Polar Earth Motion and evolution
Thomas Auriel, 11th March 2024
Article previously published on Twitter.
As you know, Earth is a rotating (almost spherical) sphere. It is composed of molten and solid rocks (depending on the timescale), solid and liquid water and an atmosphere. Since it is not perfectly solid and not perfectly spherical, influences on its rotation (direction and speed) can appear. Two kinds of influence exist: External influences: this is due to the gravitational interaction between the Earth and other celestial bodies as the Moon, the Sun and a bit from other planets. Internal influence: this is due to distribution and displacement of internal masses.
External influences
The external influence of the Moon, Sun and planets on Earth rotation are numerous. We can list several of them: The precession motion of the rotation axis. This means for the earth rotation axis to move through the sky in a circle. Today, the axis is pointing toward Polaris star, but it is moving away from it. It takes 26 000 years to complete this cycle. This is due to the shape of the Earth. Due to its equatorial bulbe and earth rotation axis obliquity (inclination of the Earth rotating axis compared to the ecliptic plane), the attraction on Earth by other celestial body is not evenly distributed, creating a torque on the rotation axis, thus the precession motion.
Once you remove the 26 000 years precession cycle you can observe, there is this still a little but quick motion. This is the nutation. What is beautiful about space mechanism and celestial motion is that everything is moving, and no orbit, attitude or shapes are constant on a long time. It is true also for the orbit plans. The Earth orbit plane is not exactly on the solar system ecliptic plane. Then the Earth orbit cross it on two points: the ascending and descending point. This is also true for the moon orbit around the Earth. Its orbit does not match the equator and there is also ascending and descending point. These two points for both orbits are moving over time due to the gravitational influences. Then the precession motion and obliquity are affected by this and express a little cycle of 20 years: the nutation.
In all the figures, we saw those motions as perfect circle and perfectly cyclic. In reality, they change over time since other celestial bodies are also affected and no one follows perfect stable orbit.
Internal Influences
Here we had a quick look at the external influences but there are also internal causes. Since the Earth is not a perfect solid body, matter motion can have an impact on the day length and rotation axis. Most obvious case is when the Earth quadratic moment change. The quadratic moment is the equivalent of inertia but for rotational motions. Higher it is, more difficult it is for a torque to increase or slow rotation. And if the quadratic motion change over time the rotation speed will change too, even if no torque is applied. This is usually illustrated by the skater example. Another interesting element is the case where the quadratic moment change, but not in a symmetric way. In the skater illustration, both arms are moved closer to the body, increasing the speed. However, what appends if only one arm is moved or weight in one hand increase? The rotation axis is no longer in the body axe and the skater fall (unless it is done slowly, and the skater can adjust its position). This happens in space too. When on a rotating body the mass distribution change not evenly, the rotation axis change. And since mass distribution move is a slow and continuous displacement (especially for big object as a planet), we can observe the motion of the rotation axis. This is what is fundamentally causing the_polar_motion_of the Earth (PME). When mass distribution change, the rotation axis change compared to the referential north (the "true north"). There are also different cycles and contribution to this motion: We can mention a cycle of +-14 months Chandler wobble. This cycle was measured more than a century ago by Chandler (in 1891). However, the understanding of it really starts in the 2000s. Before that it was theorised by Euler but the period was incorrect.
The mismatch between the theoretical period and the measured one is due to missing hypothesises. Euler assumed the Earth was a rigid body. However, if we include the water and atmospheric motion it becomes possible to estimate the Chandler Wobble. This explains very well the annual periodic motion of the wobble. What is it interesting is the size of this periodic motion. The wobble should dump overtime. However, the interaction between the deep ocean and the oceanic crust (through barometric pressure, ocean bottom pressure, atmospheric winds and ocean currents interactions) and the interaction between atmosphere and surface ocean create two excitation modes. This was modelled by R. Gross at the JPL since 2000.
Water currents (like El Nino) change cause also variation in this wobble : Source Here you can find some thoeric approach : Source
But the story does not end here.
The average value of the wobble moves over time. Until the 2000s, it was going slowly toward Hudson Bay, Canada (we are talking of few metres). Since the 2000s, the axis took a sharp turn toward Western Europe.
This turn is explained since 2016 thanks to the S. Adhikar and al. from the JPL. With the help of gravitometer satellites as the GRACE, GOCE or SLR methods, they modelled the Earth mass distribution over time and show this match the new displacement. Since, the new articles provide better estimations of the displacement compared to measurement thanks to new models and updated data.
The evolution of this displacement was associated to water content change over continents:
- Article ice sheet, Antartic ice sheet and glaciers loss mass;
- Their is more dams in eastern Asia;
- Underground water balance is negative (more extraction than filling) Sea water level increases due to the negative balance over contient. However, the water is spread uniformly over the globe and its contribution to the wobble deviation is minor.
Here you can find the last estimation of the displacement contributor estimated in the last study and the difference between the model and the measured values.
All the influence coming from internal causes are called natural nutation. They are the response of the Earth system to external influences. All the nutations share different periods from 400 days for the Chandler Wobble to a single day due to tidal forces
They are challenging to measure but are done on a routinely basis now. This use long base gyroscopes, satellite measurement and Moon orbit observation. Using all this it becomes possible to measure variation in day length and axe orientation. This provides information on many Earth parameters as its matter displacement as ocean currents, Earth elasticity, magnetic field interaction, mantel/external core/inner core interaction (those three spheres do not spin exactly on the same axis and does not react the same way to influence). If the position error measurement of the star and satellite compared to the Earth surface due to those motions is not that much important in many cases (especially for few deci-arcseconds), it is still relevant for several applications as cosmology, satellite observation and GPS.
Be able to predict the PM also becomes a challenge for precise navigation
https://earth-planets-space.springeropen.com/articles/10.1186/s40623-021-01477-2
So yes, remarkably interesting science and quite unknown from the general public. And the potatoes on which we are all living is not as solide as we can imagine and moves a lot.
If you want to play with the different contributions you can try this nice page:
https://sealevel.nasa.gov/vesl/web/sea-level/polar-motion/
