It is frustrating (to me at least) that the current generation of Earth System Models, ESMs (e. g. CMIP5), do not adequately address dynamical climate sensitivity. Hopefully, CMIP6 and future phases of E3SM, will improve upon the accuracy of our current projections.
In this regards, the first linked reference (and associated image) calibrated an effective/specific equilibrium climate sensitivity (S) based on warming cycles during the past 784,000 years. There findings for the upper end risk (e.g. RCP 8.5) indicated that the projected GMSTA range could be between 4.78C to 7.36C by 2100, based on one set of calculations.
Tobias Friedrich, Axel Timmermann, Michelle Tigchelaar, Oliver Elison Timm and Andrey Ganopolski (09 Nov 2016), "Nonlinear climate sensitivity and its implications for future greenhouse warming", Science Advances, Vol. 2, no. 11, e1501923, DOI: 10.1126/sciadv.1501923
http://advances.sciencemag.org/content/2/11/e1501923Extract: "Global mean surface temperatures are rising in response to anthropogenic greenhouse gas emissions. The magnitude of this warming at equilibrium for a given radiative forcing—referred to as specific equilibrium climate sensitivity (S)—is still subject to uncertainties. We estimate global mean temperature variations and S using a 784,000-year-long field reconstruction of sea surface temperatures and a transient paleoclimate model simulation. Our results reveal that S is strongly dependent on the climate background state, with significantly larger values attained during warm phases. Using the Representative Concentration Pathway 8.5 for future greenhouse radiative forcing, we find that the range of paleo-based estimates of Earth’s future warming by 2100 CE overlaps with the upper range of climate simulations conducted as part of the Coupled Model Intercomparison Project Phase 5 (CMIP5). Furthermore, we find that within the 21st century, global mean temperatures will very likely exceed maximum levels reconstructed for the last 784,000 years. On the basis of temperature data from eight glacial cycles, our results provide an independent validation of the magnitude of current CMIP5 warming projections."
While Friedrich et. al. (2016) is a useful starting point, its use of an effective/specific equilibrium climate sensitivity (S) calibrated to the last 784,000 years of warming cycles, means that it is missing the aperiodic dynamical climate sensitivity illustrated in the third image, the risk of Hansen's ice-climate feedback mechanism and the risk that we may well exceed the value of S calibrated to the last 784,000 years, as the fourth attached image shows that S increases in value with increasing values of GMST.
In regards S increasing with GMST, per the following linked NOAA article is entitled: "Global Climate Report - Annual 2016"
https://www.ncdc.noaa.gov/sotc/global/201613#gtempExtract: "The average global temperature across land and ocean surface areas for 2016 was 0.94°C (1.69°F) above the 20th century average of 13.9°C (57.0°F), surpassing the previous record warmth of 2015 by 0.04°C (0.07°F)."
The immediate following linked reference clarifies the relationship of ECS and the dynamical sensitivity of climate models.:
Kevin M. Grise & Lorenzo M. Polvani (28 April 2016), "Is climate sensitivity related to dynamical sensitivity?", Journal of Geophysical Research Atmospheres, DOI: 10.1002/2015JD024687
http://onlinelibrary.wiley.com/doi/10.1002/2015JD024687/abstractAbstract: "The atmospheric response to increasing CO2 concentrations is often described in terms of the equilibrium climate sensitivity (ECS). Yet, the response to CO2 forcing in global climate models is not limited to an increase in global-mean surface temperature: for example, the mid-latitude jets shift poleward, the Hadley circulation expands, and the subtropical dry zones are altered. These changes, which are referred to here as “dynamical sensitivity,” may be more important in practice than the global-mean surface temperature.
This study examines to what degree the inter-model spread in the dynamical sensitivity of 23 CMIP5 models is captured by ECS. In the Southern Hemisphere, inter-model differences in the value of ECS explain ~60% of the inter-model variance in the annual-mean Hadley cell expansion, but just ~20% of the variance in the annual-mean mid-latitude jet response. In the Northern Hemisphere (NH), models with larger values of ECS significantly expand the Hadley circulation more during winter months, but contract the Hadley circulation more during summer months. Inter-model differences in ECS provide little significant information about the behavior of the Northern Hemisphere subtropical dry zones or mid-latitude jets.
The components of dynamical sensitivity correlated with ECS appear to be driven largely by increasing sea surface temperatures, whereas the components of dynamical sensitivity independent of ECS are related in part to changes in surface temperature gradients. These results suggest that efforts to narrow the spread in dynamical sensitivity across global climate models must also consider factors that are independent of global-mean surface temperature."
Finally, I provide the following reference related to the calibration of dynamical sensitivity of climate models using paleodata.
The first following four linked references and I note that der Heydt et. al. 2016 concludes: "Such perturbations (illustrated in Fig. 1b,d) are not normally applied in climate models used for climate predictions [IPCC, 2013], where climate sensitivity is derived from model simulations considering prescribed, non-dynamic atmospheric CO2. In our conceptual model, we have derived climate sensitivities from both types of perturbations and find that the classical climate model approach (section 2.2, Fig. 4f) leads to significantly lower values of the climate sensitivity than the perturbations away from the attractor with dynamic CO2 (section 2.3, Fig. 11a). This emphasises the importance of including dynamic carbon cycle processes into climate prediction models. Moreover, it supports the idea that the real observed climate response may indeed be larger than the model predicted one, because those models never will include all feedback processes in the climate system.“
Anna S. von der Heydt, Peter Ashwin (Submitted on 12 Apr 2016), "State-dependence of climate sensitivity: attractor constraints and palaeoclimate regimes", arXiv:1604.03311
http://arxiv.org/abs/1604.03311&
http://arxiv.org/pdf/1604.03311v1.pdfThe second linked reference on the application of "dynamical systems theory" supports the position that the current effective ECS may be as high as 4.35C (but is masked both by lag times and by aerosol impacts):
Egbert H. van Nes, Marten Scheffer, Victor Brovkin, Timothy M. Lenton, Hao Ye, Ethan Deyle and George Sugihara (2015), "Causal feedbacks in climate change", Nature Climate Change, doi:10.1038/nclimate2568
http://www.nature.com/nclimate/journal/v5/n5/full/nclimate2568.htmlThe third linked reference examines the state dependency of ECS using paledata from the past 5 millions years and similarly finds that the effective ECS is higher than more CMIP5 models assume.
Köhler, P., de Boer, B., von der Heydt, A. S., Stap, L. B., and van de Wal, R. S. W. (2015), "On the state dependency of the equilibrium climate sensitivity during the last 5 million years", Clim. Past, 11, 1801-1823, doi:10.5194/cp-11-1801-2015.
http://www.clim-past.net/11/1801/2015/cp-11-1801-2015.htmlhttp://www.clim-past.net/11/1801/2015/cp-11-1801-2015.pdfThe fourth linked reference could not make it more clear that paleo-evidence from inter-glacial periods indicates that ECS is meaningfully higher than 3C and that climate models are commonly under predicting the magnitude of coming climate change. Furthermore, these finding concur with those of Köhler et al (2015) which indicates that inter-glacial values for specific ECS was about 45% higher than during glacial periods.
Dana L. Royer (2016), "Climate Sensitivity in the Geologic Past", Annual Review of Earth and Planetary Sciences, Vol. 44
http://www.annualreviews.org/doi/abs/10.1146/annurev-earth-100815-024150?src=recsys