Comment by rrobukef

So we want to calculate the change in momentum caused by moving water from just under the surface to the surface.

Assume earth is a perfect sphere, let m be the mass of earth and r be the radius of earth. Let rdm be the relative mass of the water moved = 3e-8, let rdr be the relative distance of the water moved = 5e-6.

The change in momentum is rdm.m.(1+rdr)².r² - rdm.m.1².r² which is 2.rdm.rdr.m.r²= 3e-14mr². Looks about right for the change of axis you wanted.

There's other counter arguments but at least the oom analysis fits.