Examples for the paper

[iangrooms]

Here's a list of ideas for examples to include in the paper. Please add and discuss

1. POP 0.1 degree data, 5-day average, fixed-scale and fixed-factor filters (with different shapes: Gaussian, sharp, boxcar?) applied to salinity. Salinity does go near 0 in some places, so maybe we can use this to give an example of how the sharp filter can generate negative values from positive data. If we implement boxcar it will have to be ad-hoc because the Laplacian-based ones can't do it.
2. POP 0.1 degree data, 5-day average, compute EKE at the surface using (defined mean-square minus square-mean)? We might need to convert the raw grid-aligned velocity to lat/lon before filtering, but at least it's on a B grid.
3. Apply the filter to a discrete delta function (data is 1 at one grid point, 0 elsewhere) on the POP 0.1 degree grid so that we can see the shape of the effective kernel. We could use this to show
   • negative weights in the sharp filter
   • how the filter kernel changes shape near boundaries
   • how the shape of the fixed-factor filter changes with the local grid scale
4. Some along-track SSH obs data

[jakesteinberg]

I can provide a filtering example of along-track absolute dynamic topography and/or cross-track geostrophic velocity. I had imagined a figure like this (below). The upper panel shows one cycle of ADT filtered using the boxcar, Gaussian, and sharp filters. The lower panel shows the mean cross-term (u_bar*u_prime) magnitude averaged over ~50 cycles along the same track. Specifics are easy to change. I can also provide an example applying 2d filtering (as I believe Nora is) to surface geostrophic kinetic energy from gridded AVISO.

[rabernat]

I shared a bit of my POP code here: https://github.com/ocean-eddy-cpt/gcm-filters/issues/14

@iangrooms - could you point me to a path on glade where some POP 0.1-degree output lives? I'll try to plug them together.

[iangrooms]

The POP data is in /home/bryan/johnsonb/ on cheyenne. Once you unzip a single 5-day average, it's about a 90GB netcdf file. If I recall correctly, the data starts after a 15 year spinup using CORE-2 normal-year forcing, so you should be fine to start with year 0 if you want.

[iangrooms]

Actually it's on HPSS at /home/bryan/johnsonb, see documentation here https://www2.cisl.ucar.edu/resources/storage-and-file-systems/hpss/managing-files-hsi for how to get it.

[iangrooms]

@jakesteinberg that figure looks great to me!

[iangrooms]

@rabernat If you want to avoid HPSS I have one data volume on cheyenne at /glade/work/igrooms/current_data. current_data is a netcdf file

[NoraLoose]

I have done 1.-3. for the NeverWorld2 MOM6 lat/lon grid, so it should be straightforward for me to reproduce these figures for the POP data, with help of @rabernat's POP kernels/code examples. I was first thinking about trying 1.-3. for the MITgcm LLC4320 data using xmitgcm's wrappers to handle the different faces, but the POP data seems easier to work with.

[rabernat]

LLC-type grids will be very difficult to deal with using this method because they require exchange between the cube faces. This is not something that xgcm supports today. Even if it did, it would not work on the GPU.

[NoraLoose]

@iangrooms - what about including an example of thickness-weighted filtering in an isopycnal-coordinate model?

[iangrooms]

I think we should skip thickness-weighted since we don't want to scoop other parts of the CPT work and also since it doesn't really seem to illustrate any particular point about how these filters work. (Unless I missed something.)

[NoraLoose]

I think we should skip thickness-weighted since we don't want to scoop other parts of the CPT work and also since it doesn't really seem to illustrate any particular point about how these filters work. (Unless I missed something.)

Ok. The main motivation would be to highlight that the sharp filter has limited use if you want to preserve the volume integral when filtering in an isopycnal coordinate model (via thickness-weighted filtering, $\bar{uh}/\bar{h}$). But since this issue arises from negative values in filtered thickness, we could instead show the concept of unwanted negative values via Example 1 or 2. (And then reference to these examples in the CPT papers.)

[jbusecke]

I can provide a filtering example of along-track absolute dynamic topography and/or cross-track geostrophic velocity. I had imagined a figure like this (below). The upper panel shows one cycle of ADT filtered using the boxcar, Gaussian, and sharp filters. The lower panel shows the mean cross-term (u_bar*u_prime) magnitude averaged over ~50 cycles along the same track. Specifics are easy to change. I can also provide an example applying 2d filtering (as I believe Nora is) to surface geostrophic kinetic energy from gridded AVISO.

This is an amazing figure @jakesteinberg!

[iangrooms]

@NoraLoose we should definitely show the problem with negative values somehow. One way is just to show that the filter can produce values outside (eps. below) of the range of the data, so we might be able to make that point with temperature or salinity even if we don't produce negative temperature or salinity.

It might be useful to show that mean(square) - square(mean) is not necessarily positive when the weights are negative. Maybe we could do that with @jakesteinberg's along-track data? Does the sharp filter produce negative "EKE" in your along-track data?

[NoraLoose]

@iangrooms, I posted a figure in this comment that shows all locations where the taper filter generates negative values for EKE. Negative EKE is ubiquitous!

[iangrooms]

I'm wondering if we should also compare how the different filters interact with the two definitions of variance. Nora's EKE example shows how the taper filter produces lots of negative EKE under the definition $\bar{u^2} - \bar{u}^2$. Jake's example includes the cross term, which is more relevant to the other definition $\bar{(u')^2}$. The cross term should be a lot smaller (globally-integrated) for the Taper filter than for the Gaussian (which should be better than the boxcar). We could compare the global integral of the cross term for the three filters, since it will suggest that people using the second definition might prefer to use the Taper filter.

[iangrooms]

I had a useful call with Nora and Scott this morning where we took stock of the status and what needs to be done for the examples section of the paper.

1. @sdbachman has a figure from a high-res MITgcm simulation over Drake Passage showing how we can use kappa to vary the filter length scale over the domain. Done. Thanks @sdbachman!
2. The figure showing filter kernels appears to be pretty much done. Thanks @NoraLoose! I think #9 can be closed. I don't think we need more panels or another figure showing the fixed-factor kernel at widely disparate latitudes.
3. The 2D AVISO KE/MKE/EKE figure looks great! Thanks @jakesteinberg.
4. The along-track figure #13 looks great! Thanks @jakesteinberg.
5. The figure computing smoothed vorticity 2 ways is done (#18). Thanks Elizabeth!
6. The figure from #7 looks good to me (the one with Panama) as a way to show the effect of Hussein's "set values on land to zero" strategy. Thanks Nora!

For all of the figures we'll need background on where the data came from, and where it can be accessed. If it's not already public then (assuming it's not too large) we can put it on figshare, or somewhere else (TBD). Once all the figures for the example section are ready I can write up the text for section 3 of the paper.

[ElizabethYankovsky]

Attached is the figure from #18
I've updated the land boundaries and projection using cartopy. This figure includes both smoothed vorticities, @iangrooms please let me know if you'd prefer just the 3 panels with only one of the smoothed vorticities. Also, it's a bit hard to see the differences around the coasts, we could add a closeup view of one coastal regions

[iangrooms]

Thanks @ElizabethYankovsky! This figure looks good to me. We might have to edit later if co-authors or reviewers want, but for now I think this is good. I updated my post above with the list of figures to reflect that this one is done.

[iangrooms]

I've added all the figures you provided to the draft on overleaf. Almost everything has a paragraph or two describing it (excepting along-track SLA, which I hope to get to soon). I would be grateful if you could go on overleaf and provide a sentence or two about where the data came from. Specifically:

1. @sdbachman's figure: something about the MITgcm configuration if there's no paper to cite
2. @ElizabethYankovsky's figure: a citation to the relevant CM2.6 paper and/or brief description of the configuration
3. @jakesteinberg's figures: some kind of hook to the observational data - citations if possible.

Also please correct any mistakes I might have made in describing the figures. I think the "examples" section is almost complete.

[ElizabethYankovsky]

@iangrooms I've added a description of Figure 6 as well as text and references on CM2.6/MOM5. Please see line 765 in the overleaf document. I wasn't sure what you meant with the Pangeo reference, so I included both text and a citation (feel free to remove either).

[iangrooms]

Looks great! The only change I made is to replace 1/10 degrees by 0.1 degrees, not because it's wrong but just for consistency.

For the pangeo reference I just wanted to make sure you'd cite more than just the pangeo url for the data, so your current version is perfect. Thanks!