## 4 Discussion
### Link between Parameter Sets and Model Structures  
A revision of parameters in GPP simulation could cancel errors caused by model structure, including coupled stomatal conductance and carbon assimilation scheme [7], two-stream radiative transfer, and leaf photosynthesis [2]. We evaluated the application of parameter adjustment in the MODIS land algorithm. The results demonstrated that the performances of parameter-optimized LUE and LUE-SW were identical in terms of GPP estimation (Figure 1), but the optimized \(\varepsilon_{max}\) in the latter model had lower standard deviation than the former for sites within the same PFT (Table 2), even though the parameters categorized according to PFTs are not the best option. After optimizing parameters in simple photosynthesis and transpiration models using measurements from 101 EC flux towers, [PERSON] _et al._[81] pointed out that a simple PFT classification could induce the uncertainties in the photosynthesis and water vapor flux estimates, and site-year parameters gave the best predictions. However, this parameter uncertainty could be reduced by adding control factors, such as considering the scale of soil moisture in the one-leaf model (Table 2). Furthermore, we quantified the relationships between annual average soil water factors with optimized \(\varepsilon_{max}\) in LUE and in LUE-SW, excluding four sites for which \(\varepsilon_{max}\) was greater than 1.3 gC\(\cdot\)MJ\({}^{-1}\) (Figure 5). The regression analysis shows that the \(\varepsilon_{max}\) in LUE decreased linearly with the soil water factor. The reduction was as much as a half in LUE-SW, as evidenced by the slopes reducing from 0.77 to 0.38 and by the constants increasing from 0.32 to 0.73, especially for sites with low annual average soil water factors and large soil water changes. It should be noted that the annual rainfall values of our selected sites were all greater than 200 mm\(\cdot\)yr\({}^{-1}\) (Table 1). More validations were needed in those water-limited regions with annual precipitation less than 100 mm\(\cdot\)yr\({}^{-1}\)[8,96]. Moreover, parameter adjustment could not compensate all structural errors, such as the error caused by the canopy upscaling strategy. Although we optimized the parameters using data assimilation, GPP estimated by both LUE and LUE-SW still had large negative biases in summer (Table 3). The biases were reduced by 81.9% using the two-leaf Farquhar model. [PERSON] _et al._[36] compared 26 models with standard parameters at 39 EC flux tower sites across North America and found that the average GPP bias was \(-0.87\) gC\(\cdot\)m\({}^{-2}\cdot\)day\({}^{-1}\) in summer (Figure 2a), which is between the biases of LUE-SW (\(-1.21\) gC\(\cdot\)m\({}^{-2}\cdot\)day\({}^{-1}\)) and the Farquhar model (0.17 gC\(\cdot\)m\({}^{-2}\cdot\)day\({}^{-1}\)) in the same season that we estimated (Table 3). In their study, more than half of the models adopted the one-leaf upscaling strategy. An underestimation in the MODIS GPP product during summer was also reported by [PERSON] _et al._[24], who evaluated different regions across the conterminous U.S. The reason for underestimation is that the one-leaf strategy ignores a large contribution of diffuse PAR to the shaded leaves, and the contribution is more efficiently absorbed by the canopy for photosynthesis than direct PAR. In the strategy of separating the canopy into two parts, the sunlit leaves achieve a high rate of light-saturated photosynthesis and have a low light use efficiency, whereas shaded leaves are only limited by the electron transport related to direct and diffused radiation, which lead to a high light use efficiency [25, 73, 97, 98]. Many efforts have been made to improve the structure of the MODIS land algorithm by considering photosynthesis rate saturation or light saturation. [PERSON] _et al._[71] adopted a saturating function for light use efficiency adjustment that allowed for saturation of gross photosynthesis at a high irradiance.