## 1 Introduction  
Vegetation growth is regarded as crucial portion of global carbon and water cycling, and its role has been receiving more attention due to global climate change including increases in the atmospheric carbon dioxide concentration [1, 2, 3, 4]. The continued increase in atmospheric concentrations of carbon dioxide due to anthropogenic emissions is predicted to lead significant changes in climate [5]. Explicit changes in other factors such as land use, land cover types and atmospheric which influence the water budget, plant water use strategy, and the global carbon cycle are expected due to the result of global climate change [6, 7]. The monitoring of the carbon cycle has been emphasized in many ecological studies [1, 8, 9], particularly focused on the relationship between the carbon cycle and vegetation production in the ecosystem, and parameters for detecting vegetation production. The gross primary productivity (GPP) and net primary productivity (NPP) have been widely used [10, 11, 12, 13, 14] in traditional methods to study the carbon cycle. The GPP is calculated using observations of vegetation at the beginning of the carbon cycle and is the primary indicator of vegetation carbon fluxes. The GPP is essential in order to control parameter estimations of global carbon variation. [PERSON] _et al._[10] developed the theoretical basis for the global-scaled NPP algorithm. [PERSON] and [PERSON] [13] noted that the NPP was based on the dynamic vegetation model of the Biosphere Energy Transfer Hydrology (BETHY/DLR) study in Germany and Austria during 2000 and 2001. [PERSON] and [PERSON] [6] developed a method for estimation of the NPP in East Asia by implementing the Boreal Ecosystem Productivity Simulator (BEPS) model, which combines several sets of data for global applications of the algorithm. [PERSON] _et al._[15] and [PERSON] _et al._[16] used the Global Production Efficiency Model (GLO-PEM) to calculate the spatio-temporal variation of the NPP between 1981 and 2000 at global scale. [PERSON] _et al._[17] developed satellite-based Vegetation Photosynthesis Model (VPM) to analyze the seasonal variation of GPP in evergreen needleleaf forests. [PERSON] _et al._[11] conducted various spatial and temporal resolutions to quantify the global carbon cycle using EC-LUE (Eddy covariance Light Use Efficiency) model, generated by only four parameters: normalized difference vegetation index (NDVI), photosynthetically active radiation (PAR), air temperature, and the energy flux terms. The parameters used in these models were limited because they did not consider water circulation. There are many methods for analyzing of the relationships between the water and carbon cycles. The WUE, ratio of carbon gain during plant photosynthesis to water loss during evapotranspiration (ET), is an imperative concept to study these interactive effects, because it couples the water and carbon cycles very effectively [18, 19, 20, 21]. The WUE can be defined in various ways, such as in different spatial scales, for different study objectives [18, 22, 23]. [PERSON] _et al._[22] used an eco-hydrological model, the Regional Hydro-Ecological Simulation System (RHESSys), as a scaling tool at regional catchment scale. The RHESSys represented the spatial variation of the water and carbon cycles in a forest ecosystem. [PERSON] _et al._[18] analyzed the seasonal variation of the WUE in an ecosystem and demonstrated spatial patterns of ecosystem variables such as GPP, ET, and WUE at 1 km spatial resolution over three local flux tower sites in China between 2003 and 2005. Despite the completion of many studies focused on flux tower measurements, only a limited number of flux tower field measurements for WUE have been available in recent decades, and for only a few ecosystems, in comparison to the development of eddy covariance systems [24, 25, 26]. Due to the limited number offield measurements, it is also difficult to determine representative data at regional scale.