## Question

Hello again,

In my opinion the implementation of

**gpstk::PoleTides::getPoleTide** function is wrong.
Here is my argumentation.

According to Eq.(3) (Wahr, 1985, pp.9364), the greek letter 'theta' denotes the

**co-latitude**. This notation is also used by IERS conventions (IERS, 2003). In Chapter 7 of their last update (

ftp://tai.bipm.org/iers/convupdt/chapter7/icc7.pdf), Eq.(24) is given at page 13 in order to calculate the displacements at the reference point due to polar motion. The displacements are calculated in a

**USE** reference frame as mentioned right after Eq.(20).

Kouba (2003) gives in Section 5.2.2 same formulas as IERS.

On the other hand, according to gpstk's implementation, the term

**latitude** is used. This means

**latitude = 90 degrees - co-latitude**.

Based on above mentioned, the formulas given at rows 92-94 are wrong and should be changed in

- res[0] = -0.033 * sin2lat * ( m1*coslon + m2*sinlon );
- res[1] = +0.009 *
**sinlat** * ( m1*sinlon - m2*coslon );
- res[2] =
**-** 0.009 * cos2lat * ( m1*coslon + m2*sinlon ); (*please note the minus sign*)

to obtain the displacements in a

**UEN** reference frame using the

**latitude**.

## Reference:

IERS Conventions (2003). Dennis D.

McCarthy and Gérard Petit. (IERS Technical Note ; 32) Frankfurt am Main: Verlag des Bundesamts für Kartographie und Geodäsie, 2004. 127 pp. (The updated version is available at

http://tai.bipm.org/iers/convupdt/convupdt.html)

Kouba J., (2003), A Guide to Using International GPS Service (IGS) Products.

http://igscb.jpl.nasa.gov/igscb/resource/pubs/GuidetoUsingIGSProducts.pdf
Wahr, J. M., 1985, “Deformation Induced by Polar Motion,” J. Geophys. Res., Vol. 90, No. B11, p. 9363 - 9368

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OctavianAndrei - 30 May 2008

## Answer

**If you answer a question - or have a question you asked answered by someone - please remember to edit the page and set the status to answered. The status is in a drop-down list below the edit box.**
Dear Mr. Andrei:

Thanks very much for your thorough feedback. I'll check carefully the documentation and the source code you are pointing at, and I'll tell you something about it as soon as possible.

Best regards,

Dagoberto Salazar

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DagobertoSalazar - 04 Jun 2008

Dear Mr. Andrei:

After carefully checking your proposition, as well as the references cited, I arrived to the conclusion that you are right. I will commit the corrections as soon as possible.

On the other hand, be aware that your included reference Kouba, 2003, is ALSO IN ERROR.

Section 5.2.2 implies it is using latitude instead of co-latitude, and
therefore the LONGITUDE correction should be:

deltaLambda = 9 SIN(lat) * (Xp * sin(Lambda) +Yp * cos(Lambda))

In the current version, it uses COS(lat).

The problem is difficult to see at first glance because trigonometrical identities for co-latitude and latitude are similar, and IERS' document uses a southward correction, mixing up signs a little bit.

Thanks again for your through feedback. This kind of user comments helps us a lot to improve the GPSTk quality.

Best regards,

Dagoberto Salazar

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DagobertoSalazar - 04 Jun 2008

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