Make figure for example 1

[NoraLoose]

Example 1 in #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.

To summarize, highlight the following aspects with POP 0.1 degree data:

• [ ] fixed-scale vs. fixed-factor filters
• [x] Gaussian vs. sharp filter shape
• [ ] Sharp filter can generate negative values from positive data
• [x] filter which takes into account boundaries vs. filter which ignores boundaries

[NoraLoose]

A simple figure that shows differences in Gaussian vs. sharp filter:

We might want to substitute this figure by the model-obs figure (#16).

[NoraLoose]

Boundary-aware vs. boundary-unaware filter. For a change, we are now looking at the Agulhas Current:

Notice the "cold" band/shadow hugging the coast, which arises from filling land values with 0. This figure shows how fill values on land artificially affect the filtered fields in oceanic coastal regions. Apart from the differences near the coast, the filtered fields are identical.

[iangrooms]

"Sharp filter can generate negative values from positive data" we can actually demonstrate this using the alternate definition of EKE \bar{(u')^2}. I think Jake's along-track example might do this already; in any case it might be easier to demonstrate this using a "variance" than using salinity

[NoraLoose]

"Sharp filter can generate negative values from positive data" we can actually demonstrate this using the alternate definition of EKE \bar{(u')^2}. I think Jake's along-track example might do this already; in any case it might be easier to demonstrate this using a "variance" than using salinity

Agreed. I was also planning to show the alternative definition \bar{(u')^2} for the POP data, and maybe compute a global integral, as you suggest here. Unless we don't want to do the same thing twice, because Jake has kind of done this for the obs data...

There is something odd about salinity, see cells 9 and 10 in this notebook.

[iangrooms]

Yes, negative values of SSS is very suspicious. Might as well just do the alternative version of EKE instead. Jake's notebook shows local negatives using the alternative definition of EKE, but we could still use the alternative definition on POP data to demonstrate the global integrals so it's not redundant.

[NoraLoose]

I updated the figure that illustrates the effect of boundary-unaware filters. I switched to a warmer region with maximal shoreline length to make the contamination by zero fill values on land even more clear:

In the right panel, SST values close to the coast are as low as 6 degree C.

[iangrooms]

This looks great! Thanks @NoraLoose. I think we can close this issue, and I'll update my post on #1 to reflect that this figure is done.