## 2 Materials and Methods
### Satellite-Derived MODIS Products and Processing  
Currently, satellite-based products of terrestrial GPP and ET from NASA MODIS have been developed and experienced ongoing improvement during the past decade [17,24]. [PERSON] _et al._[16] identified important errors in the old GPP product (Collection 4) owing to the problems in the upstream inputs. Then, these GPP estimates were amended through improving the algorithms and perfecting the necessary parameters, which generated the enhanced Collection 5 MOD17 products. The 8-day composites of MODIS LAI/FPAR (fraction of photosynthetically active radiation) data with the resolution of 1-km were introduced into the processing methods of GPP as remote sensing-based vegetation properties. The information in the QA (quality-assessment) flags were used to gap-fill the missing data in the time-series MODIS LAI/FPAR product resulting from clouds. Near real-time meteorological data are obtained from the National Center for Environmental Prediction (NCEP) to drive the algorithm. The continuous 8-day MODIS GPP values are summed up to generate monthly and annual GPP estimates. Further, the global evapotranspiration data can be used to quantitatively evaluate the regional soil water status and energy balance, which is key for agricultural water management. The potential effects of changes in global climate, land use/land cover, as well as natural disturbances such as wildfires on regional surface energy change and water cycles can also be examined with long-term ET products. [PERSON] _et al._[32] developed the global satellite remote sensing-based ET product (MOD16A2) with an improved algorithm using MODIS and ground-based meteorological observations. These improvements included: (1) separating dry canopy surface from the wet that caused water consumption by evaporation from the intercepted water and the plant transpiration; (2) treating land surface evaporation as the sum of the saturated and moist soil surface; (3) inclusion of daytime and nighttime components; (4) estimation of the soil heat flux value as radiation partitioned from the land surface; and (5) improving the estimates of canopy and aerodynamic resistances, as well as the vegetation cover fraction. Both NTSG (Numerical Terradynamic Simulation Group of the University of Montana) MODIS GPP and ET products with an 8-day time scale can be obtained freely from the web site [33].  
In addition, the 8-day composite land surface reflectance (MOD09A1, with resolution of 500 m) data from one MODIS pixel where the US-Bo1 and US-Ro1 lie were downloaded from the Oak Ridge National Laboratory's Distributed Active Archive Center web site [34]. The version of MODIS data is collection 5. The enhanced vegetation index (EVI) derived from blue, red, and near-infrared (NIR) bands has proved to be sensitive to vegetation production, plant transpiration and growth stages [35, 36, 37]. [PERSON] _et al._[38] defined EVI as:  
\[EVI=2.5\frac{\rho_{air}-\rho_{rod}}{\rho_{air}+(6\rho_{rad}-7.5\rho_{blue})+1} \tag{1}\]where \(\rho_{\text{mir}}\), \(\rho_{\text{red}}\), and \(\rho_{\text{blue}}\) are the spectral reflectances in MODIS bands 2, 1, and 3, respectively. Time-series EVI data are used to analyze the correlation with variations in ecosystem WUE, and to develop an alternative method for quantifying crop WUE.