Flierl1978 quotes Karl Marx:
A second and, in my opinion, more persuasive argument for our studies is that, in sensitive systems, a small quantitative error may lead to large qualitative errors1.
_1 "Quantitative changes suddenly become qualitative changes" (Karl Marx)
Holte2009 throw shade at under-performing Canadian Argo floats:
Most floats sampled at regular pressure levels, though the Canadian Argo floats often sampled at irregular pressures and required substantial editing.
Sutyrin1994 note insufficient printer resolution in their Figure 2.
A frequently asked question related to this work is “Which mixing processes matter most for climate?”. As with many alluringly comprehensive sounding questions, the answer is “it depends”.
and then end on an inspiring note
At the same time, the epiphanies, new ideas and novel observations that fundamentally drive the field forward frequently come not from big science, but from a cornucopia of much smaller exploratory efforts and the continued small-scale development of innovative observing technology and numerical techniques. We must not lose the ability to be surprised.
Wunsch2016 cites the Bible
That which is far off, and exceeding deep, who can find it out? — Ecclesiastes 7:24 (King James Version)
Enrico Fermi quotes John von Neumann to Freeman Dyson, critizing the latter's model (Dyson2004):
"I remember my friend Johnny von Neumann used to say, with four parameters I can fit an elephant, and with five I can make him wiggle his trunk." - Enrico Fermi
Mayer2010 take on the challenge yielding:
The resulting shape is schematic and cartoonlike but is still recognizable as an elephant. Although the use of the Fourier coordinate expansion is not new,2,3 our approach clearly demonstrates its usefulness in reducing the number of parameters needed to describe a two-dimensional contour. In the special case of fitting an elephant, it is even possible to lower it to four complex parameters and therein implement a well-known saying.
With five, they give the elephant an eye and make it's trunk wiggle!
Python implementation here.
As it turns out, the observations provide a clue to the problem.
- Smyth textbook + the dude abides
- [Flierl1978] Flierl, Models of Vertical Structure and the Calibration of Two-Layer Models, Dynamics of Atmospheres and Oceans, 2(4), 341-381 (1978). doi.
- [Holte2009] Holte & Talley, A New Algorithm for Finding Mixed Layer Depths with Applications to Argo Data and Subantarctic Mode Water Formation*, Journal of Atmospheric and Oceanic Technology, 26(9), 1920-1939 (2009). doi.
- [Sutyrin1994] Sutyrin & Flierl, Intense Vortex Motion on the Beta Plane: Development of the Beta Gyres, Journal of the Atmospheric Sciences, 51(5), 773-790 (1994). doi.
- [MacKinnon2017] MacKinnon, Alford, Ansong, Arbic, Barna, Briegleb, Bryan, Buijsman, Chassignet, Danabasoglu, Diggs, Griffies, Hallberg, Jayne, Jochum, Klymak, Kunze, Large, Legg, Mater, Melet, Merchant, Musgrave, Nash, Norton, Pickering, Pinkel, Polzin, Simmons, Laurent, Sun, Trossman, Waterhouse, Whalen & Zhao, Climate Process Team on Internal-Wave Driven Ocean Mixing, Bulletin of the American Meteorological Society, , (2017). doi.
- [Wunsch2016] Wunsch, Global Ocean Integrals and Means, with Trend Implications, Annual Review of Marine Science, 8(1), 1-33 (2016). doi.
- [Dyson2004] Dyson, A Meeting with Enrico Fermi, Nature, 427(6972), 297-297 (2004). doi.
- [Mayer2010] Mayer, Khairy & Howard, Drawing an Elephant with Four Complex Parameters, American Journal of Physics, 78(6), 648 (2010). doi.
- [Lindzen1988] Lindzen & Hou, Hadley Circulations for Zonally Averaged Heating Centered off the Equator, Journal of the Atmospheric Sciences, 45(17), 2416-2427 (1988). doi.