advection and spurious mixing

[rduran]

I have a few questions regarding spurious mixing in ROMS-Rutgers:

1) Is the cppdefs option TS_U3ADV_SPLIT something similar to what is described here:
Marchesiello, P., Debreu, L., Couvelard, X. 2009. Spurious diapycnal mixing in terrain-following coordinate models: The problem and a solution. Ocean Modelling 26, 156-169.

or here:
http://www.myroms.org/Workshops/ROMS201 ... emarie.pdf ?

2) If I choose TS_U3ADV_SPLIT globaldefs will have me use
TS_DIF4
TS_C4HADVECTION
TS_C4VADVECTION

But Hernan has mentioned in this forum:

I have also recommended in all ROMS workshops to use TS_A4HADVECTION and TS_A4VADVECTION with explicit diffusivity (TS_DIF2 and MIX_TS_GEO). For vertical advection of momentum you should useUV_C4VADVECTION.

 Just try the recommendation and compare the solutions. Then, you will know what I am talking about. This is the best advice that I can give to any ROMS user...

Do Hernan's suggestions take care of spurious diapycnal mixing in sigma-coordinates in a different way?

It would seem that mixing TS along isopycnals would be more physical (at least for a baroclinic ocean) than along geopotentials ...

3) Any suggestions and guidance regarding this topic are very welcome. I would like to be able to reproduce a warm and salty tongue of water moving over the slope where isopycnals are sloping up above the tongue and sloping down below it.

[rduran]

Should I add an item to the wish list?

[arango]

If I recall correctly, your application is idealized and you don't need to worried about the problems described in Marchesiello et al. (2009). The numerical diapycnal mixing due to horizontal advection is a function of bathymetry, horizontal and vertical resolution, terrain-following transformation coordinates, and stretching parameters. I had shown in previous ROMS Workshops that the 4th-order Akima advection and Vtransform=2 works as well or better than the split scheme proposed by Marchesiello et al. (2009).

Therefore, you need to experiment with advection schemes and vertical transformation parameters and monitor the evolution of T-S properties of the water masses. In particular, deep water masses.

[rduran]

thank you very much Hernan.

Just for the record my case is a realistic simulation of the Oregon coast (simulating 2005).

R.

[patrickm]

I did not have much success with the Akima advection scheme. I think that the only progress from the scheme proposed in Marchesiello et al. (2009) is coming from Lemarié et al. (a paper that will soon be published). It is a significant update from my work that will allow isopycnal mixing (with no addition constraint on the timestep).

cheers
Patrick

[arango]

Yes, the problem with the numerical diapycnal mixing in the tracer advection operator is that it depend on the application resolution and bathymetry.

[ilicakme]

Hi,

I just have one question and one comment:
My comment is we just have a new paper coming out about numerical mixing in idealized test cases and global experiments using ROMS, GOLD, MOM and MITgcm. We found that ROMS performs better than the MOM and MITgcm since it uses a high-order upwind biased momentum-advection scheme which has implicit numerical viscosity. In fact, ROMS performs better in the idealized cases if I use the Marchesiello et al. (2009) option again just for the momentum-advection scheme.

My question is I'm not sure it's proper thing to do to use a non-monotonic advection scheme for temperature and salinity. Am I wrong? I mean if we have the option we should use a monotonic scheme which is MPDATA in ROMS case. At the end of the day, temperature and salinity are conserved between max and min values.

I guess my conclusion is that I agreed that numerical mixing depends on a lot of things such as resolution, stretching etc. But at the same idealized experiment, Marchesiello et al. (2009) option shows less numerical mixing if I use just for the momentum-advection scheme.

Please let me know what you guys think.
Best Regards,
Mehmet

[patrickm]

The scheme in Marchesiello et al (2009), let's call it RSUP3, is not meant to outperform UP3 (the standard ROMS upstream-biased advection scheme) in terms of numerical properties (accuracy, dispersion ...). It is only an attempt to correct excess diapycnal mixing that arises with steep slopes (even at relatively high resolution).

In your idealized experiment, I don't know why the results appear better with RSUP3 used in the momentum equation only. It would probably help to know what kind of idealized experiment we are talking about (with or without topography, boundary currents ...).

As for monotone schemes, my experience is that they may be useful at avoiding false extrema but not diapycnal mixing. They seem to often produce more implicit diffusion than non-monotonic schemes (of the same order). S. Griffies has shown that high order accurate monotone schemes are needed to lower their implicit diapycnal mixing but they are very expensive. Of course the level of accuracy that is required depends on the size of your domain, i.e. the flushing time scale of water masses passing through the lateral boundaries. In a global domain, you need a weakly diffusive scheme ...

Patrick

[ilicakme]

Thanks for the quick response.

I used RSUP3 for the lock-exchange example which is a standard two layer dam breaking.
There was no topography so I evenly spaced the sigma layers to compare with the z-models and RSUP3 had
less numerical mixing in that config. In fact, it has a nice convergence when I decreased horizontal grid resolution.

For the monotonic scheme, let's say I want to setup a model (realistic or idealized), I think I should choose a monotonic scheme for tracer advection since it is more physical. Then I should worry about numerical mixing and try to reduce it as much as I can (resolution, diffusion etc.).
In general, community looks for the erosion of the deep water masses as a criteria for numerical mixing.
However, deep water masses might not be disappearing because of non-monotonicity of the tracer advection. Maybe new extrama occur and it looked like cold water is not eroding. That's why I was thinking a monotonic scheme is more proper.

Mehmet

[patrickm]

monotonocity is far from being the only issue with tracer advection. An example of lock exchange experiment in different models is given by Flavien Gouillon (PhD thesis) at http://coaps.fsu.edu/~gouillon/Spurious.html

again, monotone schemes have implicit diffusion, which becomes a problem with steep slopes: not only deep waters are affected but also thermocline and surface waters, barotropic and baroclinic circulation ...

Patrick

[ilicakme]

Thank you, I'm aware of the Flavien's work.

I didn't say that monotonic schemes don't have any problems.
All advection schemes have either dispersion or dissipation or both, but that shouldn't mean that we can use a scheme which is not physical and assume that it's fine because deep waters are not affected too much.
Mixed layer, barotropic/baroclinic circulations are also affected by non-monotonic schemes.

I bring up this issue because I think we should discuss the choice between monotonic and non-monotonic schemes.

Mehmet

[patrickm]

the circulation is not that affected by local extrema (unless out of control) but is greatly affected by diapycnal mixing.

a discussion on the need for monotonicity is good of course ...

[kate]

The NPZ type models don't tolerate negative values for at least some of their fields. A typical reaction to the advection problem is to introduce a clamping, setting all negative values of bio tracers to zero. Of course we don't want to talk about this and conservation of nitrate in the same sentence.

[ilicakme]

> the circulation is not that affected by local extrema (unless out of control) but is greatly affected by diapycnal mixing.

I didn't say otherwise. But, when you have a very sharp front, convection zones or overflows, nonmonotnic schemes will also have diapycnal mixing due to local extrama and it will not be physical.

We cannot simply say that we don't obey the second law of thermodynamics.

[lemarief]

Hi,

Relevant details about part of the topic discussed here can be found in a recent ocean modelling
paper written by Matthew Hecht <http://www.sciencedirect.com/science/ar ... 031000106X>

In the framework of a z-level model, it is shown that the use of a quasi-monotonic advection scheme
for tracers induces too much of a diapycnal mixing (with a particular emphasis on the Pacific
Equatorial jets). It is also shown that the usual UP3 (a.k.a. UB3, a.k.a UBS) produces very
moderate overshooting which is of course true only if we assume some regularity in the tracer field
(As Mehmet said, sharp fronts could produce significant overshoots).
Moreover, usually one has to sacrifice the scale-selectivity property of the mixing operator
to pursue monotonicity.

For non-isopycnic models, there is so far no perfect scheme ensuring both monotonicity and small inherent
diapycnal mixing. This is essentially due to the fact that it is not possible to derive a discretized
isoneutral mixing scheme which is monotonic (see Beckers et al. 2000). This means that when we intend
to reduce the spurious diapycnal mixing by rotating the diffusion (or the hyper-diffusion) along
isopycnals, in the same spirit as the RSUP3 scheme, we also increase the potential for more spurious extrema.
This may or may not be harmful depending on the situations.

I'm quite doubtful about the adequacy of the Akima scheme in the horizontal direction.
Looking at the truncation error associated with this scheme (see Shchepetkin & McWilliams, 2008)
we see that the dominant term is of dispersive nature and thus this scheme should require an
additional diffusion to maintain physically realistic results over long temporal integrations.


As Patrick said, a paper showing (among other things) the clear advantage of using an isoneutral
instead of an isosigma mixing operator for long-term basin-scale ROMS simulations is under revision
and will be published very soon.

Florian,

[arango]

Numerical diapycnal diffusion and spurious extrema from the lack of monotonicity in advection schemes are two different problems. Ideally, we would like to minimize such errors to a tolerant level. The monotonicity is only possible in lower order schemes. It is very important in passive tracers, like biology and sediment tracers, because negative concentrations are unphysical. In deep water masses circulations, I have observed equivalent numerical diffusion in the monotonic scheme (MPDATA). In my opinion, in such case is more important to control the numerical diapycnal diffusion error than the lack of monotonicity. The over mixing of water masses can be catastrophic for long simulations (order of years).

[gouillon]

Dear all,

I think that everything has been written. I just like to add one point (that maybe does not fit into this topic, feel free to move it).
When I did the lock exchange problem on my personal computer (if you want details on its config contact me) with no other load than running ROMS, the UP3 took about 5min to run while the MPDATA took about 12min... I was surprised by this difference for such a simple experiment and always wondered what it could be for realistic simulations.
After talking to John (Warner) he told me that the scheme could surely be optimized... I wonder if people realized that maybe the computational expense to remove over- (under-) shoot is huge... Or maybe I am not aware of MPDATA modifications and recent optimizations. Has anybody tried to quantify this and/or work on the MPDATA scheme itself?

Flav