Continuum fits about internal_waves_barkley_canyon HOT 9 CLOSED

• Use np.polyfit to get better values for A and k.
• Put these on the standard PSD plots, no need for new plots.
• Don't use depth-mean PSD.
• Add/remove plot fluff and important details (WKB scaling, units, depth-mean, long titles that aren't important, etc.).

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• Used a SciPy power law fitting method to get the a and b values for each PSD, for a fit line of y = ax^b.
• Narrowed the range for the 'continuum' as 7e5 Hz (above the notable tidal harmonics) to 2e4 Hz (below both N and a notable whitening zone). This was applied to other analyses that use the 'continuum' range.
• This was done for the lowest depth evaluated for each instrument, and at mid-depths.
• Added fits to standard PSD for reference, rather than zoomed plots.
• Slopes amplified and steeper near the bottom (they don't need to 'flatten' to reach the high-frequency roll-off).
• Compare amplitudes and slopes to GM in this frequency range.

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OK - to get a time series you will need to fit c f^-2, which should be easier. So I see two products:

• A time series of a and b from a f^b
• A time series of c from c f^-2 (shown as c/GM)

the first tells us how GM-like the spectrum is. The second compares amplitude in a consistent way, where of course we need to be careful if b deviates substantially from -2.

Kurtis' note: For the second one, multiply by f^2 (whiten) and take average over band.

• Afterwards: estimate dissipation rates (epsilon, etc.).

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Rough notes:

• Time series for a and b at each site, for each year.
• Still working on time series of c.
• Values are obtained for each window in the spectrograms (~9 days, 50% overlap), at ~50 m AB.
• At this temporal resolution the variability of both a and b is very large (e.g. for b, from -5 to 0).

9-day windows:

• Question for Jody: I didn't expect the a and b time series to be so variable. Is ~9 days too short of a window to get a good estimate of the continuum? I thought so, so either the slope varies significantly or I'm wrong. I doubled nperseg (~18 days, 50% overlap) to get better frequency resolution (but worse temporal resolution, of course). Thoughts?

18-day windows:

• When a is displayed with a log scale, a and b time series appear to have identical shape (positive correlation).
• There are no recurring seasonal features (similar to integrated continuum power).
• Pulses in integrated continuum power do not align with time series features.

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I'm not sure what the last plot is showing.

a and b will be correlated, but that doesn't mean anything because if you increase the power law you need to decrease the amplitude.

Still suggest fitting c f^2 and plotting c. b is useful info as well, but its hard to get an amplitude if it is changing. We are looking for amplitude changes.

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@jklymak the last plot is for visually comparing integrated continuum power features to what's seen in the a and b plots (they aren't similar).

I'm already in process working on the cf^-2 fits!

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• Time series of cf^-2. Compare w/ GM over time (could plot GM line, divide by GM, or take difference).

• Do this for each depth to get depth-time-amplitude plots.

• At each window whitened the spectrum, and then took the average over the band.

• Same method applied to GM (1/2 for components).

• After doing this at a single depth, I ran the process for all depths to get depth-time-amplitude.

• These were divided by the GM amplitude to produce the c/GM comparison plots, below.

• Cross-slope and cross-canyon generally stronger (as in spectra).

• Inter-annually trends are similar but amplitudes vary.

  • At Slope, lulls in summer (as in integrated continuum power plots). Over 3x GM (1/2) amplitude near topography.
  • At Axis, seasonality is less obvious. Over 5x GM (1/2) amplitude near topography; all depths somewhat elevated.

• Plots are very similar to the previous depth-band integrated power plots that I made for the continuum. When continuum power increases so does its amplitude vs GM. I would say this is an expected result.

All depths:

Depth-band integrated power for comparison:

• Get other years for the c/GM comparison.

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• See #47. Redo c/GM with better time resolution, narrower bandwidth (6e-5 to 1e-4). Keep this one as components to show not GM-like (components differ).

Optional:

• Could try c without whitening, just fit -2 to get amplitude? I think the way I'm doing it is fine, as long as the process is the same.
• Fit -2 to Axis75 and Axis55 to show deviation if narrower bandwidth doesn't help.
  • Or even just whiten PSD to better show slope deviation.

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Combined this with Dissipation Estimates, Issue #47.

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