Dear, Prof. Alexander

Thanks for helping me

Abdel Rahim

Recollection

Imagine the 3 gravity fields:

(1) the gravity field of the Earth, described in the rotating Earth-fixed coordinate

system, under the assumption that Moon and Sun do not exist ==> tide free gravity field model

(2) the gravity field of the Earth, described in the rotating Earth-fixed coordinate

system, plus the gravity fields of the Moon and the Sun averaged over a long time (which is called the permanent tidal effect), plus the effect of Earth's deformation, caused by Moon and Sun, on the gravity field (also averaged over time)   ==> mean tide gravity field model

(3) the gravity field of the Earth, described in the rotating Earth-fixed coordinate

system, without the gravity fields of the Moon and the Sun, but, with the indirect effect of Earth's deformation ==> zero tide gravity field model

The differences of these three gravity fields can be described (as the gravity

field itself) in terms of spherical harmonics. Strictly, these spherical harmonic series go up to infinity.

But, because the permanent (i.e. averaged over time) tidal effects change the gravity field only very globally, it turned out that it is sufficient to change only the coefficient C20, which describes the flattening of the equipotential surfaces of the gravity field.

This answer I received from Dr. Franz Barthelmes (Section 1.2: Global Geomonitoring and Gravity Field, Department 1: Geodesy and e-mail:    [email protected])

Dear, Prof. Alexander

Thanks again for helping me

I know the formulas which used for transformation between different permanent tides

For example: When converting the model such as EGM2008 (tide free) to zero tides, we will use the following formula:

C2,0 (zero tide) = C2,0 (tide free)  (0.30 * -1.39*10^-8)     

I am looking for why use the coefficient C2,0 (only) in the above equations

Regards

Abdel Rahim

Dear Abdel Rahim, the C20 coefficient linked to the flattening of the earth, and it is the main contribution in the spherical harmonic development of the gravity field which includes all the gravity perturbations as the earth tides. When we want to have an approximation of its contribution, I think that the use of all the other coefficients is not necessary.

Sincerely yours

Salem Kahlouche

Dear, Dr. Salem

Many thank for this answer

Abdel Rahim