Make figure for example 2 (EKE)

[NoraLoose]

Example 2 in #1:

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.

Note: In the context of this example, we could also highlight that the sharp filter can generate negative EKE values.

[NoraLoose]

In #11 I added a notebook that computes EKE for the POP 0.1 degree data. Here is a preliminary plot from the notebook, which compares EKE = \bar{u^2} - \bar{u}^2 in the Gulf Stream region for the Gaussian vs. sharp filter (both 0.1 --> 1 degree):

Left: EKE computed with Gaussian filter (generates only positive values). Right: EKE computed with sharp filter (generates both positive and negative values).

Obviously, the figure is not yet publication-ready. I tried to plot the POP data on a lon/lat grid (rather than a "nlon/nlat grid") using cartopy, but ran into some issues (see last two cells in this notebook). I will have to look more into this. Or maybe @jbusecke has experience with making nice maps from POP data?

[NoraLoose]

I'm inserting another figure from this notebook:

Yellow shading corresponds to positive EKE, while black shading corresponds to negative EKE. (EKE amplitude is ignored.) Left: Gaussian filter; right: Taper filter. Everything close to the northern boundary should be ignored, because I am currently not handling the northern boundary of the POP tripolar grid correctly, as mentioned in this comment.

I am surprised to see 4-5 locations in the Pacific and Southern Ocean where even the Gaussian filter gives negative EKE values (albeit of very small amplitude: -0.0003<EKE<0, whereas negative EKE values for the taper filter go down to -0.6). The only possible explanation is that the filter weights of the approximated Gaussian filter are not strictly positive, and must have a tiny negative contribution. This issue can probably be resolved by increasing N even further. Edit: Looking at the plot on the left again, it seems that the issue of negative EKE values for the Gaussian filter arises at continental boundaries or small islands. There are actually a lot of small spots in the Canadian Arctic that I am just seeing now. Will have to look more into this boundary issue...

[NoraLoose]

Obviously, the figure is not yet publication-ready. I tried to plot the POP data on a lon/lat grid (rather than a "nlon/nlat grid") using cartopy, but ran into some issues (see last two cells in this notebook). I will have to look more into this. Or maybe @jbusecke has experience with making nice maps from POP data?

Ok, I figured out how to map (regional) POP data onto a lon/lat grid. Here is the updated figure:

[iangrooms]

This comment might be helpful here. Also this.

[NoraLoose]

This comment might be helpful here. Also this.

Thanks, Ian! These suggestions will be really helpful for computing global integrals of filtered data, e.g., what you suggest here. But I think we want to stick to regional plots for showing EKE and how the filters act ( #7 and #9), because I found it hard to illustrate some of our points if you look at the global picture. (Unless you make 0/1 masks, as the yellow/black one above.) For instance, I find the above figure - zoomed into the Gulf Stream region - more illuminating than something like:

[iangrooms]

Agreed - regional plots are a lot better here. If we do a section on computational aspects (#4) then we should do the full global version for a fair comparison.

[jbusecke]

Sorry, I saw the mention too late. Those maps look quite nice @NoraLoose, did you have any more questions for the map plotting part?

[NoraLoose]

Sorry, I saw the mention too late. Those maps look quite nice @NoraLoose, did you have any more questions for the map plotting part?

@jbusecke, thanks for checking! I haven't figured out how to plot the global POP data yet. (This seems to be a common issue, but even using cartopy and adding a cyclic point didn't solve the issue for me.) But maybe we will only need regional plots, so no need to go down that rabbit hole now. In case we need the global plots and I can't figure it out myself, I may ask you again :smiley:

[jbusecke]

Anytime. What was the issue exactly? A gap or weird striping? Or something else?

[iangrooms]

We decided not to use POP data for surface EKE, and instead to just use Jake's surface KE/MKE/EKE plot from AVISO data. So I'm closing this issue.