Use area-scaled biharmonic viscosity in coarse examples

[glwagner]

Summary

• Add area_scaled_biharmonic_viscosity() in src/Oceans/ocean_simulation.jl returning a HorizontalScalarBiharmonicDiffusivity with ν = Az² / timescale (default 15 days), so the effective viscosity adapts to local cell area.
• Export area_scaled_biharmonic_viscosity from NumericalEarth and the Oceans submodule.
• Use it as the viscous closure in the one_degree_simulation and global_climate_simulation examples, alongside the existing Gent-McWilliams IsopycnalSkewSymmetricDiffusivity. In global_climate_simulation it replaces the constant ν=1e12 biharmonic viscosity; in one_degree_simulation it is added next to GM and CATKE.

Test plan

• Verify the one-degree simulation runs with the new closure
• Verify the global climate simulation runs with the new closure
• Check that grid-scale artifacts are suppressed

🤖 Generated with Claude Code

[xkykai]

out of curiosity why don't we want GM, especially in the 1degree model?

[codecov]

Codecov Report

❌ Patch coverage is 0% with 3 lines in your changes missing coverage. Please review.

Files with missing lines	Patch %	Lines
src/Oceans/ocean_simulation.jl	0.00%	3 Missing ⚠️

📢 Thoughts on this report? Let us know!

[glwagner]

out of curiosity why don't we want GM, especially in the 1degree model?

didn't you find that it has no effect? I've been telling people this...

[glwagner]

out of curiosity why don't we want GM, especially in the 1degree model?

@xkykai are you saying that we should keep GM? I am happy to do that if that is your recommendation.

[xkykai]

out of curiosity why don't we want GM, especially in the 1degree model?

didn't you find that it has no effect? I've been telling people this...

They have an effect, just less significant than expected/on other models.

For 0.5 degree I'll be running another test against ECCO data and fluxes in the next few days, but by and large without GM is ok.

For 1 degree:

here are some meridional sections to compare after 200 years of repeat forcing. Even though the solutions are less sensitive to GM than initially expected, I would still recommend having some GM at 1 degree as the solutions are less noisy.

[glwagner]

I would still recommend having some GM at 1 degree as the solutions are less noisy.

Do these solutions have biharmonic viscosity?

[glwagner]

@xkykai did you try running with only the symmetric part of the diffusivity? Theoretically we might expect that we don't need the skew part (baroclinic conversion is represented) but we still a symmetric diffusivity (bc tracer stirring not captured if no eddies)

[xkykai]

I would still recommend having some GM at 1 degree as the solutions are less noisy.

Do these solutions have biharmonic viscosity?

No they don't. I haven't run comparison of GM with biharmonic viscosity as well.

[glwagner]

I would still recommend having some GM at 1 degree as the solutions are less noisy.

Do these solutions have biharmonic viscosity?

No they don't. I haven't run comparison of GM with biharmonic viscosity as well.

In the previous runs, the solutions have grid imprinting without biharmonic viscosity (unsure what other dissipation you might have though). So I am not sure GM is the right fix for noise, strictly speaking, even though it may be good to include for other reasons.

[xkykai]

@xkykai did you try running with only the symmetric part of the diffusivity? Theoretically we might expect that we don't need the skew part (baroclinic conversion is represented) but we still a symmetric diffusivity (bc tracer stirring not captured if no eddies)

no, don't think we ever turned off skew viscosity completely

[glwagner]

@xkykai did you try running with only the symmetric part of the diffusivity? Theoretically we might expect that we don't need the skew part (baroclinic conversion is represented) but we still a symmetric diffusivity (bc tracer stirring not captured if no eddies)

no, don't think we ever turned off skew viscosity completely

I'll add ISSD back here, but with only the symmetric turned on. Maybe that will provide some inspiration for future work.

[xkykai]

I would still recommend having some GM at 1 degree as the solutions are less noisy.

Do these solutions have biharmonic viscosity?

No they don't. I haven't run comparison of GM with biharmonic viscosity as well.

In the previous runs, the solutions have grid imprinting without biharmonic viscosity (unsure what other dissipation you might have though). So I am not sure GM is the right fix for noise, strictly speaking, even though it may be good to include for other reasons.

GM also brings about a bit more subduction and the flattening of the isopycnals (from the figure), to what degree of that is needed still remains to be seen.

[xkykai]

up to your discretion to merge!

[navidcy]

@simone-silvestri was also claiming we do need (at least a bit?) GM, but not sure about the rationale behind it...

[simone-silvestri]

yeah at 1 degree we probably still need it. I am unsure at 0.5, I think I still see some differences with + without although I see a lot of other biases I am trying to debug so we need much more investigation before being conclusive. I would also keep GM for the practical reason of seeing that it works as intended (although maybe in 1 year of simulation the impact is not that large)

[glwagner]

yeah at 1 degree we probably still need it. I am unsure at 0.5, I think I still see some differences with + without although I see a lot of other biases I am trying to debug so we need much more investigation before being conclusive. I would also keep GM for the practical reason of seeing that it works as intended (although maybe in 1 year of simulation the impact is not that large)

I think it's important that the examples reflect a "recommended" configuration --- so if GM is not a good idea at 1 degree, and we want an example that uses GM, we should add a coarser case / any case which does actually require it.

If we can't find a case that benefits then its questionable why we need an example that uses it...

[simone-silvestri]

then remove the "probably". At one degree we need it for sure. I wouldn't know the value we should use though. Maybe 500? Typically people use 1000. I am planning to run a complete OMIP with the orca grid and after we have understood what parameters we need we can use that one as an example.

[glwagner]

Typically people use 1000.

Isn't it also the case that the Oceananigans solution is quite unusual and expresses more variability than other models at this resolution? So we should not expect to use the same value as others.

[glwagner]

@xkykai @simone-silvestri changing this PR so that it just adds viscosity to the coarse example, but does not remove GM. Let me know what you think.

[xkykai]

lgtm!

[navidcy]

Docs break because of Metadataset fixes included in #277 or #283

[simone-silvestri]

I think tests should pass now. If docs pass I will merge