<p>You are asking about a phenomenon called &quot;polar motion&quot;. Scientists have a fairly good, but definitely not perfect, set of analytical models of the Earth's orientation in space. These are <a href="https://en.wikipedia.org/wiki/Axial_precession" rel="nofollow noreferrer">precession</a>, <a href="https://en.wikipedia.org/wiki/Astronomical_nutation" rel="nofollow noreferrer">nutation</a>, and <a href="https://en.wikipedia.org/wiki/Earth%27s_rotation" rel="nofollow noreferrer">rotation</a>. Precession and nutation are caused by external gravitational torques on the Earth, thus changing the orientation of the Earth's rotational axis. The only difference between precession and nutation is frequency. There's a large gap in the frequencies at which those external torques operate. Precession describes the very low frequency changes while nutation describes the much high frequency changes. Finally, rotation is the daily rotation of the Earth about that rotational axis.</p>
<p>As mentioned above, these analytic models are good but definitely are not perfect.  The Earth's rotation rate is not constant, and the axis about which the Earth rotates is not fixed with respect to the more or less solid Earth. Moreover, the organizations that model precession and nutation have decided to cut the very high frequency nutation effects off at one per every other day. This makes the precession/nutation models more accurate but at the expense of missing higher frequency nutations.</p>
<p>The non-constant rotation rate is measured in terms of <a href="https://en.wikipedia.org/wiki/%CE%94T_(timekeeping)" rel="nofollow noreferrer"><span class="math-container">$\Delta T$</span></a> (that <span class="math-container">$\Delta T$</span> is a link, but it doesn't appear as one), or equivalently as, <a href="https://en.wikipedia.org/wiki/DUT1" rel="nofollow noreferrer">DUT1</a>. I'm not going to discuss this topic in detail.</p>
<p>The other, <a href="https://en.wikipedia.org/wiki/Polar_motion" rel="nofollow noreferrer">polar motion</a>, is the subject of the rest of this answer. Together, the image that follows portrays this polar motion.
<a href="https://i.sstatic.net/2TxHksM6.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/2TxHksM6.jpg" alt="Polar motion, with the horizontal axis denoting rotation about the X axis and the vertical axis denoting rotation about the Y axis. Details follow in the text below." /></a><br />
<sup><a href="https://www.iers.org/IERS/EN/Home/home_node.html" rel="nofollow noreferrer">Source: iers.org</a></sup></p>
<p>The horizontal axis in the above plot denotes rotation of the Celestial Intermediate Origin (the &quot;true&quot; North Pole), measured in milliarcseconds (mas) about the terrestrial reference frame X axis, and the vertical axis denotes rotation about the once-rotated Y-axis, also expressed in milliarcseconds. Two curves are plotted, a red curve that portrays polar motion over the last two years, and a black curve that portrays polar motion with the quasi-period variations (more on this below) averaged out. It is the black curve that the article referenced in the question addressed.</p>
<p>What about the location of the rotational pole itself? The image below portrays the location of the mean (average) pole in polar coordinates, with distance south of the pole in concentric circles and longitude as radial lines extending from the poles.</p>
<p><a href="https://i.sstatic.net/UAHMKmED.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/UAHMKmED.jpg" alt="Polar motion since 1900" /></a><br />
<sup>Source: <a href="https://www.jpl.nasa.gov/images/pia26120-meandering-path-of-earths-spin-axis/" rel="nofollow noreferrer">JPL</a></sup></p>
<p>Note that polar motion is measured with respect to where the poles were at some time around 1900. Our current latitudes and longitudes are based on the orientation of the Earth at that somewhat arbitrary choice of time. Polar motion means that the North Pole and South Pole are not quite where they were then. It also means that not only do the southward (or northward) motion have meaning but so do the eastward (or westward) motion have meaning.</p>
<p>Polar motion is dominated by two quasi-periodic effects, the Chandler wobble with a period of about 435 days, and an annual variation. Which of the two is larger varies, and neither is predictable over the long term. The Chandler wobble results from the fact that the Earth is not a perfect sphere (it has an equatorial bulge) coupled with an angular momentum and angular velocity vectors that are not perfectly aligned. The Chandler wobble would have a period shorter than one year and a more or less constant magnitude if the Earth was a rigid solid, which it isn't. The Chandler wobble instead has a period longer than one year (435 days) and the magnitude varies over the years.</p>
<p>The annual effect is mostly due to seasonal atmospheric changes, and also to snow cover in the far Northern Hemisphere in Northern Hemisphere winter. This annual variation from little if any snow cover in the summer to a lot of snow cover in the winter results in two effects, an annual variation in the Earth's rotation rate due to a net migration of water between equatorial regions and those northern regions, and an annual variation in the direction of the Earth's instantaneous rotation axis due to a slightly uneven distribution of land (and snowfall) in the far north.</p>
<p>Those two quasi-periodic effects can be averaged out using statistical techniques, resulting in the apparently secular black curve in the above plots. Something happened around the year 2000, when the curve changed from a strongly southward motion to a strongly southeastward motion.</p>
<p>The CNN article cited in the question links to the scientific journal article, <a href="https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2023GL103509" rel="nofollow noreferrer">Seo, Ki‐Weon, et al. &quot;Drift of Earth's pole confirms groundwater depletion as a significant contributor to global sea level rise 1993–2010.&quot; Geophysical Research Letters 50.12 (2023): e2023GL103509.&quot;</a></p>

CC BY-SA 4.0
2024-11-25T16:48:03.383Z
So "east" doesn't have its normal meaning here: it's the direction the 90 degree east meridian points from the pole. Usually, "east" is perpendicular to whatever the local meridian is.
John Doty
CC BY-SA 4.0
2024-11-25T19:25:23.280Z
@JohnDoty The only places on Earth where east and west are undefined are the frozen geographic north and south poles. The time-varying location of those poles based on astronomy differ from the frozen geographic poles.
David Hammen
CC BY-SA 4.0
2024-11-25T19:32:09.930Z
The OP was about eastward drift at precisely that point where east and west are undefined.
John Doty
CC BY-SA 4.0
2024-11-26T06:28:36.737Z
Ok, I think I get it. We freeze a reference location of the "north pole", which the actual rotational north pole can move around. And since this rotational north pole was headed west for approximately 100 years, the fact that it has virtually stop moving west over the past 20 years, they said it has "tilted eastward". Though, I do think that it would make more sense (at least in news article headlines) to just say that since 2000 the pole has moved almost due south, as that does not require the added context that for 100 years the pole was drifting west.
Aphyd
CC BY-SA 4.0
2024-11-26T06:29:41.573Z
Though, what do they mean by the axis tilting "31 inches" east? From that graph, it seems the pole did not move east at all, it just basically stopped moving west.
Aphyd
CC BY-SA 4.0
2024-11-26T12:00:56.067Z
@Aphyd Quoting from the underlying scientific journal article (emphasis mine), "Earth's pole has drifted toward 64.16°E at a speed of 4.36 cm/yr during 1993–2010 **due to groundwater depletion and resulting sea level rise.**"  That is not describing the overall drift of the pole's location. It is the portion of the drift attributable (per the article) per the article to groundwater depletion and that depletion's contribution to sea level rise.
David Hammen
CC BY-SA 4.0
2024-11-26T12:11:40.410Z
@Aphyd If one accepts the 4.36 cm/year as truth, then 4.36 cm/year multiplied by 18 years (the period of the study) and converted to inches results in 30.9 includes. Note well: It is usually a dubious prospect to accept as fact something that comes from a recently published scientific journal article. Getting something published in a peer-reviewed scientific journal is where science starts rather than ends.
David Hammen
CC BY-SA 4.0
2024-11-26T12:21:13.057Z
@JohnDoty Many political boundaries are based on lines of latitude or longitude. We do not want those boundaries shifting, so the North and South Poles are cartographically frozen. The locations of the poles as marked on a map are not the true locations of the poles. This means that east and west are well defined regarding motion of the true poles.
David Hammen
CC BY-SA 4.0
2024-11-26T12:43:35.683Z
@DavidHammen You quoted "Earth's pole has drifted toward 64.16°E". Why give an angle? The reason is that the direction is not ill-defined east, but a well-defined meridian.
John Doty
CC BY-SA 4.0
2024-11-26T17:25:52.003Z
I see. The statement isn't that the pole traveled 31 inches in an eastward direction, it is that it traveled 31 inches in some direction that is much more eastward than the direction the pole has been moving in the past hundred or so years. Thanks for the clarification! I think this claim in the paper could be summarized in a much better way in news articles and such.
Aphyd
CC BY-SA 4.0
2024-11-26T17:36:08.353Z
Or is it that if we hadn't been pumping groundwater, they're claiming that the pole would be 31 inches more west than it currently is?
Aphyd
CC BY-SA 4.0
2024-11-27T10:59:03.693Z
@JohnDoty You appear to be stuck on the idea that the as-observed North Pole and the as-observed prime meridian are how we measure latitude and longitude. That simply is not the case. The cartographic poles and prime meridian are frozen; we would not want borders based on latitude and longitude to change just because the poles are moving. Being frozen, the rotational north pole intersects the Earth's surface slightly away from the cartographic north pole, so north, south, east, and west all exist at the location of the rotational north pole.
David Hammen
CC BY-SA 4.0
2024-11-27T13:06:14.773Z
@DavidHammen No, I'm not stuck on that idea at all. You are stuck on the idea that the direction "toward 64.16°E" is the same as "east".
John Doty
CC BY-SA 4.0
2024-11-27T13:15:55.260Z
@DavidHammen "the rotational north pole intersects the Earth's surface slightly away from the cartographic north pole, so north, south, east, and west all exist at the location of the rotational north pole." It would be a nightmare to define coordinates in this manner, since which direction "east" is would change as the rotational pole wanders. The plot you include above doesn't use north, south, etc: it uses Cartesian X and Y, with X parallel to the prime meridian, and Y parallel to the 90 degree east meridian.
John Doty
CC BY-SA 4.0
2024-12-05T17:34:34.857Z
@JohnDoty, and others: I posted an update to the answer.
David Hammen
CC BY-SA 4.0
2024-11-25T16:16:32.423Z
2024-12-05T17:30:03.620Z
2024-12-05T17:30:03.620Z
David Hammen
<p>I recently read <a href="https://www.cnn.com/2023/06/26/world/pumping-groundwater-earth-axis-shifting-scn/index.html" rel="nofollow noreferrer">this article</a> that states that groundwater pumping has caused an eastward tilt of the Earth's rotational axis.</p>
<p>I am confused about which direction an &quot;eastward tilt&quot; is in regards to the rotational axis, as it seems to me that &quot;east&quot; is not well defined at the pole.</p>
<p>Is it simply that since the rotational axis is different from magnetic north, they are saying that the rotational axis moved east as defined by the magnetic north pole?</p>
<p>If this isn't astronomical enough, I guess the question could be generalized to ask what an eastward movement of an arbitrary planetary body's rotational axis is defined as. Bonus points for also considering the case where the planetary body's magnetic north and rotational axis are the same, or even a planetary body without a magnetic field.</p>

CC BY-SA 4.0
2024-11-25T06:32:15.200Z
I assume it means "towards the Eastern Hemisphere", ie south, along the 090 meridian
James K
CC BY-SA 4.0
2024-11-25T07:02:15.553Z
Some useful background info:  https://en.wikipedia.org/wiki/Earth_orientation_parameters & https://www.iers.org/IERS/EN/Science/EarthRotation/EarthRotation.html and a related question: https://astronomy.stackexchange.com/q/53233/16685 Note that the IERS site can be very sluggish.
PM 2Ring
CC BY-SA 4.0
2024-11-25T16:18:21.060Z
@JohnDoty That is not the case. It is motion of the Earth's rotation axis relative to the rotation axis at some time prior to 1900, after accounting for Earth precession and nutation.
David Hammen
CC BY-SA 4.0
2024-11-25T16:37:22.793Z
@DavidHammen Which gets us back to the puzzle: which direction is east in that system?
John Doty
CC BY-SA 4.0
2024-11-25T16:43:20.517Z
@DavidHammen OK, I see. It's not "tilt" of the axis relative to an external reference, but rather a change in the balance of the Earth, more moving the Earth relative to the axis than changing the axis.
John Doty
CC BY-SA 4.0
2024-11-25T21:25:59.823Z
In the paper, it’s specifically referenced as “We found that groundwater depletion was the second largest (4.36 cm/yr) component of PM [polar motion] excitation trend toward 64.16°E during 1993–2010”.  For what that’s worth.
Peter Erwin
CC BY-SA 4.0
2024-11-25T21:29:36.493Z
@DavidHammen “motion of the Earth's rotation axis relative to the rotation axis at some time prior to 1900” — I’m not sure that’s entirely correct; it’s more like the motion of the rotation axis *relative to the crust* (or possibly vice-versa).
Peter Erwin
CC BY-SA 4.0
2024-11-26T09:38:10.200Z
Also see [New parameters for the orientation of the Earth in the ICRS](https://syrte.obspm.fr/~capitaine/discEOP/EOP.html) by Nicole Capitaine.
PM 2Ring
CC BY-SA 4.0
2024-11-26T17:25:29.660Z
And https://space.stackexchange.com/q/55174/38535 & http://www.neoprogrammics.com/obliquity-of-the-ecliptic/
PM 2Ring
<fundamental-astronomy><movement>
What is an eastward tilt of the Earth's rotational axis?
Aphyd
# What is an eastward tilt of the Earth's rotational axis?

(Asked by: username_0 on 2024-11-25)

I recently read [this article](https://www.cnn.com/2023/06/26/world/pumping-groundwater-earth-axis-shifting-scn/index.html) that states that groundwater pumping has caused an eastward tilt of the Earth's rotational axis.

I am confused about which direction an "eastward tilt" is in regards to the rotational axis, as it seems to me that "east" is not well defined at the pole.

Is it simply that since the rotational axis is different from magnetic north, they are saying that the rotational axis moved east as defined by the magnetic north pole?

If this isn't astronomical enough, I guess the question could be generalized to ask what an eastward movement of an arbitrary planetary body's rotational axis is defined as. Bonus points for also considering the case where the planetary body's magnetic north and rotational axis are the same, or even a planetary body without a magnetic field.

**Tags:** fundamental-astronomy, movement
> **Comments:**
> **username_1**: I assume it means "towards the Eastern Hemisphere", ie south, along the 090 meridian  
> **username_2**: Some useful background info:  https://en.wikipedia.org/wiki/Earth_orientation_parameters & https://www.iers.org/IERS/EN/Science/EarthRotation/EarthRotation.html and a related question: https://astronomy.stackexchange.com/q/53233/16685 Note that the IERS site can be very sluggish.  
> **username_3**: @JohnDoty That is not the case. It is motion of the Earth's rotation axis relative to the rotation axis at some time prior to 1900, after accounting for Earth precession and nutation.  
> **username_4**: @DavidHammen Which gets us back to the puzzle: which direction is east in that system?  
> **username_4**: @DavidHammen OK, I see. It's not "tilt" of the axis relative to an external reference, but rather a change in the balance of the Earth, more moving the Earth relative to the axis than changing the axis.  
> **username_5**: In the paper, it’s specifically referenced as “We found that groundwater depletion was the second largest (4.36 cm/yr) component of PM [polar motion] excitation trend toward 64.16°E during 1993–2010”.  For what that’s worth.  
> **username_5**: @DavidHammen “motion of the Earth's rotation axis relative to the rotation axis at some time prior to 1900” — I’m not sure that’s entirely correct; it’s more like the motion of the rotation axis *relative to the crust* (or possibly vice-versa).  
> **username_2**: Also see [New parameters for the orientation of the Earth in the ICRS](https://syrte.obspm.fr/~capitaine/discEOP/EOP.html) by Nicole Capitaine.  
> **username_2**: And https://space.stackexchange.com/q/55174/38535 & http://www.neoprogrammics.com/obliquity-of-the-ecliptic/  

---

## 1 answers

### Answer by username_3 on 2024-11-25. Score: 4 | Accepted answer

You are asking about a phenomenon called "polar motion". Scientists have a fairly good, but definitely not perfect, set of analytical models of the Earth's orientation in space. These are [precession](https://en.wikipedia.org/wiki/Axial_precession), [nutation](https://en.wikipedia.org/wiki/Astronomical_nutation), and [rotation](https://en.wikipedia.org/wiki/Earth%27s_rotation). Precession and nutation are caused by external gravitational torques on the Earth, thus changing the orientation of the Earth's rotational axis. The only difference between precession and nutation is frequency. There's a large gap in the frequencies at which those external torques operate. Precession describes the very low frequency changes while nutation describes the much high frequency changes. Finally, rotation is the daily rotation of the Earth about that rotational axis.

As mentioned above, these analytic models are good but definitely are not perfect. The Earth's rotation rate is not constant, and the axis about which the Earth rotates is not fixed with respect to the more or less solid Earth. Moreover, the organizations that model precession and nutation have decided to cut the very high frequency nutation effects off at one per every other day. This makes the precession/nutation models more accurate but at the expense of missing higher frequency nutations.

The non-constant rotation rate is measured in terms of [$\Delta T$](https://en.wikipedia.org/wiki/%CE%94T_(timekeeping)) (that $\Delta T$ is a link, but it doesn't appear as one), or equivalently as, [DUT1](https://en.wikipedia.org/wiki/DUT1). I'm not going to discuss this topic in detail.

The other, [polar motion](https://en.wikipedia.org/wiki/Polar_motion), is the subject of the rest of this answer. Together, the image that follows portrays this polar motion.
[![Polar motion, with the horizontal axis denoting rotation about the X axis and the vertical axis denoting rotation about the Y axis. Details follow in the text below.](https://i.sstatic.net/2TxHksM6.jpg)](https://i.sstatic.net/2TxHksM6.jpg)  
[Source: iers.org](https://www.iers.org/IERS/EN/Home/home_node.html)

The horizontal axis in the above plot denotes rotation of the Celestial Intermediate Origin (the "true" North Pole), measured in milliarcseconds (mas) about the terrestrial reference frame X axis, and the vertical axis denotes rotation about the once-rotated Y-axis, also expressed in milliarcseconds. Two curves are plotted, a red curve that portrays polar motion over the last two years, and a black curve that portrays polar motion with the quasi-period variations (more on this below) averaged out. It is the black curve that the article referenced in the question addressed.

What about the location of the rotational pole itself? The image below portrays the location of the mean (average) pole in polar coordinates, with distance south of the pole in concentric circles and longitude as radial lines extending from the poles.

[![Polar motion since 1900](https://i.sstatic.net/UAHMKmED.jpg)](https://i.sstatic.net/UAHMKmED.jpg)  
Source: [JPL](https://www.jpl.nasa.gov/images/pia26120-meandering-path-of-earths-spin-axis/)

Note that polar motion is measured with respect to where the poles were at some time around 1900. Our current latitudes and longitudes are based on the orientation of the Earth at that somewhat arbitrary choice of time. Polar motion means that the North Pole and South Pole are not quite where they were then. It also means that not only do the southward (or northward) motion have meaning but so do the eastward (or westward) motion have meaning.

Polar motion is dominated by two quasi-periodic effects, the Chandler wobble with a period of about 435 days, and an annual variation. Which of the two is larger varies, and neither is predictable over the long term. The Chandler wobble results from the fact that the Earth is not a perfect sphere (it has an equatorial bulge) coupled with an angular momentum and angular velocity vectors that are not perfectly aligned. The Chandler wobble would have a period shorter than one year and a more or less constant magnitude if the Earth was a rigid solid, which it isn't. The Chandler wobble instead has a period longer than one year (435 days) and the magnitude varies over the years.

The annual effect is mostly due to seasonal atmospheric changes, and also to snow cover in the far Northern Hemisphere in Northern Hemisphere winter. This annual variation from little if any snow cover in the summer to a lot of snow cover in the winter results in two effects, an annual variation in the Earth's rotation rate due to a net migration of water between equatorial regions and those northern regions, and an annual variation in the direction of the Earth's instantaneous rotation axis due to a slightly uneven distribution of land (and snowfall) in the far north.

Those two quasi-periodic effects can be averaged out using statistical techniques, resulting in the apparently secular black curve in the above plots. Something happened around the year 2000, when the curve changed from a strongly southward motion to a strongly southeastward motion.

The CNN article cited in the question links to the scientific journal article, [Seo, Ki‐Weon, et al. "Drift of Earth's pole confirms groundwater depletion as a significant contributor to global sea level rise 1993–2010." Geophysical Research Letters 50.12 (2023): e2023GL103509."](https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2023GL103509)

> **Comments:**
> **username_4**: So "east" doesn't have its normal meaning here: it's the direction the 90 degree east meridian points from the pole. Usually, "east" is perpendicular to whatever the local meridian is.  
> **username_3**: @JohnDoty The only places on Earth where east and west are undefined are the frozen geographic north and south poles. The time-varying location of those poles based on astronomy differ from the frozen geographic poles.  
> **username_4**: The OP was about eastward drift at precisely that point where east and west are undefined.  
> **username_0**: Ok, I think I get it. We freeze a reference location of the "north pole", which the actual rotational north pole can move around. And since this rotational north pole was headed west for approximately 100 years, the fact that it has virtually stop moving west over the past 20 years, they said it has "tilted eastward". Though, I do think that it would make more sense (at least in news article headlines) to just say that since 2000 the pole has moved almost due south, as that does not require the added context that for 100 years the pole was drifting west.  
> **username_0**: Though, what do they mean by the axis tilting "31 inches" east? From that graph, it seems the pole did not move east at all, it just basically stopped moving west.  
> **username_3**: @Aphyd Quoting from the underlying scientific journal article (emphasis mine), "Earth's pole has drifted toward 64.16°E at a speed of 4.36 cm/yr during 1993–2010 **due to groundwater depletion and resulting sea level rise.**"  That is not describing the overall drift of the pole's location. It is the portion of the drift attributable (per the article) per the article to groundwater depletion and that depletion's contribution to sea level rise.  
> **username_3**: @Aphyd If one accepts the 4.36 cm/year as truth, then 4.36 cm/year multiplied by 18 years (the period of the study) and converted to inches results in 30.9 includes. Note well: It is usually a dubious prospect to accept as fact something that comes from a recently published scientific journal article. Getting something published in a peer-reviewed scientific journal is where science starts rather than ends.  
> **username_3**: @JohnDoty Many political boundaries are based on lines of latitude or longitude. We do not want those boundaries shifting, so the North and South Poles are cartographically frozen. The locations of the poles as marked on a map are not the true locations of the poles. This means that east and west are well defined regarding motion of the true poles.  
> **username_4**: @DavidHammen You quoted "Earth's pole has drifted toward 64.16°E". Why give an angle? The reason is that the direction is not ill-defined east, but a well-defined meridian.  
> **username_0**: I see. The statement isn't that the pole traveled 31 inches in an eastward direction, it is that it traveled 31 inches in some direction that is much more eastward than the direction the pole has been moving in the past hundred or so years. Thanks for the clarification! I think this claim in the paper could be summarized in a much better way in news articles and such.  
> **username_0**: Or is it that if we hadn't been pumping groundwater, they're claiming that the pole would be 31 inches more west than it currently is?  
> **username_3**: @JohnDoty You appear to be stuck on the idea that the as-observed North Pole and the as-observed prime meridian are how we measure latitude and longitude. That simply is not the case. The cartographic poles and prime meridian are frozen; we would not want borders based on latitude and longitude to change just because the poles are moving. Being frozen, the rotational north pole intersects the Earth's surface slightly away from the cartographic north pole, so north, south, east, and west all exist at the location of the rotational north pole.  
> **username_4**: @DavidHammen No, I'm not stuck on that idea at all. You are stuck on the idea that the direction "toward 64.16°E" is the same as "east".  
> **username_4**: @DavidHammen "the rotational north pole intersects the Earth's surface slightly away from the cartographic north pole, so north, south, east, and west all exist at the location of the rotational north pole." It would be a nightmare to define coordinates in this manner, since which direction "east" is would change as the rotational pole wanders. The plot you include above doesn't use north, south, etc: it uses Cartesian X and Y, with X parallel to the prime meridian, and Y parallel to the 90 degree east meridian.  
> **username_3**: @JohnDoty, and others: I posted an update to the answer.  

---

