This work aims at studying how the representation of physical processes of the surface layers, known to be critical for biogeochemistry, can be improved by SSH and SST data assimilation with a reduced order Kalman filter into a coupled physical-biogeochemical model of the North Atlantic. First, it is shown that the original assimilation scheme is not adapted to the problem, as hydrostatic stability, dynamic stability and temporal continuity are not respected. Two new schemes enforcing hydrostatic stability, and a continuous correction scheme are proposed and evaluated through annual simulations over 1998. The nutrient input in the euphotic zone is used to quantify the coupling quality. Diffusive inputs are improved, but advective inputs are overestimated in the subtropics. Annual primary productivity is improved, but its annual cycle remains unchanged. The biogeochemical model flaws limit improvements of the biogeochemical response at high latitudes and in the subtropical gyre centre.
