Water does not find its own level....
Water levels so that the hydrostatic force at the surface is constant. So if gravity changes, the surface changes "level". Gestational field strength (in newtons/kg) is varies from the equator to the pole, so the force on the sea is different. It is stronger at the pole, of course, so the sea is pulled stronger toward the center of Earth.
Now at the equator, the distance is longer, so gravitational field is less, so the water is pulled less toward Earth.
Curiously, as one moves from the pole to the equator, the spinning of the Earth creates a greater centripetal force effect, which reduces net force holding the sea (and land) at the equator. Water will be a greater distance from the center of the Earth as a result of this.
All this is to explain your delimina on sea level. Water will seek its own level on Earth if the Gravitational Field is constant, and if other forces on it (centripetal) are constant. But due to changing relative spin velocity, and changing distances to the the center of Earth, such is not the case.
Yes, on the peaks of Mountains, gravity is less, as distance to the center of the Earth is more.
One last thing on your distinction of land vs water. There is no distinction, what we see as solid land is floating on a molten core.
Radius of Earth is normally taken from the geometric center of the Earth to average sea level, and in mountainous regions, the distance to the surface is slightly farther.
Goodness. Gestational? It was meant to be gravitational (field strength). I type in the dark, and am losing vision in my left eye. Sorry.
If you want to explore this in some depth, there are many good introductory books on geophysics, you might call your local library.
Thank you BOB, Fantastic reply! My problem all along has being in my understanding of how a NM is determined. I have been imagining a dot in the centre of the earth with degrees and minutes extending outwards from this dot. In fact I have been looking at the problem from the wrong end. I now understand subject to your further confirmation that the curvature of the earth at a given point creates its own centre. This is where the word subtended is relevant. There is no such thing as an individual centre of the earth. Considering all the different locations on the earths surface creating curvatures that are then subtended. There will be billions of centres of the earth.
Am I getting the hang of it?
There is a geometric center of the Earth, as is there a gravitational center. They are different because of the uneven distribution of the Matter in Earth (Earth does wobble).
The center of curvature is indeed different from the center of the Earth, and in fact, for each segement on the surface of the Earth, there is a specific center of curvature. Yes, there are billions of center of curvature, one each for any arbitrary arc on the surface chosen.