# What is polar movement

## encyclopedia

Movement of the earth's axis of rotation relative to its crust

^{[1]}

**Polar motion of the earth** is the movement of the earth's axis of rotation relative to its crust.^{[2]}^{::1} This is measured in relation to a frame of reference in which the solid earth is fixed (a so-called *Earth-centered, earth-fixed* or ECEF reference framework). This variation is only a few meters.

### Analysis [edit]

Polar motion is defined relative to a conventionally defined reference axis, with the CIO (Conventional International Origin) being the average location of the pole in 1900. It consists of three main components: a free oscillation called Chandler wobble with a duration of about 435 days, an annual oscillation and an irregular drift towards the 80th meridian west,^{[3]} which has recently been moved east.^{[4]}^{[5]}^{::1}

The slow drift, around 20 m since 1900, is partly due to movements in the earth's core and mantle, partly to the redistribution of the water mass when the Greenland ice cover melts and to the isostatic rebound, i.e. the slow rise of the country earlier burdened with ice sheets or glaciers .^{[2]}^{::2} The drift runs roughly along the 80th west meridian. Since around 2000 the pole has found a new drift direction that lies roughly along the central meridian. This dramatic shift in the drift direction to the east is attributed to the worldwide mass transport between the oceans and the continents.^{[5]}^{::2}

Severe earthquakes cause abrupt polar movements by changing the volume distribution of the earth's solid mass. These displacements are relatively small relative to the long term core / shell and isostatic rebound components of polar motion.^{[6]}

### Principle [edit]

In the absence of external torques, the vector of angular momentum **M.** of a rotating system remains constant and is directed to a fixed point in space. If the earth were perfectly symmetrical and rigid **M.** would stay aligned with its axis of symmetry, which would also be its axis of rotation. In the case of the earth, it is almost identical to its axis of rotation, the discrepancy being due to mass displacements on the planet's surface. The vector of the figure axis **F.** of the system (or the maximum major axis, the axis that gives the greatest value of the moment of inertia) wobbles around **M.**. This movement is called Euler's free nutation. For a rigid earth, which is a flattened spheroid to a good approximation, the figure axis is **F.** would be its geometric axis defined by the geographic north and south poles and identical to the axis of its polar moment of inertia. The Euler period of free nutation is

(1) τ_{E.} = 1 / ν_{E.} = A / (C - A) sidereal days ≈ 307 sidereal days ≈ 0.84 sidereal years

ν_{E.} = 1.19 is the normalized Euler frequency (in units of reciprocal years), C = 8.04 × 10^{37} kg m^{2} is the Earth's polar moment of inertia, A is the mean equatorial moment of inertia, and C - A = 2.61 × 10^{35} kg m^{2}.^{[2]}^{[7]}

The observed angle between the figure axis of the earth **F.** and its angular momentum **M.** is a few hundred milliseconds (mas). This rotation can be interpreted as a linear displacement of one of the two geographic poles at a height of several meters on the earth's surface: 100 mas form an arc length of 3.082 m when converted into radians and with the polar radius of the earth (6,356,752.3 m ) are multiplied. Using the geometric axis as the main axis of a new body-fixed coordinate system, one arrives at the Euler equation of a gyroscope, which describes the apparent movement of the axis of rotation around the geometric axis of the earth. This is what is known as the polar movement.^{[8]}

Observations show that the figure axis exhibits an annual wobble, which is forced by the displacement of the surface mass via the atmospheric and / or oceanic dynamics, while the free nutation is much larger than the Euler period and on the order of 435 to 445 star days. This observed free nutation is known as the Chandler wobble. In addition, there are polar motions with smaller periods on the order of decades.^{[9]} Finally, a secular polar drift of about 0.10 m per year towards 80 ° West was observed, which is due to a mass redistribution in the Earth's interior due to continental drift and / or slow movements within the mantle and core, which lead to changes in the moment of inertia.^{[8]}

The annual variation was discovered in 1885 by Karl Friedrich Küstner through precise measurements of the variation in the latitude of the stars, while SC Chandler found free nutation in 1891.^{[8]} Both periods overlap and lead to a beat frequency with a period of about 5 to 8 years (see Figure 1).

This polar movement should not be confused with the change in direction of the earth's axis of rotation relative to the stars with different periods, mainly caused by the torques on the geoid due to the gravitational pull of the moon and sun. They are also called nutations, with the exception of the slowest, the precession of the equinoxes.

### Observations [edit]

Polar motion is routinely observed by very long baseline interferometry.^{[10]}Moon laser distance and satellite laser distance.^{[11]} The annual component has a fairly constant amplitude, and its frequency does not vary by more than 1 to 2%. However, the amplitude of the Chandler wobble varies by a factor of three and its frequency by up to 7%. Its maximum amplitude in the last 100 years has never exceeded 230 mas.

Chandler wobble is usually thought of as a resonance phenomenon, a free nutation that is excited by a source and then disappears with a time constant τ_{D.} on the order of 100 years. It is a measure of the earth's elastic response.^{[12]} It is also the explanation for the deviation of the Chandler period from the Euler period. However, instead of dying off, the Chandler wobble, which has been continuously observed for more than 100 years, varies in amplitude and shows a sometimes rapid frequency shift within a few years.^{[13]} This mutual behavior between amplitude and frequency was described by the empirical formula:^{[14]}

(2) m = 3.7 / (ν - 0.816) (for 0.83 <ν>

**m**the annual component of polar movement as a function of the year. Numbers and ticks indicate the beginning of each calendar month. The dash-dotted line runs in the direction of the main axis. The line in the direction of the minor axis is the location of the excitation function in relation to the season. (100 mas (milliseconds) = 3,082 m on the earth's surface at the poles)

There is now general agreement that the annual component of polar motion is a forced motion, mainly stimulated by atmospheric dynamics.^{[21]} There are two external forces to stimulate polar movement: atmospheric winds and pressure loading. The main component is the pressure drive, which is a standing wave of the form:^{[17]}

(3) p = p_{Ö}Θ_{−3}^{1}(θ) cos [(2πν_{A.}

(t - t_{O})] cos (λ - λ_{Ö})

with P_{Ö} a pressure amplitude, Θ_{−3}^{1} a Hough function, which describes the latitude distribution of the atmospheric pressure on the ground, θ the geographical co-latitude, t the season, t_{Ö} a time delay, ν_{A} = 1.003 the normalized frequency of a solar year, λ the length and λ_{Ö} the length of the maximum pressure. As a first approximation, the Hough function is proportional to sinθ cosθ. Such a standing wave represents the seasonally varying spatial difference in the earth's surface pressure. In the northern winter there is high pressure over the North Atlantic and low pressure over Siberia with temperature differences of the order of 50 ° and vice versa in summer, which results in an unbalanced mass distribution on the earth's surface. The position of the vector **m** the annual component describes an ellipse (Figure 2). The calculated ratio between the major and minor axes of the ellipse is

(4) m_{1}/ m_{2} = ν_{C.}

where ν_{C.} is the Chandler resonance frequency. The result agrees well with the observations.^{[2]}^{[22]}

From Fig. 2, together with equation (4), ν is obtained_{C.} = 0.83, corresponding to a Chandler resonance period of

(5) τ_{C.} = 441 star days = 1.20 star years

p_{Ö} = 2.2 hPa, λ_{Ö} = - 170 ° the latitude of the maximum pressure and t_{Ö} = - 0.07 years = - 25 days.

It is difficult to gauge the effect of the ocean, which can slightly increase the value of the maximum ground pressure required to produce the annual wobble. This ocean effect has been estimated at 5–10%.^{[23]}

### Chandler wiggles [edit]

It is unlikely that the Earth's internal parameters responsible for the Chandler wobble are time dependent on such short time intervals. In addition, the observed stability of the annual component speaks against any hypothesis of a variable Chandler resonance frequency. A possible explanation for the observed frequency-amplitude behavior would be a forced but slowly changing quasi-periodic excitation by interannually varying atmospheric dynamics. In fact, a period of almost 14 months was found in coupled general circulation models of the ocean atmosphere.^{[24]} and a 14 month regional signal in regional sea surface temperature was observed.^{[25]}

To describe such behavior theoretically, one begins with the Euler equation with pressure load as in equation (3), but now with a slowly changing frequency ν, and replaces the frequency ν with a complex frequency ν + iν_{D.}, where ν_{D.} simulates the dissipation due to the elastic reaction of the earth's interior. As in Figure 2, the result is the sum of a progressive and a retrograde circularly polarized wave. For frequencies ν

(6) m = 14.5 p_{Ö} ν_{C.}/.[(ν - ν_{C.})^{2} + ν_{D.}^{2}]^{1/2} (for ν

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