Subject: [Forwarded: Re: Jason models]
From: "Frank Lemoine" <[email-masked]>
To: [email-masked]
Date: Thu, 19 Oct 2006 05:53:26 -0000 (GMT)

---------------------------- Original Message ----------------------------
Subject: Re: Jason models
From:    "John C. Ries" <[email-masked]>
Date:    Thu, October 19, 2006 12:28 am
To:      [email-masked]
Cc:      [email-masked]
         [email-masked]
         "Nikita Zelensky" <[email-masked]>
         "Dr. Erricos C. Pavlis" <[email-masked]>
         [email-masked]
         "Pascal Bonnefond" <[email-masked]>
         "Cerri Luca" <[email-masked]>
         "Mercier Flavien" <[email-masked]>
         "Laurent Soudarin" <[email-masked]>
         [email-masked]
--------------------------------------------------------------------------

At 4:50 PM +0200 10/17/06, Jean-Paul Berthias wrote:
>Hi John,
>
>In your last Email you propose to
>>1)* We adopt the IERS2003 values for C21/S21 at epoch 2000.0 as
>>well as the rates. These are consistent with the mean pole and
>>rates adopted for the pole tide, also in the standards.* Because
>>the rates were not used  for EIGEN-GL04C, this is the only way I
>>see to ensure consistency with the pole tide model.
>
>Just to make sure that we all understand the same thing, the
>standards tell us (at the beginning of chapter 6) how to compute the
>C21/S21 and associated rates from the values of the mean pole and
>C20, C22 and S22. We should adopt the mean pole (and mean pole rate
>from the standards), but the C20, C22 and S22 of the gravity model
>that we plan to use (EIGEN-GL04C).
>
>When we do that we obtain values of C21/S21 slightly different than
>those given in the standards which are valid for EGM96. The EIGEN
>based standards are
>
>C21 = -2.36e-10
>S21 = 15.12e-10
>C21dot = -0.341e-12
>S21dot =  1.602e-12
>

Hi Jean-Paul,

I found some older emails where you had raised related questions
about C21/S21, and I'm not sure what conclusion we had come to. But
perhaps now we can try to clarify this.

When I calculate C21/S21 from the standards, using EGM96 (C20 mapped
to epoch 2000), I get

C21/S21: -2.23E-10 1.447E-09

rates:  -0.337E-11 1.606E-11

My calculation differs by just 1 from IERS2003 in the last digit for
S21; otherwise I match it. The small difference for S21 may just have
been some rounding. The rates are calculated by simply replacing xbar
and ybar with xbardot and ybardot from chapter 7 and ignoring the
C22/S22 contributions. If the C22/S22 contributions are included, the
rates become

-0.341E-11 1.602E-11

which matches your calculation for the rates. Not enough difference
to worry about and probably well under the uncertainty in the
determination of the mean pole rates. But it is inconsistent, and I'm
not sure why the C22/S22 contributions were ignored for the rates in
the standards.

The estimated uncertainty in C21/S21 is ~2e-11 from EIGEN-GL04C. The
difference in the rate calculation (with and without C22/S22) is
4e-14. It would take hundreds of years for the difference to be
significant.

When I use EIGEN_GL04C's values for C20, C22 and S22, I get the same
numbers. This is expected since C20, C22 and S22 differ only in the
fourth or fifth digit at most.

There must be some error in your calculations. I can't duplicate it.
I'm attaching a simple piece of code so that you can check my
calculations.

My conclusion is that the IERS2003 standards are more or less model
independent. The difference in the calculation of the rates is
unimportant, but perhaps we should propose they make it consistent,
since it is otherwise a bit confusing.

See ya,
JR

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