## 1 Introduction  
Water use efficiency (WUE) is defined as the ratio of photosynthetic carbon uptake over transpiration, and has been widely recognized as an important link between global carbon and water cycles in terrestrial ecosystems [1,2]. Plants assimilate CO\({}_{2}\) through photosynthetic activity, which is always accompanied by the water loss that regulates the land surface exchanges between the biosphere and the atmosphere [3]. The exchanges of both CO\({}_{2}\) and water vapor are controlled by stomatal aperture for leaf-level WUE [4]. However, ecosystem-level WUE changes with vegetation types and the surrounding environmental conditions [5]. The variability in WUE is closely related to the reasonable utilization of water resources and survival strategies, as well as responses to the changing hydrological environment [6,7]. Especially for agriculture, WUE is important for agronomy and making optimal irrigation management decisions. Increasing atmospheric CO\({}_{2}\) concentration has increased global mean temperature in the 20 th and early 21 st centuries [8]. In response to the higher temperature, plant transpiration and soil evaporation can enhance water consumption, which has the potential to increase the severity, frequency, and duration of soil moisture stress. Conversely, higher CO\({}_{2}\) concentration can trigger stomatal closure that may limit the extent of water loss by plant transpiration [9]. Further, in some systems, the higher temperatures will extend the plant's phenological period with an earlier spring and a later fall, which can cause more water to be consumed by terrestrial ecosystems [10]. In addition, land use/land cover changes, primarily the expansion of cropland from forest, grassland, and wetland, are deemed responsible for 20%-25% of the increase in atmospheric CO\({}_{2}\) over the past 150 years [11]. Given the rapid expansion of urbanization and industrialization, the demands on water are continuously increasing which further ramp up the pressure to decrease agricultural water consumption [12]. Technologies for improving crop WUE are critical for sustainable yield and food security. Therefore, quantifying large-scale ecosystem WUE is vital for diagnosing how current farming practices influence WUE and identifying opportunities for improvement without yield penalty. At the ecosystem level, the eddy covariance (EC) technique has become one of the powerful tools used to characterize the dynamics of WUE as the ratio of gross primary production (GPP) over evapotranspiration (ET) [13, 14, 15]. By combining EC fluxes with remote sensing information, it is possible to extrapolate these site-level measurements of plant functional characteristics to a much larger area with ecosystem models [16; 17; 18; 19]. As an important proxy of terrestrial carbon and water coupling, both processes of CO\({}_{2}\) sequestration through photosynthesis and loss of water by evapotranspiration are closely related to the biophysical properties (e.g., biomass, leaf area, and growth stage) and environmental factors [20; 21; 22; 23]. With the development of MODIS GPP and ET algorithms, currently large-scale ecosystem WUE can be calculated as the ratio of GPP to ET in accordance to its definition. Although [PERSON] _et al._[24] evaluated how global WUE of terrestrial ecosystems distributed and changed in the past decade using remotely-sensed products on an annual time scale, the correspondence between MODIS WUE estimates and tower-based WUE measurements at short time scales remains unclear. In fact, precise information on seasonal variations in WUE is more significant for agricultural water management [25; 26; 27]. There is an important need to examine the capacity of applying MODIS GPP and ET products to monitor the variability in crop WUE. Meanwhile, alternative approaches involving direct estimation of WUE from satellite data need to be explored. Therefore, this study aims to answer:  
1. How do environmental factors control the changes in WUE from flux measurements in corn/soybean rotation systems? 2.