Apparently the "Ice Age Effect", which has caused rotation to quicken by making the planet more spherical, dominated over the last 20k yrs. More recently, "polar ice sheet/glacier melting" has moved water mass from the poles to the ocean, causing rotation to slow. It isn't clear from TFA how these phenomena can be differentiated: in both cases ice is melting in polar regions. However they seem to have opposite effects? I'm sure Mitrovica has a way to tease out these opposite effects, and I'm sure they're not exactly offsetting, but without those details TFA is just confusing.
The Earth is growing more spherical because 20,000 years ago we had a lot more ice at the poles. When ice sheets were at the poles they kind of squished the Earth from both poles and the Earth flattened a little bit. When those ice sheets melted, that flattening started to rebound and we’re becoming spherical, so our spin rate should be increasing, like a ballerina or a figure skater. The ice age correction is a speeding up of the rotation rate.
In both cases, polar ice is melting. Since it's claimed that this melting has two opposite effects, it's unclear how to separate one effect from the other.
The timescale, I think. If the ice at the poles melts, the water immediately (days?) distributes itself along the geoid, the earth's moment of rotational inertia increases, it slows down. But, once the weight is taken off the poles, the crust rebounds over a period of thousands of years, making the earth less oblate, its moment decreases, it speeds up.
This article is fascinating...this man--Jerry Mitrovica--is obviously a genius...the techniques used to arrive at the conclusions he's reached...just wow...
My takeaway is that the gravitational attraction of ocean waters that the Arctic, Anarctic and Greenland ice sheets currently provide will diminish as those ice sheets melt...
This means that water previously attracted to those ares will move south...
The polar regions will experience lowered sea levels...the temperate regions will experience a rise well beyond what was earlier predicted...
In the area he's working here, it's totally fine. You only need relativity when you have extreme speeds or masses. Knowing which approximations are fine to use when is a skill too.
Specifically angular momentum. The Earth's moment of inertia changes as the mass distribution about the axis of rotation changes. Given a constant angular momentum, this redistribution causes it to gain or lose angular velocity.