On determining the point of no return in climate change

van Zalinge, Brenda C.; Feng, Qing Yi; Aengenheyster, Matthias; Dijkstra, Henk A.

doi:https://doi.org/10.5194/esd-8-707-2017

Articles | Volume 8, issue 3

https://doi.org/10.5194/esd-8-707-2017

© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.

https://doi.org/10.5194/esd-8-707-2017

© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.

Articles | Volume 8, issue 3

Research article

|

09 Aug 2017

Research article |

| 09 Aug 2017

On determining the point of no return in climate change

Brenda C. van Zalinge, Qing Yi Feng, Matthias Aengenheyster, and Henk A. Dijkstra

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Final revised paper (published on 09 Aug 2017)
Preprint (discussion started on 16 Sep 2016)

Interactive discussion

Status: closed

AC: Author comment | RC: Referee comment | SC: Short comment | EC: Editor comment

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- Supplement

RC1: 'review', Anonymous Referee #1, 25 Sep 2016
- AC1: 'Point by point reply to reviewer #1', Qing Yi Feng, 24 Nov 2016
RC2: 'Referee comment from K. Rypdal', Kristoffer Rypdal, 26 Sep 2016
- AC2: 'Point by point reply to reviewer #2', Qing Yi Feng, 24 Nov 2016

Peer-review completion

AR: Author's response | RR: Referee report | ED: Editor decision

ED: Reconsider after major revisions (25 Nov 2016) by Christian Franzke

AR by Qing Yi Feng on behalf of the Authors (18 Mar 2017) Author's response Manuscript

ED: Referee Nomination & Report Request started (20 Mar 2017) by Christian Franzke

RR by Anonymous Referee #3 (04 Apr 2017)

RR by Jobst Heitzig (26 Apr 2017)

Suggestions for revision or reasons for rejection

1. Clarify definitions and their relationship to classical viability theory.

2. Change terminology from "point of no return" to something more appropriate.

3. Compare results for low-dimensional model to existing frameworks and make a case why the actual dimensionality of the 2nd model used exceed the capacity of these frameworks.

(see report below for details)

Report on manuscript
On determining the Point of no Return in Climate Change
by Brenda C. van Zalinge, Qing Yi Feng, and Henk A. Dijkstra

The authors suggest a very simple approach to define what they call a "point of no return". It seems it simply consists in finding that point in time t so that when GHG emissions are switched at time t from business as usual to an extreme mitigation scenario, there will still be some considerable probability that global mean temperature will exceed some given threshold value for either longer than 20 years or in the year 2100.

While this is an interesting numerical exercise, I am unsure about its significance and have several issues with the current presentation.

1. The authors claim to apply some form of viability theory for their analysis, but their presentation and usage of viability theory is confusing if not misleading. Viability theory is mainly about control problems in which the trajectory of some system can be influenced at many time points rather than just once as in this paper. In viability theory, the (stochastic) viability kernel of a system given control options and a desirable region in state space consists of all states starting from which one can force the system to stay within the desirable region (with at least some given probability) forever or until some target time by using a suitable (and typically non-constant!) control policy. The (somewhat unclear) definition of viability kernel the authors give instead seems to suggest that only those states should be considered viable starting at which the system will stay within the desirable region if the control is NOT changed but stays constant, which is not a control problem at all but rather a question of dynamical forward invariance (in the cited paper Heitzig et al., 2016, this was called an (open) invariant kernel). Later they seem to use an even more trivial definition of "viable" by apparently identifying a viable state simply with one in which a given temperature threshold is not crossed. In the caption of Fig. 1, they suggest that by using the right policy, the state may become viable again. In viability theory, a viable state can be reached from a non-viable one only if the latter is outside the desirable region, and this reachability question is normally analysed with the concept of capture basin which is however not even mentioned here.

2. The study does not seem to be about a "point of no return" at all but rather about what one might call a "point of sure exceedance". For one thing, in all presented scenarios it is always possible to return to a 280 ppm world and thus to a below-threshold temperature world, so being able to return is not a question. The question is rather, at what point in time t does a (temporary) exceedance of a given temperature threshold become highly likely if no mitigation has happened before t? While this is an important question, it will typically be the case that, due to the inertia of the system, this point in time is somewhat earlier than the point in time at which the threshold will actually be exceeded. So, at the critical point in time, the system is still in the desirable region but is deemed to leave it later. But this means that calling this critical point in time a "point of no RETURN" quite confusing since at this point the system has not even LEFT the desirable region.

3. Since the authors use a one-dimensional model in section 3 and cite both classical viability theory and the framework in Heitzig et al. 2015, which are readily applicable to 1d-problems, it would be very interesting to see a comparison of their resuls with what these two established frameworks would yield. In section 4, they use a model which I cannot judge due to missing experience, but which seems to be still one-dimensional (dealing again with global mean temperature alone) rather than high-dimensional as claimed in the introduction. If the authors mean to say that the high dimensionality arises because of the stochastic nature of the models, I would agree in general if they really attempted to model arbitrary nonpararmeterized probability distributions. But on line 273 they say they assume it to be a normal distribution, so the actual model dimension is still only two (mean and variance of the distribution suffice to describe the state) and the established frameworks would again be readily applicable.

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ED: Reconsider after major revisions (27 Apr 2017) by Christian Franzke

AR by Qing Yi Feng on behalf of the Authors (21 Jun 2017) Author's response Manuscript

ED: Referee Nomination & Report Request started (24 Jun 2017) by Christian Franzke

RR by Anonymous Referee #3 (29 Jun 2017)

ED: Publish as is (03 Jul 2017) by Christian Franzke

AR by Qing Yi Feng on behalf of the Authors (04 Jul 2017)

Short summary

The increase in atmospheric greenhouse gases (GHGs) is one of the main causes for the increase in global mean surface temperature. There is no good quantitative measure to determine when it is too late to start reducing GHGs in order to avoid dangerous anthropogenic interference. We develop a method for determining a so-called point of no return (PNR) for several GHG emission scenarios. The innovative element in this approach is the applicability to high-dimensional climate models.