Climate change: Sea level rising faster in the Pacific?

Factual Questions
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One of the problems with mental models of how the sea surface changes is that we often don’t account for how shallow the sea is compared to its extent.
The bathtub example fails because the water has a depth of a similar magnitude to its extent. Change the example one that is representative of the real geometry with of the order of a thousand to one aspect ratio and it is apparent that mixing at the edges of regions of different sea surface temperatures is going to be very slow relative to the extent of the water. There isn’t likely much of any sort of flow where the warmer water overtops the cooler water and drives a large scale mixing. Even if there was, the region of mixing would only have an extent of the same size as the depth of the water.
But a few centimetres of difference between bodies a couple of kilometres deep is going to drive a very slow mixing.

The thermohaline circulations take of the order hundreds to a thousand years to perform a circuit. They are driven in part by temperature but mostly from differences in density due to different salt concentrations. The circuit time gives us an insight to the time we might expect any levelling of inhomogeneities to occur.

22

What can be accomplished is remarkable.
From the satellite sea surface measurements we can derive the local gravitational field. Which is nuts. This is really useful as getting reasonably high resolution gravitational measurements over water is expensive and messy.

Why do we want this? Because we can use it to create reasonable models of the underlying geology. A company I worked for ages ago used such data to help look for oil and gas. The sea surface derived gravity was exquisitely sensitive to all manner of things. We did need to adjust for things like the way the sea surface bulged over the continental shelf when tides or currents pushed it up. We could see the residual presence of ocean waves in the energy spectra. But we could also see the large scale geological structures under the sea floor. These could provide used guidance on where to concentrate more costly data acquisition. Stuff like shipboard seismic and magnetic surveys.

The depth of water imposes a spatial low pass filter on the measurements, but it is way closer to the geology than the satellite, which makes a huge difference.