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

-- OctavianAndrei - 30 May 2008

Answer

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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

-- 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

-- DagobertoSalazar - 04 Jun 2008