Mathematics for Climate Change Detection and Attribution school

The question of detecting and attributing causes in our current context of global warming is basically a statistical problem, one that can be thought of as establishing cause-and-effect relationships in a regression analysis study. In conventional detection schemes, model-predicted anthropogenic climate change is required to be as distinguishable as possible from spatial patterns associated with natural climate variability in order to facilitate attribution of specific physical mechanisms.


Our planet is experiencing rapid atmospheric warming with consequences for weather and sea ice. This change results in shifts in Earth’s water cycle, such as extended periods of drought and shorter but more intense rainfall that can have negative effects on health, contribute to food insecurity, migration, increased conflict, and severely affect poor and socially marginalized people. Unless convincing detection is accomplished and the source of the climate change signal clearly attributed, failure of mitigation planning and adaptation action remains the global risk with the biggest potential impact for communities in the future.

To train a new generation of early career scientists looking for a solid mathematical framework to handle detection and attribution (D&A;) questions, a school was held in September 2017 at the CNRS Center in Aussois, France (


This interdisciplinary effort brought together 30 masters, PhD students and postdocs in the fields of atmospheric sciences, oceanography, statistics and mathematics for 5 days of lectures and practical sessions on recent applied mathematical developments geared towards climate change studies.

For the week duration of MathDACC at the Paul Langevin conference centre, lectures took place in the mornings and the practical application of the theory covered were devoted to the afternoons. The main statistical language was the open source R language.

Introductory lab sessions scheduled during the first 2 afternoons, helped us develop some familiarity with reading netCDF files and plotting maps using the R packages commonly used in climate.

Each student was randomly paired with a partner also, and in the context of a small challenge. A list of the 15 teams was given and across 3 evenings, paired-up students had five minutes, to present in three slides of the research of their partner. It was the opportunity for participants and lecturers to learn more about the current research interest of each participant.

Projects were varied and included – to name only a few of them: The 1998-2012 ocean surface warming hiatus’ (Max-Planck-Institute Für Meteorologie); Temporal response of NDVI to precipitation in North Africa (University of Southampton); Evaluating climate models performances at simulating extreme events (University of Oxford); Coupling atmosphere and circulation models with waves in the Baltic Sea (Leibniz Institute for Baltic Sea Research); Recent trends in the regime of extreme rainfall on the central plateau of Burkina Faso (National Meteorological Services of Burkina Faso); and The climate response to five trillion tonnes of carbon (University of Victoria).
The school was organized around 5 broad topic areas:

  1. Statistical regression and application to D&A;
  2. Attribution of rare events and atmospheric mechanisms involved in extending the duration of some specific extreme events;
  3. Atmospheric flows, causal theories and teleconnections;
  4. Global sensitivity analysis and metamodeling; and
  5. Statistical theory underpinning extreme value analysis.

Among the case studies covered in the afternoon, was an investigation on how the so-called Lorentz butterfly (Lorentz 1963) approach could be used to describe the day-by-day properties of the atmosphere, visualize its evolution as a series of points along a two-dimensional (latitude by longitude) trajectory and for the predictability of extremes as well.


Just after lunch, office hours were also held by lecturers, all prominent experts in their fields. It was an invaluable opportunity to interact and build-up a scientific network. Many of those conversations occasionally continued out of doors while hiking in groups the beautiful surroundings located at an elevation of 1500m near the conference centre.



  • Hedemann, C., T. Mauritsen, J. Jungclaus and J. Marotzke (2017) The subtle origins of surface warming hiatuses. Nature Climate Change, doi: 10.1038/nclimate3274
  • B. Tokarska, K., N. Gillett, A. Weaver, V. Arora and M. Eby (2016). The climate response to five trillion tonnes of carbon. Nature Climate Change, doi: 10.1038/nclimate3036
  • Faranda, D., G. Messori and P. Yiou (2017). Dynamical proxies of North Atlantic predictability and extremes. Scientific Reports, 7, 41278, doi: 10.1038/srep41278.
  • Zwiers, F.W., X. Zhang, and Y. Feng, 2011: Anthropogenic Influence on Long Return Period Daily Temperature Extremes at Regional Scales. J. Climate, 24, 881– 892, doi:10.1175/2010JCLI3908

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