The NESSC workshop “Mathematical approaches to (palaeo-)climate sensitivity” was held on 12/13-November 2015, organised by Anna von der Heydt, Henk Dijkstra and Roderik van de Wal (IMAU). NESSC Post Docs Sebastian Bathiany and Itzel Ruvalcaba wrote a summary.

Climate sensitivity is a key number to quantify the effect of greenhouse gas emissions on climate. It is often defined as the long-term global mean temperature change that follows from doubling the atmospheric CO2 content. Several problems related to climate sensitivity are widely discussed in the scientific community: How can the large uncertainty of this number be reduced? How can theoretical approaches and observations or reconstructions of past climates be combined to this purpose? And do we need a different definition of climate sensitivity to make progress?  The recent NESSC workshop on “Mathematical approaches to (palaeo-)climate sensitivity” united principle investigators, Post Docs and PhD students from within and outside NESSC to address these fundamental questions.

A few dedicated presentations together with repeated discussion sessions in smaller groups has resulted in lively and fruitful exchange of ideas Soesterberg’s conference hotel “Kontakt der Kontinenten“.

A central part of the meeting was to become more aware of the many limitations of the definition of climate sensitivity. A good start is to recognize that a global mean temperature is easy to calculate in climate models, but not easy to obtain from reconstructions, which often yield only local information. This leads to several problems that need attention. In particular, perturbations in the global mean temperature depend on the nature and spatial pattern of the forcing, as well as on the background climate. For example, the effect of the continental distribution on global temperature has to be separated from the influence of CO₂ and other forcings. Also, in climates that are very different from today, the (linear) approach of climate sensitivity becomes less adequate. For instance, climate model simulations that were presented on the meeting show a rapid decrease in tropical clouds once the Earth warms by several degrees. This would cause a substantial increase in climate sensitivity.

Another important problem with such data-based approaches is that the climate is never in equilibrium with the forcing. In a climate model, one can in principle suddenly double the CO₂ content of the atmosphere and then wait to see at what temperature the model settles again. In the real world, however, the forcing will have changed before the equilibration has occurred because the changes in forcing and the climate’s response happen on overlapping time scales. It is therefore important to be aware of what time scales are considered in a certain analysis, and how one should define forcing and response, especially when comparing results to other studies. One result of the discussions about these problems was that a close collaboration will be needed between theoretical approaches and climate reconstruction activities. It also became evident that there is a need to improve/develop proxies to reconstruct past atmospheric conditions, especially for CO₂ levels, to build models for specific proxies, such as carbon and oxygen isotopes, and to include them in climate models. While a theoretician can hardly make progress without data, a palaeo-scientist may need advice on where to look for data, at what resolution and what feature to look for.

Another important aspect is the possibility that climate change is not always a gradual process but can be punctuated by abrupt shifts, often referred to as tipping points. It is even possible that the evolution of climate is not unique, but that qualitatively distinct solutions exist for the same orbital forcing. Such nonlinear phenomena cannot be captured by the classical definition of climate sensitivity. While abrupt changes have been found in models and in reconstructions, it remains a challenge to come up with a robust assessment of tipping points that are relevant for anthropogenic climate change. Therefore, the workshop also discussed on how local discontinuities of climate change can be incorporated in an improved definition of climate sensitivity, and what mathematical approaches may contribute to this end. While an alternative definition should overcome at least some of the limitations, it should still be simple enough to allow an easy communication between disciplines and possibly also between scientists and the rest of society. This trade-off between simplicity and adequacy, and the challenges mentioned above, will probably remain important topics of discussion in the future of NESSC and beyond.