[MITgcm-devel] Fwd: [MITgcm-support] GM: Skew flux vs Advective form

Fri Jun 14 05:35:26 EDT 2013

Hi guys,

I just got a call from Carsten Eden, who wanted to raise awareness for the apparent problem with the skew flux formulation of GM. Here's the thread again: <http://mitgcm.org/pipermail/mitgcm-support/2013-June/008344.html>

Do you agree, that this is a serious issue? How can we fix that? May the adjoint stability even be affected in a positive way by this?

Martin

Begin forwarded message:

> From: Lars Czeschel <lars.czeschel at zmaw.de>
> Subject: Re: [MITgcm-support] GM: Skew flux vs Advective form
> Date: June 12, 2013 12:50:08 PM GMT+02:00
> To: <mitgcm-support at mitgcm.org>
> Reply-To: <mitgcm-support at mitgcm.org>
> 
> Hi Ryan,
> it seems it is not a problem of the layer diagnostic.
> I calculated the eddy-MOC from the bolus velocities in z-levels 
> for the 'tutorial_global_oce_latlon' for year 10 with similar results.
> 
> I attached some figures showing the global eddy MOC for both cases and the differences.
> The last two figures show the eddy MOC in the deepest level to give an impression of the 
> divergence when using the skew flux formulation.
> 
> I also attached the matlab code in case I am missing something in my calculation.  
> 
> Thanks, Lars
> 
> 
> 
> 
> 
> 
> 
> %Eddy MOC from skew flux formulation
> clear all
> % load data
> DXG = rdmds('DXG');
> hFacS = rdmds('hFacS');
> YG = rdmds('YG');
> DRF = rdmds('DRF');
> DRF = squeeze(DRF);
> KWY = rdmds('GM_Kwy-T.0000172800');
> 
> % compute mer. bolus velocity
> KWY(:,:,16)=0.0;
> for i=1:90
> for j=1:40
> for k=1:15
> Vb(i,j,k)=KWY(i,j,k+1)*0.5-KWY(i,j,k)*0.5;
> end
> end
> end
> DX=repmat(DXG,[1,1,15]);
> ddz=repmat(DRF,[1, 40, 90]);
> ddz=permute(ddz,[3 2 1]);
> n=find(hFacS > 0); 
> Vb(n)=Vb(n)./(ddz(n).*hFacS(n));
> 
> % integrate MOC
> Xint=sum(Vb.*DX.*hFacS);
> Xint=squeeze(Xint);
> dz=repmat(DRF,[1,40]);
> dz=permute(dz,[2 1]);
> MOC=cumsum(Xint.*dz./1e6, 2);
> 
> %Plotting
> [hcl cl]=contourf(YG(1,:),cumsum(DRF),MOC',[-30:5:-10 -10:2:10 10:5:30 ]);
> set(gca,'YDIR','reverse')
> clabel(hcl,cl)
> caxis([-30,30])
> colorbar
> title('Skew Flux MOC [Sv]');
> 
> ----
> 
> %Eddy MOC from advective formulation
> clear all
> DXG = rdmds('DXG');
> hFacS = rdmds('hFacS');
> YG = rdmds('YG');
> DRF = rdmds('DRF');
> DRF = squeeze(DRF);
> PSIY = rdmds('GM_PsiYtave.0000172800');
> 
> % compute mer. bolus velocity
> PSIY(:,:,16)=0.0;
> for i=1:90
> for j=1:40
> for k=1:15
> Vb(i,j,k)=PSIY(i,j,k+1)-PSIY(i,j,k);
> end
> end
> end
> DX=repmat(DXG,[1,1,15]);
> ddz=repmat(DRF,[1, 40, 90]);
> ddz=permute(ddz,[3 2 1]);
> n=find(hFacS > 0);
> Vb(n)=Vb(n)./(ddz(n).*hFacS(n));
> 
> % compute eddy MOC
> Xint=sum(Vb.*DX.*hFacS);
> Xint=squeeze(Xint);
> dz=repmat(DRF,[1,40]);
> dz=permute(dz,[2 1]);
> MOC=cumsum(Xint.*dz./1e6, 2);
> 
> %Plotting
> [hcl cl]=contourf(YG(1,:),cumsum(DRF),MOC',[-30:5:-10 -10:2:10 10:5:30 ]);
> set(gca,'YDIR','reverse')
> clabel(hcl,cl)
> caxis([-30,30])
> colorbar
> title('Advective form MOC [Sv]');
> 
> 
> 
> 
> On 06.06.2013, at 18:04, Ryan Abernathey wrote:
> 
>> Lars,
>> Unfortunately, I can't really comment on climatological differences between the skew flux vs adv form.
>> But I am curious whether using adv form fixed the problems you were having with the layers diagnostics.
>> -Ryan
>> 
> 
>> 
>> On Thu, Jun 6, 2013 at 2:24 AM, Lars Czeschel <lars.czeschel at zmaw.de> wrote:
>> Hi all,
>> 
>> i am running a 1deg global model with version MITgcm_63q. Using the layers pkg I noticed
>> that my global overturning in density space is divergent (up to 5 Sv in ACC latitudes).
>> Without bolus velocities or using  ' GM_AdvForm    = .TRUE.,' in data.gmredi
>> the overturning becomes non-divergent.
>> 
>> As we used the skew flux version frequently in the past (which is also the default) I hoped to find
>> a bug in the layers pkg but without success. As a further test I ran the tutorial example
>> 'tutorial_global_oce_latlon'  for 10 years with   GM_AdvForm    = .False. compared
>> to GM_AdvForm    = .TRUE. in data.gmredi. I attached the quite strong differences in theta (z=85m)
>> below.
>> 
>> To my understanding the differences should be very small even if the small slope assumption
>> is made using the skew flux version.
>> 
>> Did I miss something here or do we have an undiscovered bug in the skew flux code and
>> the advective form should be recommended ?
>> 
>>   Thanks , Lars
>> 
>> p.s: Several years ago Christopher Wolfe reported a related problem
>> http://mitgcm.org/pipermail/mitgcm-support/2008-January/005180.html
>> 
>> 
>> ----------------------------------------------
>> Lars Czeschel
>> Theoretical Oceanography
>> Institut für Meereskunde
>> KlimaCampus Universität Hamburg
>> Bundesstr. 53
>> 20146 Hamburg
>> 
>> 
>> _______________________________________________
>> MITgcm-support mailing list
>> MITgcm-support at mitgcm.org
>> http://mitgcm.org/mailman/listinfo/mitgcm-support
>> 
>> 
>> _______________________________________________
>> MITgcm-support mailing list
>> MITgcm-support at mitgcm.org
>> http://mitgcm.org/mailman/listinfo/mitgcm-support
> 
> _______________________________________________
> MITgcm-support mailing list
> MITgcm-support at mitgcm.org
> http://mitgcm.org/mailman/listinfo/mitgcm-support

-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://mitgcm.org/pipermail/mitgcm-devel/attachments/20130614/9db5b0bc/attachment-0001.htm>
-------------- next part --------------
A non-text attachment was scrubbed...
Name: Skew_MOC.jpg
Type: image/jpg
Size: 44501 bytes
Desc: not available
URL: <http://mitgcm.org/pipermail/mitgcm-devel/attachments/20130614/9db5b0bc/attachment-0005.jpg>
-------------- next part --------------
A non-text attachment was scrubbed...
Name: Adv_MOC.jpg
Type: image/jpg
Size: 44661 bytes
Desc: not available
URL: <http://mitgcm.org/pipermail/mitgcm-devel/attachments/20130614/9db5b0bc/attachment-0006.jpg>
-------------- next part --------------
A non-text attachment was scrubbed...
Name: MOC_difference.jpg
Type: image/jpg
Size: 48367 bytes
Desc: not available
URL: <http://mitgcm.org/pipermail/mitgcm-devel/attachments/20130614/9db5b0bc/attachment-0007.jpg>
-------------- next part --------------
A non-text attachment was scrubbed...
Name: Skew_MOC_bottom.jpg
Type: image/jpg
Size: 18447 bytes
Desc: not available
URL: <http://mitgcm.org/pipermail/mitgcm-devel/attachments/20130614/9db5b0bc/attachment-0008.jpg>
-------------- next part --------------
A non-text attachment was scrubbed...
Name: Adv_MOC_bottom.jpg
Type: image/jpg
Size: 20988 bytes
Desc: not available
URL: <http://mitgcm.org/pipermail/mitgcm-devel/attachments/20130614/9db5b0bc/attachment-0009.jpg>