Oceanic eddies are not negligible, especially in climate modeling. There’s the work of Dr Emily Shuckburgh of the BAS on this, but more specifically there’s section 6.3.3 of Gettelman and Rood, Demystifying Climate Models: A Users Guide to Earth System Models, 2016, an open source book. Generally speaking, oceans transport otherwise un-transportable heat energy from tropics north. As Gettelman and Rood say, “It is as if the large scales (think of the highway or the concrete drainage ditch) require the small scales to handle the flow (or energy) of the circulation” (6.3.3, on page 97).

And while climate models are the best we’ve got, they need a lot more work, and Gettelman and Rood cover areas for improvement. There’s also:

• R. Frigg, L. A. Smith, D. A. Stainforth, “The myopia of imperfect climate models: The case of UKCP09”, Philosophy of Science, 2013, 80(5).
• D. Dommenget, M. Rezny, “A caveat note on tuning in the development of Coupled
  Climate Models”, Journal of Advances in Modeling Earth Systems, 10, 2018.
• F. Pattyn, L. Favier, S. Sun, · G. Durand, “Progress in numerical modeling of Antarctic ice-sheet dynamics”, Current Climate Change Reports, September 2017, 3(3), 174-184.
• R. L. Smith, C. Tebaldi, D. Nychka, L. O. Mearns, “Bayesian modeling of uncertainty
  in ensembles of climate models”, Journal of the American Statistical Association, 2009, 104(485), 97-116.

This is not to say model projections are useless. As many say, Uncertainty is not our friend, and that’s what I mean when I write here and elsewhere that forecasts based upon climate models might well underestimate rates of climate change.

Facts are, especially when used in ensembles, numerical climate models have to be fast enough to be able to be run many times simulating Earth’s climate over many years. Even with the fastest computers and specialized hardware, this means compromises are inevitably necessary. For example, although variable grids are common, these are static, and the best dynamical models of fluids (e.g., FVCOM, and see also) use variable mesh grids where the fineness of the grid gets dropped when gradients have too large magnitudes. On the large specialized hardware, such software architectures are presently unworkable because they mean cores have to communicate with one another too much.

Then there’s the interaction with ice sheets, and various simplifications of oceans.

So, my point is, while I certainly would not feel assured that outcomes could be better than they are projected by CMIP5 going on CMIP6, I wouldn’t feel assured either that they are no worse than the models say.

[FVCOM example:]