[MITgcm-support] Production of spurious negative tracer values by GM

[Jean-Michel Campin]

Hi,

This is a response to a unanswered (very) old message, but since the issue has 
been brought back recently and since the discretisation used in pkg/gmredi has not 
changed much since that time, might still be useful.

pkg/gmredi discretisation:
--------------------------
The current implementation of the Redi tensor (isopycnal diffusion) ensures
that tracer are mixed along isopycnal and, if using linear EOS, the density is 
not affected by the isopycnal diffusion, with or without tapering scheme
(this is not true when using the slope clipping method).

However, the implementation is not the "best" one, since one would prefer a more
local scheme involving less averaging, such as the one described in this paper:
Griffies etal, 1998a, JPO, 28, pp 805-830. (also known as "triads method").

And regarding the GM part, the implementation of the skew flux form (Griffies,
1998b, JPO, 28, pp 831–841) affects the coefficients of the Redi tensor but 
relies on the same pieces of code (=> same discretisation).

The implementation of advective form of GM is somehow more local: the slope is
evaluated from the locally-referenced potential density field at only 4 points, 
which is the minimum to form the ratio of 2 gradients in each direction, 
and then the stream-function is set directly from the slope.

Skew-flux vs advective form:
----------------------------
If I remember well, the superiority of skew-flux compared to the advective form 
that Stephen Griffies obtained are partly due to the triads-method.
When doing the comparison skew-flux / advective form with pkg/gmredi (MITgcm),
my interpretation is that the less local implementation of the Redi-tensor 
produces some differences, specially near boundaries, that would probably not 
been seen if the triads method was used.

monotonous property (no false extrema):
---------------------------------------
It is interesting to note that (any) linear scheme (i.e., without any type of 
non-linear flux limiter that depends on each tracer distribution) used for the 
isopycnal diffusion is not monotonous (can produce false extrema), see: 
Beckers, 1998, JPO, 28, pp 1552-1559.
However, the problem of false extrema is reduced when using the triads-method
(Griffies etal, 1998a).

In MITgcm, with the advective form of GM and assuming the default: 
GM_AdvSeparate=False is used, the eulerian and bolus velocity are combined 
(= residual-mean transport) and, with the choice of a monotonous advection 
scheme, false extrema can be avoided/controlled; note that this does not take 
care of the false extrema occurring because of isopycnal diffusion.

But Oliver Jahn implemented in MITgcm a type of (flux) correction 
(CPP option: GAD_SMOLARKIEWICZ_HACK, in GAD_OPTIONS.h, pkg/generic_advdiff).
to prevent negative passive tracer concentration (that the isopycnal diffusion
might produce). 

Cheers,
Jean-Michel

On Thu, Jan 24, 2008 at 02:42:07PM -0800, Christopher L. Wolfe wrote:
> 
> Hi,
> 
> I'm doing some tracer release experiments in a low resolution model
> using the ptracers package. The initial condition is a strip of
> positive tracer on the surface and zero everywhere else. The tracers
> are advected by scheme 33 and diffused by a very low diffusion
> (1e-7). If I set PTRACERS_useGMRedi(1)=.TRUE., I get rather
> significant (>30% RMS tracer value) negative tracer values pretty
> quickly (less than a year). If I turn GM off, the negative values
> are at the level of single precision numerical noise (see attached
> figure). I'm using the plain vanilla skew flux GM scheme with all
> the default values.
> 
> My understanding is that the skew flux GM is mathematically
> equivalent to advection by a non-divergent bolus velocity---which
> shouldn't be able to produce negative values from positive
> data---and that the skew flux form is preferred because it is
> numerically more accurate. In the present case, however, the skew
> flux form seems to be significantly in error.
> 
> I'll run a test using the advective form of GM, but until then, does
> anyone have any idea what's going on?
> 
> Thanks,
> Christopher
> 


> 
> -----------------------------------------------------------
> Dr. Christopher L. Wolfe                   858-534-4560
> Physical Oceanography Research Division    OAR 357
> Scripps Institution of Oceanography, UCSD  clwolfe at ucsd.edu
> -----------------------------------------------------------
> 
> 

> _______________________________________________
> MITgcm-support mailing list
> MITgcm-support at mitgcm.org
> http://mitgcm.org/mailman/listinfo/mitgcm-support