# Linking Remotely Sensed Carbon and Water Use Efficiencies with In Situ Soil Properties
## 1 Introduction  
Plant growth is tightly coupled with soil nutrients, particularly nitrogen (N) and phosphorus (P) [1, 2, 3, 4], and limitation of these nutrients is assumed to be one of the drivers of observed spatial variability in ecosystem carbon (C) fluxes [5, 6, 7], particularly terrestrialecosystem productivity [8; 9; 10; 11]. Soil P is also a limiting factor of global terrestrial ecosystem productivity [12; 13], and studies have shown that P limitation on plant growth occurs more frequently than previously thought [3]. Because soil nutrients modify plant growth [14], a change in the soil-nutrient composition can alter plant responses to elevated atmospheric carbon dioxide (CO\({}_{2}\)) concentration and climate change [15; 16; 17; 18; 19; 20]. Physical and chemical soil properties, such as texture, soil moisture content, and pH can influence soil nutrient concentration [21; 22]. For instance, high soil pH can reduce the availability of soil N and P resulting in nutrient deficiencies [23; 24]. Soil age is also a key factor determining nutrient content and the type of nutrients that limit vegetation productivity [25; 26]. For example, older and more developed soils can be leached of important rock-derived nutrients such as P [27]. Conversely, soil N may be derived from external processes, such as atmospheric N disposition and biological N fixation. The concentrations of soil nutrients also vary with soil depth [28]. For instance, microbial activity can move nutrients upward into the root zone [29; 30], while translocation and infiltration may increase the nutrient concentration with depth by moving nutrients downward. Thus, root systems and plant uptake along with hydrology and microbial communities have strong effects on the vertical distribution of soil nutrients [28; 31]. Previous studies showed strong relationships between soil nutrient and vegetation carbon use efficiency (CUE) and water use efficiency (WUE) for different ecosystems [32; 33; 34]. However, the combined effects of multiple nutrients and soil characteristics on CUE and WUE have been rarely examined. CUE, defined as the ratio of net primary production (NPP) to gross primary production (GPP), measures the ecosystem proficiency to store absorbed atmospheric carbon (C) [9]. CUE plays an important role in regulating the terrestrial ecosystem's carbon balance and determines the amount of carbon allocated to biomass [35]. An additional metric of plant resource economy quantifies the rate of carbon uptake per unit of water use. WUE measures the effect of water on the ecosystem to absorb atmospheric C [36] and varies with soil nutrients content [37]. WUE, a key physiological parameter linking carbon and water cycles, quantifies the amount of water that terrestrial ecosystems use relative to carbon gained [38; 39]. CUE and WUE are important indicators of plants' ability to adapt to changing environmental conditions, such as atmospheric CO\({}_{2}\), precipitation, and temperature. Satellite-based remote sensing of vegetation can be used to estimate global WUE and CUE from NASA's Moderate Resolution Imaging Spectroradiometer (MODIS) GPP, evapotranspiration (ET), and NPP products starting from year 2000. The MODIS NPP and GPP algorithms were also modified to generate GPP and NPP at 30 m resolution from Landsat and meteorological data for the conterminous United States [40]. Estimates of global GPP are also available from the Max Planck Institute for Biogeochemistry (MPI-BGC) based on upscaling of eddy covariance-based measurements [41]. Currently, NASA ECOSTRESS onboard the space station is producing ET and WUE starting from July 2018 [42] and can also lead to instantaneous GPP estimates [43]. In addition, satellite-based solar-induced fluorescence (SIF) has been related to GPP [44; 45; 46]. All these satellite-derived data can be used to quantify WUE and CUE. For example, MODIS data have been applied to quantify the spatial variability and drivers of global WUE and CUE [39; 47; 48; 49] and drought impacts on vegetation WUE [50; 51].