[MITgcm-devel] stevens boundary conditions

[Jean-Michel Campin]

Hi Martin,

To summarize, you want to add, for T & S, (mostly surface) forcing 
and vertical diffusion to the stevens OBC values (= those @ OB_Jn,OB_Js
and @ OB_Ie,OB_Iw, so outside the OB interior region).  

I think vertical advection should be "zero out" like horizontal advection
which is treated separately, as you say. 
Regarding horizontal diffusion, it does not make sense to me to keep part 
of those fluxes for this partial update of OBC value (e.g., @ i=OB_Ie, 
we don't have any valid tracer value @ i=OB_Ie-1, so diffusive flux in
X dir @ i=OB_Ie is meaningless) and it's better to cancel all of them
when computing flux divergence (but we should not zero out fluxes
at i=OB_Ie+1, right ? )

As I wrote earlier (outside the list), it's not yet clear to me which one of 
the 2 solutions is best.

In the option 2 way:
I think in gad_advection (because of OBC multi-dimensional implementation),
all horizontal advection flux divergence are already canceled.
But I would argue that vertical advection should be canceled too
(this is also what you propose).
And in gad_calc_rhs, only vertical diffusive flux should be kept
in the divergence, with the divergence of all the others (including 
gmredi vertical component) being zero out.

Is it what you tried ? or something different ?
Because this looks quite different:
> I need to separate advective flux from the rest (in fZon/fMer),

Going to look at EmPmR forcing issue.

However, I am little bit concern that with vertical mixing scheme 
(KPP, GGL90) and may be also some surface forcing computation,
because of horizontal averaging, it might be difficult to get a 
clean solution in those columns (in fact, in seaice_obcs test.exp. 
which is using KPP, some of the western OB values already 
influence the Eastern side).

Cheers,
Jean-Michel

On Thu, Dec 08, 2011 at 10:20:18AM +0100, Martin Losch wrote:
> Hi Jean-Michel,
> 
> following up on my previous post: my initial tests show, that for option 2, adding a maskInC in gad_advection "works" in the sense that I does not affect the results, but masking the contribution from advection in gad_calc_rhs is problematic: I need to separate advective flux from the rest (in fZon/fMer), and this separation alone (naively, I added two new afZona,afMeri, but no further masking or anything) changes the results of exp4 by 4-6 digits for cg2d (reducing the agreement to 12, 11 and 10), so just the order of summation. Is this expected?
> This would make option 2 not very attractive (for non-multidimAdvection), would it?
> 
> Martin
> 
> On Dec 7, 2011, at 4:59 PM, Martin Losch wrote:
> 
> > Jean-Michel,
> > 
> > it turns out that the Stevens BC story continues. So far, I implemented updating the tracer (T/S) value on the boundary only based on advection (modified model "mean" velocity and some kind of phase velocity that is similar to orlanski), and a restoring term. 
> > 
> > Now it turns out that it is necessary to include surface forcing and vertical diffusion for the boundary values as well. Stepping back this means that basically all terms in the tracer advection/diffusion equation on the boundary should be used, except for the advection. The advection is added in a modified version, and the restoring term added. How can that be implemented technically? I see two options:
> > 1. my quick fix is to add the desired terms to OB?t/s as required. In the case of surface forcing and vertical diffusion, I add these contributions at the end of do_oceanic_physics, and everything else remains the same.
> > 2. Far more elegant: Do you think it's possible to have the model do all computations, except for advection, compute advection and restoring tendencies in obcs (_calc_stevens), and apply these as a correction in obcs_apply_ts (is useStevens)? As far as I can see, this requires a maskInC in gad_advection (at the very end) and gad_calc_rhs (advFac*maskInC) and that's it. Is my thinking too simple?
> > 
> > A related problem is that the surface forcing for salinity is incomplete on the open boundary for useRealFreshWaterFlux=.true., because EmPmR is masked by maskInC in this case. Do you see a way to add that back in?
> > 
> > Martin
> > 
> > PS. In Stevens (1990), the phase velocity to correct to model advection on the boundary is computed from time steps n-1 and n-2: 
> > c=dy/dt * ( t(i,j+1,k,n-1) - t(i,j+1,k,n-2) )/( t(i,j+2,k,n-2)-t(i,j+1,k,n-2) )
> > I use
> > c=dy/dt * ( t(i,j+1,k,n-1) - t(i,j+1,k,n-2) )/( t(i,j+2,k,n-1)-t(i,j+1,k,n-1) )
> > to save me from storing t(i,j+2,k,n-2)-t(i,j+1,k,n-2). In orlanski_south, things are done "properly". I am not sure if this is an issue or not. For it does not cause any problems. One could think of merging the orlanski and the stevens code. What do you think?
> > 
> > 
> > 
> > 
> > 
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> 
> 
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