AbstractMechanisms controlling the heat budget of the North Sea are investigated based on a combination of satellite sea surface temperature measurements and numerical model simulations. Lateral heat fluxes across the shelf edge and into the Baltic Sea as well as vertical ocean-atmosphere heat exchange are considered. A 3-D variational (3DVAR) data assimilation (DA) scheme is applied, which contains assumed model error correlations that depend on the mixed layer depth derived from a coupled circulation/ocean wave model. The analysis balances pressure gradients introduced by temperature modifications. Significant hydrodynamic model response to DA was found, which should be considered in the heat budget estimations. The observed change of the current velocity field decreases the lateral advective volume/heat exchanges between the North Sea and the Atlantic, yielding an increased heat flux from the Atlantic into the North Sea and more heat flux from the sea to the atmosphere. The largest DA impact on volume/heat transport is in the Norwegian Channel, where the dominant process is Eulerian transport, followed by tidal pumping and wind pumping. Further analysis reveals an acceleration of the along-shelf current at the northern edge of the North Sea, a decrease in the horizontal pressure gradient from the Atlantic to the North Sea, and a reduction of the Eulerian transport of volume/heat outward the North Sea. Furthermore, the coupling between the circulation model and the wave model has significant impacts on lateral heat advection in the DA run, which is due to the wave impact on the mixed layer depth.