Wind friction at the ocean surface introduces energetic variations in the net mass transport across the oceanic basins. To conserve mass, the whole water column adjusts rapidly, introducing a depth‐independent perturbation in the pressure field. This signal is analyzed in a high resolution numerical model of the Atlantic Ocean. While the pressure perturbation cannot be extracted from the energetic sea surface height signals, it represents up to 90% of the bottom pressure signal when integrated across the Atlantic Ocean in the daily and monthly frequencies. This signal will be an important part of the signal measured by the GRACE (Gravity Recovery And Climate Experiment) mission.