Quantifying the effect of interannual ocean variability on the attribution of extreme climate events to human influence


In recent years, the climate change research community has become highly interested in describing the anthropogenic influence on extreme weather events, commonly termed “event attribution.” Limitations in the observational record and in computational resources motivate the use of uncoupled, atmosphere/land-only climate models with prescribed ocean conditions run over a short period, leading up to and including an event of interest. In this approach, large ensembles of high-resolution simulations can be generated under factual observed conditions and counterfactual conditions that might have been observed in the absence of human interference; these can be used to estimate the change in probability of the given event due to anthropogenic influence. However, using a prescribed ocean state ignores the possibility that estimates of attributable risk might be a function of the ocean state. Thus, the uncertainty in attributable risk is likely underestimated, implying an over-confidence in anthropogenic influence. In this work, we estimate the year-to-year variability in calculations of the anthropogenic contribution to extreme weather based on large ensembles of atmospheric model simulations. Our results both quantify the magnitude of year-to-year variability and categorize the degree to which conclusions of attributable risk are qualitatively affected. The methodology is illustrated by exploring extreme temperature and precipitation events for the northwest coast of South America and northern-central Siberia; we also provides results for regions around the globe. While it remains preferable to perform a full multi-year analysis, the results presented here can serve as an indication of where and when attribution researchers should be concerned about the use of atmosphere-only simulations.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15


  1. Allen M (2003) Liability for climate change. Nature 421:891–892

    Article  Google Scholar 

  2. Angélil O, Stone DA, Pall P (2014a) Attributing the probability of South African weather extremes to anthropogenic greenhouse gas emissions: spatial characteristics. Geophy Res Lett 41:3238–3243. doi:10.1002/2014GL059760

  3. Angélil O, Stone DA, Tadross M, Tummon F, Wehner M, Knutti R (2014b) Attribution of extreme weather to anthropogenic greenhouse gas emissions: sensitivity to spatial and temporal scales. Geophys Res Lett 41:2150–2155. doi:10.1002/2014GL059234

  4. Angélil O, Perkins-Kirkpatrick S, Alexander LV, Stone D, Donat MG, Wehner M, Shiogama H, Ciavarella A, Christidis N (2016a) Comparing1 regional precipitation and temperature extremes in climate model and reanalysis products. Weather Clim Extremes 13:35–43. doi:10.1016/j.wace.2016.07.001. http://www.sciencedirect.com/science/article/pii/S2212094716300202

  5. Angélil O, Stone D, Wehner M, Paciorek CJ, Krishnan H, Collins W (2016b) An independent assessment of anthropogenic attribution statements for recent extreme temperature and rainfall events. J Clim. doi:10.1175/JCLI-D-16-0077.1

  6. DerSimonian R, Laird N (1986) Meta-analysis in clinical trials. Controlled Clin Trials 7(3):177–188. doi:10.1016/0197-2456(86)90046-2. http://www.sciencedirect.com/science/article/pii/0197245686900462

  7. Gelman A, Carlin JB, Stern HS, Dunson DB, Vehtari A, Rubin DB (2013) Bayesian Data Analysis, 3rd edn. Chapman and Hall/CRC

  8. Hansen G, Auffhammer M, Solow AR (2014) On the attribution of a single event to climate change. J Clim 27:8297–8301

    Article  Google Scholar 

  9. Hurrell JW, Hack JJ, Shea D, Caron JM, Rosinski J (2008) A new sea surface temperature and sea ice boundary dataset for the Community Atmosphere Model. J Clim 21:5145–5153

    Article  Google Scholar 

  10. Jeon S, Paciorek CJ, Wehner MF (2016) Quantile-based bias correction and uncertainty quantification of extreme event attribution statements. Weather Clim Extremes. doi:10.1016/j.wace.2016.02.001. http://www.sciencedirect.com/science/article/pii/S2212094715300220

  11. McCulloch CE, Searle SR (2004) Generalized linear mixed models. In: Wiley series in probability and statistics: applied probability and statistics. Wiley. https://books.google.com/books?id=XpL38GzFqL0C

  12. National Academies of Sciences, Engineering, and Medicine (2016) Attribution of extreme weather events in the context of climate change. The National Academies Press, Washington, DC. doi:10.17226/21852

  13. Neale RB, Chen CC, Gettelman A, Lauritzen PH, Park S, Williamson DL, Conley AJ, Garcia R, Kinnison JF D Lamarque, Marsh D, Mills M, Smith AK, Tilmes F S Vitt, Morrison H, Cameron-Smith P, Collins WD, Iacono MJ, Easter RC, Ghan SJ, Liu X, Rasch PJ, Taylor MA (2012) Description of the NCAR community atmosphere model (CAM 5.0). Tech. rep., NCAR Technical Note NCAR/TN-486+STR

  14. Otto FEL, Boyd E, Jones RG, Cornforth RJ, James R, Parker HR, Allen MR (2015) Attribution of extreme weather events in Africa: a preliminary exploration of the science and policy implications. Clim Change 132:531–543. doi:10.1007/s10584-015-1432-0

  15. Pall P, Aina T, Stone DA, Stott PA, Nozawa T, Hilberts AGJ, Lohmann D, Allen MR (2011) Anthropogenic greenhouse gas contribution to flood risk in England and Wales in Autumn 2000. Nature 470:382–385

    Article  Google Scholar 

  16. Stone DA, Allen MR (2005) The end-to-end attribution problem: from emissions to impacts. Clim Change 71:303–318

    Article  Google Scholar 

  17. Stone DA, Pall P (2016) A benchmark estimate of the effect of anthropogenic emissions on the ocean surface (In preparation)

  18. Trenberth K, Jones P, Ambenje P, Bojariu R, Easterling D, Tank AK, Parker D, Rahimzadeh F, Renwick J, Rusticucci M, Soden B, Zhai P (2007) Observations: Surface and Atmospheric Climate Change. In: Climate Change 2007: The Physical Science Basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change. Cambridge University Press, Cambridge

  19. Wolski P, Stone D, Tadross M, Wehner M, Hewitson B (2014) Attribution of floods in the Okavango Basin, Southern Africa. J Hydrol 511:350–358

    Article  Google Scholar 

Download references


This work was supported by the Regional and Global Climate Modeling Program of the Office of Biological and Environmental Research in the Department of Energy Office of Science under contract number DE-AC02-05CH11231. This document was prepared as an account of work sponsored by the United States Government. While this document is believed to contain correct information, neither the United States Government nor any agency thereof, nor the Regents of the University of California, nor any of their employees, makes any warranty, express or implied, or assumes any legal responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by its trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof, or the Regents of the University of California. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof or the Regents of the University of California.

Author information



Corresponding author

Correspondence to Mark D. Risser.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (PDF 210 kb)


Appendix 1: Details for the derivation of the confidence interval of \(\phi _p\)

Recall the setting introduced in Sect. 7, the goal being to make a confidence statement regarding the population distribution of risk from all possible years, using only a risk estimate from a single year.

The sampling distribution of \(\widehat{\xi }_t\) conditional on \(\mu\) is derived as follows. Again, recall that the sampling distribution of \(\widehat{\xi }_t\) conditional on \(\xi _t\) is \(N(\xi _t, \nu ^2/n):\) also \(\xi _t \sim N(\mu , \sigma ^2).\) The sampling distribution of interest is calculated by averaging over \(\xi _t:\)

$$\begin{aligned} p(\widehat{\xi }_t | \mu ) = \int _{\xi _t} p(\widehat{\xi }_t | \xi _t) p(\xi _t | \mu ) d\xi _t, \end{aligned}$$

where the implicit conditioning on \(\nu ^2\) and \(\sigma ^2\) is suppressed in the notation. Given that \(p(\widehat{\xi }_t | \xi _t) = N(\xi _t, \nu ^2/n)\) and \(p(\xi _t | \mu ) = N(\mu , \sigma ^2),\) the closed-form solution is well-known (this setup is identical to the derivation for the marginal distribution of the data in a Normal-Normal Bayesian posterior calculation). The result is that

$$\begin{aligned} p(\widehat{\xi }_t | \mu ) = N(\mu , \nu ^2/n + \sigma ^2). \end{aligned}$$

Next, to derive a confidence interval for \(\phi _p,\) first note that using (12) we can obtain a \(100(1-\alpha )\%\) confidence interval for \(\mu\) as

$$\begin{aligned} \left( \widehat{\xi }_t - z_{\alpha /2} \sqrt{\nu ^2/n + \sigma ^2}, \widehat{\xi }_t + z_{\alpha /2} \sqrt{\nu ^2/n + \sigma ^2}\right) . \end{aligned}$$

Because \(\phi _p = f(\mu ) = \mu + c_p\sqrt{\nu ^2/n + \sigma ^2}\) is a linear function of \(\mu\), statistical theory says that \(f(\widehat{\xi }_t) \sim N\big (f(\mu ), \text {Var}[f(\widehat{\xi }_t)]\big ),\) so that a \(100(1-\alpha )\%\) confidence interval for \(\phi _p = f(\mu )\) is

$$\begin{aligned} \left( f(\widehat{\xi }_t) - z_{\alpha /2} \sqrt{\text {Var} [f(\widehat{\xi }_t)]}, f(\widehat{\xi }_t) + z_{\alpha /2}\sqrt{\text {Var}[f(\widehat{\xi }_t)]} \right) . \end{aligned}$$

Since \(\text {Var}[f(\widehat{\xi }_t)] = \text {Var}\widehat{\xi }_t = \nu ^2/n + \sigma ^2,\) the confidence interval for \(\phi _p\) is

$$\begin{aligned} \left( \left[ \widehat{\xi }_t - c_p\sqrt{\nu ^2/n + \sigma ^2}\right] - z_{\alpha /2}\sqrt{\nu ^2/n + \sigma ^2}, \left[ \widehat{\xi }_t - c_p\sqrt{\nu ^2/n + \sigma ^2}\right] + z_{\alpha /2}\sqrt{\nu ^2/n + \sigma ^2} \right) \end{aligned}$$


$$\begin{aligned} \left( \widehat{\xi }_t + (c_p - z_{\alpha /2}) \sqrt{\nu ^2/n + \sigma ^2}, \widehat{\xi }_t + (c_p + z_{\alpha /2}) \sqrt{\nu ^2/n + \sigma ^2} \right) , \end{aligned}$$

which is what is given in (10).

Appendix 2: Supplemental Figures

See Figs. 13, 14 and 15.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Risser, M.D., Stone, D.A., Paciorek, C.J. et al. Quantifying the effect of interannual ocean variability on the attribution of extreme climate events to human influence. Clim Dyn 49, 3051–3073 (2017). https://doi.org/10.1007/s00382-016-3492-x

Download citation


  • Climate change
  • Anthropogenic
  • Event attribution
  • Extreme weather
  • Risk ratio