Beyond equilibrium climate sensitivity

Abstract

Equilibrium climate sensitivity characterizes the Earth's long-term global temperature response to increased atmospheric CO2 concentration. It has reached almost iconic status as the single number that describes how severe climate change will be. The consensus on the 'likely' range for climate sensitivity of 1.5 °C to 4.5 °C today is the same as given by Jule Charney in 1979, but now it is based on quantitative evidence from across the climate system and throughout climate history. The quest to constrain climate sensitivity has revealed important insights into the timescales of the climate system response, natural variability and limitations in observations and climate models, but also concerns about the simple concepts underlying climate sensitivity and radiative forcing, which opens avenues to better understand and constrain the climate response to forcing. Estimates of the transient climate response are better constrained by observed warming and are more relevant for predicting warming over the next decades. Newer metrics relating global warming directly to the total emitted CO2 show that in order to keep warming to within 2 °C, future CO2 emissions have to remain strongly limited, irrespective of climate sensitivity being at the high or low end.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Figure 1: Overview of published best estimates and ranges for the transient climate response constrained by different lines of evidence.
Figure 2: Overview of published best estimates and ranges for equilibrium climate sensitivity constrained by different lines of evidence.
Figure 3: Overview of published best estimates and ranges for equilibrium climate sensitivity constrained by different lines of evidence.
Figure 4: Illustration of feedbacks changing in result to various boundary conditions.
Figure 5: Illustrative example of combining multiple constraints for climate sensitivity.

References

  1. 1

    Arrhenius, S. On the influence of carbonic acid in the air upon the temperature of the ground. Philos. Mag. Ser. 5 41, 237–276 (1896).

    Article  Google Scholar 

  2. 2

    Callendar, G. S. The artificial production of carbon dioxide and its influence on temperature. Q. J. R. Meteorol. Soc. 64, 223–240 (1938).

    Article  Google Scholar 

  3. 3

    Knutti, R. & Rugenstein, M. A. A. Feedbacks, climate sensitivity and the limits of linear models. Philos. Trans. R. Soc. A 373, 20150146 (2015).

    Article  Google Scholar 

  4. 4

    Richardson, M., Cowtan, K., Hawkins, E. & Stolpe, M. B. Reconciled climate response estimates from climate models and the energy budget of Earth. Nat. Clim. Change 6, 931–935 (2016).

    Article  Google Scholar 

  5. 5

    Hope, C. The $10 trillion value of better information about the transient climate response. Philos. Trans. R. Soc. A 373, 20140429 (2015).

    Article  Google Scholar 

  6. 6

    Knutti, R. & Hegerl, G. C. The equilibrium sensitivity of the Earth's temperature to radiation changes. Nat. Geosci. 1, 735–743 (2008).

    Article  Google Scholar 

  7. 7

    IPCC Climate Change 2013: The Physical Science Basis (eds Stocker, T. F. et al.) (Cambridge University Press, 2013).

  8. 8

    PALEOSENS Project Members. Making sense of palaeoclimate sensitivity. Nature 491, 683–691 (2012).

  9. 9

    Charney, J. et al. Carbon Dioxide and Climate: A Scientific Assessment (National Acadamies of Sciences Press, 1979).

    Google Scholar 

  10. 10

    Hegerl, G. & Zwiers, F. Use of models in detection and attribution of climate change. Wiley Interdiscip. Rev. Clim. Change 2, 570–591 (2011).

    Article  Google Scholar 

  11. 11

    Otto, A. et al. Energy budget constraints on climate response. Nat. Geosci. 6, 415–416 (2013).

    Article  Google Scholar 

  12. 12

    Huber, M., Beyerle, U. & Knutti, R. Estimating climate sensitivity and future temperature in the presence of natural climate variability. Geophys. Res. Lett. 41, 2086–2092 (2014).

    Article  Google Scholar 

  13. 13

    Olson, R. et al. What is the effect of unresolved internal climate variability on climate sensitivity estimates? J. Geophys. Res. Atmos. 118, 4348–4358 (2013).

    Article  Google Scholar 

  14. 14

    Stevens, B. Rethinking the lower bound on aerosol radiative forcing. J. Clim. 28, 4794–4819 (2015).

    Article  Google Scholar 

  15. 15

    Medhaug, I., Stolpe, M. B., Fischer, E. M. & Knutti, R. Reconciling controversies about the 'global warming hiatus'. Nature 545, 41–47 (2017).

    Article  Google Scholar 

  16. 16

    Johansson, D. J. A., O'Neill, B. C., Tebaldi, C. & Häggström, O. Equilibrium climate sensitivity in light of observations over the warming hiatus. Nat. Clim. Change 5, 449–453 (2015).

    Article  Google Scholar 

  17. 17

    Lewis, N. & Curry, J. A. The implications for climate sensitivity of AR5 forcing and heat uptake estimates. Clim. Dyn. 45, 1009–1023 (2015).

    Article  Google Scholar 

  18. 18

    Lewis, N. Objective inference for climate parameters: Bayesian, transformation-of-variables, and profile likelihood approaches. J. Clim. 27, 7270–7284 (2014).

    Article  Google Scholar 

  19. 19

    Annan, J. D. & Hargreaves, J. C. On the generation and interpretation of probabilistic estimates of climate sensitivity. Clim. Change 104, 423–436 (2011).

    Article  Google Scholar 

  20. 20

    Annan, J. D. Recent developments in Bayesian estimation of climate sensitivity. Curr. Clim. Change Rep. 1, 263–267 (2015).

    Article  Google Scholar 

  21. 21

    Skeie, R. B., Berntsen, T., Aldrin, M., Holden, M. & Myhre, G. A lower and more constrained estimate of climate sensitivity using updated observations and detailed radiative forcing time series. Earth Syst. Dyn. 5, 139–175 (2014).

    Article  Google Scholar 

  22. 22

    Karl, T. R. et al. Possible artifacts of data biases in the recent global surface warming hiatus. Science 348, 1469–1472 (2015).

    Article  Google Scholar 

  23. 23

    Tebaldi, C. & Knutti, R. The use of the multi-model ensemble in probabilistic climate projections. Philos. Trans. R. Soc. A 365, 2053–2075 (2007).

    Article  Google Scholar 

  24. 24

    Dessler, A. E. A determination of the cloud feedback from climate variations over the past decade. Science 330, 1523–1527 (2010).

    Article  Google Scholar 

  25. 25

    Mauritsen, T. & Stevens, B. Missing Iris effect as a possible cause of muted hydrological change and high climate sensitivity in models. Nat. Geosci. 8, 346–351 (2015).

    Article  Google Scholar 

  26. 26

    Zelinka, M. D., Zhou, C. & Klein, S. A. Insights from a refined decomposition of cloud feedbacks. Geophys. Res. Lett. 43, 9259–9269 (2016).

    Article  Google Scholar 

  27. 27

    Caldwell, P. M., Zelinka, M. D., Taylor, K. E. & Marvel, K. Quantifying the sources of intermodel spread in equilibrium climate sensitivity. J. Clim. 29, 513–524 (2016).

    Article  Google Scholar 

  28. 28

    Stevens, B. & Bony, S. Water in the atmosphere. Phys. Today 66, 29 (2013).

    Article  Google Scholar 

  29. 29

    Donohoe, A., Armour, K. C., Pendergrass, A. G. & Battisti, D. S. Shortwave and longwave radiative contributions to global warming under increasing CO2 . Proc. Natl. Acad. Sci. USA 111, 16700–16705 (2014).

    Article  Google Scholar 

  30. 30

    Harris, G. R., Sexton, D. M. H., Booth, B. B. B., Collins, M. & Murphy, J. M. Probabilistic projections of transient climate change. Clim. Dyn. 40, 2937–2972 (2013).

    Article  Google Scholar 

  31. 31

    Hawkins, E., Dong, B., Robson, J., Sutton, R. & Smith, D. The interpretation and use of biases in decadal climate predictions. J. Clim. 27, 2931–2947 (2014).

    Article  Google Scholar 

  32. 32

    Stevens, B., Sherwood, S. C., Bony, S. & Webb, M. J. Prospects for narrowing bounds on Earth's equilibrium climate sensitivity. Earth's Future 4, 512–522 (2016).

    Article  Google Scholar 

  33. 33

    Cess, R. D. et al. Interpretation of cloud-climate feedback as produced by 14 atmospheric general circulation models. Science 245, 513–516 (1989).

    Article  Google Scholar 

  34. 34

    Samset, B. H., Myhre, G. & Schulz, M. Upward adjustment needed for aerosol radiative forcing uncertainty. Nat. Clim. Change 4, 230–232 (2014).

    Article  Google Scholar 

  35. 35

    Carslaw, K. S. et al. Large contribution of natural aerosols to uncertainty in indirect forcing. Nature 503, 67–71 (2013).

    Article  Google Scholar 

  36. 36

    Gregory, J. M. A new method for diagnosing radiative forcing and climate sensitivity. Geophys. Res. Lett. 31, L03205 (2004).

    Google Scholar 

  37. 37

    Boer, G. J., Hamilton, K. & Zhu, W. Climate sensitivity and climate change under strong forcing. Clim. Dyn. 24, 685–700 (2005).

    Article  Google Scholar 

  38. 38

    Armour, K. C., Bitz, C. M. & Roe, G. H. Time-varying climate sensitivity from regional feedbacks. J. Clim. 26, 4518–4534 (2013).

    Article  Google Scholar 

  39. 39

    Rose, B. E. J., Armour, K. C., Battisti, D. S., Feldl, N. & Koll, D. D. B. The dependence of transient climate sensitivity and radiative feedbacks on the spatial pattern of ocean heat uptake. Geophys. Res. Lett. 41, 1071–1078 (2014).

    Article  Google Scholar 

  40. 40

    Feldl, N. & Roe, G. H. The nonlinear and nonlocal nature of climate feedbacks. J. Clim. 26, 8289–8304 (2013).

    Article  Google Scholar 

  41. 41

    Rugenstein, M. A. A., Caldeira, K. & Knutti, R. Dependence of global radiative feedbacks on evolving patterns of surface heat fluxes. Geophys. Res. Lett. 43, 9877–9885 (2016).

    Article  Google Scholar 

  42. 42

    Rose, B. E. J. & Rayborn, L. The effects of ocean heat uptake on transient climate sensitivity. Curr. Clim. Change Rep. 2, 190–201 (2016).

    Article  Google Scholar 

  43. 43

    Winton, M. et al. Has coarse ocean resolution biased simulations of transient climate sensitivity? Geophys. Res. Lett. 41, 8522–8529 (2014).

    Article  Google Scholar 

  44. 44

    Knutti, R. & Tomassini, L. Constraints on the transient climate response from observed global temperature and ocean heat uptake. Geophys. Res. Lett. 35, L09701 (2008).

    Google Scholar 

  45. 45

    Murphy, J. M. Transient response of the Hadley Centre coupled ocean–atmosphere model to increasing carbon dioxide. Part III: Analysis of global-mean response using simple models. J. Clim. 8, 496–514 (1995).

    Article  Google Scholar 

  46. 46

    Senior, C. A. & Mitchell, J. F. B. The time-dependence of climate sensitivity. Geophys. Res. Lett. 27, 2685–2688 (2000).

    Article  Google Scholar 

  47. 47

    Andrews, T., Gregory, J. M. & Webb, M. J. The dependence of radiative forcing and feedback on evolving patterns of surface temperature change in climate models. J. Clim. 28, 1630–1648 (2015).

    Article  Google Scholar 

  48. 48

    Gregory, J. M., Andrews, T. & Good, P. The inconstancy of the transient climate response parameter under increasing CO2 . Philos. Trans. R. Soc. A 373, 20140417 (2015).

    Article  Google Scholar 

  49. 49

    Winton, M., Takahashi, K. & Held, I. M. Importance of ocean heat uptake efficacy to transient climate change. J. Clim. 23, 2333–2344 (2010).

    Article  Google Scholar 

  50. 50

    Geoffroy, O. et al. Transient climate response in a two-layer energy-balance model. Part I: Analytical solution and parameter calibration using CMIP5 AOGCM experiments. J. Clim. 26, 1841–1857 (2013).

    Article  Google Scholar 

  51. 51

    Geoffroy, O. et al. Transient climate response in a two-layer energy-balance model. Part II: Representation of the efficacy of deep-ocean heat uptake and validation for CMIP5 AOGCMs. J. Clim. 26, 1859–1876 (2013).

    Article  Google Scholar 

  52. 52

    Yoshimori, M. et al. A review of progress towards understanding the transient global mean surface temperature response to radiative perturbation. Prog. Earth Planet. Sci. 3, 21 (2016).

    Article  Google Scholar 

  53. 53

    Bloch-Johnson, J., Pierrehumbert, R. T. & Abbot, D. S. Feedback temperature dependence determines the risk of high warming. Geophys. Res. Lett. 42, 4973–4980 (2015).

    Article  Google Scholar 

  54. 54

    Gregory, J. M. & Andrews, T. Variation in climate sensitivity and feedback parameters during the historical period. Geophys. Res. Lett. 43, 3911–3920 (2016).

    Article  Google Scholar 

  55. 55

    Boer, G. J. & Yu, B. Climate sensitivity and climate state. Clim. Dyn. 21, 167–176 (2003).

    Article  Google Scholar 

  56. 56

    Loeb, N. G., Su, W. & Kato, S. Understanding climate feedbacks and sensitivity using observations of Earth's energy budget. Curr. Clim. Change Rep. 2, 170–178 (2016).

    Article  Google Scholar 

  57. 57

    Long, D. J. & Collins, M. Quantifying global climate feedbacks, responses and forcing under abrupt and gradual CO2 forcing. Clim. Dyn. 41, 2471–2479 (2013).

    Article  Google Scholar 

  58. 58

    Williams, K. D., Ingram, W. J. & Gregory, J. M. Time variation of effective climate sensitivity in GCMs. J. Clim. 21, 5076–5090 (2008).

    Article  Google Scholar 

  59. 59

    Armour, K. C. Energy budget constraints on climate sensitivity in light of inconstant climate feedbacks. Nat. Clim. Change 7, 331–335 (2017).

    Article  Google Scholar 

  60. 60

    Proistosescu, C. & Huybers, P. J. Slow climate mode reconciles historical and model-based estimates of climate sensitivity. Sci. Adv. 3, e1602821 (2017).

    Article  Google Scholar 

  61. 61

    Meraner, K., Mauritsen, T. & Voigt, A. Robust increase in equilibrium climate sensitivity under global warming. Geophys. Res. Lett. 40, 5944–5948 (2013).

    Article  Google Scholar 

  62. 62

    Zhou, C., Zelinka, M. D. & Klein, S. A. Impact of decadal cloud variations on the Earth's energy budget. Nat. Geosci. 9, 871–874 (2016).

    Article  Google Scholar 

  63. 63

    Mauritsen, T. et al. Climate feedback efficiency and synergy. Clim. Dyn. 41, 2539–2554 (2013).

    Article  Google Scholar 

  64. 64

    Schaller, N., Sedlacek, J. & Knutti, R. The asymmetry of the climate system's response to solar forcing changes and its implications for geoengineering scenarios. J. Geophys. Res. Atmos. 119, 5171–5184 (2014).

    Article  Google Scholar 

  65. 65

    Shindell, D. T. Inhomogeneous forcing and transient climate sensitivity. Nat. Clim. Change 4, 274–277 (2014).

    Article  Google Scholar 

  66. 66

    Davin, E. L., de Noblet-Ducoudré, N. & Friedlingstein, P. Impact of land cover change on surface climate: Relevance of the radiative forcing concept. Geophys. Res. Lett. 34, L13702 (2007).

    Article  Google Scholar 

  67. 67

    Marvel, K. et al. Do responses to different anthropogenic forcings add linearly in climate models? Environ. Res. Lett. 10, 104010 (2015).

    Article  Google Scholar 

  68. 68

    Marvel, K., Schmidt, G. A., Miller, R. L. & Nazarenko, L. S. Implications for climate sensitivity from the response to individual forcings. Nat. Clim. Change 6, 386–389 (2015).

    Article  Google Scholar 

  69. 69

    Crook, J. A., Forster, P. M. & Stuber, N. Spatial patterns of modeled climate feedback and contributions to temperature response and polar amplification. J. Clim. 24, 3575–3592 (2011).

    Article  Google Scholar 

  70. 70

    Colman, R. & McAvaney, B. Climate feedbacks under a very broad range of forcing. Geophys. Res. Lett. 36, L01702 (2009).

    Article  Google Scholar 

  71. 71

    Huneeus, N. et al. Forcings and feedbacks in the GeoMIP ensemble for a reduction in solar irradiance and increase in CO2 . J. Geophys. Res. Atmos. 119, 5226–5239 (2014).

    Article  Google Scholar 

  72. 72

    Kummer, J. R. & Dessler, A. E. The impact of forcing efficacy on the equilibrium climate sensitivity. Geophys. Res. Lett. 41, 3565–3568 (2014).

    Article  Google Scholar 

  73. 73

    Stott, P. A., Jones, G. S. & Mitchell, J. F. B. Do models underestimate the solar contribution to recent climate change? J. Clim. 16, 4079–4093 (2003).

    Article  Google Scholar 

  74. 74

    Wang, W.-C., Dudek, M. P., Liang, X.-Z. & Kiehl, J. T. Inadequacy of effective CO2 as a proxy in simulating the greenhouse effect of other radiatively active gases. Nature 350, 573–577 (1991).

    Article  Google Scholar 

  75. 75

    Good, P. et al. Nonlinear regional warming with increasing CO2 concentrations. Nat. Clim. Change 5, 138–142 (2015).

    Article  Google Scholar 

  76. 76

    Gregory, J. M., Andrews, T., Good, P., Mauritsen, T. & Forster, P. M. Small global-mean cooling due to volcanic radiative forcing. Clim. Dyn. 47, 3979–3991 (2016).

    Article  Google Scholar 

  77. 77

    Andrews, T., Ringer, M. A., Doutriaux-Boucher, M., Webb, M. J. & Collins, W. J. Sensitivity of an Earth system climate model to idealized radiative forcing. Geophys. Res. Lett. 39, L10702 (2012).

    Google Scholar 

  78. 78

    Hansen, J. E., Sato, M. & Ruedy, R. Radiative forcing and climate response. J. Geophys. Res. 102, 6831–6864 (1997).

    Article  Google Scholar 

  79. 79

    Modak, A., Bala, G., Cao, L. & Caldeira, K. Why must a solar forcing be larger than a CO2 forcing to cause the same global mean surface temperature change? Environ. Res. Lett. 11, 44013 (2016).

    Article  Google Scholar 

  80. 80

    Rieger, V. S., Dietmüller, S. & Ponater, M. Can feedback analysis be used to uncover the physical origin of climate sensitivity and efficacy differences? Clim. Dyn. http://dx.doi.org/10.1007/s00382-016-3476-x (2016).

  81. 81

    Gettelman, A., Lin, L., Medeiros, B. & Olson, J. Climate feedback variance and the interaction of aerosol forcing and feedbacks. J. Clim. 29, 6659–6675 (2016).

    Article  Google Scholar 

  82. 82

    Andrews, T. & Forster, P. M. CO2 forcing induces semi-direct effects with consequences for climate feedback interpretations. Geophys. Res. Lett. 35, L04802 (2008).

    Article  Google Scholar 

  83. 83

    Gregory, J. & Webb, M. Tropospheric adjustment induces a cloud component in CO2 forcing. J. Clim. 21, 58–71 (2008).

    Article  Google Scholar 

  84. 84

    Rugenstein, M. A. A., Gregory, J. M., Schaller, N., Sedláček, J. & Knutti, R. Multiannual ocean–atmosphere adjustments to radiative forcing. J. Clim. 29, 5643–5659 (2016).

    Article  Google Scholar 

  85. 85

    Colman, R. A. & McAvaney, B. J. On tropospheric adjustment to forcing and climate feedbacks. Clim. Dyn. 36, 1649–1658 (2011).

    Article  Google Scholar 

  86. 86

    Sherwood, S. C. et al. Adjustments in the forcing-feedback framework for understanding climate change. Bull. Am. Meteorol. Soc. 96, 217–228 (2015).

    Article  Google Scholar 

  87. 87

    Hansen, J. et al. Efficacy of climate forcings. J. Geophys. Res. D 110, D18104 (2005).

    Article  Google Scholar 

  88. 88

    Stuber, N., Ponater, M. & Sausen, R. Why radiative forcing might fail as a predictor of climate change. Clim. Dyn. 24, 497–510 (2005).

    Article  Google Scholar 

  89. 89

    Andrews, T., Gregory, J. M., Forster, P. M. & Webb, M. J. Cloud adjustment and its role in CO2 radiative forcing and climate sensitivity: a review. Surv. Geophys. 33, 619–635 (2011).

    Article  Google Scholar 

  90. 90

    Kamae, Y., Watanabe, M., Ogura, T., Yoshimori, M. & Shiogama, H. Rapid adjustments of cloud and hydrological cycle to increasing CO2: a review. Curr. Clim. Change Rep. 1, 103–113 (2015).

    Article  Google Scholar 

  91. 91

    Forster, P. M. et al. Recommendations for diagnosing effective radiative forcing from climate models for CMIP6. J. Geophys. Res. Atmos. 121, 460–475 (2016).

    Article  Google Scholar 

  92. 92

    Paynter, D. & Frölicher, T. L. Sensitivity of radiative forcing, ocean heat uptake, and climate feedback to changes in anthropogenic greenhouse gases and aerosols. J. Geophys. Res. Atmos. 120, 9837–9854 (2015).

    Article  Google Scholar 

  93. 93

    Knutti, R., Krähenmann, S., Frame, D. J. & Allen, M. R. Comment on 'Heat capacity, time constant, and sensitivity of Earth's climate system' by S. E. Schwartz. J. Geophys. Res. 113, D15103 (2008).

    Article  Google Scholar 

  94. 94

    Annan, J. D. & Hargreaves, J. C. Using multiple observationally-based constraints to estimate climate sensitivity. Geophys. Res. Lett. 33, L06704 (2006).

    Article  Google Scholar 

  95. 95

    Hegerl, G. C., Crowley, T. J., Hyde, W. T. & Frame, D. J. Climate sensitivity constrained by temperature reconstructions over the past seven centuries. Nature 440, 1029–1032 (2006).

    Article  Google Scholar 

  96. 96

    Knutti, R. & Sedláček, J. Robustness and uncertainties in the new CMIP5 climate model projections. Nat. Clim. Change 3, 369–373 (2012).

    Article  Google Scholar 

  97. 97

    Urban, N. M., Holden, P. B., Edwards, N. R., Sriver, R. L. & Keller, K. Historical and future learning about climate sensitivity. Geophys. Res. Lett. 41, 2543–2552 (2014).

    Article  Google Scholar 

  98. 98

    Myhre, G., Boucher, O., Bréon, F.-M., Forster, P. & Shindell, D. Declining uncertainty in transient climate response as CO2 forcing dominates future climate change. Nat. Geosci. 8, 181–185 (2015).

    Article  Google Scholar 

  99. 99

    Fasullo, J. T., Sanderson, B. M. & Trenberth, K. E. Recent progress in constraining climate sensitivity with model ensembles. Curr. Clim. Change Rep. 1, 268–275 (2015).

    Article  Google Scholar 

  100. 100

    Li, F., Rosa, D., Collins, W. D. & Wehner, M. F. 'Super-parameterization': a better way to simulate regional extreme precipitation? J. Adv. Model. Earth Syst. 4, M04002 (2012).

    Article  Google Scholar 

  101. 101

    Schneider, T. et al. Climate goals and computing the future of clouds. Nat. Clim. Change 7, 3–5 (2017).

    Article  Google Scholar 

  102. 102

    Hargreaves, J. C. & Annan, J. D. Could the Pliocene constrain the equilibrium climate sensitivity? Clim. Past 12, 1591–1599 (2016).

    Article  Google Scholar 

  103. 103

    Weitzman, M. L. Fat-tailed uncertainty in the economics of catastrophic climate change. Rev. Environ. Econ. Policy 5, 275–292 (2011).

    Article  Google Scholar 

  104. 104

    Allen, M. R. & Frame, D. J. Call off the quest. Science 318, 582–583 (2007).

    Article  Google Scholar 

  105. 105

    van der Sluijs, J., van Eijndhoven, J., Shackley, S. & Wynne, B. Anchoring devices in science for policy: the case of consensus around climate sensitivity. Soc. Stud. Sci. 28, 291–323 (1998).

    Article  Google Scholar 

  106. 106

    Otto, A., Todd, B. J., Bowerman, N., Frame, D. J. & Allen, M. R. Climate system properties determining the social cost of carbon. Environ. Res. Lett. 8, 24032 (2013).

    Article  Google Scholar 

  107. 107

    Shiogama, H. et al. Predicting future uncertainty constraints on global warming projections. Sci. Rep. 6, 18903 (2016).

    Article  Google Scholar 

  108. 108

    Stott, P., Good, P., Jones, G., Gillett, N. & Hawkins, E. The upper end of climate model temperature projections is inconsistent with past warming. Environ. Res. Lett. 8, 14024 (2013).

    Article  Google Scholar 

  109. 109

    Gillett, N. P. Weighting climate model projections using observational constraints. Philos. Trans. R. Soc. A 373, 20140425 (2015).

    Article  Google Scholar 

  110. 110

    Sanderson, B. M., Knutti, R. & Caldwell, P. Addressing interdependency in a multimodel ensemble by interpolation of model properties. J. Clim. 28, 5150–5170 (2015).

    Article  Google Scholar 

  111. 111

    Rowlands, D. J. et al. Broad range of 2050 warming from an observationally constrained large climate model ensemble. Nat. Geosci. 5, 256–260 (2012).

    Article  Google Scholar 

  112. 112

    Knutti, R. et al. A Fig of uncertainties in global temperature projections over the twenty-first century. J. Clim. 21, 2651–2663 (2008).

    Article  Google Scholar 

  113. 113

    Rogelj, J., Meinshausen, M., Sedláček, J. & Knutti, R. Implications of potentially lower climate sensitivity on climate projections and policy. Environ. Res. Lett. 9, 31003 (2014).

    Article  Google Scholar 

  114. 114

    Knutti, R., Rogelj, J., Sedláček, J. & Fischer, E. M. A scientific critique of the two-degree climate change target. Nat. Geosci. 9, 13–18 (2016).

    Article  Google Scholar 

  115. 115

    Rogelj, J. et al. Differences between carbon budget estimates unravelled. Nat. Clim. Change 6, 245–252 (2016).

    Article  Google Scholar 

  116. 116

    Hawkins, E. et al. Estimating changes in global temperature since the pre-industrial period. Bull. Am. Meteorol. Soc. http://doi.org/10.1175/BAMS-D-16-0007.1 (2017).

  117. 117

    Schurer, A. P., Mann, M. E., Hawkins, E., Tett, S. F. B. & Hegerl, G. C. Importance of pre-industrial baseline for determining the likelihood of exceeding the Paris limits. Nat. Clim. Change 7, 563–567 (2017).

    Article  Google Scholar 

  118. 118

    Rogelj, J. et al. Disentangling the effects of CO2 and short-lived climate forcer mitigation. Proc. Natl Acad. Sci. USA 111, 2–7 (2014).

    Article  Google Scholar 

  119. 119

    Robiou du Pont, Y. et al. Equitable mitigation to achieve the Paris Agreement goals. Nat. Clim. Change 7, 38–43 (2016).

    Article  Google Scholar 

  120. 120

    Knutti, R. & Rogelj, J. The legacy of our CO2 emissions: a clash of scientific facts, politics and ethics. Clim. Change 133, 361–373 (2015).

    Article  Google Scholar 

  121. 121

    Raupach, M. R. et al. Sharing a quota on cumulative carbon emissions. Nat. Clim. Change 4, 873–879 (2014).

    Article  Google Scholar 

  122. 122

    Sanderson, B. M. & Knutti, R. Delays in US mitigation could rule out Paris targets. Nat. Clim. Change (2016).

  123. 123

    Rogelj, J. et al. Paris Agreement climate proposals need a boost to keep warming well below 2 °C. Nature 534, 631–639 (2016).

    Article  Google Scholar 

  124. 124

    Hulburt, E. O. The temperature of the lower atmosphere of the Earth. Phys. Rev. 38, 1876–1890 (1931).

    Article  Google Scholar 

  125. 125

    Plass, G. N. The carbon dioxide theory of climatic change. Tellus 8, 140–154 (1956).

    Article  Google Scholar 

  126. 126

    Möller, F. On the influence of changes in the CO2 concentration in air on the radiation balance of the Earth's surface and on the climate. J. Geophys. Res. 68, 3877–3886 (1963).

    Article  Google Scholar 

  127. 127

    North, G. R., Cahalan, R. F. & Coakley J. A. Jr Energy balance climate models. Rev. Geophys. 19, 91–121 (1981).

    Article  Google Scholar 

  128. 128

    Hansen, J. et al. Climate response times: dependence on climate sensitivity and ocean mixing. Science 229, 857 (1985).

    Article  Google Scholar 

  129. 129

    Budyko, M. I. The effect of solar radiation variations on the climate of the Earth. Tellus 21, 611–619 (1969).

    Article  Google Scholar 

  130. 130

    Wigley, T. M. L. & Schlesinger, M. Analytical solution for the effect of increasing CO2 on global mean temperature. Nature 315, 649–652 (1985).

    Article  Google Scholar 

  131. 131

    Sellers, W. D. A global climate model based on the energy balance of the Earth–atmosphere system. J. Appl. Meteorol. 8, 392–400 (1969).

    Article  Google Scholar 

  132. 132

    Wigley, T. M. L. & Raper, S. Natural variability of the climate system and detection of the greenhouse effect. Nature 344, 324–326 (1990).

    Article  Google Scholar 

  133. 133

    Manabe, S. & Wetherald, R. T. The effects of doubling the CO2 concentration on the climate of a general circulation model. J. Atmos. Sci. 32, 3–15 (1975).

    Article  Google Scholar 

  134. 134

    Manabe, S. & Stouffer, R. J. Sensitivity of a global climate model to an increase of CO2 concentration in the atmosphere. J. Geophys. Res. 85, 5529–5554 (1980).

    Article  Google Scholar 

  135. 135

    Wetherald, R. T. & Manabe, S. Cloud cover and climate sensitivity. J. Atmos. Sci. 37, 1485–1510 (1980).

    Article  Google Scholar 

  136. 136

    Hansen, J. E. et al. Climate sensitivity: analysis of feedback mechanisms. Clim. Process. Clim. Sensit. 5, 130–163 (1984).

    Article  Google Scholar 

  137. 137

    Manabe, S. & Wetherald, R. T. Thermal equilibrium of the atmosphere with a given distribution of relative humidity. J. Atmos. Sci. 24, 241–259 (1967).

    Article  Google Scholar 

  138. 138

    Ramanathan, V. Increased atmosheric CO2 — zonal and seasonal estimates of the effect on the radiation energy balance and surface temperature. J. Geophy. Res. 84, 4949–4958 (1979).

    Article  Google Scholar 

  139. 139

    Augustsson, T. & Ramanathan, V. A radiative-convective model study of the CO2 climate problem. J. Atmos. Sci. 34, 448–451 (1977).

    Article  Google Scholar 

  140. 140

    Lorius, C., Jouzel, J., Raynaud, D., Hansen, J. E. & Le Treut, H. The ice-core record: climate sensitivity and future greenhouse warming. Nature 347, 139–145 (1990).

    Article  Google Scholar 

  141. 141

    Hoffert, M. I. & Covey, C. Deriving global climate sensitivity from palaeoclimate reconstructions. Nature 360, 573–575 (1992).

    Article  Google Scholar 

  142. 142

    Covey, C., Sloan, L. C. & Hoffert, M. I. Paleoclimate data constraints on climate sensitivity: the paleocalibration method. Clim. Change 32, 165–184 (1996).

    Article  Google Scholar 

  143. 143

    Specht, E., Redemann, T. & Lorenz, N. Simplified mathematical model for calculating global warming through anthropogenic CO2 . Int. J. Therm. Sci. 102, 1–8 (2016).

    Article  Google Scholar 

  144. 144

    Harde, H. Advanced two-layer climate model for the assessment of global warming by CO2 . Open J. Atmos. Clim. Chang. 2014, 1–51 (2014).

    Article  Google Scholar 

  145. 145

    Idso, S. B. CO2-induced global warming: a skeptic's view of potential climate change. Clim. Res. 10, 69–82 (1998).

    Article  Google Scholar 

  146. 146

    Roe, G. H. & Armour, K. C. How sensitive is climate sensitivity? Geophys. Res. Lett. 38, L14708 (2011).

    Article  Google Scholar 

  147. 147

    Harde, H. Radiation transfer calculations and assessment of global warming by CO2 . Int. J. Atmos. Sci. 2017, 1–30 (2017).

    Google Scholar 

  148. 148

    Stouffer, R. J. Time scales of climate response. J. Clim. 17, 209–217 (2004).

    Article  Google Scholar 

  149. 149

    Held, I. M. et al. Probing the fast and slow components of global warming by returning abruptly to preindustrial forcing. J. Clim. 23, 2418–2427 (2010).

    Article  Google Scholar 

  150. 150

    Hansen, J., Sato, M., Kharecha, P. & von Schuckmann, K. Earth's energy imbalance and implications. Atmos. Chem. Phys. 11, 13421–13449 (2011).

    Article  Google Scholar 

  151. 151

    Rugenstein, M. A. A., Sedláček, J. & Knutti, R. Nonlinearities in patterns of long-term ocean warming. Geophys. Res. Lett. 43, 3380–3388 (2016).

    Article  Google Scholar 

  152. 152

    Caldeira, K. & Myhrvold, N. P. Projections of the pace of warming following an abrupt increase in atmospheric carbon dioxide concentration. Environ. Res. Lett. 8, 34039 (2013).

    Article  Google Scholar 

  153. 153

    Dickinson, R. E. & Schaudt, K. J. Analysis of timescales of response of a simple climate model. J. Clim. 11, 97–106 (1998).

    Article  Google Scholar 

  154. 154

    Harvey, L. D. D. & Schneider, S. H. Transient climate response to external forcing on 100–104 year time scales. Part 1: Experiments with globally averaged, coupled, atmosphere and ocean energy balance models. J. Geophys. Res. 90, 2191–2205 (1985).

    Article  Google Scholar 

  155. 155

    Jarvis, A. The magnitude–timescale relationship of surface temperature feedbacks in climate models. Earth Syst. Dyn. Discuss. 2, 467–491 (2011).

    Article  Google Scholar 

  156. 156

    Li, S. & Jarvis, A. Long run surface temperature dynamics of an A-OGCM: the HadCM3 4 × CO2 forcing experiment revisited. Clim. Dyn. 33, 817–825 (2009).

    Article  Google Scholar 

  157. 157

    Watts, R. G., Morantine, M. C. & Achutarao, K. Timescales in energy balance climate models. 1: The limiting case solutions. J. Geophys. Res. 99, 3631–3641 (1994).

    Article  Google Scholar 

  158. 158

    Morantine, M. C. & Watts, R. G. Time scales in energy balance climate models. 2: The intermediate time solutions. J. Geophys. Res. 99, 3643–3653 (1994).

    Article  Google Scholar 

  159. 159

    Olivié, D. J. L., Peters, G. P. & Saint-Martin, D. Atmosphere response time scales estimated from AOGCM experiments. J. Clim. 25, 7956–7972 (2012).

    Article  Google Scholar 

  160. 160

    Schneider, S. H. & Thompson, S. L. Atmospheric CO2 and climate: importance of the transient response. J. Geophys. Res. 86, 3135–3147 (1981).

    Article  Google Scholar 

  161. 161

    Padilla, L. E., Vallis, G. K. & Rowley, C. W. Probabilistic estimates of transient climate sensitivity subject to uncertainty in forcing and natural variability. J. Clim. 24, 5521–5537 (2011).

    Article  Google Scholar 

  162. 162

    Knutti, R. Probabilistic climate change projections for CO2 stabilization profiles. Geophys. Res. Lett. 32, L20707 (2005).

    Article  Google Scholar 

  163. 163

    Frame, D. J., Stone, D. A., Stott, P. A. & Allen, M. R. Alternatives to stabilization scenarios. Geophys. Res. Lett. 33, L14707 (2006).

    Article  Google Scholar 

  164. 164

    Gregory, J. M. & Forster, P. M. Transient climate response estimated from radiative forcing and observed temperature change. J. Geophys. Res. 113, D23105 (2008).

    Article  Google Scholar 

  165. 165

    Armour, K. C. & Roe, G. H. Climate commitment in an uncertain world. Geophys. Res. Lett. 38, L01707 (2011).

    Article  Google Scholar 

  166. 166

    Meehl, G. A., Washington, W. M. & Collins, W. D. How much more global warming and sea level rise? Science 307, 1769–1773 (2005).

    Article  Google Scholar 

  167. 167

    Hare, B. & Meinshausen, M. How much warming are we committed to and how much can be avoided? Clim. Change 75, 111–149 (2006).

    Article  Google Scholar 

  168. 168

    Harvey, L. D. D. Transient climatic response to an increase of greenhouse gases. Clim. Change 15, 15–30 (1989).

    Article  Google Scholar 

  169. 169

    Allen, M. R. et al. in Avoiding Dangerous Climate Change (ed. Schellnhuber, H. J.) 281–290 (Cambridge Univ. Press, 2005).

    Google Scholar 

  170. 170

    Plattner, G. K. et al. Long-term climate commitments projected with climate–carbon cycle models. J. Clim. 21, 2721–2751 (2008).

    Article  Google Scholar 

  171. 171

    Siegenthaler, U. & Oeschger, H. Transient temperature changes due to increasing CO2 using simple models. Ann. Glaciol. 5, 153–159 (1984).

    Article  Google Scholar 

  172. 172

    Bryan, K., Komro, F., Manabe, S. & Spelman, M. Transient climate response to increasing atmospheric carbon dioxide. Science 215, 56 (1982).

    Article  Google Scholar 

  173. 173

    Myhre, G., Highwood, E. J., Shine, K. P. & Stordal, F. New estimates of radiative forcing due to well mixed greenhouse gases. Geophys. Res. Lett. 25, 2715–2718 (1998).

    Article  Google Scholar 

  174. 174

    Chung, E.-S. & Soden, B. J. An assessment of direct radiative forcing, radiative adjustments, and radiative feedbacks in coupled ocean–atmosphere models. J. Clim. 28, 4152–4170 (2015).

    Article  Google Scholar 

  175. 175

    Roe, G. H. & Baker, M. B. Comment on 'Another look at climate sensitivity' by Zaliapin and Ghil (2010). Nonlinear Process. Geophys. 18, 125–127 (2011).

    Article  Google Scholar 

  176. 176

    Zaliapin, I. & Ghil, M. Another look at climate sensitivity. Nonlinear Process. Geophys. 17, 113–122 (2010).

    Article  Google Scholar 

  177. 177

    Roe, G. H. & Baker, M. B. Why is climate sensitivity so unpredictable? Science 318, 629–632 (2007).

    Article  Google Scholar 

  178. 178

    Hannart, A., Dufresne, J.-L. & Naveau, P. Why climate sensitivity may not be so unpredictable. Geophys. Res. Lett. 36, L16707 (2009).

    Article  Google Scholar 

  179. 179

    Baker, M. B. & Roe, G. H. The shape of things to come: why is climate change so predictable? J. Clim. 22, 4574–4589 (2009).

    Article  Google Scholar 

  180. 180

    Klein, S. A. & Hall, A. Emergent constraints for cloud feedbacks. Curr. Clim. Change Rep. 1, 276–287 (2015).

    Article  Google Scholar 

  181. 181

    Knutti, R., Stocker, T. F., Joos, F. & Plattner, G.-K. Constraints on radiative forcing and future climate change from observations and climate model ensembles. Nature 416, 719–723 (2002).

    Article  Google Scholar 

  182. 182

    Knutti, R., Stocker, T. F., Joos, F. & Plattner, G.-K. K. Probabilistic climate change projections using neural networks. Clim. Dyn. 21, 257–272 (2003).

    Article  Google Scholar 

  183. 183

    Forest, C. E., Stone, P. H., Sokolov, A. P., Allen, M. R. & Webster, M. D. Quantifying uncertainties in climate system properties with the use of recent climate observations. Science 295, 113–117 (2002).

    Article  Google Scholar 

  184. 184

    Andronova, N. G. & Schlesinger, M. E. Objective estimation of the probability density function for climate sensitivity. J. Geophys. Res. Atmos. 106, 22605–22611 (2001).

    Article  Google Scholar 

  185. 185

    Frame, D. J. Constraining climate forecasts: the role of prior assumptions. Geophys. Res. Lett. 32, L09702 (2005).

    Article  Google Scholar 

  186. 186

    Forster, P. M. D. F. & Gregory, J. M. The climate sensitivity and its components diagnosed from Earth radiation budget data. J. Clim. 19, 39–52 (2006).

    Article  Google Scholar 

  187. 187

    Forster, P. M. F. & Taylor, K. E. Climate forcings and climate sensitivities diagnosed from coupled climate model integrations. J. Clim. 19, 6181–6194 (2006).

    Article  Google Scholar 

  188. 188

    Gregory, J. M., Stouffer, R. J., Raper, S. C. B., Stott, P. A. & Rayner, N. A. An observationally based estimate of the climate sensitivity. J. Clim. 15, 3117–3121 (2002).

    Article  Google Scholar 

  189. 189

    Masters, T. Observational estimate of climate sensitivity from changes in the rate of ocean heat uptake and comparison to CMIP5 models. Clim. Dyn. 42, 2173–2181 (2014).

    Article  Google Scholar 

  190. 190

    Aldrin, M. et al. Bayesian estimation of climate sensitivity based on a simple climate model fitted to observations of hemispheric temperatures and global ocean heat content. Environmetrics 23, 253–271 (2012).

    Article  Google Scholar 

  191. 191

    Tomassini, L. et al. Robust Bayesian uncertainty analysis of climate system properties using Markov Chain Monte Carlo methods. J. Clim. 20, 1239 (2007).

    Article  Google Scholar 

  192. 192

    Meinshausen, M. et al. Greenhouse-gas emission targets for limiting global warming to 2 °C. Nature 458, 1158–1162 (2009).

    Article  Google Scholar 

  193. 193

    Lewis, N. An objective Bayesian improved approach for applying optimal fingerprint techniques to estimate climate sensitivity. J. Clim. 26, 7414–7429 (2013).

    Article  Google Scholar 

  194. 194

    Olson, R. et al. A climate sensitivity estimate using Bayesian fusion of instrumental observations and an Earth System model. J. Geophys. Res. Atmos. 117, D04103 (2012).

    Article  Google Scholar 

  195. 195

    J. Ring, M. & E. Schlesinger, M. Bayesian learning of climate sensitivity I: Synthetic observations. Atmos. Clim. Sci. 2, 464–473 (2012).

    Google Scholar 

  196. 196

    Sanso, B., Forest, C. E. & Zantedeschi, D. Inferring climate system properties using a computer model. Bayesian Anal. 3, 1–37 (2008).

    Article  Google Scholar 

  197. 197

    Forest, C. E., Stone, P. H. & Sokolov, A. P. Constraining climate model parameters from observed 20th century changes. Tellus A 60, 911–920 (2008).

    Article  Google Scholar 

  198. 198

    Forest, C. E., Stone, P. H. & Sokolov, A. P. Estimated PDFs of climate system properties including natural and anthropogenic forcings. Geophys. Res. Lett. 33, L01705 (2006).

    Article  Google Scholar 

  199. 199

    Sansó, B. & Forest, C. Statistical calibration of climate system properties. J. R. Stat. Soc. C 58, 485–503 (2009).

    Article  Google Scholar 

  200. 200

    Tomassini, L. et al. A smoothing algorithm for estimating stochastic, continuous time model parameters and its application to a simple climate model. J. R. Stat. Soc. C 58, 679–704 (2009).

    Article  Google Scholar 

  201. 201

    Libardoni, A. G. & Forest, C. E. Correction to “Sensitivity of distributions of climate system properties to the surface temperature data set”. Geophys. Res. Lett. 40, 2309–2311 (2013).

    Article  Google Scholar 

  202. 202

    Bengtsson, L. & Schwartz, S. E. Determination of a lower bound on Earth's climate sensitivity. Tellus B 65, 21533 (2013).

    Article  Google Scholar 

  203. 203

    Schwartz, S. E. Determination of Earth's transient and equilibrium climate sensitivities from observations over the twentieth century: strong dependence on assumed forcing. Surv. Geophys. 33, 745–777 (2012).

    Article  Google Scholar 

  204. 204

    Schwartz, S. E., Charlson, R. J., Kahn, R. & Rodhe, H. Earth's climate sensitivity: apparent inconsistencies in recent assessments. Earth's Future 2, 601–605 (2014).

    Article  Google Scholar 

  205. 205

    Storelvmo, T., Leirvik, T., Lohmann, U., Phillips, P. C. B. & Wild, M. Disentangling greenhouse warming and aerosol cooling to reveal Earth's climate sensitivity. Nat. Geosci. 9, 286–289 (2016).

    Article  Google Scholar 

  206. 206

    Tanaka, K., Raddatz, T., O'Neill, B. C. & Reick, C. H. Insufficient forcing uncertainty underestimates the risk of high climate sensitivity. Geophys. Res. Lett. 36, L16709 (2009).

    Article  Google Scholar 

  207. 207

    Tanaka, K. & Raddatz, T. Correlation between climate sensitivity and aerosol forcing and its implication for the 'climate trap'. Clim. Change 109, 815–825 (2011).

    Article  Google Scholar 

  208. 208

    Urban, N. M. & Keller, K. Complementary observational constraints on climate sensitivity. Geophys. Res. Lett. 36, L04708 (2009).

    Article  Google Scholar 

  209. 209

    Webster, M. et al. Uncertainty analysis of climate change and policy response. Clim. Change 61, 295–320 (2003).

    Article  Google Scholar 

  210. 210

    Harvey, L. D. D. & Kaufmann, R. K. Simultaneously constraining climate sensitivity and aerosol radiative forcing. J. Clim. 15, 2837–2861 (2002).

    Article  Google Scholar 

  211. 211

    Andreae, M. O., Jones, C. D. & Cox, P. M. Strong present-day aerosol cooling implies a hot future. Nature 435, 1187–1190 (2005).

    Article  Google Scholar 

  212. 212

    Loehle, C. Global temperature trends adjusted for unforced variability. Univers. J. Geosci. 3, 183–187 (2015).

    Article  Google Scholar 

  213. 213

    Lewis, N. & Grünwald, P. Objectively combining AR5 instrumental period and paleoclimate climate sensitivity evidence. Clim. Dyn. http://dx.doi.org/10.1007/s00382-017-3744-4 (2017).

  214. 214

    van Hateren, J. H. A fractal climate response function can simulate global average temperature trends of the modern era and the past millennium. Clim. Dyn. 40, 2651–2670 (2013).

    Article  Google Scholar 

  215. 215

    van der Werf, G. R. & Dolman, A. J. Impact of the Atlantic Multidecadal Oscillation (AMO) on deriving anthropogenic warming rates from the instrumental temperature record. Earth Syst. Dyn. 5, 375–382 (2014).

    Article  Google Scholar 

  216. 216

    Rypdal, M. & Rypdal, K. Long-memory effects in linear response models of Earth's temperature and implications for future global warming. J. Clim. 27, 5240–5258 (2014).

    Article  Google Scholar 

  217. 217

    Loutre, M. F. et al. Evaluating climate model performance with various parameter sets using observations over the recent past. Clim. Past 7, 511–526 (2011).

    Article  Google Scholar 

  218. 218

    Rowlands, D. J. et al. Broad range of 2050 warming from an observationally constrained large climate model ensemble. Nat. Geosci. 5, 256–260 (2012).

    Article  Google Scholar 

  219. 219

    Stott, P. A., Huntingford, C., Jones, C. D. & Kettleborough, J. A. Observed climate change constrains the likelihood of extreme future global warming. Tellus B 60B, 76–81 (2008).

    Article  Google Scholar 

  220. 220

    Stott, P. A. & Kettleborough, J. A. Origins and estimates of uncertainty in predictions of twenty-first century temperature rise. Nature 416, 723–726 (2002).

    Article  Google Scholar 

  221. 221

    Gillett, N. P., Arora, V. K., Flato, G. M., Scinocca, J. F. & von Salzen, K. Improved constraints on 21st-century warming derived using 160 years of temperature observations. Geophys. Res. Lett. 39, L01704 (2012).

    Article  Google Scholar 

  222. 222

    Stott, P. A. et al. Observational constraints on past attributable warming and predictions of future global warming. J. Clim. 19, 3055–3069 (2006).

    Article  Google Scholar 

  223. 223

    Gillett, N. P., Arora, V. K., Matthews, D. & Allen, M. R. Constraining the ratio of global warming to cumulative CO2 emissions using CMIP5 simulations. J. Clim. 26, 6844–6858 (2013).

    Article  Google Scholar 

  224. 224

    Lewis, N. Implications of recent multimodel attribution studies for climate sensitivity. Clim. Dyn. 46, 1387–1396 (2016).

    Article  Google Scholar 

  225. 225

    Forster, P. M. Inference of climate sensitivity from analysis of Earth's energy budget. Annu. Rev. Earth Planet. Sci. 44, 85–106 (2016).

    Article  Google Scholar 

  226. 226

    DelSole, T., Yan, X. & Tippett, M. K. Inferring aerosol cooling from hydrological sensitivity. J. Clim. 29, 6167–6178 (2016).

    Article  Google Scholar 

  227. 227

    Millar, R. J. et al. Model structure in observational constraints on transient climate response. Clim. Change 131, 199–211 (2015).

    Article  Google Scholar 

  228. 228

    Cowtan, K. et al. Robust comparison of climate models with observations using blended land air and ocean sea surface temperatures. Geophys. Res. Lett. 42, 6526–6534 (2015).

    Article  Google Scholar 

  229. 229

    Huber, M. & Knutti, R. Anthropogenic and natural warming inferred from changes in Earth's energy balance. Nat. Geosci. 5, 31–36 (2012).

    Article  Google Scholar 

  230. 230

    Lacis, A. A., Schmidt, G. A., Rind, D. & Ruedy, R. A. Atmospheric CO2: principal control knob governing Earth's temperature. Science 330, 356–359 (2010).

    Article  Google Scholar 

  231. 231

    Murphy, D. M. et al. An observationally based energy balance for the Earth since 1950. J. Geophys. Res. 114, D012105 (2009).

    Google Scholar 

  232. 232

    Allan, R. P. et al. Changes in global net radiative imbalance 1985–2012. Geophys. Res. Lett. 41, 5588–5597 (2014).

    Article  Google Scholar 

  233. 233

    Loeb, N. G. et al. Advances in understanding top-of-atmosphere radiation variability from satellite observations. Surv. Geophys. 33, 359–385 (2012).

    Article  Google Scholar 

  234. 234

    Stephens, G. L. et al. An update on Earth's energy balance in light of the latest global observations. Nat. Geosci. 5, 691–696 (2012).

    Article  Google Scholar 

  235. 235

    Loeb, N. G. et al. Observed changes in top-of-the-atmosphere radiation and upper-ocean heating consistent within uncertainty. Nat. Geosci. 5, 110–113 (2012).

    Article  Google Scholar 

  236. 236

    Kato, S. et al. Detection of atmospheric changes in spatially and temporally averaged infrared spectra observed from space. J. Clim. 24, 6392–6407 (2011).

    Article  Google Scholar 

  237. 237

    Church, J. A. et al. Revisiting the Earth's sea-level and energy budgets from 1961 to 2008. Geophys. Res. Lett. 38, L18601 (2011).

    Article  Google Scholar 

  238. 238

    Loeb, N. G. et al. Toward optimal closure of the Earth's top-of-atmosphere radiation budget. J. Clim. 22, 748–766 (2009).

    Article  Google Scholar 

  239. 239

    Smith, D. M. et al. Earth's energy imbalance since 1960 in observations and CMIP5 models. Geophys. Res. Lett. 42, 1205–1213 (2015).

    Article  Google Scholar 

  240. 240

    Trenberth, K. E. & Fasullo, J. T. Tracking Earth's energy: from El Niño to global warming. Surv. Geophys. 33, 413–426 (2011).

    Article  Google Scholar 

  241. 241

    Trenberth, K. E., Fasullo, J. T. & Balmaseda, M. A. Earth's energy imbalance. J. Clim. 27, 3129–3144 (2014).

    Article  Google Scholar 

  242. 242

    Norris, J. R. et al. Evidence for climate change in the satellite cloud record. Nature 536, 72–75 (2016).

    Article  Google Scholar 

  243. 243

    He, J., Winton, M., Vecchi, G., Jia, L. & Rugenstein, M. Transient climate sensitivity depends on base climate ocean circulation. J. Clim. 30, 1493–1504 (2017).

    Article  Google Scholar 

  244. 244

    Liang, M.-C., Lin, L.-C., Tung, K.-K., Yung, Y. L. & Sun, S. Transient climate response in coupled atmospheric–ocean general circulation models. J. Atmos. Sci. 70, 1291–1296 (2013).

    Article  Google Scholar 

  245. 245

    Trossman, D. S., Palter, J. B., Merlis, T. M., Huang, Y. & Xia, Y. Large-scale ocean circulation–cloud interactions reduce the pace of transient climate change. Geophys. Res. Lett. 43, 3935–3943 (2016).

    Article  Google Scholar 

  246. 246

    Allen, M. R., Forest, C. E., Stone, P. H. & Sokolov, A. P. Constraining uncertainties in climate models using climate change detection techniques. Geophys. Res. Lett. 27, 569–572 (2000).

    Article  Google Scholar 

  247. 247

    Stott, P. A., Kettleborough, J. A. & Allen, M. R. Uncertainty in continental-scale temperature predictions. Geophys. Res. Lett. 33, L02708 (2006).

    Article  Google Scholar 

  248. 248

    Rogelj, J., Meinshausen, M. & Knutti, R. Global warming under old and new scenarios using IPCC climate sensitivity range estimates. Nat. Clim. Change 2, 248–253 (2012).

    Article  Google Scholar 

  249. 249

    Sokolov, A. P. et al. Probabilistic forecast for twenty-first-century climate based on uncertainties in emissions (without policy) and climate parameters. J. Clim. 22, 5175–5204 (2009).

    Article  Google Scholar 

  250. 250

    Sokolov, A. P., Forest, C. E. & Stone, P. H. Sensitivity of climate change projections to uncertainties in the estimates of observed changes in deep-ocean heat content. Clim. Dyn. 34, 735–745 (2010).

    Article  Google Scholar 

  251. 251

    Jones, G. S., Stott, P. A. & Mitchell, J. F. B. Uncertainties in the attribution of greenhouse gas warming and implications for climate prediction. J. Geophys. Res. Atmos. 121, 6969–6992 (2016).

    Article  Google Scholar 

  252. 252

    Kaufmann, R. K. & Stern, D. I. Cointegration analysis of hemispheric temperature relations. J. Geophys. Res. 107, D000174 (2002).

    Google Scholar 

  253. 253

    Lovejoy, S. Scaling fluctuation analysis and statistical hypothesis testing of anthropogenic warming. Clim. Dyn. 42, 2339–2351 (2014).

    Article  Google Scholar 

  254. 254

    Lovejoy, S. & Schertzer, D. Stochastic and scaling climate sensitivities: solar, volcanic and orbital forcings. Geophys. Res. Lett. 39, L11702 (2012).

    Article  Google Scholar 

  255. 255

    Stern, D. I. An atmosphere–ocean time series model of global climate change. Comput. Stat. Data Anal. 51, 1330–1346 (2006).

    Article  Google Scholar 

  256. 256

    Bell, T. L. Climate sensitivity from fluctuation dissipation — some simple model tests. J. Atmos. Sci. 37, 1700–1707 (1980).

    Article  Google Scholar 

  257. 257

    Ragone, F., Lucarini, V. & Lunkeit, F. A new framework for climate sensitivity and prediction: a modelling perspective. Clim. Dyn. 46, 1459–1471 (2016).

    Article  Google Scholar 

  258. 258

    Cooper, F. C. & Haynes, P. H. Climate sensitivity via a nonparametric fluctuation–dissipation theorem. J. Atmos. Sci. 68, 937–953 (2011).

    Article  Google Scholar 

  259. 259

    Kirk-Davidoff, D. B. On the diagnosis of climate sensitivity using observations of fluctuations. Atmos. Chem. Phys. 9, 813–822 (2009).

    Article  Google Scholar 

  260. 260

    Majda, A. J., Gershgorin, B. & Yuan, Y. Low-frequency climate response and fluctuation–dissipation theorems: theory and practice. J. Atmos. Sci. 67, 1186–1201 (2010).

    Article  Google Scholar 

  261. 261

    Abramov, R. V. & Majda, A. J. A new algorithm for low-frequency climate response. J. Atmos. Sci. 66, 286–309 (2009).

    Article  Google Scholar 

  262. 262

    Leith, C. E. Climate response and fluctuation dissipation. J. Atmos. Sci. 32, 2022–2026 (1975).

    Article  Google Scholar 

  263. 263

    Thuburn, J. Climate sensitivities via a Fokker–Planck adjoint approach. Q. J. R. Meteorol. Soc. 131, 73–92 (2005).

    Article  Google Scholar 

  264. 264

    Lucarini, V., Ragone, F. & Lunkeit, F. Predicting climate change using response theory: global averages and spatial patterns. J. Stat. Phys. 166, 1036–1064 (2017).

    Article  Google Scholar 

  265. 265

    Zhou, C., Zelinka, M. D., Dessler, A. E. & Klein, S. A. The relationship between interannual and long-term cloud feedbacks. Geophys. Res. Lett. 42, 10463–10469 (2015).

    Article  Google Scholar 

  266. 266

    Dessler, A. E., Zhang, Z. & Yang, P. Water-vapor climate feedback inferred from climate fluctuations, 2003–2008. Geophys. Res. Lett. 35, L20704 (2008).

    Article  Google Scholar 

  267. 267

    Dessler, A. E. Observations of climate feedbacks over 2000–10 and comparisons to climate models. J. Clim. 26, 333–342 (2013).

    Article  Google Scholar 

  268. 268

    Tsushima, Y. & Manabe, S. Assessment of radiative feedback in climate models using satellite observations of annual flux variation. Proc. Natl. Acad. Sci. USA 110, 7568–7573 (2013).

    Article  Google Scholar 

  269. 269

    Xie, S.-P., Kosaka, Y. & Okumura, Y. M. Distinct energy budgets for anthropogenic and natural changes during global warming hiatus. Nat. Geosci. 9, 29–33 (2016).

    Article  Google Scholar 

  270. 270

    Brown, P. T., Li, W., Jiang, J. H. & Su, H. Unforced surface air temperature variability and its contrasting relationship with the anomalous TOA energy flux at local and global spatial scales. J. Clim. 29, 925–940 (2016).

    Article  Google Scholar 

  271. 271

    Lin, B. et al. Estimations of climate sensitivity based on top-of-atmosphere radiation imbalance. Atmos. Chem. Phys. 10, 1923–1930 (2010).

    Article  Google Scholar 

  272. 272

    Lin, B., Min, Q., Sun, W., Hu, Y. & Fan, T.-F. Can climate sensitivity be estimated from short-term relationships of top-of-atmosphere net radiation and surface temperature? J. Quant. Spectrosc. Radiat. Transf. 112, 177–181 (2011).

    Article  Google Scholar 

  273. 273

    Trenberth, K. E., Zhang, Y., Fasullo, J. T. & Taguchi, S. Climate variability and relationships between top-of-atmosphere radiation and temperatures on Earth. J. Geophys. Res. Atmos. 120, 3642–3659 (2015).

    Article  Google Scholar 

  274. 274

    Masters, T. On the determination of the global cloud feedback from satellite measurements. Earth Syst. Dyn. 3, 97–107 (2012).

    Article  Google Scholar 

  275. 275

    Trenberth, K. E., Fasullo, J. T. & Abraham, J. P. Issues in establishing climate sensitivity in recent studies. Remote Sens. 3, 2051–2056 (2011).

    Article  Google Scholar 

  276. 276

    Lyman, J. M. Estimating global energy flow from the global upper ocean. Surv. Geophys. 33, 387–393 (2011).

    Article  Google Scholar 

  277. 277

    Abraham, J. Issues related to the use of one-dimensional ocean-diffusion models for determining climate sensitivity. J. Earth Sci. Clim. Change 5, (2014).

  278. 278

    Murphy, D. M. & Forster, P. M. On the accuracy of deriving climate feedback parameters from correlations between surface temperature and outgoing radiation. J. Clim. 23, 4983–4988 (2010).

    Article  Google Scholar 

  279. 279

    Richardson, M., Hausfather, Z., Nuccitelli, D. A., Rice, K. & Abraham, J. P. Misdiagnosis of Earth climate sensitivity based on energy balance model results. Sci. Bull. 60, 1370–1377 (2015).

    Article  Google Scholar 

  280. 280

    Lindzen, R. S. & Choi, Y.-S. On the determination of climate feedbacks from ERBE data. Geophys. Res. Lett. 36, L16705 (2009).

    Article  Google Scholar 

  281. 281

    Lindzen, R. S. & Choi, Y.-S. On the observational determination of climate sensitivity and its implications. Asia-Pacific J. Atmos. Sci. 47, 377–390 (2011).

    Article  Google Scholar 

  282. 282

    Spencer, R. W. & Braswell, W. D. Potential biases in feedback diagnosis from observational data: a simple model demonstration. J. Clim. 21, 5624–5628 (2008).

    Article  Google Scholar 

  283. 283

    Spencer, R. W. & Braswell, W. D. On the diagnosis of radiative feedback in the presence of unknown radiative forcing. J. Geophys. Res. 115, D16109 (2010).

    Article  Google Scholar 

  284. 284

    Spencer, R. W. & Braswell, W. D. On the nisdiagnosis of surface temperature feedbacks from variations in Earth's radiant energy balance. Remote Sens. 3, 1603–1613 (2011).

    Article  Google Scholar 

  285. 285

    Choi, Y.-S. et al. Influence of non-feedback variations of radiation on the determination of climate feedback. Theor. Appl. Climatol. 115, 355–364 (2014).

    Article  Google Scholar 

  286. 286

    Koumoutsaris, S. What can we learn about climate feedbacks from short-term climate variations? Tellus A 65, 1–17 (2013).

    Article  Google Scholar 

  287. 287

    Bodman, R. W. & Jones, R. N. Bayesian estimation of climate sensitivity using observationally constrained simple climate models. Wiley Interdiscip. Rev. Clim. Change 7, 461–473 (2016).

    Article  Google Scholar 

  288. 288

    Chung, E.-S., Soden, B. J. & Sohn, B.-J. Revisiting the determination of climate sensitivity from relationships between surface temperature and radiative fluxes. Geophys. Res. Lett. 37, L10703 (2010).

    Google Scholar 

  289. 289

    Murphy, D. M. Constraining climate sensitivity with linear fits to outgoing radiation. Geophys. Res. Lett. 37, L09704 (2010).

    Article  Google Scholar 

  290. 290

    Monckton, C., Soon, W. W.-H., Legates, D. R. & Briggs, W. M. Why models run hot: results from an irreducibly simple climate model. Sci. Bull. 60, 122–135 (2015).

    Article  Google Scholar 

  291. 291

    Bates, J. R. Estimating climate sensitivity using two-zone energy balance models. Earth Space Sci. 3, 207–225 (2016).

    Article  Google Scholar 

  292. 292

    Bates, J. R. Climate stability and sensitivity in some simple conceptual models. Clim. Dyn. 38, 455–473 (2012).

    Article  Google Scholar 

  293. 293

    Schwartz, S. E. Reply to comments by G. Foster. et al., R. Knutti. et al., and N. Scafetta on 'Heat capacity, time constant, and sensitivity of Earth's climate system'. J. Geophys. Res. 113, D15105 (2008).

    Article  Google Scholar 

  294. 294

    Schwartz, S. E. Heat capacity, time constant, and sensitivity of Earth's climate system. J. Geophys. Res. 112, D24S05 (2007).

    Article  Google Scholar 

  295. 295

    Foster, G., Annan, J. D., Schmidt, G. A. & Mann, M. E. Comment on 'Heat capacity, time constant, and sensitivity of Earth's climate system' by S. E. Schwartz. J. Geophys. Res. 113, D15102 (2008).

    Article  Google Scholar 

  296. 296

    Schwartz, S. E. Uncertainty in climate sensitivity: causes, consequences, challenges. Energy Environ. Sci. 1, 430–453 (2008).

    Article  Google Scholar 

  297. 297

    Chylek, P. et al. Limits on climate sensitivity derived from recent satellite and surface observations. J. Geophys. Res. 112, D24S04 (2007).

    Article  Google Scholar 

  298. 298

    Trenberth, K. E., Fasullo, J. T., O'Dell, C. & Wong, T. Relationships between tropical sea surface temperature and top-of-atmosphere radiation. Geophys. Res. Lett. 37, L03702 (2010).

    Article  Google Scholar 

  299. 299

    Loehle, C. A minimal model for estimating climate sensitivity. Ecol. Modell. 276, 80–84 (2014).

    Article  Google Scholar 

  300. 300

    Cawley, G. C., Cowtan, K., Way, R. G., Jacobs, P. & Jokimäki, A. On a minimal model for estimating climate sensitivity. Ecol. Modell. 297, 20–25 (2015).

    Article  Google Scholar 

  301. 301

    Ollila, A. The potency of carbon dioxide (CO2) as a greenhouse gas. Dev. Earth Sci. 2, (2014).

  302. 302

    Soden, B. J. Global cooling after the eruption of Mount Pinatubo: a test of climate feedback by water vapor. Science 296, 727–730 (2002).

    Article  Google Scholar 

  303. 303

    Bender, F. A.-M., Ekman, A. M. L. & Rodhe, H. Response to the eruption of Mount Pinatubo in relation to climate sensitivity in the CMIP3 models. Clim. Dyn. 35, 875–886 (2010).

    Article  Google Scholar 

  304. 304

    Merlis, T. M., Held, I. M., Stenchikov, G. L., Zeng, F. & Horowitz, L. W. Constraining transient climate sensitivity using coupled climate model simulations of volcanic eruptions. J. Clim. 27, 7781–7795 (2014).

    Article  Google Scholar 

  305. 305

    Wigley, T. M. L. Effect of climate sensitivity on the response to volcanic forcing. J. Geophys. Res. 110, D09107 (2005).

    Article  Google Scholar 

  306. 306

    Boer, G. J., Stowasser, M. & Hamilton, K. Inferring climate sensitivity from volcanic events. Clim. Dyn. 28, 481–502 (2007).

    Article  Google Scholar 

  307. 307

    Yokohata, T. et al. Climate response to volcanic forcing: Validation of climate sensitivity of a coupled atmosphere–ocean general circulation model. Geophys. Res. Lett. 32, L21710 (2005).

    Article  Google Scholar 

  308. 308

    Santer, B. et al. Volcanic effects on climate. Nat. Clim. Change 6, 3–4 (2015).

    Article  Google Scholar 

  309. 309

    Ollila, A. Climate sensitivity parameter in the test of the Mount Pinatubo eruption. Phys. Sci. Int. J. 9, 1–14 (2016).

    Article  Google Scholar 

  310. 310

    Lehner, F., Schurer, A. P., Hegerl, G. C., Deser, C. & Frölicher, T. L. The importance of ENSO phase during volcanic eruptions for detection and attribution. Geophys. Res. Lett. 43, 2851–2858 (2016).

    Article  Google Scholar 

  311. 311

    Douglass, D. H., Knox, R. S., Pearson, B. D. & Clark, A. Thermocline flux exchange during the Pinatubo event. Geophys. Res. Lett. 33, L19711 (2006).

    Article  Google Scholar 

  312. 312

    Tung, K. K., Zhou, J. & Camp, C. D. Constraining model transient climate response using independent observations of solar-cycle forcing and response. Geophys. Res. Lett. 35, L17707 (2008).

    Article  Google Scholar 

  313. 313

    Raper, S. C. B., Gregory, J. M. & Stouffer, R. J. The role of climate sensitivity and ocean heat uptake on AOGCM transient temperature response. J. Clim. 15, 124–130 (2002).

    Article  Google Scholar 

  314. 314

    Räisänen, J. Probability distributions of CO2-induced global warming as inferred directly from multimodel ensemble simulations. Geophysica 41, 19–30 (2005).

    Google Scholar 

  315. 315

    Forster, P. M. et al. Evaluating adjusted forcing and model spread for historical and future scenarios in the CMIP5 generation of climate models. J. Geophys. Res. Atmos. 118, 1139–1150 (2013).

    Article  Google Scholar 

  316. 316

    Knutti, R. Why are climate models reproducing the observed global surface warming so well? Geophys. Res. Lett. 35, L18704 (2008).

    Article  Google Scholar 

  317. 317

    Kiehl, J. T. Twentieth century climate model response and climate sensitivity. Geophys. Res. Lett. 34, L22710 (2007).

    Article  Google Scholar 

  318. 318

    Bony, S. et al. How well do we understand and evaluate climate change feedback processes? J. Clim. 19, 3445–3482 (2006).

    Article  Google Scholar 

  319. 319

    Soden, B. J. & Held, I. M. An assessment of climate feedbacks in coupled ocean–atmosphere models. J. Clim. 19, 3354–3360 (2006).

    Article  Google Scholar 

  320. 320

    Huybers, P. Compensation between model feedbacks and curtailment of climate sensitivity. J. Clim. 23, 3009–3018 (2010).

    Article  Google Scholar 

  321. 321

    Whetton, P., Macadam, I., Bathols, J. & O'Grady, J. Assessment of the use of current climate patterns to evaluate regional enhanced greenhouse response patterns of climate models. Geophys. Res. Lett. 34, L14701 (2007).

    Article  Google Scholar 

  322. 322

    Scherrer, S. C. Present-day interannual variability of surface climate in CMIP3 models and its relation to future warming. Int. J. Climatol. 31, 1518–1529 (2011).

    Article  Google Scholar 

  323. 323

    Knutti, R., Furrer, R., Tebaldi, C., Cermak, J. & Meehl, G. A. Challenges in combining projections from multiple climate models. J. Clim. 23, 2739–2758 (2010).

    Article  Google Scholar 

  324. 324

    Masson, D. & Knutti, R. Predictor screening, calibration, and observational constraints in climate model ensembles: an illustration using climate sensitivity. J. Clim. 26, 887–898 (2013).

    Article  Google Scholar 

  325. 325

    Sanderson, B. M. On the estimation of systematic error in regression-based predictions of climate sensitivity. Clim. Change 118, 757–770 (2013).

    Article  Google Scholar 

  326. 326

    Knutti, R., Meehl, G. A., Allen, M. R. & Stainforth, D. A. Constraining climate sensitivity from the seasonal cycle in surface temperature. J. Clim. 19, 4224–4233 (2006).

    Article  Google Scholar 

  327. 327

    Reichler, T. & Kim, J. How well do coupled models simulate today's climate? Bull. Am. Meteorol. Soc. 89, 303 (2008).

    Article  Google Scholar 

  328. 328

    Knutti, R., Masson, D. & Gettelman, A. Climate model genealogy: generation CMIP5 and how we got there. Geophys. Res. Lett. 40, 1194–1199 (2013).

    Article  Google Scholar 

  329. 329

    Sanderson, B. M. & Knutti, R. On the interpretation of constrained climate model ensembles. Geophys. Res. Lett. 39, L16708 (2012).

    Article  Google Scholar 

  330. 330

    Hall, A. & Qu, X. Using the current seasonal cycle to constrain snow albedo feedback in future climate change. Geophys. Res. Lett. 33, L03502 (2006).

    Google Scholar 

  331. 331

    Boé, J., Hall, A. & Qu, X. September sea-ice cover in the Arctic Ocean projected to vanish by 2100. Nat. Geosci. 2, 341–343 (2009).

    Article  Google Scholar 

  332. 332

    Mahlstein, I. & Knutti, R. September Arctic sea ice predicted to disappear near 2 °C global warming above present. J. Geophys. Res. 117, D06104 (2012).

    Article  Google Scholar 

  333. 333

    Sanderson, B. M. et al. Constraints on model response to greenhouse gas forcing and the role of subgrid-scale processes. J. Clim. 21, 2384–2400 (2008).

    Article  Google Scholar 

  334. 334

    Sanderson, B. M., Piani, C., Ingram, W. J., Stone, D. A. & Allen, M. R. Towards constraining climate sensitivity by linear analysis of feedback patterns in thousands of perturbed-physics GCM simulations. Clim. Dyn. 30, 175–190 (2008).

    Article  Google Scholar 

  335. 335

    Piani, C., Frame, D. J., Stainforth, D. A. & Allen, M. R. Constraints on climate change from a multi-thousand member ensemble of simulations. Geophys. Res. Lett. 32, L23825 (2005).

    Article  Google Scholar 

  336. 336

    Stainforth, D. A. et al. Uncertainty in predictions of the climate response to rising levels of greenhouse gases. Nature 433, 403–406 (2005).

    Article  Google Scholar 

  337. 337

    Huber, M., Mahlstein, I., Wild, M., Fasullo, J. & Knutti, R. Constraints on climate sensitivity from radiation patterns in climate models. J. Clim. 24, 1034–1052 (2011).

    Article  Google Scholar 

  338. 338

    Klocke, D., Pincus, R. & Quaas, J. On constraining estimates of climate sensitivity with present-day observations through model weighting. J. Clim. 24, 6092–6099 (2011).

    Article  Google Scholar 

  339. 339

    Fasullo, J. T. & Trenberth, K. E. A less cloudy future: the role of subtropical subsidence in climate sensitivity. Science 338, 792–794 (2012).

    Article  Google Scholar 

  340. 340

    Shukla, J., DelSole, T., Fennessy, M., Kinter, J. & Paolino, D. Climate model fidelity and projections of climate change. Geophys. Res. Lett. 33, L07702 (2006).

    Article  Google Scholar 

  341. 341

    Tett, S. F. B., Rowlands, D. J., Mineter, M. J. & Cartis, C. Can top-of-atmosphere radiation measurements constrain climate predictions? Part II: Climate sensitivity. J. Clim. 26, 9367–9383 (2013).

    Article  Google Scholar 

  342. 342

    Tett, S. F. B., Mineter, M. J., Cartis, C., Rowlands, D. J. & Liu, P. Can top-of-atmosphere radiation measurements constrain climate predictions? Part I: Tuning. J. Clim. 26, 9348–9366 (2013).

    Article  Google Scholar 

  343. 343

    Sherwood, S. C., Bony, S. & Dufresne, J.-L. Spread in model climate sensitivity traced to atmospheric convective mixing. Nature 505, 37–42 (2014).

    Article  Google Scholar 

  344. 344

    Zhai, C., Jiang, J. H. & Su, H. Long-term cloud change imprinted in seasonal cloud variation: more evidence of high climate sensitivity. Geophys. Res. Lett. 42, 8729–8737 (2015).

    Article  Google Scholar 

  345. 345

    Tian, B. Spread of model climate sensitivity linked to double-Intertropical Convergence Zone bias. Geophys. Res. Lett. 42, 4133–4141 (2015).

    Article  Google Scholar 

  346. 346

    Tan, I., Storelvmo, T. & Zelinka, M. D. Observational constraints on mixed-phase clouds imply higher climate sensitivity. Science 352, 224–227 (2016).

    Article  Google Scholar 

  347. 347

    Brient, F. & Schneider, T. Constraints on climate sensitivity from space-based measurements of low-cloud reflection. J. Clim. 29, 5821–5835 (2016).

    Article  Google Scholar 

  348. 348

    Kamae, Y., Ogura, T., Shiogama, H. & Watanabe, M. Recent progress toward reducing the uncertainty in tropical low cloud feedback and climate sensitivity: a review. Geosci. Lett. 3, 1–10 (2016).

    Article  Google Scholar 

  349. 349

    Volodin, E. M. Relation between temperature sensitivity to doubled carbon dioxide and the distribution of clouds in current climate models. Izv. Atmos. Ocean. Phys. 44, 288–299 (2008).

    Article  Google Scholar 

  350. 350

    Trenberth, K. E. & Fasullo, J. T. Simulation of present-day and twenty-first-century energy budgets of the Southern Oceans. J. Clim. 23, 440–454 (2010).

    Article  Google Scholar 

  351. 351

    Su, H. et al. Weakening and strengthening structures in the Hadley Circulation change under global warming and implications for cloud response and climate sensitivity. J. Geophys. Res. Atmos. 119, 5787–5805 (2014).

    Article  Google Scholar 

  352. 352

    Levis, S., Bonan, G. B. & Lawrence, P. J. Present-day springtime high-latitude surface albedo as a predictor of simulated climate sensitivity. Geophys. Res. Lett. 34, L17703 (2007).

    Article  Google Scholar 

  353. 353

    Tsushima, Y., Abe-Ouchi, A. & Manabe, S. Radiative damping of annual variation in global mean surface temperature: comparison between observed and simulated feedback. Clim. Dyn. 24, 591–597 (2005).

    Article  Google Scholar 

  354. 354

    Wu, Q. Statistics of calendar month averages of surface temperature: a possible relationship to climate sensitivity. J. Geophys. Res. 108, D002218 (2003).

    Google Scholar 

  355. 355

    Sexton, D. M. H. & Murphy, J. M. Multivariate probabilistic projections using imperfect climate models. Part II: Robustness of methodological choices and consequences for climate sensitivity. Clim. Dyn. 38, 2543–2558 (2012).

    Article  Google Scholar 

  356. 356

    Siler, N., Po-Chedley, S. & Bretherton, C. S. Variability in modeled cloud feedback tied to differences in the climatological spatial pattern of clouds. Clim. Dyn. http://dx.doi.org/10.1007/s00382-017-3673-2 (2017).

  357. 357

    Gordon, N. D. & Klein, S. A. Low-cloud optical depth feedback in climate models. J. Geophys. Res. Atmos. 119, 6052–6065 (2014).

    Article  Google Scholar 

  358. 358

    Gettelman, A. & Sherwood, S. C. Processes responsible for cloud feedback. Curr. Clim. Change Rep. 2, 179–189 (2016).

    Article  Google Scholar 

  359. 359

    Bretherton, C. S. Insights into low-latitude cloud feedbacks from high-resolution models. Philos. Trans. R. Soc. A 373, 20140415 (2015).

    Article  Google Scholar 

  360. 360

    Clement, A. C., Burgman, R. & Norris, J. R. Observational and model evidence for positive low-level cloud feedback. Science 325, 460–464 (2009).

    Article  Google Scholar 

  361. 361

    Lemoine, D. M. Climate sensitivity distributions dependence on the possibility that models share biases. J. Clim. 23, 4395–4415 (2010).

    Article  Google Scholar 

  362. 362

    Hourdin, F. et al. The art and science of climate model tuning. Bull. Am. Meteorol. Soc. 98, 589–602 (2017).

    Article  Google Scholar 

  363. 363

    Schmidt, G. A. et al. Practice and philosophy of climate model tuning across six U. S. modeling centers. Geosci. Model Dev. Discuss. http://dx.doi.org/10.5194/gmd-2017-30 (2017).

  364. 364

    Grise, K. M., Polvani, L. M. & Fasullo, J. T. Reexamining the relationship between climate sensitivity and the Southern Hemisphere radiation budget in CMIP models. J. Clim. 28, 9298–9312 (2015).

    Article  Google Scholar 

  365. 365

    Caldwell, P. M. et al. Statistical significance of climate sensitivity predictors obtained by data mining. Geophys. Res. Lett. 41, 1803–1808 (2014).

    Article  Google Scholar 

  366. 366

    Sanderson, B. M. A multimodel study of parametric uncertainty in predictions of climate response to rising greenhouse gas concentrations. J. Clim. 24, 1362–1377 (2011).

    Article  Google Scholar 

  367. 367

    Sanderson, B. M., Shell, K. M. & Ingram, W. Climate feedbacks determined using radiative kernels in a multi-thousand member ensemble of AOGCMs. Clim. Dyn. 35, 1219–1236 (2009).

    Article  Google Scholar 

  368. 368

    Rodwell, M. J. & Palmer, T. Using numerical weather prediction to assess climate models. Q. J. R. Meteorol. Soc. 133, 129–146 (2007).

    Article  Google Scholar 

  369. 369

    Zhao, M. et al. Uncertainty in model climate sensitivity traced to representations of cumulus precipitation microphysics. J. Clim. 29, 543–560 (2016).

    Article  Google Scholar 

  370. 370

    Dufresne, J.-L. & Bony, S. An assessment of the primary sources of spread of global warming estimates from coupled atmosphere–ocean models. J. Clim. 21, 5135 (2008).

    Article  Google Scholar 

  371. 371

    Soden, B. J. et al. Quantifying climate feedbacks using radiative kernels. J. Clim. 21, 3504–3520 (2008).

    Article  Google Scholar 

  372. 372

    Medeiros, B. et al. Aquaplanets, climate sensitivity, and low clouds. J. Clim. 21, 4974–4991 (2008).

    Article  Google Scholar 

  373. 373

    Bony, S. et al. Thermodynamic control of anvil cloud amount. Proc. Natl. Acad. Sci USA 113, 8927–8932 (2016).

    Article  Google Scholar 

  374. 374

    Qu, X., Hall, A., Klein, S. A. & Caldwell, P. M. On the spread of changes in marine low cloud cover in climate model simulations of the 21st century. Clim. Dyn. 42, 2603–2626 (2014).

    Article  Google Scholar 

  375. 375

    Webb, M. J., Lambert, F. H. & Gregory, J. M. Origins of differences in climate sensitivity, forcing and feedback in climate models. Clim. Dyn. 40, 677–707 (2013).

    Article  Google Scholar 

  376. 376

    Tomassini, L., Voigt, A. & Stevens, B. On the connection between tropical circulation, convective mixing, and climate sensitivity. Q. J. R. Meteorol. Soc. 141, 1404–1416 (2015).

    Article  Google Scholar 

  377. 377

    Vial, J., Dufresne, J.-L. & Bony, S. On the interpretation of inter-model spread in CMIP5 climate sensitivity estimates. Clim. Dyn. 41, 3339–3362 (2013).

    Article  Google Scholar 

  378. 378

    Bony, S. Marine boundary layer clouds at the heart of tropical cloud feedback uncertainties in climate models. Geophys. Res. Lett. 32, L20806 (2005).

    Article  Google Scholar 

  379. 379

    Bony, S. et al. Clouds, circulation and climate sensitivity. Nat. Geosci. 8, 261–268 (2015).

    Article  Google Scholar 

  380. 380

    Parker, W. S. Understanding pluralism in climate modeling. Found. Sci. 11, 349–368 (2006).

    Article  Google Scholar 

  381. 381

    Pincus, R., Batstone, C. P., Hofmann, R. J. P., Taylor, K. E. & Glecker, P. J. Evaluating the present-day simulation of clouds, precipitation, and radiation in climate models. J. Geophys. Res. 113, D14209 (2008).

    Article  Google Scholar 

  382. 382

    Gleckler, P. J., Taylor, K. E. & Doutriaux, C. Performance metrics for climate models. J. Geophys. Res. 113, D06104 (2008).

    Article  Google Scholar 

  383. 383

    Knutti, R. et al. Good Practice Guidance Paper on Assessing and Combining Multi Model Climate Projections (IPCC, 2010).

    Google Scholar 

  384. 384

    Pierce, D. W., Barnett, T. P., Santer, B. D. & Gleckler, P. J. Selecting global climate models for regional climate change studies. Proc. Natl Acad. Sci. USA 106, 8441–8446 (2009).

    Article  Google Scholar 

  385. 385

    Eyring, V. et al. A strategy for process-oriented validation of coupled chemistry–climate models. Bull. Am. Meteorol. Soc. 86, 1117–1133 (2005).

    Article  Google Scholar 

  386. 386

    Wenzel, S., Eyring, V., Gerber, E. P. & Karpechko, A. Y. Constraining future summer austral jet stream positions in the CMIP5 Ensemble by process-oriented multiple diagnostic regression. J. Clim. 29, 673–687 (2016).

    Article  Google Scholar 

  387. 387

    Borodina, A., Fischer, E. M. & Knutti, R. Emergent constraints in climate projections: a case study of changes in high-latitude temperature variability. J. Clim. 30, 3655–3670 (2017).

    Article  Google Scholar 

  388. 388

    Sanderson, B. M., Knutti, R. & Caldwell, P. A representative democracy to reduce interdependency in a multimodel ensemble. J. Clim. 28, 5171–5194 (2015).

    Article  Google Scholar 

  389. 389

    Knutti, R. et al. A climate model projection weighting scheme accounting for performance and interdependence. Geophys. Res. Lett. 44, 1909–1918 (2017).

    Google Scholar 

  390. 390

    Sanderson, B. M., Wehner, M. & Knutti, R. Skill and independence weighting for multi-model assessments. Geosci. Model Dev. 10, 2379–2395 (2017).

    Article  Google Scholar 

  391. 391

    Masson, D. & Knutti, R. Climate model genealogy. Geophys. Res. Lett. 38, L08703 (2011).

    Article  Google Scholar 

  392. 392

    Jun, M., Knutti, R. & Nychka, D. W. Local eigenvalue analysis of CMIP3 climate model errors. Tellus A 60, 992–1000 (2008).

    Article  Google Scholar 

  393. 393

    Annan, J. D. & Hargreaves, J. C. Understanding the CMIP3 multimodel ensemble. J. Clim. 24, 4529–4538 (2011).

    Article  Google Scholar 

  394. 394

    Bishop, C. H. & Abramowitz, G. Climate model dependence and the replicate Earth paradigm. Clim. Dyn. 41, 885–900 (2012).

    Article  Google Scholar 

  395. 395

    Abramowitz, G. & Bishop, C. H. Climate model dependence and the ensemble dependence transformation of CMIP projections. J. Clim. 28, 2332–2348 (2015).

    Article  Google Scholar 

  396. 396

    Abramowitz, G. & Gupta, H. Toward a model space and model independence metric. Geophys. Res. Lett. 35, L032834 (2008).

    Article  Google Scholar 

  397. 397

    DelSole, T. & Shukla, J. Artificial skill due to predictor screening. J. Clim. 22, 331–345 (2009).

    Article  Google Scholar 

  398. 398

    Räisänen, J., Ruokolainen, L. & Ylhäisi, J. Weighting of model results for improving best estimates of climate change. Clim. Dyn. 35, 407–422 (2009).

    Article  Google Scholar 

  399. 399

    Weigel, A. P., Knutti, R., Liniger, M. A. & Appenzeller, C. Risks of model weighting in multimodel climate projections. J. Clim. 23, 4175–4191 (2010).

    Article  Google Scholar 

  400. 400

    Edwards, T. L., Crucifix, M. & Harrison, S. P. Using the past to constrain the future: how the palaeorecord can improve estimates of global warming. Prog. Phys. Geogr. 31, 481–500 (2007).

    Article  Google Scholar 

  401. 401

    Harrison, S. P. et al. Evaluation of CMIP5 palaeo-simulations to improve climate projections. Nat. Clim. Change 5, 735–743 (2015).

    Article  Google Scholar 

  402. 402

    Braconnot, P. et al. Evaluation of climate models using palaeoclimatic data. Nat. Clim. Change 2, 417–424 (2012).

    Article  Google Scholar 

  403. 403

    Schmidt, G. A. et al. Using palaeo-climate comparisons to constrain future projections in CMIP5. Clim. Past 10, 221–250 (2014).

    Article  Google Scholar 

  404. 404

    Dowsett, H. J. et al. Assessing confidence in Pliocene sea surface temperatures to evaluate predictive models. Nat. Clim. Change 2, 365–371 (2012).

    Article  Google Scholar 

  405. 405

    Lunt, D. J. et al. Warm climates of the past — a lesson for the future? Philos. Trans. R. Soc. A 371, 20130146 (2013).

    Article  Google Scholar 

  406. 406

    Schneider von Deimling, T., Held, H., Ganopolski, A. & Rahmstorf, S. Climate sensitivity estimated from ensemble simulations of glacial climate. Clim. Dyn. 27, 149–163 (2006).

    Article  Google Scholar 

  407. 407

    Hargreaves, J. C., Abe-Ouchi, A. & Annan, J. D. Linking glacial and future climates through an ensemble of GCM simulations. Clim. Past 3, 77–87 (2007).

    Article  Google Scholar 

  408. 408

    Hargreaves, J. C., Annan, J. D., Yoshimori, M. & Abe-Ouchi, A. Can the Last Glacial Maximum constrain climate sensitivity? Geophys. Res. Lett. 39, L24702 (2012).

    Article  Google Scholar 

  409. 409

    Hopcroft, P. O. & Valdes, P. J. How well do simulated last glacial maximum tropical temperatures constrain equilibrium climate sensitivity? Geophys. Res. Lett. 42, 5533–5539 (2015).

    Article  Google Scholar 

  410. 410

    Schmittner, A. et al. Climate sensitivity estimated from temperature reconstructions of the Last Glacial Maximum. Science 334, 1385–1388 (2011).

    Article  Google Scholar 

  411. 411

    Annan, J. D., Hargreaves, J. C., Ohgaito, R., Abe-Ouchi, A. & Emori, S. Efficiently constraining climate sensitivity with ensembles of paleoclimate simulations. SOLA 1, 181–184 (2005).

    Article  Google Scholar 

  412. 412

    Annan, J. D. & Hargreaves, J. C. A perspective on model-data surface temperature comparison at the Last Glacial Maximum. Quat. Sci. Rev. 107, 1–10 (2015).

    Article  Google Scholar 

  413. 413

    Köhler, P. et al. What caused Earth's temperature variations during the last 800,000 years? Data-based evidence on radiative forcing and constraints on climate sensitivity. Quat. Sci. Rev. 29, 129–145 (2010).

    Article  Google Scholar 

  414. 414

    Friedrich, T., Timmermann, A., Tigchelaar, M., Elison Timm, O. & Ganopolski, A. Nonlinear climate sensitivity and its implications for future greenhouse warming. Sci. Adv. 2, e1501923 (2016).

    Article  Google Scholar 

  415. 415

    Came, R. E. et al. Coupling of surface temperatures and atmospheric CO2 concentrations during the Palaeozoic era. Nature 449, 198–201 (2007).

    Article  Google Scholar 

  416. 416

    Crucifix, M. Does the Last Glacial Maximum constrain climate sensitivity? Geophys. Res. Lett. 33, L18701 (2006).

    Article  Google Scholar 

  417. 417

    Holden, P. B., Edwards, N. R., Oliver, K. I. C., Lenton, T. M. & Wilkinson, R. D. A probabilistic calibration of climate sensitivity and terrestrial carbon change in GENIE-1. Clim. Dyn. 35, 785–806 (2010).

    Article  Google Scholar 

  418. 418

    Lea, D. W. The 100 000-yr cycle in tropical SST, greenhouse gorcing, and climate sensitivity. J. Clim. 17, 2170–2179 (2004).

    Article  Google Scholar 

  419. 419

    Manabe, S. & Broccoli, A. A comparison of climate model sensitivity with data from the last glacial maximum. J. Atmos. Sci. 42, 2643–2651 (1985).

    Article  Google Scholar 

  420. 420

    Skinner, L. A long view on climate sensitivity. Science 337, 917–919 (2012).

    Article  Google Scholar 

  421. 421

    Chylek, P. & Lohmann, U. Aerosol radiative forcing and climate sensitivity deduced from the Last Glacial Maximum to Holocene transition. Geophys. Res. Lett. 35, L04804 (2008).

    Google Scholar 

  422. 422

    Hargreaves, J. C. & Annan, J. D. Comment on 'Aerosol radiative forcing and climate sensitivity deduced from the Last Glacial Maximum to Holocene transition' by P. Chylek and U. Lohmann. Clim. Past 5, 143–145 (2009).

    Article  Google Scholar 

  423. 423

    Ganopolski, A. & Schneider von Deimling, T. Comment on 'Aerosol radiative forcing and climate sensitivity deduced from the Last Glacial Maximum to Holocene transition' by Petr Chylek and Ulrike Lohmann. Geophys. Res. Lett. 35, L23703 (2008).

    Article  Google Scholar 

  424. 424

    Chylek, P. & Lohmann, U. Reply to comment by Andrey Ganopolski and Thomas Schneider von Deimling on 'Aerosol radiative forcing and climate sensitivity deduced from the Last Glacial Maximum to Holocene transition'. Geophys. Res. Lett. 35, L23704 (2008).

    Article  Google Scholar 

  425. 425

    Dunkley Jones, T. et al. A Palaeogene perspective on climate sensitivity and methane hydrate instability. Philos. Trans. R. Soc. A 368, 2395–2415 (2010).

    Article  Google Scholar 

  426. 426

    Rohling, E. J., Medina-Elizalde, M., Shepherd, J. G., Siddall, M. & Stanford, J. D. Sea surface and high-latitude temperature sensitivity to radiative forcing of climate over several glacial cycles. J. Clim. 25, 1635–1656 (2012).

    Article  Google Scholar 

  427. 427

    Shaffer, G., Huber, M., Rondanelli, R. & Pepke Pedersen, J. O. Deep time evidence for climate sensitivity increase with warming. Geophys. Res. Lett. 43, 6538–6545 (2016).

    Article  Google Scholar 

  428. 428

    Kutzbach, J. E., He, F., Vavrus, S. J. & Ruddiman, W. F. The dependence of equilibrium climate sensitivity on climate state: applications to studies of climates colder than present. Geophys. Res. Lett. 40, 3721–3726 (2013).

    Article  Google Scholar 

  429. 429

    Köhler, P., de Boer, B., von der Heydt, A. S., Stap, L. B. & van de Wal, R. S. W. On the state dependency of the equilibrium climate sensitivity during the last 5 million years. Clim. Past 11, 1801–1823 (2015).

    Article  Google Scholar 

  430. 430

    Royer, D. L., Pagani, M. & Beerling, D. J. Geobiological constraints on Earth system sensitivity to CO2 during the Cretaceous and Cenozoic. Geobiology 10, 298–310 (2012).

    Article  Google Scholar 

  431. 431

    Caballero, R. & Huber, M. State-dependent climate sensitivity in past warm climates and its implications for future climate projections. Proc. Natl Acad. Sci. USA 110, 14162–14167 (2013).

    Article  Google Scholar 

  432. 432

    Royer, D. L., Berner, R. A. & Park, J. Climate sensitivity constrained by CO2 concentrations over the past 420 million years. Nature 446, 530–532 (2007).

    Article  Google Scholar 

  433. 433

    Anagnostou, E. et al. Changing atmospheric CO2 concentration was the primary driver of early Cenozoic climate. Nature 533, 380–384 (2016).

    Article  Google Scholar 

  434. 434

    Martínez-Botí, M. a. et al. Plio–Pleistocene climate sensitivity evaluated using high-resolution CO2 records. Nature 518, 49–54 (2015).

    Article  Google Scholar 

  435. 435

    Goelzer, H. et al. Impact of Greenland and Antarctic ice sheet interactions on climate sensitivity. Clim. Dyn. 37, 1005–1018 (2011).

    Article  Google Scholar 

  436. 436

    Swingedouw, D. et al. Antarctic ice-sheet melting provides negative feedbacks on future climate warming. Geophys. Res. Lett. 35, L17705 (2008).

    Article  Google Scholar 

  437. 437

    Lunt, D. J. et al. Earth system sensitivity inferred from Pliocene modelling and data. Nat. Geosci. 3, 60–64 (2010).

    Article  Google Scholar 

  438. 438

    Pagani, M., Liu, Z., LaRiviere, J. & Ravelo, A. C. High Earth-system climate sensitivity determined from Pliocene carbon dioxide concentrations. Nat. Geosci. 3, 27–30 (2010).

    Article  Google Scholar 

  439. 439

    Hansen, J., Sato, M., Russell, G. & Kharecha, P. Climate sensitivity, sea level and atmospheric carbon dioxide. Philos. Trans. A 371, 20120294 (2013).

    Article  Google Scholar 

  440. 440

    Zeebe, R. E. Time-dependent climate sensitivity and the legacy of anthropogenic greenhouse gas emissions. Proc. Natl Acad. Sci. USA 110, 13739–13744 (2013).

    Article  Google Scholar 

  441. 441

    Kiehl, J. Lessons from Earth' s past. Science 331, 158–159 (2011).

    Article  Google Scholar 

  442. 442

    Previdi, M. et al. Climate sensitivity in the Anthropocene. Q. J. R. Meteorol. Soc. 139, 1121–1131 (2013).

    Article  Google Scholar 

  443. 443

    Dyez, K. A. & Ravelo, A. C. Late Pleistocene tropical Pacific temperature sensitivity to radiative greenhouse gas forcing. Geology 41, 23–26 (2013).

    Article  Google Scholar 

  444. 444

    Hansen, J. et al. Target atmospheric CO2: where should humanity aim? Open Atmos. Sci. J. 2, 217–231 (2008).

    Article  Google Scholar 

  445. 445

    Park, J. & Royer, D. L. Geologic constraints on the glacial amplification of Phanerozoic climate sensitivity. Am. J. Sci. 311, 1–26 (2011).

    Article  Google Scholar 

  446. 446

    von der Heydt, A. S. et al. Lessons on climate sensitivity from past climate changes. Curr. Clim. Chang. Rep. 2, 148–158 (2016).

    Article  Google Scholar 

  447. 447

    Morgan, M. G. & Keith, D. W. Subjective judgements by climate experts. Environ. Sci. Technol. 29, 468–476 (1995).

    Google Scholar 

  448. 448

    Zickfeld, K., Morgan, M. G., Frame, D. J. & Keith, D. W. Expert judgments about transient climate response to alternative future trajectories of radiative forcing. Proc. Natl Acad. Sci. USA 107, 12451–12456 (2010).

    Article  Google Scholar 

  449. 449

    Millner, A., Calel, R., Stainforth, D. A. & MacKerron, G. Do probabilistic expert elicitations capture scientists' uncertainty about climate change? Clim. Change 116, 427–436 (2013).

    Article  Google Scholar 

  450. 450

    Oppenheimer, M., Little, C. M. & Cooke, R. M. Expert judgement and uncertainty quantification for climate change. Nat. Clim. Change 6, 445–451 (2016).

    Article  Google Scholar 

  451. 451

    Raupach, M. R. The exponential eigenmodes of the carbon-climate system, and their implications for ratios of responses to forcings. Earth Syst. Dyn. 4, 31–49 (2013).

    Article  Google Scholar 

  452. 452

    Raupach, M. R. et al. The relationship between peak warming and cumulative CO2 emissions, and its use to quantify vulnerabilities in the carbon–climate–human system. Tellus B 63, 145–164 (2011).

    Article  Google Scholar 

  453. 453

    Friedlingstein, P. et al. Persistent growth of CO2 emissions and implications for reaching climate targets. Nat. Geosci. 7, 709–715 (2014).

    Article  Google Scholar 

  454. 454

    MacDougall, A. H. The transient response to cumulative CO2 emissions: a review. Curr. Clim. Change Rep. 2, 39–47 (2016).

    Article  Google Scholar 

  455. 455

    Zickfeld, K., MacDougall, A. H. & Matthews, H. D. On the proportionality between global temperature change and cumulative CO2 emissions during periods of net negative CO2 emissions. Environ. Res. Lett. 11, 55006 (2016).

    Article  Google Scholar 

  456. 456

    Matthews, H. D., Gillett, N. P., Stott, P. A. & Zickfeld, K. The proportionality of global warming to cumulative carbon emissions. Nature 459, 829–832 (2009).

    Article  Google Scholar 

  457. 457

    Zickfeld, K., Eby, M., Matthews, H. D. & Weaver, A. J. Setting cumulative emissions targets to reduce the risk of dangerous climate change. Proc. Natl Acad. Sci. USA 106, 16129–16134 (2009).

    Article  Google Scholar 

  458. 458

    Allen, M. R. et al. Warming caused by cumulative carbon emissions towards the trillionth tonne. Nature 458, 1163–1166 (2009).

    Article  Google Scholar 

  459. 459

    Gregory, J. M., Jones, C. D., Cadule, P. & Friedlingstein, P. Quantifying carbon cycle feedbacks. J. Clim. 22, 5232–5250 (2009).

    Article  Google Scholar 

  460. 460

    Steinacher, M., Joos, F. & Stocker, T. F. Allowable carbon emissions lowered by multiple climate targets. Nature 499, 197–201 (2013).

    Article  Google Scholar 

  461. 461

    Steinacher, M. & Joos, F. Transient Earth system responses to cumulative carbon dioxide emissions: linearities, uncertainties, and probabilities in an observation-constrained model ensemble. Biogeosciences 13, 1071–1103 (2016).

    Article  Google Scholar 

  462. 462

    Tokarska, K. B., Gillett, N. P., Weaver, A. J., Arora, V. K. & Eby, M. The climate response to five trillion tonnes of carbon. Nat. Clim. Change 6, 851–855 (2016).

    Article  Google Scholar 

  463. 463

    Williams, R. G., Goodwin, P., Roussenov, V. M. & Bopp, L. A framework to understand the transient climate response to emissions. Environ. Res. Lett. 11, 15003 (2016).

    Article  Google Scholar 

  464. 464

    Frölicher, T. L., Winton, M. & Sarmiento, J. L. Continued global warming after CO2 emissions stoppage. Nat. Clim. Change 4, 40–44 (2013).

    Article  Google Scholar 

  465. 465

    Gillett, N. P., Arora, V. K., Zickfeld, K., Marshall, S. J. & Merryfield, W. J. Ongoing climate change following a complete cessation of carbon dioxide emissions. Nat. Geosci. 4, 83–87 (2011).

    Article  Google Scholar 

  466. 466

    Solomon, S., Plattner, G.-K., Knutti, R. & Friedlingstein, P. Irreversible climate change due to carbon dioxide emissions. Proc. Natl Acad. Sci. USA 106, 1704–1709 (2009).

    Article  Google Scholar 

  467. 467

    Solomon, S. et al. Persistence of climate changes due to a range of greenhouse gases. Proc. Natl Acad. Sci. USA 107, 18354–18359 (2010).

    Article  Google Scholar 

  468. 468

    Ehlert, D. & Zickfeld, K. What determines the warming commitment after cessation of CO2 emissions? Environ. Res. Lett. 12, 15002 (2017).

    Article  Google Scholar 

  469. 469

    Zickfeld, K., Arora, V. K. & Gillett, N. P. Is the climate response to CO2 emissions path dependent? Geophys. Res. Lett. 39, L05703 (2012).

    Article  Google Scholar 

Download references

Acknowledgements

R.K. acknowledges support by the European Union's Horizon 2020 research and innovation program under grant agreement 641816 (CRESCENDO), and by NCAR and the Regional and Global Climate Modeling Program (RGCM) of the US Department of Energy, Office of Science (BER), Cooperative Agreement DE-FC02-97ER62402. The National Center for Atmospheric Research is sponsored by the National Science Foundation. G.C.H. was supported by the ERC funded project TITAN (EC-320691), by the Wolfson Foundation and the Royal Society as a Royal Society Wolfson Research Merit Award (WM130060) holder, and by the NERC-funded SMURPHS project. We acknowledge the World Climate Research Programme's Working Group on Coupled Modelling, which is responsible for CMIP, and we thank the climate modelling groups for producing and making available their model output. For CMIP the US Department of Energy's Program for Climate Model Diagnosis and Intercomparison provides coordinating support and led development of software infrastructure in partnership with the Global Organization for Earth System Science Portals.

Author information

Affiliations

Authors

Contributions

All authors wrote the Review. M.A.A.R. produced Figs 1, 2, 3, 4. R.K. produced Fig. 5.

Corresponding author

Correspondence to Reto Knutti.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

Supplementary Figure (PDF 313 kb)

Supplementary Information

Supplementary Table (XLSX 53 kb)

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Knutti, R., Rugenstein, M. & Hegerl, G. Beyond equilibrium climate sensitivity. Nature Geosci 10, 727–736 (2017). https://doi.org/10.1038/ngeo3017

Download citation

Further reading

Search

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing