The accurate estimation of carbon and heat fluxes at global scale is paramount for future policy decisions in the context of global climate change. This paper analyzes the relative relevance of potential remote sensing and meteorological drivers of global carbon and energy fluxes over land. The study is done in an indirect way via upscaling both Gross Primary Production (GPP) and latent energy (LE) using Gaussian Process regression (GPR). In summary, GPR is successfully compared to multivariate linear regression (RMSE gain of +4.17% in GPP and +7.63% in LE) and kernel ridge regression (+2.91% in GPP and +3.07% in LE). The best GP models are then studied in terms of explanatory power based on the analysis of the lengthscales of the anisotropic covariance function, sensitivity maps of the predictive mean, and the robustness to distortions in the input variables. It is concluded that GPP is predominantly mediated by several vegetation indices and land surface temperature (LST), while LE is mostly driven by LST, global radiation and vegetation indices.