What effect does climate change have on the Earth's rotation?

Question

I recently read a blog entry from a leap-second expert explaining that in near term (i.e. last 3 years) the Earth has been spinning ever so slightly faster, delaying the need to insert a leap-second (that accounts for the Earth spinning at a different speed than once per 24 * 60 * 60 seconds).

That got me wondering what effect Climate Change might have had on the spin of the Earth over the last century, and into the next.

I reasoned that melting ice caps would bring mass closer to the centre, lowering the moment of inertia and speeding up the spin (which was a silly thought - see comments).

But then I reasoned that warming oceans would lower the density of water, pushing the mass away.

Then I realised I had no idea what effect of the changing atmosphere might have.

I came away knowing I had a very poor understanding of the problem.

What predictions do the scientific models make about the effect of climate change on the previous rate of gradual slowing of the Earth's spin?

[Note: This is an idle curiosity question from a non-expert. Please tailor your answering efforts appropriately.]

Answer 1

The only answer I can come up with is related to isostasy.

1 - Poles melt, so there's more water in the oceans. 2 - As there's more water in the oceans, there's more weight on the oceanic crusts, so they bend, making deeper some parts of the oceans. 3 - The parts of the ocean that are deeper are in the centre of the oceans, far from continental crust. It should be mainly the Pacific Ocean, Indic and Atlantic, but not near Antarctica, as this area is continental crust (lighter) and will be also unloaded from ice. 4 - As a result, the shape of the Earth crust becomes a bit longer in N-S direction. 5 - As the mass of the Earth is closer to the rotation axis, it accelerates the spin.

Lithospheric density is approximately 2.5 times that of water, so amount of water in the ocean isn't as important as crust flexion.

Answer 2

This study seems to suggest that global warming will change oceanic circulation and transfer a net increase of mass to the poles, closer to the axis of rotation, therefore speeding up the spin.

article: https://www.newscientist.com/article/dn11555-global-warming-will-make-earth-spin-faster/ study: https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2006GL029106

Much of this transfer of mass seems to be to do with water flooding low-lying areas in the northern hemisphere, and I assume that adding to this effect will be lower density frozen water being replaced by higher density liquid water around the poles.