer forest. \(\theta=45^{\circ}\). Ta = 15 \({}^{\circ}\)C. Overstory canopy temperature = 14 \({}^{\circ}\)C. Understory canopy temperature = 12 \({}^{\circ}\)C. Ground temperature = 12 \({}^{\circ}\)C. Relative humidity = 80%. Wind speed is set as 6.0 m s\({}^{-1}\). Downward shortwave radiation above the canopy is set as 500 W m\({}^{-2}\). The albedo of overstory and understory leaves in visible- and near-infrared bands are set as 0.035 and 0.23, respectively. The red open and filled diamonds represent the overstory sunlit and shaded components, respectively; the blue open and filled circles represent the understory sunlit and shaded components, respectively; the crosses represent the total of the four components. For the same L\({}_{\rm e}\), the overstory or understory shaded LAI as well as total LAI increased with the decrease of \(\Omega\) (more clumped) while overstory or understory sunlit LAI were invariant (Figure 11c). When L\({}_{\rm e}\) is used in estimating \(T\) ignoring clumping, leaf-level absorbed PPFD, R\({}_{\rm n}\), g\({}_{\rm sw}\), and \(T\) of the overstory representative sunlit leaf were invariant while those of the overstory representative shaded leaf were overestimated (Figure 11). Canopy-level overstory sunlit T was invariant while the shaded T and total T were negatively biased when effective LAI is used ignoring clumping (Figure 11f). Using the same example as mentioned above, effective LAI for the overstory and understory canopies are set as a constant of 2.0 and 0.2, respectively. If \(\Omega\) is 0.5, absorbed PPFD, R\({}_{\rm n}\), g\({}_{\rm sw}\) and T for the overstory representative shaded leaf at \(\theta=45^{\circ}\) is 75.8 umol m\({}^{-2}\)s\({}^{-1}\), 24.3 W m\({}^{-2}\), 1.76 mm s\({}^{-1}\) and 0.0053 g H\({}_{2}\)O m\({}^{-2}\) s\({}^{-1}\), respectively, when clumping is considered, while they are 155.7 umol m\({}^{-2}\)s\({}^{-1}\), 42.5 W m\({}^{-2}\), 2.64 mm s\({}^{-1}\) and 0.0089 g H\({}_{2}\)O m\({}^{-2}\) s\({}^{-1}\), if clumping is ignored (Figure 11). The RE in the estimation of PPFD, R\({}_{\rm n}\), g\({}_{\rm s}\),w, and T when clumping is ignored will be 105.3%, 74.8%, 50.0%, and 67.9%, for the overstory representative shaded leaf. Meanwhile, the sunlit LAI in overstory and understory are unchanged and the shaded LAI in overstory and understory were negatively biased by 68.2% and 56.3% (\(\Omega\) = 0.5). Total LAI was underestimated by 50.0% if \(\Omega\) is 0.5 (Figure 11c). Accordingly, T of the overstory sunlit canopy would be unchanged while that of the shaded counterpart was underestimated by 46.8% (Figure 11f). On the other hand, \(T\) of understory sunlit canopy would be underestimated by 11.1% while that of the shaded counterpart was underestimated by 33.3%. The total canopy-level transpiration rate was underestimated by 13.6% in this Case (Figure 11f).