## 1 Introduction  
Gross primary productivity (GPP) is a fundamental variable in assessing controls on carbon dynamics because it varies with soil water availability, incident solar radiation, temperature, vegetation composition and nutrient availability [1, 2]. Therefore, GPP is important in studying terrestrial vegetation carbon cycling and climate change [3]. GPP can be observed using eddy covariance systems at flux towers, which quantify the carbon exchange. However, the observed data can only reflect the carbon exchange to the extent to which the measurement taken in a spatial-temporal domain describes the actual environmental conditions in the space-temporal domain [4]. Remote sensing technology is a good way to simulate regional or global GPP, and to study carbon sources and carbon sinks; however, there is a scale difference between the remote sensing data and footprint of ground-observed GPP. In this context, studying the representativeness of the observed GPP from flux towers, and ways to match ground GPP and satellite-derived GPP is important in validating ecosystem models and remote sensing products. To summarize, the issue of spatial-temporal representativeness is of great significance in model-data benchmarking and remote sensing products' validation ([PERSON] et al., 2018). Several studies have been conducted to analyze flux network-to-region representativeness, i.e., to analyze if the measured data from flux towers reflect the carbon flux in a region. For example, [PERSON] et al. (2018) analyzed the representativeness of the eddy covariance sites of AmeriFlux based on the ecosystem functional types categories represented by each network. [PERSON] and [PERSON] (2018) assessed the representativeness of registered FLUXNET sites across Latin America using GPP and evapotranspiration. [PERSON] et al. (2018) compared the environmental conditions observed at the tower locations and those within the larger Arctic domain, and mapped the representativeness of these eddy covariance network. Other studies have focused on analysis of the point-to-area representativeness ([PERSON] et al., 2018), i.e., to what extent do measurements taken at the carbon flux tower reflect the carbon exchange around the measurement instruments. Over the last two decades, a number of footprint models have been proposed to simulate the source area for eddy covariance observations, such as the simple analytical footprint model based on Eulerian coordinates for scalar concentration (SAFE-C) ([PERSON] et al., 2018), the flux source area model (FSAM) ([PERSON] et al., 2018; [PERSON] et al., 2018), the Hsieh model ([PERSON] et al., 2018), and the Horst-Weil model ([PERSON] et al., 2018). Studies of the representativeness of flux tower data for different land cover types have also been conducted. For example, [PERSON] et al. (2018) analyzed the sensitivity of the vertical fluxes at a single measurement point, and estimated the systematic uncertainty of eddy covariance flux measurements in annual cumulative values due to missing data for an urban area based on two towers. [PERSON] et al. (2018) analyzed the spatial representativeness of the source area for the vegetation characteristics (density variation and magnitude) within the surrounding area of a flux tower in a mixed forest. [PERSON] et al. (2018) studied the representativeness of observed carbon flux data in a Mediterranean urban area with equipment setup restrictions. [PERSON] et al. (2018) examined the land cover composition and vegetation characteristics in flux footprints and target areas across AmeriFlux sites, and analyzed the potential biases as a consequence of the footprint-to-target-area mismatch. With the implementation of the Heihe Watershed Allied Telemetry Experiment Research (HiWATER) in the Heihe River Basin in Northwestern China, many algorithms have been developed and several remote sensing products have been generated in this area ([PERSON] et al., 2018; [PERSON] et al., 2018; [PERSON] et al., 2018).