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# Pole Tide

Fundamentals | |
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Title | Pole Tide |

Author(s) | J. Sanz Subirana, J.M. Juan Zornoza and M. Hernández-Pajares, Technical University of Catalonia, Spain. |

Level | Intermediate |

Year of Publication | 2011 |

The instantaneous earth rotation axis shifts inside a square of about meters in relation to a point with fixed coordinates on the earth (i.e., Chandler wobble with a period of months). This entails a varying elastic response of the earth's crust. This has an effect smaller than centimetres in vertical and centimetres in horizontal, but must be taken into account if the observations are carried out over periods longer than two months.

From the IERS Conventions [Denis et al., 2004] ^{[1]}, pages 83-84, the following expression ^{[footnotes 1]} can be derived for the displacement at a point of geocentric latitude and longitude :

where (,) are the displacements (in meters) from the 1903.0 CIO, pole position, and , are the Love numbers.

Taking the earth's angular rotation , the earth's equatorial radius and the gravitational acceleration , it follows:

where (,) are the displacements (given in seconds of arc). Pole displacements can be found at ftp://hpiers.obspm.fr/iers/eop/eop.others.

The displacement is given in the radial, longitude and latitude vectors (positive upwards, eastwards and northwards, respectively).
Thus, the displacement vector in the (x, y, z) ECEF Cartesian coordinates is given by

where are the rotations in latitude (1) and longitude (2) indicated in figure 1 (see Reference Frames in GNSS).

## Notes

- ^ Notice the use of latitude in equations (1 and 2), instead of the co-latitude used in the IERS equations.

## References

- ^ [Denis et al., 2004] Denis, D., McCarthy and Petit, G., 2004. IERS Conventions (2003). IERS Technical Note 32.. IERS Convention Center., Frankfurt am Main.