Analysis Tools - dhruvbalwada/sogos GitHub Wiki

Analysis tools commonly used.

Established:

Observational studies:

  • Estimating PV to give a qualitative summary of instabilities. It is often done using only hydrography, but works better if velocities are also measured. (issue: instability suggests little about non-linear evolution)
  • Estimate heat fluxes due to instabilities. This also relies on hydrography, and uses different parameterizations of heat fluxes due to instabilities. These can then be compared to surface fluxes, to gauge relative importance.
  • Estimate vertical velocities. This is a hard one. Siegelman et al showed that it can be quantified using only QG omega equation, SSH derived FSLE and hydrography. Might be more accurate if the glider drift is used to estimate velocities. (issue: knowing a snap shot of vertical velocity has little use to explain the vertical subduction, which is in essence a Lagrangian process)
  • Tracer anomalies/ visual inspection. This is a qualitative tool, where the data is visually parsed and interesting looking tracer anomalies are found. (issue: visual signatures are usually statistically inconclusive, but this should not deter you).
  • Tracer Spectra. A quantitative estimate of the small-scale variance in tracers, can be then compared against theoretical estimates. (In lot of places these slopes appear to be -2, and there is no model to explain it yet. The process might be filaments being dragged into interior from boundaries, which looks more front like, rather than the -1 slope that would appear if something maintained a constant background gradient).
  • Comparing Gradients. Some studies have compared PDFs of gradients across regions or seasons. It should be noted that this is exactly equivalent to looking at the distribution in the smallest possible bin of second order structure functions; and it makes more sense to look at the distribution of differences at different distances. This gives a quantitative sense of the multiscale structure.
  • Turner angle. Quantify what fraction of density gradients result from temp vs salinity contributions. There is some theory that I am unfamiliar with, but this angle can help inform the process that is working. (e.g Rudnick and Ferrari)
  • Tracer anomalies+mean gradient == length scales. Use them to quantify a diffusivity/proxy for the rate of stirring.
  • Tracer anomaly slopes

Models to help obs:

  • It is also useful to use a model to justify or refute the assumptions that might be made when approximating terms using observations (since some information is always missing, and assumptions are needed) (issue: this is always questionable when using finite resolution models that have less variance than obs)

Experimental:

  • Variograms. We can look at space-time variograms, since they are the most amenable and least assumptive statistics about variability that can easily be plotted.
    • Some way to convert from 2D to 1D? Average along dR = (dr^2 + Cdt^2), where C is chosen to max/min something.
  • Fitting spectra using Gaussian Processes. Using max likelihood estimation we can try to find the most probably spectral shapes by fitting a parametric form for the spectra. This can in the future also help in mapping.
  • Multiple linear regression to infer patterns of unmeasured variables.
  • Quantification of the vertical spectra. Klymak et al tried to this a bit, but largely open question as to how tracer shapes in the vertical are being set.

Extra:

  • Turner angles. Ferrari and Rudnick find that the turner ratio is 1 (compensated) in the mixed layer at scales less than 10km, 2 at larger scales, and 2 below the mixed layer. They hypothesize that maybe it is only the large scale ratio that gets subducted into the interior, and sets the ratio in the interior (or alternatively it is double diffusion). The compensation at the surface is a result of the non-compensated fronts being quickly eroded away as mixing depends on density gradients. The compensated T/S gradients that are subducted get stirred and mixed. Regions that have weak compensation will also have a density gradient associated with it, so geostrophic stirring can't easily wipe this away - while the compensated regions get stirred away preferentially. This presumably returns the interior waters to the large scale R values.