## 3 Results
### Model-Data Agreement on Half-Hourly and Daily Time Scales  
Two methods of parameter adjustment, optimizing the key parameter \(\varepsilon_{max}\) and adding the soil water factor, had the same effects on performances of the MODIS GPP algorithm. Examples are presented for one representative year of each site (Table 1) because the behavior is comparable from year to year in each simulation. On half-hourly time scale, \(\sigma_{norm}\) values tended to increase linearly from 0.77 to 0.97 for LUE and from 0.80 to 0.97 for LUE-SW, in \(R\) of 0.74-0.92 and 0.78-0.92, respectively (Figure 1a), indicating that adding the soil water factor to the algorithm could only improve GPP simulation slightly. The two-leaf simulation could well quantify canopy carbon assimilation, in which the average \(R\) and \(\sigma_{norm}\) were 0.882(\(\pm\)0.042) and 1.007(\(\pm\)0.118), respectively, on a half-hourly time scale. LUE and LUE-SW still had same performances after accumulating half-hourly GPP into 8-daily average values (Figure 1b). Note that although the key parameters had been optimized for all three models at each site, the standard deviations of estimates by two one-leaf models were lower than those of observation systematically. The average \(\sigma_{norm}\) values in LUE-SW decreased by 0.102 and 0.162 on half-hourly and 8-day average time scales, respectively, compared with the two-leaf model. These analyses suggest that parameter optimization is available for compensating the error caused by ignoring soil moisture, but is not for the model structural errors caused by the canopy upscaling strategy. Moreover, we quantified differences among MOD17A2, \(\mathrm{LUE_{def}}\) and three parameter-adjusted simulations (Figure 1b). Site-specific parameters made the simulations more robust than when default values for light use efficiency models were used overall. For most sites we selected, \(\sigma_{\mathrm{norm}}\), which were ranged from 0.55 to 1.12, increased with \(R\) in MOD17A2. The excluded sites are the CA-NS1 (site number 10), FR-Pue (site number 12), IT-Cpz (site number 13), DK-Sor (site number 17), CA-Mer (site number 18), and CA-NS6 (site numbers 19), most of which are deciduous ecosystems. There was no consistency in sites with large or small \(\sigma_{\mathrm{norm}}\) between \(\mathrm{LUE_{def}}\) and MOD17A2. For instance, in the CA-NS1 site, \(\sigma_{\mathrm{norm}}\) increased by 0.45 from LUE (0.76) to \(\mathrm{LUE_{def}}\) (1.21), and then by 0.70 from \(\mathrm{LUE_{def}}\) to MOD17A2 (1.91), which were similar for FR-Pue and CA-NS6. In the ES-ES1 site (site number 5), the value increased by 0.40 from LUE (1.19) to \(\mathrm{LUE_{def}}\) (1.59), but decreased by 0.25 from LUE to MOD17A2 (0.94). These results implied that poor parameterization is one reason for errors in MOD17A2, but not for all sites. Errors introduced by parameters could be compensated or intensified by uncertainty in meteorological and vegetation data. \end{table}
Table 2: Model parameters \({}^{\mathrm{a}}\) derived from the 21 selected tower sites for nine plant functional types. Parameter differences among plant functional types, biome types and climate zones were determined using the one-way analysis of variance. We further compared the daily simulations with the EC observations using the linear regression analyses for each PFT, as shown in Figure 2, whereas the daily observations were averaged into 8-day values to compare with MOD17A2. The slopes of the MODIS product varied largely from 0.49 to 1.50, and the \(R^{2}\) ranged from 0.46 to 0.89. Adopting site-specific parameters and input data effectively improved the accuracy of simulations. Further improvements in both correlation and variability were achieved by using the two-leaf strategy. The biases of GPP simulated by the two-leaf Farquhar model were relatively small for nine PFTs, with the slopes of 0.81-1.07 and \(R^{2}\) of 0.67-0.92. Overall, model-data agreement across the selected 21 sites was better for the two-leaf model than for the one-leaf model.