## 3 Results
### Performance of the PMLv2 and MODIS Products in eWUE Estimations  
Figure 6 shows the comparison of the eight-day observed eWUE and RS-based eWUE from the PMLv2 and MODIS products for C4 maize and C3 soybean at the five cropland sites. Overall, the PMLv2 product was able to achieve higher-accuracy eWUE estimates in contrast to the MODIS product, as indicated by the RMSE reducing from 2.14 g C Kg\({}^{-1}\) H\({}_{2}\)O to 1.36 g C Kg\({}^{-1}\) H\({}_{2}\)O and the R\({}^{2}\) increasing from 0.06 to 0.52 for maize, with the RMSE reducing from 1.33 g C Kg\({}^{-1}\) H\({}_{2}\)O to 0.89 g C Kg\({}^{-1}\) H\({}_{2}\)O and the R\({}^{2}\) increasing from 0.05 to 0.49 for soybean. Moreover, the MODIS product exhibited considerable underestimations and overestimations of high and low observed eWUE for both maize and soybean, respectively. By contrast, the PMLv2 product greatly reduced these above-mentioned biases found in the MODIS product but still showed moderate underestimations of high observed eWUE for maize and slight overestimations of low observed eWUE for both maize and soybean. Figure 7 shows the time series of the eight-day observed eWUE and RS-based eWUE from the PMLv2 and MODIS products at the five cropland sites. Overall, the eWUE calculated from the MODIS product was commonly much lower than the observed eWUE during the peak of growing seasons and much higher than the observed eWUE during the start and end of growing seasons for both maize and soybean. By contrast, the PMLv2 product overall better captured the seasonal variation of observed eWUE compared to the MODIS product. In particular, the eWUE calculated from the PMLv2 product was generally moderately lower than the observed eWUE for maize and was consistent with the observed eWUE for soybean during the peak of growing seasons. Moreover, the eWUE calculated from the PMLv2 product tended to be slightly higher than the observed eWUE for both maize and soybean during the start and end of growing seasons (e.g., the year 2002 at the US-Ne1 and US-Ne2 sites). Figure 6: Scatter plots of the eight-day observed eWUE and RS-based eWUE from the PMLv2 and MODIS products for C4 maize and C3 soybean at the five cropland sites. The PMLv2 eWUE was calculated as the ratio of GPP and ET from the PMLv2 product. The MODIS eWUE was calculated as the ratio of GPP from the MOD17 product and ET from the MOD16 product. Figure 8 shows the comparison of the annual observed GPP, ET, and eWUE and RS-based GPP, ET, and eWUE from the PMLv2 and MODIS products for C4 maize and C3 soybean at the five cropland sites. Overall, the PMLv2 annual GPP, ET, and eWUE performed better than the MODIS annual GPP, ET, and eWUE with lower Bias and RMSE, and higher R\({}^{2}\). For GPP and ET estimations, the PMLv2 product with a Bias of \(-256.3\) g C m\({}^{-2}\) year\({}^{-1}\) and \(26.1\) mm year\({}^{-1}\) and an RMSE of \(332.57\) g C m\({}^{-2}\) year\({}^{-1}\) and \(76.65\) mm year\({}^{-1}\) for maize  
Figure 7: Time series of the eight-day observed eWUE and RS-based eWUE from the PMLv2 and MODIS products at the five cropland sites. The PMLv2 eWUE was calculated as the ratio of GPP and ET from the PMLv2 product. The MODIS eWUE was calculated as the ratio of GPP from the MOD17 product and ET from the MOD16 product. The years with white backgrounds represent that C4 maize was planted this year. The years with grey backgrounds represent that C3 soybean was planted this year. performed better than that with a Bias of 365.36 g C m\({}^{-2}\) year\({}^{-1}\) and 72.58 mm year\({}^{-1}\) and an RMSE of 396.87 g C m\({}^{-2}\) year\({}^{-1}\) and 82.53 mm year\({}^{-1}\) for soybean, respectively. For eWUE estimations, the PMLv2 product for soybean with a Bias of 0.43 g C Kg\({}^{-1}\) H\({}_{2}\)O and an RMSE of 0.52 g C Kg\({}^{-1}\) H\({}_{2}\)O outperformed that for maize with a Bias of \(-\)0.55 g C Kg\({}^{-1}\) H\({}_{2}\)O and an RMSE of 0.71 g C Kg\({}^{-1}\) H\({}_{2}\)O.