For those confused how they managed that geometric analysis, the sea level rise mentioned in the paper [1] is caused by groundwater depletion. The tilt is caused by groundwater depletion. The sea level rise is not caused by the tilt.

[1] https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2023GL10...

Link to the original study:

https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2023GL10...

  Drift of Earth's Pole Confirms Groundwater Depletion as a Significant Contributor to Global Sea Level Rise 1993–2010

I would guess that when there were gigatons of frozen water where there now is none that also changed the rotation of the earth.

Large magma flows and volcanic eruptions also change the rotation.

The earth is not a static system.

The earth is such a large and variable system that over the long term, humans can't significantly permantly change something like weight distribution.

How much would that be in degrees?

How is that surprising? It seems pretty obvious to me that pumping groundwater would accelerate how quickly that water ends up in the ocean, and could thus lead to rising sea levels.

My intuition is that, if changing the altitude only affects the magnitude of the angular velocity, the other 2 degrees of freedom (longitude and altitude) must determine the direction of the angular velocity.

You start with a model of mass distribution of Earth over time, let us say M(x, y, z, t). Let us call w(t) the Earth's angular velocity at time t. If you know w(t_0) for some time t_0, you can calculate what the model says w(t) will be. The givens are: M(x, y, z, t_0), M(x, y, z, t), w(t_0), and conservation of angular momentum. You want to calculate w(t) from the model, then compare that calculation to the measurement to test the model. Your hypothesis is the model is accurate; your experiment is comparing the model's prediction of w(t) against the measured w(t).

I'm immensely curious to know how M(x, y, z, t) is calculated. They show some satellite images but it seems like they would only measure lakes, rivers, and maybe surface level soil saturation. But to me "groundwater" implies things like aquifers and underground storage, how do they measure that? You'd need to not only know the amount of water but also its change in latitude and longitude. Do you assume that if groundwater is used it ends up in the oceans? That seems a bit presumptuous, wouldn't a lot of it soak into the ground, get taken up by plants, find its way back down into an aquifer, etc.? Having water soak into the soil and become integrated into a plant is literally the point of watering crops, if we assume agricultural water ends up in the ocean doesn't that mean farmers are using too much water, which would be economically irrational because water is not free?

For that matter, why focus so much on water? Solid matter also has mass and we change its latitude, longitude and altitude when we mine it and turn it into products that we ship all over the world. For that matter, people and cars and ships and airplanes and wild animals all have mass and move around every day.

I'm a bit lost trying to follow the paper, it says "Changes in terrestrial water and oceanic mass loads were converted to spherical harmonic (SH) coefficients of the geoid..." but I only have a vague notion of what spherical harmonics are, and I don't really understand the given formulas.

[1] Latitude: Along the surface in the direction it's spinning. Longitude: Along the surface parallel to the axis of rotation. Altitude: Toward or away from the center of the sphere.