## 3 Results and discussion
### Independent Validation of the Proposed Models  
Although the calibrated model developed at the US-Bo1 site provided fairly good estimates of crop WUE directly from MODIS EVI data, its applicability to other crop sites needs to be evaluated before spatial up-scaling of site-level observations to regional scale. Therefore, flux measurements at additional US-Ro1 crop site were used for independent validation. Comparisons between both WUEs and WUEGR with 8-day tower-based WUEEC are shown in Figures 7-9. Validation of the empirical model at the independent US-Ro1 site also exhibited a significant improvement in ecosystem WUE simulation, especially for the soybean-planting year. The WUE estimates by exclusive use of MODIS EVI data captured the seasonal variations in ecosystem WUE in spite of a slight underestimation during the peak-growth period of the corn year, which may be ascribed to the effects of different farming practices on the vegetation index. Although both US-Bo1 and US-Ro1 sites are annual corn/soybean rotation fields, US-Bo1 is under continuous no-till treatment whereas US-Ro1 adopts conventional tillage management [10,29]. The scatter plots showed that _R\({}^{2}\)_ and _RMSE_ between WUERS with WUEEC were 0.02 and 2.21 g C kg\({}^{-1}\) H\({}_{2}\)O _vs_ the values of 0.86 and 1.15 g C kg\({}^{-1}\) H\({}_{2}\)O between WUEGR and WUEEC, respectively in 2005. During the soybean-planting year--2006, _R\({}^{2}\)_ and _RMSE_ between WUERS with WUEEC were 0.23 and 1.61 g C kg\({}^{-1}\) H\({}_{2}\)O _vs_ 0.82 and 0.72 g C kg\({}^{-1}\) H\({}_{2}\)O between WUEGR and WUEEC, respectively. Therefore, all crop WUE estimates have been improved substantially with the use of EVI. However, owing to the diversity in climate conditions, crop types, and management practices [37,45,61,62], it is still challenging to develop a general a robust model for WUE estimation. For agriculture, monitoring ecosystem WUE of croplands in view of C3 and C4 photosynthetic pathways needs to be considered. Nevertheless, although our calibrated model for estimating 8-day WUE of corn and soybean captured the general tendencies, there still existed large discrepancies for individual periods such as the peak growing season of the corn-year at US-Ro1 (Figure 7). Normally, tower-based WUE of corn is generally higher than that of soybean. But the proposed models resulted in almost the same WUE values for both corn and soybean, which was notobserved in the flux tower measurements. On one hand, the flux sites and dataset used for calibration remained rather limited, whereas diverse farming practices are implemented across the globe. This challenges the general application of such models. On the other hand, our analyses and simple model for typical cropping systems in the United States indicate there is good potential for upscaling WUE especially when water is not severely limited. [PERSON] _et al._[63] showed that under water stress, plant WUE usually increased and GPP decreased. Therefore, it is necessary to examine the EVI-based models' sensitivities to drought during drought and non-drought years. [PERSON] _et al._[64] also compared four EVI-based models including the Vegetation Photosynthesis Model (VPM), Temperature and Greenness (TG) model, Greenness and Radiation (GR) model and Vegetation Index (VI) model to estimate GPP of corn and soybean croplands and grasslands under drought conditions. They found that these four models had reasonably good agreement with the GPP estimated from EC-based observations in non-drought years, while the VPM model performed best, followed by the VI, GR and TG model in drought years that may be ascribed to the VPM model incorporating a satellite-based water index. In addition to this, ecosystem WUE ultimately reflected the photosynthetic productivity per amount of water consumption; therefore, how to explain and quantify the variability of crop WUE from the environmental mechanisms remains essential.