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The dynamics of learning about a climate threshold

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Abstract

Anthropogenic greenhouse gas emissions may trigger threshold responses of the climate system. One relevant example of such a potential threshold response is a shutdown of the North Atlantic meridional overturning circulation (MOC). Numerous studies have analyzed the problem of early MOC change detection (i.e., detection before the forcing has committed the system to a threshold response). Here we analyze the early MOC prediction problem. To this end, we virtually deploy an MOC observation system into a simple model that mimics potential future MOC responses and analyze the timing of confident detection and prediction. Our analysis suggests that a confident prediction of a potential threshold response can require century time scales, considerably longer that the time required for confident detection. The signal enabling early prediction of an approaching MOC threshold in our model study is associated with the rate at which the MOC intensity decreases for a given forcing. A faster MOC weakening implies a higher MOC sensitivity to forcing. An MOC sensitivity exceeding a critical level results in a threshold response. Determining whether an observed MOC trend in our model differs in a statistically significant way from an unforced scenario (the detection problem) imposes lower requirements on an observation system than the determination whether the MOC will shut down in the future (the prediction problem). As a result, the virtual observation systems designed in our model for early detection of MOC changes might well fail at the task of early and confident prediction. Transferring this conclusion to the real world requires a considerably refined MOC model, as well as a more complete consideration of relevant observational constraints.

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References

  • Adams RM, Crocker TD, Katz RW (1984) Assessing the adequacy of natural science information—a Bayesian approach. Rev Econ Stat 66:568–575

    Article  Google Scholar 

  • Alley RB, Marotzke J, Nordhaus WD, Overpeck JT, Peteet DM, Pielke RA, Pierrehumbert RT, Rhines PB, Stocker TF, Talley LD, Wallace JM (2003) Abrupt climate change. Science 299:2005–2010

    Article  Google Scholar 

  • Baehr J, Keller K, Marotzke J (2007a) Detecting potential changes in the meridional overturning circulation at 26 °N in the Atlantic. Clim Change, http://www.dx.doi.org/10.1007/s10584-006-9153-z

  • Baehr J, McInerney D, Keller K, Marotzke J (2007) Global optimization of an observing system design for the North Atlantic meridional overturning circulation, J Atmos Oceanic Technol (in review). Available at: http://www.geosc.psu.edu/∼kkeller/publications.html

  • Brennan C, Matear R, Keller K (2007) Observing oxygen improves the detection capabilities of an ocean observation array. J Geophys Res Oceans (in review). Available at: http://www.geosc.psu.edu/∼kkeller/publications.html

  • Bence JR (1995) Analysis of short-time series—correcting for autocorrelation. Ecology 76:628–639

    Article  Google Scholar 

  • Box GEP, Tiao GC (2002) Bayesian inference in statistical analysis. Wiley, New York

    Google Scholar 

  • Cubasch U et al (2001) Projections of future climate change. Climate change 2001—the scientific basis. Contribution of working group I of the third assessment report of the intergovernmental panel on climate change. Cambridge University Press, Cambridge, pp 526–582

  • Challenor PG, Hankin RKS, March R (2006) Towards the probability of rapid climate change. In: Schellnhuber HJ (ed) Avoiding dangerous climate change. Cambridge University Press, Cambridge

  • Collins M, Sinha B (2003) Predictability of decadal variations in the thermohaline circulation and climate. Geophys Res Lett 30:1306

    Article  Google Scholar 

  • Dai AG, Hu A, Meehl GA, Washington WM, Strand WG (2005) Atlantic thermohaline circulation in a coupled general circulation model: unforced variations versus forced changes. J Clim 18(16):3270–3293

    Article  Google Scholar 

  • Delworth TL, Mann ME (2000) Observed and simulated multidecadal variability in the Northern Hemisphere. Clim Dyn 16:661–676

    Article  Google Scholar 

  • Delworth TL, Greatbatch RJ (2000) Multidecadal thermohaline circulation variability driven by atmospheric surface flux forcing. J Clim 13(9):1481–1495

    Article  Google Scholar 

  • Dixon KW, Delworth TL, Spelman MJ, Stouffer RJ (1999) The influence of transient surface fluxes on North Atlantic overturning in a coupled GCM climate change experiment. Geophys Res Lett 26:2749–2752

    Article  Google Scholar 

  • Draper D (1995) Assessment and propagation of model uncertainty. J Roy Stat Soc Ser B Methodol 57:45–97

    Google Scholar 

  • Evensen G (1997) Advanced data assimilation for strongly nonlinear dynamics. Monthly Weather Rev 125:1342–1354

    Article  Google Scholar 

  • Fichefet T, Poncin C, Goosse H, Huybrechts P, Janssens I, Le Treut H (2003) Implications of changes in freshwater flux from the Greenland ice sheet for the climate of the 21st. century. Geophys Res Lett 30. doi:10.1029/2003GL017826

  • Ganachaud A (2003) Error budget of inverse box models: the North Atlantic. J Atmos Oceanic Technol 20:1641–1655

    Article  Google Scholar 

  • Ganopolski A, Rahmstorf S (2001) Rapid changes of glacial climate simulated in a coupled climate model. Nature 409:153–158

    Article  Google Scholar 

  • Goldstein M, Rougier JC (2006) Bayes linear calibrated prediction for complex systems. J Am Stat Assoc 101:1132–1143

    Article  Google Scholar 

  • Gregory JM, Dixon KW, Stouffer RJ, Weaver AJ, Driesschaert E, Eby M, Fichefet T, Hasumi H, Hu A, Jungclaus JH, Kamenkovich IV, Levermann A, Montoya M, Murakami S, Nawrath S, Oka A, Sokolov AP, Thorpe RB (2005) A model intercomparison of changes in the Atlantic thermohaline circulation in response to increasing atmospheric CO2 concentration. Geophys Res Lett 32:L12703

    Article  Google Scholar 

  • Griffies SM, Bryan K (1997) Predictability of North Atlantic multidecadal climate variability. Science 275:181–184

    Article  Google Scholar 

  • Hankin RKS (2005) Introducing BACCO, an R bundle for Bayesian analysis of computer code output. J Stat Softw 14(16):21

    Google Scholar 

  • Hargreaves JC, Annan JD (2002) Assimilation of paleo-data in a simple Earth system model. Clim Dyn 19:371–381

    Article  Google Scholar 

  • Hargreaves JC, Annan JD (2006) Using ensemble prediction methods to examine regional climate variation under global warming scenarios. Ocean Model 11:174–192

    Article  Google Scholar 

  • Hargreaves JC, Annan JD, Edwards NR, Marsh R (2004) An efficient climate forecasting method using an intermediate complexity Earth System Model and the ensemble Kalman filter. Clim Dyn 23:745–760

    Article  Google Scholar 

  • Harmon R, Challenor P (1997) A Markov chain Monte Carlo method for estimation and assimilation into models. Ecol Model 101:41–59

    Article  Google Scholar 

  • Hastings WK (1970) Monte-Carlo sampling methods using Markov chains and their applications. Biometrika 57:97–109

    Article  Google Scholar 

  • Hasselmann K (1993) Optimal fingerprints for the detection of time-dependent climate-change. J Clim 6(10):1957–1971

    Article  Google Scholar 

  • Held H, Kleinen T (2004) Detection of climate system bifurcations by degenerate fingerprinting. Geophys Res Lett 31(23):L23207

    Article  Google Scholar 

  • Holland MM, Brasket AJ, Weaver AJ (2000) The impact of rising atmospheric CO2 on simulated sea ice induced thermohaline circulation variability. Geophys Res Lett 27(10):1519–1522

    Article  Google Scholar 

  • Hu AX, Meehl GA, Han WQ (2004) Detecting thermohaline circulation changes from ocean properties in a coupled model. Geophys Res Lett 31:L13204

    Article  Google Scholar 

  • Joos F, Plattner G-K, Stocker TF, Körtzinger A, Wallace DWR (2003) Trends in marine dissolved oxygen: implications for ocean circulation changes and the carbon budget. EOS 84:197–204

    Article  Google Scholar 

  • Keller K, Bolker BM, Bradford DF (2004) Uncertain climate thresholds and optimal economic growth. J Environ Econ Manage 48:723–741

    Article  Google Scholar 

  • Keller K, Deutsch C, Hall MG, Bradford DF (2007a) Early detection of changes in the North Atlantic meridional overturning circulation: implications for the design of ocean observation systems. J Clim 20:145–157

    Article  Google Scholar 

  • Keller K, Schlesinger M, Yohe G (2007b) Managing the risks of climate thresholds: Uncertainties and information needs. Clim Change. http://www.dx.doi.org/10.1007/s10584-006-9114-6

  • Keller K, Miltich LI, Robinson A, Tol RSJ (2007c) How overconfident are current projections of carbon dioxide emissions? Working Paper Series, Research Unit Sustainability and Global Change, Hamburg University. FNU-124: http://www.ideas.repec.org/s/sgc/wpaper.html

  • Keller K, Slater R, Bender M, Key RM (2002) Possible biological or physical explanations for decadal scale trends in North Pacific nutrient concentrations and oxygen utilization. Deep-Sea-Res II 49:345–362

    Article  Google Scholar 

  • Keller K, Tan K, Morel FMM, Bradford DF (2000) Preserving the ocean circulation: implications for climate policy. Clim Change 47:17–43

    Article  Google Scholar 

  • Kim S, Eyink GL, Restrepo JM, Alexander FJ, Johnson G (2003) Ensemble filtering for nonlinear dynamics. Monthly Weather Rev 131:2586–2594

    Article  Google Scholar 

  • Kleinen T, Held H, Petschel-Held G (2003) The potential role of spectral properties in detecting thresholds in the Earth system: application to the thermohaline circulation. Ocean Dyn 53:53–63

    Article  Google Scholar 

  • Knight JR, Allan RJ, Folland CK, Vellinga M, Mann ME (2005) A signature of persistent natural thermohaline circulation cycles in observed climate. Geophys Res Lett 32:L20708

    Article  Google Scholar 

  • Knutti R, Stocker TF, Joos F, Plattner GK (2003) Probabilistic climate change projections using neural networks. Clim Dyn 21:257–272

    Article  Google Scholar 

  • Latif M, Roeckner E, Mikolajewski U, Voss R (2000) Tropical stabilization of the thermohaline circulation in a greenhouse warming simulation. J Clim 13:1809–1813

    Article  Google Scholar 

  • Lea DJ, Allen MR, Haine TWN (2000) Sensitivity analysis of the climate of a chaotic system. Tellus Series A-Dyn Meteorol Oceanogr 52:523–532

    Google Scholar 

  • Lempert RJ (2002) A new decision sciences for complex systems. Proc Natl Acad Sci USA 99:7309–7313

    Article  Google Scholar 

  • Link PM, Tol RSJ (2006) The economic impact of a slowdown of the thermohaline circulation: an application of fund. Working paper, Hamburg University, Department of Economics, Research Unit Sustainability and Global Change, Center for Marine and Atmospheric Sciences (ZMAW), pp 14. Available at http://www.uni-hamburg.de/Wiss/FB/15/Sustainability/Working_Papers.htm

  • Lohmann G, Schneider J (1999) Dynamics and predictability of Stommel’s box model. A phase-space perspective with implications for decadal climate variability. Tellus Series A-Dyn Meteorol Oceanogr 51:326–336

    Google Scholar 

  • Lorenz EN (1963) Deterministic nonperiodic flow. J Atmos Sci 20:130–141

    Article  Google Scholar 

  • Lorenz EN (1975) Climate Predictability. In: The physical basis of climate modeling, World Meteorological Organization, Washington

  • Manabe S, Stouffer RJ (1994) Multiple-century response of a coupled ocean–atmosphere model to an increase of atmospheric carbon dioxide. J Clim 7:5–23

    Article  Google Scholar 

  • Marotzke J (2000) Abrupt climate change and thermohaline circulation: mechanisms and predictability. Proc Natl Acad Sci USA 97:1347–1350

    Article  Google Scholar 

  • Marotzke J, Cunningham SA, Bryden HL (2002) Monitoring the Atlantic meridional overturning circulation at 26.5 N., Proposal accepted by the Natural Environment Research Council (UK). Available at: http://www.noc.soton.ac.uk/rapidmoc/

  • Marsh R, Yool A, Lenton TM, Gulamati MY, Edwards NR, Shepherd JG, Krznaric M, Newhouse S, Cox SJ (2004) Bistability of the thermohaline circulation identified through comprehensive 2-parameter sweeps of an efficient climate model. Clim Dyn 23:761–777

    Article  Google Scholar 

  • McManus JF, Francois R, Gherardi JM, Keigwin LD, Brown-Leger S (2004) Collapse and rapid resumption of Atlantic meridional circulation linked to deglacial climate changes. Nature 428:834–837

    Article  Google Scholar 

  • Metropolis N, Rosenbluth AW, Rosenbluth MN, Teller AH, Teller E (1953) Equation of state calculations by fast computing machines. J Chem Phys 21:1087–1092

    Article  Google Scholar 

  • Monahan AH (2002) Stabilization of climate regimes by noise in a simple model of the thermohaline circulation. J Phys Oceanogr 32:2072–2085

    Article  Google Scholar 

  • Nordhaus WD (1994) Managing the global commons: the economics of climate change. The MIT press, Cambridge

    Google Scholar 

  • Qian SS, Stow CA, Borsuk ME (2003) On Monte Carlo methods for Bayesian inference. Ecol Model 159(2–3):269–277

    Article  Google Scholar 

  • Peterson GD, Carpenter SR, Brock WA (2003) Uncertainty and the management of multistate ecosystems: an apparently rational route to collapse. Ecology 84:1403–1411

    Article  Google Scholar 

  • Raftery AE, Lewis SM (1995) The number of iterations, convergence diagnostics, and generic Metropolis algorithms. In: Gilks WR, Spiegelhalter DJ, Richardson S (eds) Markov Chain Monte Carlo in Praxis. Chapman and Hall, London, pp 115–130

    Google Scholar 

  • Rahmstorf S, Ganopolski A (1999) Long-term global warming scenarios computed with an efficient coupled climate model. Clim Change 43:353–367

    Article  Google Scholar 

  • Rahmstorf S, Zickfeld K (2005) Thermohaline circulation changes: a question of risk assessment—an editorial review essay. Clim Change 68:241–247

    Article  Google Scholar 

  • Roeckner E, Baeuml G, Bonaventura L, Brokopf R, Esch M, Giorgetta M, Hagemann S, Kirchner I, Kornblueh L, Manzinie E, Rhodin A, Schlese U, Schulzweida U, Tompkins A (2003) The atmospheric general circulation model ECHAM5, part I: Model description, Technical Report 349, Max Planck Institute for Meteorology

  • Santer BD, Mikolajewicz U, Bruggemann W, Cubasch U, Hasselmann K, Hock H, Maierreimer E, Wigley TML (1995) Ocean variability and its influence on the detectability of greenhouse warming signals. J Geophys Res-Oceans 100:10693–10725

    Article  Google Scholar 

  • Sato M, Hansen JE, McCormick MP, Pollack JB (1993) Stratospheric aerosol optical depths, 1850–1990. J Geophys Res-Atmos 98(D12):22987–22994

    Google Scholar 

  • Simon HA (1959) Theories of decision-making in economics and behavioral-science. Am Econ Rev 49:253–283

    Google Scholar 

  • Schneider T, Neumaier A (2001) Algorithm 808: Arfit—a Matlab package for the estimation of parameters and eigenmodes of multivariate autoregressive models. ACM Trans Math Softw 27:58–65

    Article  Google Scholar 

  • Smethie WM, Fine RA (2001) Rates of North Atlantic Deep water formation calculated from chlorofluorocarbon inventories. Deep Sea Res 48:189–215

    Article  Google Scholar 

  • Sohn MD, Small MJ, Pantazidou M (2000) Reducing uncertainty in site characterization using Bayes Monte Carlo methods. J Environ Eng ASCE 126(10):893–902

    Article  Google Scholar 

  • Stocker TF (1999) Abrupt climate changes: from the past to the future—a review. Int J Earth Sci 88:365–374

    Article  Google Scholar 

  • Stommel H (1961) Thermohaline convection with two stable regimes of flow. Tellus 13:224–230

    Article  Google Scholar 

  • Stouffer RJ, Yin J, Gregory JM, Dixon KW, Spelman MJ, Hurlin W, Weaver AJ, Ebyd M, Flato GM, Hasumi H, Hu A, Jungclaus JH, Kamenkovich IV, Levermann A, Montoya M, Murakami S, Nawrath S, Oka A, Peltier WR, Robitaille DY, Sokolov A, Vettoretti G, Weber SL (2006) Investigating the causes of the response of the thermohaline circulation to past and future climate changes. J Clim 19:1365–1387

    Article  Google Scholar 

  • Swets JA (1973) Relative operating characteristic in psychology. Science 182:990–1000

    Article  Google Scholar 

  • Timmermann A, Lohmann G (2000) Noise-induced transitions in a simplified model of the thermohaline circulation. J Phys Oceanogr 30:1891–1900

    Article  Google Scholar 

  • Vellinga M, Wood RA (2004) Timely detection of anthropogenic change in the Atlantic meridional overturning circulation. Geophys Res Lett 31:L14203

    Article  Google Scholar 

  • Warnes GR (2001) The Normal Kernel Coupler: an adaptive Markov Chain Monte Carlo method for efficient sampling from multi-modal distributions, in University of Washington, Department of Statistics Working Papers, Report No. 39

  • Webster M, Scott J, Sokolov A, Stone P (2006) Estimating the probability distributions from complex models with bifurcations: The case of ocean circulation collapse, in Joint Program on the Science and Policy of Global Change, Report Number 133. MIT, Boston

  • Wilks DS (2001) A skill score based on economic value for probability forecasts. Meteorol Appl 8:209–219

    Article  Google Scholar 

  • Wunsch C (2006) Abrupt climate change: an alternative view. Quaternary Res 65:191–203

    Article  Google Scholar 

  • Zellner A, Tian GC (1964) Bayesian analysis of the regression model with autocorrelated errors. J Am Stat Assoc 59:763–778

    Article  Google Scholar 

  • Zhu XH, Fraedrich K, Blender R (2006) Variability regimes of simulated Atlantic MOC. Geophys Res Lett 33(21, L21603 Artn l21603)

  • Zickfeld K, Levermann A, Morgan MG, Kuhlbrodt T, Rahmstorf S, Keith DW (2007) Present state and future fate of the Atlantic meridional overturning circulation as viewed by experts. Clim Change 82:235–265

    Article  Google Scholar 

  • Zickfeld K, Slawig T, Rahmstorf S (2004) A low-order model for the response of the Atlantic thermohaline circulation to climate change. Ocean Dyn 54:8–26

    Article  Google Scholar 

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Acknowledgments

We thank J. Annan, B. Haupt, J. Baehr, D. Ludwig, N. Urban, M. Oppenheimer, and D. Ricciuto for helpful discussions. Nathan Urban calculated the spectra shown in Fig. 1. Any potential remaining errors and omissions are, of course, ours. K. Zickfeld kindly provided the code for the adopted MOC model. Careful reviews by R. Stouffer and H. Held considerably improved the presentation of the manuscript. We gratefully acknowledge support from the National Science Foundation (SES #0345925). Any opinions, findings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the funding entity.

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  1. Department of Geosciences, Penn State University, 208 Deike Building, University Park, PA, 16802-2714, USA

    Klaus Keller & David McInerney

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  1. Klaus Keller
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Keller, K., McInerney, D. The dynamics of learning about a climate threshold. Clim Dyn 30, 321–332 (2008). https://doi.org/10.1007/s00382-007-0290-5

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