I don’t know the rate of erosion and wasn’t considering it. It must be a contributing factor also though.
What I was referring to is thermal expansion.
Truly vast quantities of ocean water are colder both than the ocean surface above them and the Earth below them. This is because of “cold” left over from ages when the Earth was colder than now, which has been the vast majority of the time.
Even if air temperatures remain identical, these waters inevitably warm – slowly – as heat flows into them from both of these directions.
As the oceans average about 4000 meters deep, it takes a very tiny percentage of thermal expansion to yield the approximate 2 mm/year rise in sea level that has been the long term trend.
A 4 meter rise would be 1 part in 1000; a 4 mm rise one part in a million; and a 2 mm rise about one part in two million.
Or as such tiny increases in temperature or fractions of thermal expansion or such depths of water are hard to visualize, imagine that warming – from coming ever-so-slightly closer to equilibrium with temperatures above and below without air temperatures having to increase at all – comes in the form of some single layer of water increasing in temperature by one degree. Say from 10 C to 11 C.
How deep a layer of water would have to warm by that much to yield 2 mm of vertical expansion per year?
Roughly 11 meters.
Not a tremendously thick layer to have to warm so little in the course of a year.
(One could look at it as an average of about an inch thickness per day of water warming by one degree to have an idea of what sort of rate is involved.)
Now of course the actual problem of thermal expansion of the oceans is far more difficult for many reasons. For example, the coefficients of expansion are quite different at different temperatures, ocean circulation is involved, and rate of heat flow from the warmer Earth below may not be adequately known. Even if all data necessary for a good model were available, it would be a very complex task to make a good physical model.
Though certainly it would be a far simpler task than modeling the entire climate.
Anyway, the point is, it’s long been known that the oceans continually rise during interglacial periods. Most of the ocean is still cold, below thermal equilibrium, from the previous Ice Age and so it doesn’t take actual warming of the surface to warm the oceans. The same surface temperature, combined also with geothermal heat – though this is a much smaller factor: I mention the temperature difference there to show that the water is out of thermal equilibrium i in both directions and thus the coldness is not a steady-state condition) – acts to slowly (exceedingly slowly, but that is all that is required) rewarm the oceans, which inevitably raises sea level.
Whether surface air temperatures are a fraction of a degree higher or not, or even a degree or two higher, is a rather small difference compared to the temperature differences that already exist which drive rewarming of the oceans.
