Processes at the boundary

[MatthisAuger]

Last week we discussed the processes at the model frontier and how the model was behaving with boundary conditions. It seems like they are not the candidates for the large jump and trends between the models anymore, but it might be still interesting to look at what is happening there.

I made a few videos, looking at the bottom layer of Temperature, Salinity, U, and V outputs from the hycom1 model and boundary conditions. This is focused on the bottom layer as initially the interest was on the lower overturning cell, but I can make these videos in any other layer or region if needed.

Here are all the parameters along the boundary over longitudes 50W-10W. These are the outputs over the first few months of the model, boundary conditions, and differences between outputs and boundary conditions.

https://user-images.githubusercontent.com/68908668/212576484-8d820569-b8e9-4e81-af0b-e6a70f6d1ecd.mp4

Same thing but across the boundary this time, at longitude 70E if I remember correctly.

https://user-images.githubusercontent.com/68908668/212576858-1dba86a5-2a4f-4624-857c-b131f959ebd6.mp4

For both videos, T and S do not vary a lot as it is the bottom layer, but U outputs seem to go a bit crazy compared to boundary conditions. As I said just tell me if you are interested in similar plots for other regions or layers. I can make those closer to the surface if you want to see how the model reacts to stronger changes in boundary conditions temperature or salinity.

[adele-morrison]

BOUSSINESQ = True

Not sure about whether the sea ice levitates - I can't see any parameters associated with this. I suspect it doesn't levitate, because the reason for doing this in MOM5 was due to ocean - sea ice instabilities (see page 38 here). Updating SIS to SIS2 and more tightly coupling with MOM6 may have removed the need to levitate.

[aekiss]

Are we able to close the mass budget for the ice-free regional models, e.g. https://github.com/COSIMA/mom6-eac and what @ashjbarnes is developing? Maybe we're missing a term that has nothing to do with sea ice?

[PaulSpence]

Real vs virtual FW fluxes ... P-E+R is treated as a virtual freshwater flux that impacts the salt budget (not the volume) in MOM https://www.sciencedirect.com/science/article/pii/S2095927317300932#b0095

[MatthisAuger]

Discussion with Stephen Griffie.

Transport at the boundary and P-E+R should change the ocean volume accordingly.

Use ssh_ga to have the global averaged sea level, not zos_ga.

Check .wfo files. (Where are they?)

Double check the volume flux in P-E+R and at the boundary.

[aekiss]

from https://github.com/COSIMA/mom6-panan/issues/17#issuecomment-1493624446

Mean flux into the model at the boundary (after spin up)= 0.85Sv, ~ 0.87 * 10^9 kg/s

Order of magnitude, the open boundary area would be about 1e11m^2 (40,000km cos(37) 4000m), so 0.85Sv implies a mean velocity of about 8.5e-6m/s, which seems low...?

But if it was bigger the problem would be worse.

[aekiss]

More order-of-magnitude calcs:

from https://github.com/COSIMA/mom6-panan/issues/17#issuecomment-1493624446

From Paul's comment: https://github.com/COSIMA/mom6-panan/issues/17#issuecomment-1471109234 Net surface mass flux ~1.07 * 10^9 kg/s

From meridional transport into the model: https://github.com/COSIMA/mom6-panan/issues/17#issuecomment-1455225906 Mean flux into the model at the boundary (after spin up)= 0.85Sv, ~ 0.87 * 10^9 kg/s

So total boundary flux into model is ~1.9e9 kg/s

Total ocean mass =3.4e20kg, so timescale to double ocean volume is 3.4e20/1.9e9 = 1.8e11s = 5700 yr. Does that seem short?

But ocean area ~volume/depth ~ 3.4e20kg/4000m/1000 = 8.5e13 m2 so net surface mass flux ~1.07 * 10^9 kg/s is 1.2e-5 kg/s/m2 ~ 1.2e-8 m/s = 1 mm/day which seems a reasonable average precipitation - evap rate.

[aekiss]

The total ocean mass also looks ok to me. Rough numbers 1000 4pi 6000km^2 *4000m/(say) 4 = 4.5e20 kg, close to the 3.4e20kg above.

So why is the mass trend so much smaller than the net mass flux?

[MatthisAuger]

vmo2d across the boundary = 1.062e+09 kg/s out of the model NB: opposite sign to above, and now including eddy mass flux Ocean mass trend = ~1.074e+05 kg/s NB: 25x smaller than previous estimate~ 2.134e+6kg/s Panan mean of wfo = 1.083e+09 kg/s into the model

[aekiss]

vmo2d across the boundary = 1.062e+09 kg/s out of the ocean NB: opposite sign to above, and now including eddy mass flux Ocean mass trend = ~1.074e+05 kg/s NB: 25x smaller than previous estimate~ 2.134e+6kg/s Panan mean of wfo = 1.083e+09 kg/s into the ocean

~So net boundary flux into ocean is 1.083e+09 kg/s - 1.062e+09 kg/s = 2.1e7 kg/s.~ 4.97e6 kg/s - see below

So ~200x~ ~10x~ 2.3x bigger than ocean mass trend.

We would need very close (1 part in 10,000) cancellation of the boundary fluxes to match the mass trend. So everything would need to be calculated very carefully and consistently.

[MatthisAuger]

Very sorry for all the diagnostics that turned out to be wrong. Still not sure to understand how my mass flux at the boundary was so far (even opposite) from the new one computed from the vmo variable. Also spotted a mistake in the computation of Tuesday's total ocean mass trend so please refer to the new value of 2.134e+6kg/s.

I merged @PaulSpence notebook on surface fluxes and mines to compute time series of mass and fluxes. Here is the notebook used to make the following figures:

Total mass flux:

Mass budget: Total mass from diagnostics and recomputed total mass from monthly mass fluxes.

Increase of mass associated with mass fluxes is still twice higher as the total ocean mass increase. Could be because of residuals due to averaging of the surface net flux? Surface net flux is a monthly average while the vmo output at the boundary is computed from the total mass that went through the grid cell?

[PaulSpence]

Nothing to be sorry about at all. Thanks for the hard work! Seems like the budget is still not closed so we have more mistakes ahead :) Been discussing with others (e.g. @ashjbarnes) short test runs, e.g. with no (or lots of) mass flux at lateral boundaries. See what part of the budget is off. Other interpretations welcome.

On Thu, May 11, 2023 at 11:25 AM MatthisAuger @.***> wrote:

Very sorry for all the diagnostics that turned out to be wrong. Still not sure to understand how my mass flux at the boundary was so far (even opposite) from the new one computed from the vmo variable. Also spotted a mistake in the computation of Tuesday's total ocean mass trend so please refer to the new value of 2.134e+6kg/s.

I merged @PaulSpence https://github.com/PaulSpence notebook on surface fluxes and mines to compute time series of mass and fluxes. Here is the notebook https://gist.github.com/MatthisAuger/5f7087080e960ac4ff690a884a559638 used to make the following figures:

Total mass flux: [image: image] https://user-images.githubusercontent.com/68908668/237547571-25393545-1d28-496f-b6cc-8133e32aa739.png

Mass budget: Total mass from diagnostics and recomputed total mass from monthly mass fluxes. [image: image] https://user-images.githubusercontent.com/68908668/237547821-a42b110f-42dc-45b6-b397-f6b497398e34.png

Increase of mass associated with mass fluxes is still twice higher as the total ocean mass increase. Could be because of residuals due to averaging of the surface net flux? Surface net flux is a monthly average while the vmo output at the boundary is computed from the total mass that went through the grid cell?

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Paul Spence, Assoc. Prof. ARC Future Fellow Institute for Marine and Antarctic Studies https://www.imas.utas.edu.au/ University of Tasmania, Hobart, Australia https://paulspence.github.io/

[StephenGriffies]

Have you confirmed that your notebook shows that everything is self-consistent for a simulation with vmo=0 at the open boundaries? Just need to run for a few days.

[aekiss]

No need to apologise, thanks for your work on this. It seems pretty clear from your plot that the surface mass inflow drives a compensating outflow at the open boundary, so the mass accumulation involves a subtraction of two terms that are very close, so it will show up every little difference in how those numbers are calculated.

Nice to see that the discrepancy is getting smaller. Your green trend line of 4.97e6 kg/s is much less than the 2.1e7 kg/s I put in my (now updated) post above, so the mismatch is now a factor of 2.3.

Are the surface and open boundary fluxes both calculated from monthly averages, not snapshots? And are the varying month lengths taken into account for dt?