## 1 Introduction  
Recently, considerable attention has been given to the coupling relationship between carbon and water cycles in the context of profound influences on terrestrial ecosystems being exerted by the changing climate [1; 2; 3]. As an indicator of carbon-water interactions, ecosystem water use efficiency (WUE) is often defined as the amount of carbon fixed (gross primary productivity--GPP) per unit of water loss (evapotranspiration--ET) [4; 5]. Therefore, the seasonal characteristics of WUE are essentially depending on the strength of coupled GPP and ET components, as well as individual responses to environmental controls, because climate affects carbon and water processes differently [6; 7].  
With the help of continuous observations of ecosystems-level carbon and water exchanges between the Earth's biosphere and the atmosphere based on the eddy covariance (EC) technique, site-level evaluation or comparisons among multiple sites has been widely used to assess the WUE variability and its relationship with weather conditions across different time and space scales [8; 9]. Previous studies have found that seasonal dynamics in WUE varied with vegetation types and climate variables, including radiation, temperature and precipitation [10; 11]. Using flux measurements from four grasslands [12] and temperate deciduous forests [13] in northern mid- and high latitudes, WUE was found to reach its peak during the summertime, whereas [PERSON] et al. [14] revealed WUE at three Mediterranean forests with the maximum in winter and the minimum in summer, and attributed it to the effects of drought during the growth period. Similar phenomena were also exhibited in northern subtropical forests [10; 15]. Meanwhile, contrasting responses of GPP and ET to climate changes will yield significant consequences to the WUE variability under water-limited [16], light-limited [17], and thermal-limited environments [11; 18]. Nevertheless, the knowledge about seasonal cycles of WUE, as well as the potential environmental influences remains insufficient for a variety of terrestrial ecosystems because these analyses are usually rely on spatially sparse site observations. Recently, the remote sensing approaches together with process-based ecosystem models have been developed to evaluate seasonal or long-term trends of WUE through GPP and ET estimates at regional to global scales [5; 19; 20]. However, large uncertainties in both components, thereby propagating to WUE, and the inconsistency of modeled and measured WUE on short and long timescales constrained its application [21]. It remains a challenge to accurately monitor seasonal variations in WUE over large areas for water resource management.  
In the northwestern arid and semi-arid regions of China, natural grassland and irrigated agriculture are the main ecosystem types which play an important role in the regional carbon balance, hydrological patterns, and food supply [22; 23]. However, few studies addressed the interactions between carbon and water cycles in this water-limited area owing to lack of eddy covariance measurements. The overall aim of this study was (1) to examine seasonal variations in GPP, ET and ecosystem WUE, as well as the dominant environmental controls at the two grassland and cropland flux sites; (2) to evaluate the performance of MODIS WUE estimates from GPP and ET products in capturing the EC-based WUE variability and the error sources; and (3) to propose an alternative method for improving the estimation accuracy directly depending on remotely-sensed data.