# Comparison of Machine Learning Methods to Up-Scale Gross Primary Production
## 1 Introduction  
As vegetation productivity is an important part of the terrestrial carbon cycle, accurately estimating this component is significant in research on terrestrial ecosystems, carbon cycles, and climate change [1, 2, 3, 4]. Gross primary productivity (GPP) is one of the main factors to determine the carbon source and sink of the ecosystems, which could reflect the response of the ecosystems to global change [5]. Ground-observed data are most representative in an area around the field instruments; the area that defined the spatial context of the measurement means footprint scale of the field data [6, 7]. Remote sensing technology could monitor the land surface carbon exchange and carbon storage in a large area, which is at a regional or global scale. However, it is still a challenge to match the field data with GPP derived from satellite observations data, and to up-scale GPP at flux tower sites to a regional scale [8]. In this condition, studies to exploit the ways of up-scaling ground-observed GPP to regional GPP, and to validate the effectiveness of these methods, is of great significance in revealing vegetation productivity dynamics and carbon budgets [9]. Studies have been carried out to up-scale GPP at flux tower sites to a regional scale or global scale based on remote sensing data in recent years [10, 11, 12, 13]. Some regressionmodels [12; 13; 14] have been developed based on the assumption that the relationships between field data and the corresponding satellite image pixels are constant. For example, [PERSON] et al. [15; 16] up-scaled FLUXNET carbon data to a global scale, with a resolution of 0.5\({}^{\circ}\), using an integrated regression tree based on the relationship between GPP and fraction of photosynthetically active radiation (FPAR), and validated the results against Moderate Resolution Imaging Spectroradiometer (MODIS) products and GPP, using the Biome bio-geochemical cycle (Biome-BGC) model. [PERSON] et al. analyzed the relationship between GPP and near-infrared reflectance of vegetation (NIR\({}_{\
u}\)) from FLUXNET eddy covariance sites, and estimated the global annual terrestrial photosynthesis [10]. [PERSON] et al. up-scaled CO\({}_{2}\) fluxes at a relatively high spatial resolution (1 km\({}^{2}\)) across the high-latitude region, using five commonly used statistical models [17]. [PERSON] et al. [18] described a relationship between the satellite-derived growing season averaged normalized difference vegetation index (NDVI) and annual productivity for grasslands in the Greater Platte River Basin of the United States. [PERSON] et al. [19] studied long-term measurements at five Northern Great Plains to obtain relationships between carbon dioxide fluxes and photosynthetically active radiation. However, studies have also indicated that the regression models based on the relationship between GPP at flux tower sites and other variables (such as field FPAR, vegetation index) had poor robustness when up-scaling to a regional scale [12; 13; 20]. To solve this problem, some machine learning models, such as the regression tree [21], artificial neural network (ANN) [22], random forest (RF) [23; 24; 25], and support vector machine (SVM) [26], have been used to retrieve the land surface parameters from remote sensing data. Although the eco-physiological processes of the machine learning models were not clear, and the accuracy relied much on the number and representativeness of the training data. Some researches tried to up-scale GPP from the perspective of data assimilation, which could make the best of the observed data and prior knowledge of the parameters. For example, [PERSON] et al. used the Markov chain Monte Carlo (MCMC) model to up-scale carbon flux data [27]. [PERSON] et al. up-scaled GPP in the Northern United States, using the diagnostic carbon flux model (DCFM), based on the data assimilation from 17 flux net stations [28]. [PERSON] et al. optimized the parameters of the vegetation photosynthesis model (VPM) to derive GPP from an assimilation of footprint and Landsat data [29].