## 3 Results and discussion  
### Seasonal Variations in Crop WUE with Environmental and Biological Controls  
Climate of the region is northern continental, with short, moist growing periods in summer and cold, relatively dry winters, which has a profound effect on crop growth and the functional properties related to carbon and water budgets [23, 44, 45]. Crop growing season, including corn and soybean, in this region generally starts in late May to the end of October. The relationships between averaged 8-day tower-based WUE and the environmental conditions including R\({}_{\text{g}}\), T\({}_{\text{a}}\), VPD, P and MODIS-derived EVI data observed at US-Bo1 site during 2001 to 2006 are showed in Figures 2 and 3. Figure 2 shows the time-series of meteorological data and Figure 3 exhibits the variations in tower-based WUE. The statistical significance is examined using Pearson's correlation analysis (Table 1). We find that time-series of WUE data have distinct seasonal cycles that strongly covary with R\({}_{\text{g}}\) and T\({}_{\text{a}}\). During winter months, because low temperature and frozen soils inhibit the plant growth and photosynthetic activities,  
Figure 1: Overview of the research approach. R\({}_{\text{g}}\), T\({}_{\text{a}}\), VPD and P are observed at the flux tower sites. EVI are derived from the MODIS data. WUE\({}_{\text{EC}}\), WUE\({}_{\text{RS}}\), and WUE\({}_{\text{GR}}\) refer to ecosystem water use efficiency from flux tower measurements, the indirect estimates from NTSG MODIS products and the direct estimates based on MODIS EVI data, respectively. In addition, the data from US-Bo1 are used for calibration and another US-Ro1 site is used for independent validation of the developed model. WUE values are nearly zero. As temperature rises in the spring planting season, crops begin to grow and ecosystem photosynthetic capacity gradually increases accompanied by plant transpiration. Ecosystem WUE of both corn and soybean reached its peak value during about late July and early August, and then declined until the harvest in October. The C4 plant-corn showed greater sensitivity to solar radiation than temperature in contrast to the C3 plant-soybean (Table 1). In addition, despite the prominent role that R6 and T4 play as the main drivers of crop WUE, peak periods show a minor hysteresis effect. Except during the winter months, VPD remains at a suitable value over most of the growing period. The VPD around 10 hPa appear to be near optimal for stomatal aperture. Thus, VPD values are at best moderate, but not excessively high during these measurement periods. Moreover, VPD was more closely correlated to corn WUE than soybean WUE. Both of the two flux sites depend on precipitation during cultivation and no irrigation was applied. Approximately 63% of the annual precipitation occurred during the cultivation-period. Although it was not significantly correlated to WUE on 8-day periods, natural rainfall is vital to crop growth as the only water supply. Figure 2: Seasonal and interannual variations of solar radiation (R6), air temperature (T4), vapor pressure deficit (VPD), precipitation (P) and enhanced vegetation index (EVI) observed at the annual corn/soybean rotation field (US-Bo1) during 2001–2006, with the growing season highlighted. As a proxy of the biological properties that reflected the response of vegetation to environmental controls, time series MODIS-derived EVI data also showed a strong consistency with seasonal and interannual variations in ecosystem WUE. 8-day EVI data presented fairly similar patterns as WUE during the growth period of crops. Moreover, the vegetation index captured well the beginning and ending of the crop growing season in 2001-2006. EVI started to increase in late May, reached peak values during peak growth (July-August), and declined after crop senescence or harvest (October). Correlation coefficients between EVI and WUE reached 0.906 for corn and 0.950 for soybean, respectively.