Subject: [ids.analysis.forum] issue of the slope of C20 in the current EIGEN-6 releases
From: "Soudarin Laurent" <[email-masked]>
To: <[email-masked]>, <[email-masked]>
Date: Mon, 12 Sep 2011 10:19:43 +0200

Dear colleagues,

I was recently informed by Jean-Michel Lemoine about
the discussions concerning the slope of C20 in 
the current EIGEN-6 releases. (see mails below)

To sum up, the current value is valid for the time period 2003-2010
but on the long term this value is clearly far from reality (see attached plot).
A correction is proposed by GRGS for C20 et C20 dot
> >> EIGEN-6          Current Value             New Value
> >> ---------------------------------------------------------
> >>     2  0       -4.8416529982000E-04    -4.8416529995630E-04
> >>     2  0 DOT   -1.2605993970900E-11     3.1827100000000E-12

I used these new values in our DORIS data processing for Spot-2 and Topex 
arcs of January 1993.
The impact on the post-fit orbit residuals is less that 10-3 mm/s for DORIS
and 10-6 m for Topex laser.
The main effect is a radial bias on the orbit differences: 0.3 mm for Topex
and 1.2 mm for Spot-2, with maximums at high latitudes.

So it should be OK for the recent altimetric mission Jasons and Envisat,
but the new C20dot must be used for Topex and early Spots missions.

Best regards,
Laurent

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>Subject: RE: Correcting C20 slope in EIGEN-6
>Date: Wed, 27 Jul 2011 11:08:57 +0200
>Message-ID: 
><[email-masked]>
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>Thread-Topic: Correcting C20 slope in EIGEN-6
>Thread-Index: AcxGHpHm5KTeTHlpS22In7/dZtwJiwBlLi4QADbwP0AA6rTWYA==
>References: 
><[email-masked]>
>From: "Biancale Richard" <[email-masked]>
>To: "Lemoine Jean-Michel" <[email-masked]>,
>         "Christoph Foerste" <[email-masked]>,
>         "Frank Flechtner" <[email-masked]>
>Cc: "Bruinsma Sean" <[email-masked]>,
>         "BOURGOGNE Stephane" <[email-masked]>
>
>Dear all,
>I agree that we should give the C20,C20dot values proposed by Jean-Michel.
>   2  0       -4.8416529995630E-04
>   2  0 DOT    3.1827100000000E-12
>Concerning the ocean tides, the empirical adjustment at the 18.6129yr on 
>C20 (normalized) has to be converted into tides coefficients. This 
>transformation for the Om1 wave gives actually:
>   Cn20 .830 cm
>   Phase: 274.855 deg.
>We should confirm this result by adjusting directly these wave 
>coefficients in the Lageos processing what we will do next. We will have 
>then to modify the ocean tides coefficients what we could do for the next 
>release of the FES model (probably in 2012)  For the moment we simply can 
>mention that the C20dot was obtained by correcting empirically the 18.6yr 
>tide coefficients:
>Delta_C20 = 
>a1*sin(2*acos(-1)*(t-2005)/18.6129)+a2*cos(2*acos(-1)*(t-2005)/18.6129)
>with:   a1 = -9.01895e-12
>         a2 = -3.47674e-11
>That's my opinion.
>Richard
>
>-----Message d'origine-----
>De : Lemoine Jean-Michel
>Envoyé : vendredi 22 juillet 2011 19:06
>À : Christoph Foerste; Frank Flechtner
>Cc : Biancale Richard; Bruinsma Sean; Lemoine Jean-Michel; BOURGOGNE Stephane
>Objet : TR : Correcting C20 slope in EIGEN-6
>
>Dear Christoph, Frank,
>
>We have discussed, between us at GRGS, the issue of the slope of C20 in 
>the current EIGEN-6 releases. Our opinion is that we cannot stand with the 
>actual slope given in the current EIGEN-6 releases. Although the current 
>value is valid for the time period 2003-2010, as I have explained is a 
>previous mail, and as can be readily seen in the attached plot, the 
>problem is that on the long term this value is clearly far from reality 
>(see plot). There are two drawbacks to keeping the current value : one is 
>that we will get endless questions about this slope, the second and more 
>important is that EIGEN-6 will be very probably used for the reprocessing 
>of all past altimeter missions. (It is already being tested with good 
>success by Michiel Otten at ESOC and Luca Cerri at CNES ; in particular it 
>is solving quite well the problem of the increasing mean differences at 
>crossover points between ascending and descending passes.) However, while 
>the EIGEN-6 modelling of C20 is OK starting from ~1996, the problem is 
>that before that date it gets quite wrong... and the main altimetric 
>missions start in 1992.
>
>We propose a correction to the current C20 slope and to the value of the 
>equilibrium 18.6 year tide. This correction was not obtained using normal 
>equations, because unfortunately we do not have the partials for Om1 in 
>our normals, but by a regression based of the LAGEOS-1+LAGEOS-2+GRACE time 
>series. The resulting evolution of C20 is plotted in black in the attached 
>plot. Only C20 bias, slope and 18.6 year tide have been re-evaluated, the 
>annual and semi-annual coefficients have been kept to their current value. 
>Here are the values we come up with :
>
>EIGEN-6          Current Value             New Value
>---------------------------------------------------------
>   2  0       -4.8416529982000E-04    -4.8416529995630E-04
>   2  0 DOT   -1.2605993970900E-11     3.1827100000000E-12
>
>Correction to be applied to the 18.6 year tide, in terms of Delta_C20:
>
>Delta_C20 = 
>a1*sin(2*acos(-1)*(t-2005)/18.6129)+a2*cos(2*acos(-1)*(t-2005)/18.6129)
>
>with:   a1 = -9.01895e-12
>         a2 = -3.47674e-11
>
>This Delta_C20 can be converted into the following values for the 18.6 
>year tide :
>Om1 (Doodson 055.565)   Equilibrium value    Proposed (new) value
>-----------------------------------------------------------------
>C+ (cm)                  0.540594 cm             0.503722 cm
>Eps+ (°)                 270.000 °               262.323 °
>C_bar (cm)              -0.540594 cm            -0.499207 cm
>S_bar (cm)               0.000000 cm            -0.067291 cm
>
>Sean proposes that we modify the C20 and C20_DOT values and that we 
>provide Delta_C20(18.6 year tide) as an additional perturbation to the C20 
>in the file, whereas Richard objects that the Om1 belongs now to the IERS 
>standards and that therefore the only thing to do is to modify the C20 and 
>C20_DOT values and provide the non-equilibrium value of the 18.6 year tide.
>
>Please, let us know your opinion.
>
>Best regards,
>
>Jean-Michel
>-----------------------------------------------------------------
>Jean-Michel Lemoine
>CNES/GRGS
>BPI 3200
>18, avenue Édouard Belin
>31401 Toulouse cedex 4, France
>-----------------------------------------------------------------
>Email : [email-masked]
>Tel : +33-(0)5-61-33-28-94
>Lab : UMR5562
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>