Global ocean biogeochemistry models are frequently used to derive a comprehensive estimate of the global ocean carbon uptake. These models are designed to represent the most important processes of the ocean carbon cycle, but the idealized process representation and uncertainties in the initialization of model variables lead to errors in their predictions. Here, observations of ocean physics (temperature and salinity) are assimilated into the ocean biogeochemistry model FESOM2.1-REcoM3 over the period 2010-2020 to study the effect on the air-sea carbon dioxide (CO2) flux and other biogeochemical (BGC) variables. The assimilation nearly halves the model-observation differences in sea surface temperature and salinity, with modest effects on the modeled ecosystem and CO2 fluxes. The main effects of the assimilation on the air-sea CO2 flux occur on small scales in highly dynamic regions, which pose challenges to ocean models. Its largest imprint is in the Southern Ocean during winter. South of 50 degrees S, winter CO2 outgassing is reduced; thus the regional CO2 uptake increases by 0.18 Pg C yr-1 through the assimilation. Other particularly strong regional effects on the air-sea CO2 flux are located in the area of the North Atlantic Current (NAC). However, the effect on the global ocean carbon uptake is a comparatively small increase by 0.05 Pg C yr-1 induced by the assimilation, yielding a global mean uptake of 2.78 Pg C yr-1 for the period 2010-2020.