"Is it possible to have localised sea level rise?"
In a word, yes. First up, you have to keep in mind the sheer scale of the ocean. Imagine that the sea level on one side of the globe is 1m higher than the level on the other. The slope between them is then 1m in 20,000 kilometers, or 0.05 parts per million. You couldn't level a pool table to that accuracy if you tried - which means that the driving force for the two sides to level out is very weak.
Now, what can actually drive localised increases in sea level? Well, a bunch of things.
- changes in air pressure (already mentioned)
- changes in prevailing winds. A steady breeze blowing for a few hundred kilometres across open ocean will significantly lower sea levels at its origin and raise them at its destination
- changes in currents. When an oceanic current hits land (or simply shallower water) the sea level goes up there.
- changes in density. If one patch warms faster than others or gets less saline, it gets lighter, meaning it has less downward push. So, its level goes up compared to cooler/saltier parts of the ocean. Conversely, cooler and saltier regions will have lower sea levels on average.
- changes in gravity. Any sufficiently large mass will attract the oceans towards it. That includes the great ice sheets. Both Greenland and Antarctica have enough mass in their ice to significantly raise surrounding sea levels simply due to their gravitational pull.
The net effect of all these (and probably others) is that the sea level trend is far from even across the globe.
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