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# Pole Tide

Fundamentals
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



Figure 1: Transformation from UEN  to TRS  coordinates.

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

## Notes

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

## References

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