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Thursday, February 26, 2009

S. H. Schneider & M. D. Mastrandrea: Probabilistic assessment of “dangerous” climate change and emissions pathways

UPDATE: Link to most recent paper of February 26, 2009, concerning "Reasons for Concern" (free, open-access pdf file), PNAS 2009:

Proceedings of the National Academy of Sciences, November 1, 2005, Vol. 102, No. 44, 15727–15735; doi:10.1073/pnas.0507327102

Probabilistic assessment of “dangerous” climate change and emissions pathways

  1. Stephen H. Schneider*,, and
  2. Michael D. Mastrandrea*
  1. *Center for Environmental Science and Policy, Stanford University, Encina Hall East, E415, Stanford, CA 94305-6055; and Department of Biological Sciences, Stanford University, Stanford, CA 94305-5020
  1. Contributed by Stephen H. Schneider, July 26, 2005


Climate policy decisions driving future greenhouse gas mitigation efforts will strongly influence the success of compliance with Article 2 of the United Nations Framework Convention on Climate Change, the prevention of “dangerous anthropogenic interference (DAI) with the climate system.” However, success will be measured in very different ways by different stakeholders, suggesting a spectrum of possible definitions for DAI. The likelihood of avoiding a given threshold for DAI depends in part on uncertainty in the climate system, notably, the range of uncertainty in climate sensitivity. We combine a set of probabilistic global average temperature metrics for DAI with probability distributions of future climate change produced from a combination of several published climate sensitivity distributions and a range of proposed concentration stabilization profiles differing in both stabilization level and approach trajectory, including overshoot profiles. These analyses present a “likelihood framework” to differentiate future emissions pathways with regard to their potential for preventing DAI. Our analysis of overshoot profiles in comparison with non-overshoot profiles demonstrates that overshoot of a given stabilization target can significantly increase the likelihood of exceeding “dangerous” climate impact thresholds, even though equilibrium warming in our model is identical for non-overshoot concentration stabilization profiles having the same target.


  • To whom correspondence should be addressed. e-mail:

  • Author contributions: S.H.S. and M.D.M. designed research, performed research, contributed new reagents/analytic tools, analyzed data, and wrote the paper.

  • This contribution is part of the special series of Inaugural Articles by members of the National Academy of Sciences elected on April 30, 2002.

  • Abbreviations: DAI, dangerous anthropogenic interference; CDF, cumulative density function; CO2e, CO2 equivalent; SC, slow change; RC, rapid change; OS, overshoot scenario; IPCC, Intergovernmental Panel on Climate Change; TAR, Third Assessment Report; EU, European Union; PDF, probability density function; MEA, maximum exceedence amplitude; DY, degree years.

  • See accompanying Profile on page 15725.

  • § During the negotiations leading to the creation of the Kyoto Protocol, the Alliance of Small Island States submitted a draft protocol requiring 20% cuts in emissions by 2005 for industrialized nations. Clearly, the Kyoto targets are not as stringent as this target proposed by one stakeholder group.

  • Research published after the TAR has indicated that some abrupt nonlinear global changes, such as breakdown of the Greenland or Western Antarctic ice sheets, may be triggered by lower temperature thresholds than those currently indicated in Fig. 1, column V (e.g., ref. 16). Therefore, a stakeholder basing his evaluation of DAI on Fig. 1, column V would likely produce a distribution for DAI thresholds lower than the one reported here if this information were taken into account, as it is likely to be in the next IPCC assessment in 2007.

  • In this article, we make an effort, as in ref. 19, to differentiate between emissions scenarios, which represent descriptions of possible future states of the world and the characteristics relevant for emissions, emissions pathways, which represent time-evolving paths for global emissions of greenhouse gases and aerosols, and concentration profiles, which represent time-evolving trajectories for atmospheric concentrations of greenhouse gases and aerosols.

  • ** O'Neill and Oppenheimer (20) compare the future temperature profiles generated by their emissions pathways to thresholds for individual climate impacts that may be considered dangerous, and consider the sensitivity of their results to three values for climate sensitivity, but they do not produce PDFs for their results.

  • †† The two-box model is of the form: Formula where T(t) is the temperature in the upper box in year t, T LO(t) is the temperature in the lower box in year t, F(t) is the radiative forcing above preindustrial levels in year t, and λ, σ1, σ2, and σ3 are constants as defined in ref. 29. We adjust σ1 and σ3 to use a 1-year time step by dividing σ1 and σ3 by 10.

  • ‡‡ Our presentation of results is intended to demonstrate our probabilistic framework, and presenting separately the results using each climate sensitivity distribution requires, for each analysis step, either one very busy figure or three separate figures displaying essentially the same information. We believe such complexity would obscure the demonstration of our analysis methods while adding little intellectual value.

  • §§ The DAI-EU threshold is defined as 2 °C above preindustrial temperatures, while we present temperature distributions of temperature increase above 2000. Therefore, we express the DAI-EU threshold as 1.4 °C, based on the central estimate of 0.6 °C warming over the 20th century in the IPCC TAR (21).

  • ¶¶ This is strictly true when using a simple climate model with a single equilibrium warming level for a given radiative forcing. Some nonlinear processes not included in our simple model can create multiple equilibria and path dependence (e.g., ref. 35). In such models, OS could imply lower thresholds for DAI than those we report here with this linear model.

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