Does bathymetry affect ocean topography/height?

Question

Here is a map of ocean surface height or topography:

Source: http://www.esa.int/var/esa/storage/images/esa_multimedia/images/2010/12/mean_dynamic_topography_of_global_ocean/9930795-2-eng-GB/Mean_dynamic_topography_of_global_ocean.jpg

How significant is the bathymetry or seabed elevation in shaping the surface topography? What are the major causes of variations in the topography?

Answer 1

Oceanic topography of the sea surface $\zeta$ can be defined as the height of the sea surface relative to a particular level surface, the geoid. The geoid to be the level surface that coincided with the surface of the ocean at rest (a list of geoids with application to oceanography can be found in Talone et al., 2014).

Variations in sea surface height (topography) are due to processes that result in ocean motion: ocean currents, tides, and changes in barometric pressure from the inverted barometer effect. As a result, we usually call it "dynamic topography" or "dynamic height". As geoid undulations are of order 100 times larger than the dynamic height, the shape of the sea surface is dominated by local geoid variations caused by gravity with the effect of the currents being much smaller.

In the image you provide what you have is "dynamic height" and thus is a deviation from the geoid and the result of oceanic currents. By knowing the dynamic height, we can get an idea of the surface geostrophic current: $\mathrm{u_s= − {g\over f} {\delta\zeta\over\delta y}}$; $\mathrm{v_s= − {g\over f} { \delta\zeta\over\delta x}}$ where f is the Coriolis parameter, g is gravity, and $\zeta$ is the height of the sea surface above the level surface (geoid).

Now, there is a direct effect between currents and bathymetry that sometimes is referred to as Taylor columns. The Taylor-Proudman theorem enforces that vertical columns of fluid move along contours of constant fluid depth. The basic idea behind this is that in order to conserve vorticity, fluid parcels tend to follow bathymetric contours (isobaths). So to answer your question, bathymetry affects ocean topography indirectly by affecting ocean currents.