As Annan and Dessler have demonstrated that based on correlating model findings with several hundred years of observations, that ECS can increase relatively quickly with continued global warming; I repost the following linked reference that uses paleo data to remind us all how much ECS can change with climate state:
von der Heydt, A.S., Dijkstra, H.A., van de Wal, R.S.W. et al. (2016), "Lessons on Climate Sensitivity From Past Climate Changes", Curr Clim Change Rep 2: 148.
https://doi.org/10.1007/s40641-016-0049-3https://link.springer.com/article/10.1007/s40641-016-0049-3Abstract: "Over the last decade, our understanding of climate sensitivity has improved considerably. The climate system shows variability on many timescales, is subject to non-stationary forcing and it is most likely out of equilibrium with the changes in the radiative forcing. Slow and fast feedbacks complicate the interpretation of geological records as feedback strengths vary over time. In the geological past, the forcing timescales were different than at present, suggesting that the response may have behaved differently. Do these insights constrain the climate sensitivity relevant for the present day? In this paper, we review the progress made in theoretical understanding of climate sensitivity and on the estimation of climate sensitivity from proxy records. Particular focus lies on the background state dependence of feedback processes and on the impact of tipping points on the climate system. We suggest how to further use palaeo data to advance our understanding of the currently ongoing climate change."
Caption for first image: "Published paleo-based values of S [CO 2 ,LI] S[CO2,LI] (specific equilibrium climate sensitivity parameter caused by CO2 radiative forcing and corrected by variations in land-ice (LI) feedbacks) indicating its state dependence. Only studies published after the PALAEOSENS review paper [21] are considered. For comparison, the state-independent values from PALAEOSENS, and from the IPCC report [3], and the CMIP5 multi-model mean for present day [41] are also shown. All values of S [CO 2 ,LI] S[CO2,LI] were given as mean (or most likely) ±1σ, apart from IPCC, which is the 90 % confidence (CF) range. Climate background states are given by ΔT from pre-industrial and are marked as estimated ranges (or ±2σ). In [42], further corrections for other slow feedbacks have been calculated, which has been ignored here, leading to different values of ΔT than published. To increase the clarity of the figure, the data-based results are visualised by colour-coded circles (mean values), while their uncertainties are combined in a cumulative probability density distribution (grey shading) assuming normal distributed values. Results based on climate models are shown by colour-coded squares (mean) including their uncertainties (bars). G glacial, IG interglacial, LE late Eocene, EE early Eocene, LP pre-PETM/late Paleocene, PETM Paleocene-Eocene thermal maximum. Reference numbers of the given citations: IPCC 2013 [3], PALAEOSENS 2012 [21], Andrews 2012 [41], Caballero 2013 [43] vdHeydt 2014 [20], Martinez-Boti 2015 [44] Köhler 2015 [32], Anagnoustou 2016 [42], Köhler 2016 [45], and Shaffer 2016 [46]"
Caption for the second image: "Schematic of the phase diagram of a climate model with two stable coexisting climate states. The shape of the S curve follows closely that discussed in [62, 63, 64]; see also [65]. The climate sensitivity parameter S is defined on each of the stable branches as the local slope of the global mean surface temperature T versus the (logarithm of) atmospheric pCO2 (cf. Eq. 8 ). Type I state dependence: When starting at point A (e.g. the pre-industrial climate), the temperature increase after a doubling of pCO2 (point B) is smaller than when starting from a colder climate (point C) on the same branch. Type II state dependence: When the initial pCO2 is the same as in point A, but the climate is initially on the cold branch (point D), a doubling of pCO2 results in a smaller temperature increase (point E) than if starting from point A and ending in point B. S becomes undefined at the transition points (open squares) between the two branches. The conditional climate sensitivity is equal to S for small perturbations (going from points D to E), but largely increases if the perturbation in CO2 is large enough to move the system from point D beyond the bifurcation point (blue open square) and jumps to the warm branch. Note that S is generally defined as a local gradient, while the 2xCO2 definition in the ECS may involve a perturbation too large for the linear assumption along the branch to be applicable"
See also:
Title: "Future relevant climate sensitivity (part deux)"
November 12, 2016/ gavin foster
http://www.thefosterlab.org/blog/2016/11/12/future-relevant-climate-sensitivity-part-deuxExtract: "The Friedrich et al (2016) study used a new empirical estimate of Surface Air Temperature (SAT) based on a compilation of Sea Surface Temperatures (as did Snyder recently) and a complete assessment of the processes “forcing” climate change over the last ~800 thousand years (e.g. CO2, land-ice albedo, and dust) to identify that climate sensitivity changed as a function of climate state: they found it was ~1.8 K per CO2 doubling when the Earth was substantially colder than today and ~5K per doubling when the Earth was only a little bit colder than the pre-industrial."