Two different treatments in ocean dynamics are found between the gravity and pressure gradientforce. Vertical component is 5–6 orders of magnitude larger than horizontal components for the pressure gradient force in large-scale motion, and for the gravity in any scale motion. The horizontal pressure gradient force is considered as a dominant force in oceanic motion from planetary to small scales. However, the horizontal gravity is omitted in oceanography completely. A non-dimensional C number (ratio between the horizontal gravity and the Coriolis force) is used to identify the importance of horizontal gravity in the ocean dynamics. Unexpectedly large C number with the global mean around 24 is obtained using the community datasets of the marine geoid height and ocean surface currents. New large-scale ocean dynamic equations with the real gravity are presented such as hydrostatic balance, geostrophic equilibrium, thermal wind, equipotential coordinate system, and vorticity equation.

The author thanks the International Centre for Global Erath Models (ICGEM) for the EIGEN-6C4 geoid undulation data, and the NASA Jet Propulsion Laboratory for the OSCAR Tird Degree Resolution Ocean Surface Currents. He also thanks Mr. Chenwu Fan for computational assistance, and the Naval Postgraduate School Research Office for paying the publication cost.

The article of record as published may be found at https://doi.org/10.1038/s41598-021-82882-1

U.S. Government affiliation is unstated in article text.

17 USC 105 interim-entered record; under review.