Résumé : Terrestrial ecosystems absorb, at present, about one-fourth of anthropogenic CO2 emissions, which is accumulating in the carbon (C) stocks of vegetation and soils. Land-surface models are used to project the 21st century evolution of this CO2 sink, which mitigates the expected increase in atmospheric CO2 concentration and, thus, climate change. However, classical land-surface models neglect that a fraction of the anthropogenic C absorbed by terrestrial ecosystems is not accumulating on land but is instead exported through the river network. Using the Amazon basin as a case study and a novel land-surface model that represents C exports through rivers, we prove that classical land-surface models such as those used for the Assessment Reports of the IPCC underestimate the CO2 uptake by terrestrial ecosystems and overestimate the amount of anthropogenic C sequestered within vegetation and soils. We provide reasons justifying that similar biases are to be expected at global scale.