On July the 29th 2022, the Earth finished its rotation about 1.5 milliseconds earlier than the entire 24 hours. Scientists link this to climate change, saying that a possible reason could be due to the melting of polar glaciers.
I do not know for sure what dictates this would happen, but what came to my mind first was the law of conservation of angular momentum. If glaciers melt, then the water gets spread out across the oceans, so the mass located away from the rotation axis increases. This means that there is an increase in the moment of inertia.
But doesn't this mean there should be a decrease in the rotational speed?
I wonder whether there is some larger physical phenomenon at play, something with greater influence on the rotational speed.
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4 Answers
Glaciers are water that is frozen and high up in the mountains. If you thaw that ice and the water flows back to sea-level, then it would seem that mass in the water would get closer to the rotation axis; the moment of inertia of the Earth would decrease and the angular speed increase.
However, it is not such a simple calculation because ice is also melting at the poles, the sea level can rise more at the equator and in addition, the density of water is temperature dependent, the weight of water can deform the crust and the rotation axis of the Earth is also shifting in response to the distribution of water (e.g., Deng et al. 2021).
There are lots of factors besides glaciers that affect the Earth's rotation. Given the sharpness of the change, it seems unlikely to be glaciers which are notorious for moving very slowly. A more likely culprit would be the circulation patterns of air and water currents.
The wind and the ocean currents generally circulate around the Earth in a particular direction, which constitutes a component of the Earth's angular momentum. If the circulation suddenly changes in strength or direction, then the Earth rotation changes in the opposite direction to compensate. Such changes can occur in a matter of days, weeks, or months. For example, the quasi-biennial oscillation (QBO) is a circulating wind in the stratosphere that reverses direction roughly every two years. Trade winds reversing direction in the Pacific ocean are associated with El Nino. And the circulation of winds in the polar regions is known to periodically reverse. When the wind in the Arctic blows one way, the floating ice rams up against the north coast of Siberia. When it blows the other way, it is pushed southwards out of the Greenland gap and melts.
The length of day seems to have started shifting in around 2015/2016 when there was a big El Nino and a sharp jump in global mean temperature. I should think there have been some associated changes in wind and ocean circulation patterns, affecting how heat is distributed around the globe.
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For simplicity we'll take a homogenous sphere and round some numbers. The moment of inertia for such a sphere is
$$i(r)=\frac{2 M r^2}{5}$$
and its angular momentum
$$J(r,\omega)=i(r) \omega$$
If we round the mass of the earth to
$$ M=6 \rm E 24 \ kg$$
the old radius to
$$r_1=6378000 \ \rm m$$
the old angular velocity to
$$\omega_1=\frac{2 \pi}{86400 \ \rm s}$$
and the new angular velocity to
$$\omega_2=\frac{2 \pi}{(86400-15/10000) \ \rm s}$$
we need to use the conservation of angular momentum to solve for the new radius via
$$J(r_1,\omega_1)=J(r_2,\omega_2)$$
and get
$$r_2=r_1 \sqrt{\omega_1/\omega_2}$$
In order for the earth to rotate faster by the given amount of 1.5 ms per 24 hours we need
$$r_1-r_2=5.5 \ \rm cm$$
so the inhomogenous weight shifts correspond to a homogenous radius decrease of 5.5 cm, which is less than one part per 100 million.
Another possible contributing factor is the recent drought in many mid-latitude areas of the world, which would reduce the amount of water in dams, lakes, and aquifers. If these are, on average, farther from Earth's rotation axis than the ocean average, that would speed up Earth's rotation.
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