With regards to the use of paleoclimate data and strange attractors to constraint ECS, see the linked article that indicates that using this approach clearly indicates that ECS is likely higher than commonly assumed:
A.S. Von der Heydt and Peter Ashwin (2016), "State-dependence of climate sensitivity: attractor constraints and palaeoclimate regimes", arXiv:1604.03311v1http://arxiv.org/pdf/1604.03311v1.pdf
Abstract: "Equilibrium climate sensitivity is a frequently used measure to predict long-term climate change. However, both climate models and observational data suggest a rather large uncertainty on climate sensitivity (CS). The reasons for this include: the climate has a strong internal variability on many time scales, it is subject to a non-stationary forcing and it is, on many timescales, out of equilibrium with the changes in the radiative forcing. Palaeo records of past climate variations give insight into how the climate system responds to various forcings although care must be taken of the slow feedback processes before comparing palaeo CS estimates with model estimates. In addition, the fast feedback processes can change their relative strength and time scales over time. Consequently, another reason for the large uncertainty on palaeo climate sensitivity may be the fact that it is strongly state-dependent. Using a conceptual climate model, we explore how CS can be estimated from unperturbed and perturbed model time series. Even in this rather simple model we find a wide range of estimates of the distribution of CS, depending on climate state and variability within the unperturbed attractor. For climate states perturbed by instantaneous doubling of CO2, the sensitivity estimates agree with those for the unperturbed model after transient decay back the attractor. In this sense, climate sensitivity can be seen as a distribution that is a local property of the climate attractor. We also follow the classical climate model approach to sensitivity, where CO2 is prescribed and non-dynamic, leading to CS values consistently smaller than those derived from the experiments with dynamic CO2. This suggests that climate sensitivity estimates from climate models may depend significantly on future dynamics, and not just the level of CO2."
Extract: “... the presence of variability on the attractor on a number of timescales means there are clear and non-trivial distributions of sensitivities, even for unperturbed climates. The distribution of sensitivities depends strongly on the background state as well as on the timescale considered. This suggests that it could be useful to think of the unperturbed climate sensitivity as a local property of the “climate attractor”. For a perturbed system (we have considered instantaneously doubled CO2) this is still useful once an initial transient has decayed. This transient will depend in particular on ocean heat uptake, though also on carbon cycle and biosphere processes that act on time scales roughly equivalent with the forcing time scale. If the climate system has more than one attractor, the perturbed system may clearly evolve to a completely different set of states than the original attractor – a situation that did not occur in the climate model used here. In less extreme cases, there may still be very long transients for some perturbations associated parts of the climate system that are associated with slow feedbacks.
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.“
Edit, see also:
A. S. von der Heydt, H. A. Dijkstra, R. S. W. van de Wal, R. Caballero, M. Crucifix, G. L. Foster, M. Huber, P. Köhler, E. Rohling, P. J. Valdes, P. Ashwin, S. Bathiany, T. Berends, L. G. J. van Bree, P. Ditlevsen, M. Ghil, A. Haywood, J. Katzav, G. Lohmann, J. Lohmann, V. Lucarini, A. Marzocchi, H. Pälike, I. Ruvalcaba Baroni, D. Simon, A. Sluijs, L. B. Stap, A. Tantet, J. Viebahn and M. Ziegler Lessons on climate sensitivity from past climate changes, Curr. Clim. Change Rep. (2016), doi:10.1007/s40641-016-0049-3.http://link.springer.com/article/10.1007/s40641-016-0049-3
Abstract: "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."