Wind forcing

[kurtisanstey]

• Wind data was converted to u and v velocity vectors.
• CW rotary spectrograms were taken for ease of integrating over desired time periods, to determine input 'power' from storms.
• (m/s)^2 isn't actually power, though it's proportional (sort of). How would I convert this watts, which requires an additional kg/s? I still need to look this up, as it doesn't make sense (to me) that the wind input is a direct function.

[kurtisanstey]

• [x] This is directly related to the Alford (2001) slab model. Check it out. Get f from wind. Relative to abrupt changes in magnitude and/or direction.

[kurtisanstey]

Summary update

• Adjusted smoothed wind magnitude / direction plots to be more useful.

• Performed CW rotary spectrograms on the vector wind data.

• A band-pass integral on the rotary spectrograms produced CW and CCW near-inertial wind data for each year.

• It is useful to simply look at the CW near-inertial wind component, as Alford (2001) states that it is this component that contributes most to the near-inertial internal wave field (though the CCW component does contribute some small amount).

• The intensity of this contribution depends on the CW near-inertial winds, but also the depth of the mixed layer, leading to a significant (up to 12x) increase in near-inertial internal wave energy input, peaking in October and through the winter, and lowest in the summer (D'Asaro, 1985).

• Thicker mixed-layer 'strums' low modes more.

• Larger synoptic scale events do not excite much inertial energy; it is the smaller cold fronts or small lows that contribute most (~100 km).

• For the slab model, steps were taken as outlined by Alford (2001).

• First a time series of wind stress was determined as for D'Asaro (1985) using Garratt's (1977) canonical drag coefficient and the complex surface wind velocities.

• Slab layer currents and input flux computed as in D'Asaro (1985) and Alford (2001).

• [x] Look into seasonal mixed layer depth.

• [x] Check if f peak is super-inertial for local vs remote forcing.

[kurtisanstey]

• Line P station 3 seasonal mixed-layer depth as in Thomson and Fine (2003) and Li et al. (2004). The mixed-layer is thinnest mid-May through mid-November:

  

• The addition of the seasonal mixed-layer depth dampens wind contributions to mixed-layer currents in the winter/spring.

• The values for both mixed-layer currents (up to ~0.5 m/s) and flux (up to ~0.25 W/m^2) are similar to what was obtained by both D'Asaro (1985) and Alford (2001).

  

• Looking at the near-inertial CW component of the mixed-layer currents as the main contributor to near-inertial internal waves, significant wind events during thin mixed-layer months line up well with what is seen making it into the canyon, suggesting local forcing:

  

• Furthermore, in higher frequency resolution spectra, the f peak does not appear to be super-inertial, reinforcing evidence for local forcing. In previous PSD the slight shift towards higher frequencies could have been a result of over-averaging.

  

[kurtisanstey]

• [x] Correlation comparisons for wind and near-inertial depth-band (Slope and Axis, specific depth).
• [x] Add 2014, 2017, and 2018.

[kurtisanstey]

Observed:

• Correlations are weak positive at Slope (~0 - 0.15), through each year.
• At Axis, they are weak in the early months (~0 - 0.15), and stronger in the latter months (0.2 - 0.45).

Speculation:

• This suggests variable forcing of the near-inertial band at Slope and in the early months at Axis (possible wave-wave interaction, seasonal stratification and mixed-layer depth, or influence of mean currents), and more direct influence from storms in the canyon during the latter half of the year.

[kurtisanstey]

• [x] Review papers and code to ensure no mistakes were made.
• [x] Scatter plots.
• [x] Test vs random noise.
• [x] 100 m for correlation at Slope.

[kurtisanstey]

Notes for write-up:

• [x] Use pumping model additions in new papers (following Voelker et al., 2020).
• [x] Obtain vertical slab velocities (divergence pumping mechanism), take spectrogram and apply normalised window between f and N.
• [x] Calculate vertical energy flux into the internal wave field, below.
• Total 'pumped' internal wave flux is similar to models by Voelker et al. (2020) for the North Pacific (peaking around 3x10^-4 W/m^2 in the fall).
• As with the near-inertial slab response (above), qualitatively there is good general alignment between major wind events and the intermittent pulses seen in the near-inertial band. Except in the early months!
• None of the 'pumping' papers actually inspect flux to the near-inertial internal wave field, specifically (lower frame in first plot); they all just quantify total internal wave flux... I am not sure that I can extract near-inertial flux from this analysis by integrating over just the near-inertial band, like I've done with PSD in the past.
• Furthermore, in papers for both the slab and pumping models, the alignment is never perfect as there are too many variables affecting energy transfer from the wind to the internal wave field beneath the mixed layer. I believe a qualitative general correlation is the best evidence of 'forcing' for the near-inertial band that I'm going to get, and seems par for the course with these papers.

[kurtisanstey]

• [x] Research the vertical mode decomposition method (Alford), and compare with pumping results (ask Jia-Xuan about vertical mode fits > she said check Jody's GitHub for code). See next comment.
• [x] Plot the flux spectrum to see if it makes sense (NI band-pass flux levels are really low). It's actually a pretty flat (white) spectrum. I don't think band-passing this around f (bottom of plot, ~1.7xe-5 Hz) works, it could just be for internal wave flux in general? None of the papers use it specifically for near-inertial internal wave flux, either. Results for total IW flux are similar to papers.
• [x] Check window offsets for spectrograms, etc. to see if the timing lag is an artifact or real. There was a slight lag I found, due to an hourly datapoint missing about once every few days (it adds up!). This slightly affected timing (worse as the year went on) and also PSD (non-continuous data, technically). Fixed issue and results are mostly similar.
• [x] NI bandwidth should be slightly skewed above f, to account for incident NI IW. Confirmed window is about as good as I'm going to get.
• [x] Use upper bins to depth-average for Slope (as in literature, from about 35 - 155 m). And use lower bins for Axis. Only need to do this for correlation estimates, which are quite off, anyways. There's no correlation.
• [x] Check vertical modes for seasonal differences in NI flux transfer from mixed layer (see next comment).
• So far, the NI band-passed mixed layer power is the best shot for investigating wind input to NI energy, according to papers. Qualitatively (visually), the plots agree fairly well with both Slope and Axis. At Slope, near the surface, there is much more chaos and things don't line up as nicely, as well as the near-bottom attenuation. But at Axis, near the bottom (no attenuation), observed NI peaks line up well with those observed in the mixed layer, with exceptions at certain times of year (different modes?). Alford mentions that when NI energy is present near the bottom (not attenuated) the surface forcing often shows up there, immediately.

[kurtisanstey]

Gathering the pieces:

• [x] Vertical mode decomposition of band-passed NI currents in the mixed-layer (u_f).
• Find modes for water column, then use horizontal slab velocities to get amplitudes. Really it's just the variable depth of the mixed layer that should make certain modes stick out at different times.
• Use Jody's code to solve for eigenfunctions, then compare mixed layer depth and horizontal velocities to find dominant modes for those depths.
• As in Gill (Eq. 3.8, 1984):
• Jarosz et al. (2007):
• Alford and Zhao (2007):
• Alford et al. (2012):
• Zhen et al. (2017).

[kurtisanstey]

• Determined vertical modes as per Jody's code. Still interpreting the plots.
• Thinking of normalising the mode amplitudes (?) and then multiplying with the mixed-layer NI currents and seasonal mixed-layer depth to get a time-series of 'mode strength'.
• [x] These are backwards. w has boundary condition zero at surface and bottom, U does not (understand this better).
• [x] Apply this to modal analysis, as in Alford, etc.
• [x] Also can redo correlations in 4-month chunks, averaged, to evaluate correlation between seasonal cycles (should work). Then reduce time-scale until the correlations start to diverge.

Slope:

Axis:

[kurtisanstey]

• Found stratification dependent vertical modes for Slope and Axis.
• Using equations from Gill and Alford (above), the mixed-layer depths and NI slab currents as a step function, found the relative amplitudes of each mode, strummed by the mixed-layer, in time. And for each year. All results are in the archive>wind folder.
• The mixed layer deepest about -60 m in winter (January - April), thinnest about -20 m in summer.
• At Slope, when the ML is thin (~20 m), contributions from the low modes (1 and 2) and higher modes (3, 4, 5) are about equal (~53% modes 1 and 2). When the ML is thick (~60 m), modes 1 and 2 dominate (~74%).
• At Axis, when the ML is thin (~20 m), contributions from the low modes (1 and 2) and higher modes (3, 4, 5) are about equal (~50% for each group). When the ML is thick (~60 m), modes 1 and 2 dominate (~73%).
• Daily mean seasonal ML mode amplitudes are similar to those found by Jarosz et al., 2007, mode 1 up to about 0.6 m/s after notable wind events.
• At Slope, both the modes and slab do a reasonable job of lining up with the observations. However, it does seem that when the ML is thin (~equal contributions from high and low modes) that there is a greater response below the ML after notable wind events.
• There is some obvious propagation in the upper depths at Slope. The depth and time of the effect appear to vary, seasonally, up to 100 m and two weeks. Propagation from ML to ~100 m depth lasts up to 10-15 days, after which the event quickly effects the rest of the water column below (down to attenuation region at Slope, and in the near-bottom enhancement layer at Axis). This initial propagation effect is likely why the pulses at Axis show a slight delay, similar to the sub 100 m region at Slope. Could vary with seasonal changes to ML and/or pycnocline/stratification. See next comment for comparisons!
• At Axis, the ML effect is more pronounced. When the ML is thin (~equal contributions from high and low modes) there is a greater response in the canyon after notable wind events. The strongest events are in fall and early winter, with some weak events in the summer. Late winter and early spring events (February-April, when the ML is thickest) do not tend to show up, though this is not a rule.
• Results are generally similar to what has been found before (quite often, actually), that it is very difficult to consistently correlate wind forcing to NI internal waves. There is too much variability in storm characteristics and mixed-layer processes (mixing, leaking of energy below ML, propagation, trapping of NI energy by mesoscale circulation), coupled with the simplicity of the slab model, to consistently capture the near-inertial variability that is observed. Some events are qualitatively correlated, but there are some that don't line up (or show up) at all.
• A similar lack of slab model efficacy is mentioned in Jarosz et al., 2007, Alford and Zhao, 2007, Alford et al., 2016, Zheng et al., 2017, Voelker, 2020, Alford, 2020. Lots of room for further research in this field.

• Similar to those studies, I believe there is enough of a connection to say that the wind is contributing to the near-inertial intermittent seasonality, but that the ML forcing for NI IW is complex and difficult to accurately/consistently correlate.

  Some samples:

Vertical modes:

Mode amplitude seasonality, 2013:

Forcing comparison, 2013:

[kurtisanstey]

• [x] Redo vertical modes with horizontal structure, this time. Re-read papers on this, for better understanding.
• [x] Raw wind instead of two slab plots.
• [x] Is the below-ML propagation an indicative feature, from the literature?
• Gill 1984 found that NI energy density propagates from the base of the ML downward in 10-15 days, associated with the separation of the first few modes, and beyond pycnocline the vertical scale quickly increases.
• Kunze 1985 found that downward propagating NI energy could be trapped in jets of vertical relative vorticity following fronts, below the sub-ML (starting about 100 m, upper pycnocline).
• D'Asaro 1995 model results found that NI energy propagates downward to about 100 m (upper pycnocline) over about 15 days (associated with separation of the first few modes, as in Gill), and then quickly extends much deeper, that they associate with sub-ML CW rotation of NI energy (relative vorticity) and upper depth viscosity.
• Zervakis and Levine (1995, ZL) best describe the interference and separation of modes (inertial beating) in defining NI energy propagation out of the ML. Initially, sum of ML NI modal energy is constant in ML and zero below. As mode 1 rotates and adds destructively in the ML (~2-10 days after storm; now a non-zero sum of modes below ML), energy must propagate from the ML towards the upper pycnocline (~100-140 m). As mode 2 also becomes destructive (~10-20 days), much of the energy will now have been deposited into the upper pycnocline. With time, the low modes will also have 'moved away', horizontally (timing depends on N-S size of storm, horizontal mode speed, and the beta effect). These effects combined, NI energy then moves fairly quickly from the upper pycnocline to deep water, accelerating as each mode interferes and leaves (hence the big jump after modes 1 and 2 leave, observationally ~10-15 days). By the time the ML runs out of NI energy, it is distributed fairly equally between the upper pycnocline and deep water. Time-scales vary depending on storm speed, direction, rotation, etc. and both ML and pycnocline depth.
• Levine and Zervakis (1995, LZ) best observe that NI waves propagate from ML to pycnocline in slow 'packets' after some wind events, with time-scales generally between 10-15 days (as described in the ZL paper). Southward storms deposit modal energy faster than northward storms. Deep response increases as modes leave the region, generally around 10-15 days.
• Zhai et al. 2005 discuss NI energy propagating downward from below the ML (starting about 100 m, upper pycnocline) in anticyclonic (CW) 'inertial jets' which very quickly distributes NI energy through depth (> 1500 m).
• Jarosz et al., 2007, found downward propagating NI energy in packets, directly below the ML with a short depth range associated with seasonal stratification (pycnocline), and timescales greater than a week (studies only lasted a week).
• Alford et al. 2012 found that mesoscale motions perpendicular to the NI currents below the ML could raise or lower the effective inertial frequency with depth, which strongly affects NI vertical propagation.
• Alford et al. 2016 noted a 'beam' that moves NI energy very quickly downward after it leaves the ML/upper pycnocline, associated with mesoscale front-induced 'inertial jets' in this depth range. He also notes that internal ML NI energy propagation is not well defined.
• Alford 2020 suggests that shear within the ML (not accounted for in slab model) means NI energy would take time to reach the ML base, but this needs more research.
• [x] Redo correlations in seasonal chunks, time-averaged, to evaluate correlation between seasonal cycles (could work eventually, with averaging). Then reduce time-scale until the correlations start to diverge. Inter-annual comparisons.
• [x] Put Slope and Axis on same comparison plot, for modes.

• [x] Write and plots in thesis.

• NI CW power from slab model and site observations correlated in seasonal (3-month) blocks.
• To get generalised seasonal correlations, data was smoothed until correlations were 'good', then the smoothing slowly backed-off until decorrelation was evident.
• Best results were with slab data smoothed with a 3-week rolling average, and site observations smoothed with a 1-week rolling average.
• As the wind data is so patchy, results are poor, at best. Correlations are generally positive.
• Slope seems to have consistently better correlations than Axis, particularly during the notable fall events (2013 and 2014), possibly due to the shallow site being more responsive to the wind input, in general.
• Axis correlations are weaker, with best correlations during relatively quiescent periods; perhaps the typically weak response in the canyon best correlates with quiet periods at the surface, so correlation with notable events would be more promising.
• Reinforces argument that NI energy propagation is most prevalent in the fall, but is not robust, otherwise.

[kurtisanstey]

Saving this as analysis reference. New issue for writing the chapter.