## 4 Discussion  
### Problems with the Diurnal Cycle in the CLM4  
Comparison of site level observations and model simulations shows CLM4's FPAR has a slight diurnal cycle (FPAR at noon is around 80% of the maximum) but at a much smaller magnitude than site level observation (FPAR at noon is around 30% of the maximum). Sun angle could influence radiation transfer process through both between-crown gap probability and within-crown gap probability [19]. In order to identify the reasons for the insignificant angular effect in the CLM4, we used the 2-stream module from the CLM4 and conducted a sensitivity test in a two-element model that is simplified from the current CLM4 land surface scheme. In the two-element model, a grid is set consisting of two patches: one is vegetated with 100% canopy coverage, its coverage is set to be \(fc\); and the other is bare soil with a fraction of \((1-fc)\). Related parameters are set as follows: (1) leaves and stems are set as blackbodies with reflectance and transmittance of 0; (2) ground albedo is 0.2 for both visual and infrared bands, and for both direct and diffuse radiation; and (3) only direct solar radiation is considered. We calculate the fraction of canopy absorbed radiation in incident solar radiation for the whole grid under different \(fc\) and LAI conditions. A 3-D model is used for comparison. It is a new framework based on the single bush model [13, 62]. A one-layer canopy model is constructed that considers shadows, inter-canopy interactions, and the consequences of low sun (elevation) angles. It is used to build a three-layer canopy that considers ground shadow, within-crown gaps, between-crown gaps, and inter-canopy interactions, and thus is regarded as a benchmark [13, 62]. Figure 10: FPAR in relation to \(\mu\) Blue lines show simulations from the 2-stream solution in the CLM4 (blue) and green lines show simulation from the 3D scattering model at \(fc=0.2\), 0.4 and 0.8 and LAI = 0.5, 3.0 and 6.0. Experimental results (Figure 10) show the fraction of radiation absorbed by canopy would change according to the solar zenith angle when LAI is low (_i.e._, 0.5). This verifies that the minor diurnal cycle in the current CLM4 simulation is attributed to the 2-stream solution, taking into account the angular effect inside the canopy layer. Such an angular effect in the canopy radiative transfer process only contributes to only a small portion of the overall angular effect (as illustrated by the 3D scattering model in Figure 10) Therefore, the problem with the diurnal cycle in the CLM4 is not the radiative transfer process within the canopy but rather the radiative transfer process outside of the canopy. Next we examine the current CLM4 patch framework. Bare soil and plants are separately allocated into different patches. For the patch with a plant type, the canopy fraction is set to be 100%. According to this assumption, the plants become \"shadowless\"; only the soil under the canopy might be blocked from solar radiation by the canopy, but the soil between canopies can always receive solar radiation without any canopy blocking as allocated in a separate patch. As a result of this \"shadowless\" canopy assumption, the bare soil is 100% exposed to solar radiation, and such a full-exposure in bare soil is the reason for the absences of an angular effect in the current CLM4. Therefore, we need to introduce several parameters to present such an angular effect. We propose a possible solution for this problem in the current CLM4 land surface scheme and illustrate it in a two-element model. The solution is based on the boundary condition inferred from the Boolean Scene Model: (1) vegetation has 100% coverage over the grid land when the solar zenith angle is 90 \(\lx@math@degree\); and (2) a coverage of \((fc)\) when the solar zenith angle is 0 \(\lx@math@degree\), in the view of the sun.