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

Wed Jun 12 06:50:08 EDT 2013

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
> 
> 
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> 
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