Review

Beyond equilibrium climate sensitivity

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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.

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References

  1. 1.

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

  2. 2.

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

  3. 3.

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

  4. 4.

    , , & Reconciled climate response estimates from climate models and the energy budget of Earth. Nat. Clim. Change 6, 931–935 (2016).

  5. 5.

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

  6. 6.

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

  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.

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

  10. 10.

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

  11. 11.

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

  12. 12.

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

  13. 13.

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

  14. 14.

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

  15. 15.

    , , & Reconciling controversies about the 'global warming hiatus'. Nature 545, 41–47 (2017).

  16. 16.

    , , & Equilibrium climate sensitivity in light of observations over the warming hiatus. Nat. Clim. Change 5, 449–453 (2015).

  17. 17.

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

  18. 18.

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

  19. 19.

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

  20. 20.

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

  21. 21.

    , , , & 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).

  22. 22.

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

  23. 23.

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

  24. 24.

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

  25. 25.

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

  26. 26.

    , & Insights from a refined decomposition of cloud feedbacks. Geophys. Res. Lett. 43, 9259–9269 (2016).

  27. 27.

    , , & Quantifying the sources of intermodel spread in equilibrium climate sensitivity. J. Clim. 29, 513–524 (2016).

  28. 28.

    & Water in the atmosphere. Phys. Today 66, 29 (2013).

  29. 29.

    , , & Shortwave and longwave radiative contributions to global warming under increasing CO2. Proc. Natl. Acad. Sci. USA 111, 16700–16705 (2014).

  30. 30.

    , , , & Probabilistic projections of transient climate change. Clim. Dyn. 40, 2937–2972 (2013).

  31. 31.

    , , , & The interpretation and use of biases in decadal climate predictions. J. Clim. 27, 2931–2947 (2014).

  32. 32.

    , , & Prospects for narrowing bounds on Earth's equilibrium climate sensitivity. Earth's Future 4, 512–522 (2016).

  33. 33.

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

  34. 34.

    , & Upward adjustment needed for aerosol radiative forcing uncertainty. Nat. Clim. Change 4, 230–232 (2014).

  35. 35.

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

  36. 36.

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

  37. 37.

    , & Climate sensitivity and climate change under strong forcing. Clim. Dyn. 24, 685–700 (2005).

  38. 38.

    , & Time-varying climate sensitivity from regional feedbacks. J. Clim. 26, 4518–4534 (2013).

  39. 39.

    , , , & The dependence of transient climate sensitivity and radiative feedbacks on the spatial pattern of ocean heat uptake. Geophys. Res. Lett. 41, 1071–1078 (2014).

  40. 40.

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

  41. 41.

    , & Dependence of global radiative feedbacks on evolving patterns of surface heat fluxes. Geophys. Res. Lett. 43, 9877–9885 (2016).

  42. 42.

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

  43. 43.

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

  44. 44.

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

  45. 45.

    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).

  46. 46.

    & The time-dependence of climate sensitivity. Geophys. Res. Lett. 27, 2685–2688 (2000).

  47. 47.

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

  48. 48.

    , & The inconstancy of the transient climate response parameter under increasing CO2. Philos. Trans. R. Soc. A 373, 20140417 (2015).

  49. 49.

    , & Importance of ocean heat uptake efficacy to transient climate change. J. Clim. 23, 2333–2344 (2010).

  50. 50.

    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).

  51. 51.

    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).

  52. 52.

    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).

  53. 53.

    , & Feedback temperature dependence determines the risk of high warming. Geophys. Res. Lett. 42, 4973–4980 (2015).

  54. 54.

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

  55. 55.

    & Climate sensitivity and climate state. Clim. Dyn. 21, 167–176 (2003).

  56. 56.

    , & Understanding climate feedbacks and sensitivity using observations of Earth's energy budget. Curr. Clim. Change Rep. 2, 170–178 (2016).

  57. 57.

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

  58. 58.

    , & Time variation of effective climate sensitivity in GCMs. J. Clim. 21, 5076–5090 (2008).

  59. 59.

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

  60. 60.

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

  61. 61.

    , & Robust increase in equilibrium climate sensitivity under global warming. Geophys. Res. Lett. 40, 5944–5948 (2013).

  62. 62.

    , & Impact of decadal cloud variations on the Earth's energy budget. Nat. Geosci. 9, 871–874 (2016).

  63. 63.

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

  64. 64.

    , & 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).

  65. 65.

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

  66. 66.

    , & Impact of land cover change on surface climate: Relevance of the radiative forcing concept. Geophys. Res. Lett. 34, L13702 (2007).

  67. 67.

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

  68. 68.

    , , & Implications for climate sensitivity from the response to individual forcings. Nat. Clim. Change 6, 386–389 (2015).

  69. 69.

    , & Spatial patterns of modeled climate feedback and contributions to temperature response and polar amplification. J. Clim. 24, 3575–3592 (2011).

  70. 70.

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

  71. 71.

    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).

  72. 72.

    & The impact of forcing efficacy on the equilibrium climate sensitivity. Geophys. Res. Lett. 41, 3565–3568 (2014).

  73. 73.

    , & Do models underestimate the solar contribution to recent climate change? J. Clim. 16, 4079–4093 (2003).

  74. 74.

    , , & Inadequacy of effective CO2 as a proxy in simulating the greenhouse effect of other radiatively active gases. Nature 350, 573–577 (1991).

  75. 75.

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

  76. 76.

    , , , & Small global-mean cooling due to volcanic radiative forcing. Clim. Dyn. 47, 3979–3991 (2016).

  77. 77.

    , , , & Sensitivity of an Earth system climate model to idealized radiative forcing. Geophys. Res. Lett. 39, L10702 (2012).

  78. 78.

    , & Radiative forcing and climate response. J. Geophys. Res. 102, 6831–6864 (1997).

  79. 79.

    , , & 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).

  80. 80.

    , & Can feedback analysis be used to uncover the physical origin of climate sensitivity and efficacy differences? Clim. Dyn. (2016).

  81. 81.

    , , & Climate feedback variance and the interaction of aerosol forcing and feedbacks. J. Clim. 29, 6659–6675 (2016).

  82. 82.

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

  83. 83.

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

  84. 84.

    , , , & Multiannual ocean–atmosphere adjustments to radiative forcing. J. Clim. 29, 5643–5659 (2016).

  85. 85.

    & On tropospheric adjustment to forcing and climate feedbacks. Clim. Dyn. 36, 1649–1658 (2011).

  86. 86.

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

  87. 87.

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

  88. 88.

    , & Why radiative forcing might fail as a predictor of climate change. Clim. Dyn. 24, 497–510 (2005).

  89. 89.

    , , & Cloud adjustment and its role in CO2 radiative forcing and climate sensitivity: a review. Surv. Geophys. 33, 619–635 (2011).

  90. 90.

    , , , & Rapid adjustments of cloud and hydrological cycle to increasing CO2: a review. Curr. Clim. Change Rep. 1, 103–113 (2015).

  91. 91.

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

  92. 92.

    & 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).

  93. 93.

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

  94. 94.

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

  95. 95.

    , , & Climate sensitivity constrained by temperature reconstructions over the past seven centuries. Nature 440, 1029–1032 (2006).

  96. 96.

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

  97. 97.

    , , , & Historical and future learning about climate sensitivity. Geophys. Res. Lett. 41, 2543–2552 (2014).

  98. 98.

    , , , & Declining uncertainty in transient climate response as CO2 forcing dominates future climate change. Nat. Geosci. 8, 181–185 (2015).

  99. 99.

    , & Recent progress in constraining climate sensitivity with model ensembles. Curr. Clim. Change Rep. 1, 268–275 (2015).

  100. 100.

    , , & 'Super-parameterization': a better way to simulate regional extreme precipitation? J. Adv. Model. Earth Syst. 4, M04002 (2012).

  101. 101.

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

  102. 102.

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

  103. 103.

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

  104. 104.

    & Call off the quest. Science 318, 582–583 (2007).

  105. 105.

    , , & Anchoring devices in science for policy: the case of consensus around climate sensitivity. Soc. Stud. Sci. 28, 291–323 (1998).

  106. 106.

    , , , & Climate system properties determining the social cost of carbon. Environ. Res. Lett. 8, 24032 (2013).

  107. 107.

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

  108. 108.

    , , , & The upper end of climate model temperature projections is inconsistent with past warming. Environ. Res. Lett. 8, 14024 (2013).

  109. 109.

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

  110. 110.

    , & Addressing interdependency in a multimodel ensemble by interpolation of model properties. J. Clim. 28, 5150–5170 (2015).

  111. 111.

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

  112. 112.

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

  113. 113.

    , , & Implications of potentially lower climate sensitivity on climate projections and policy. Environ. Res. Lett. 9, 31003 (2014).

  114. 114.

    , , & A scientific critique of the two-degree climate change target. Nat. Geosci. 9, 13–18 (2016).

  115. 115.

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

  116. 116.

    et al. Estimating changes in global temperature since the pre-industrial period. Bull. Am. Meteorol. Soc. (2017).

  117. 117.

    , , , & Importance of pre-industrial baseline for determining the likelihood of exceeding the Paris limits. Nat. Clim. Change 7, 563–567 (2017).

  118. 118.

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

  119. 119.

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

  120. 120.

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

  121. 121.

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

  122. 122.

    & Delays in US mitigation could rule out Paris targets. Nat. Clim. Change (2016).

  123. 123.

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

  124. 124.

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

  125. 125.

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

  126. 126.

    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).

  127. 127.

    , & Energy balance climate models. Rev. Geophys. 19, 91–121 (1981).

  128. 128.

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

  129. 129.

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

  130. 130.

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

  131. 131.

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

  132. 132.

    & Natural variability of the climate system and detection of the greenhouse effect. Nature 344, 324–326 (1990).

  133. 133.

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

  134. 134.

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

  135. 135.

    & Cloud cover and climate sensitivity. J. Atmos. Sci. 37, 1485–1510 (1980).

  136. 136.

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

  137. 137.

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

  138. 138.

    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).

  139. 139.

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

  140. 140.

    , , , & The ice-core record: climate sensitivity and future greenhouse warming. Nature 347, 139–145 (1990).

  141. 141.

    & Deriving global climate sensitivity from palaeoclimate reconstructions. Nature 360, 573–575 (1992).

  142. 142.

    , & Paleoclimate data constraints on climate sensitivity: the paleocalibration method. Clim. Change 32, 165–184 (1996).

  143. 143.

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

  144. 144.

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

  145. 145.

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

  146. 146.

    & How sensitive is climate sensitivity? Geophys. Res. Lett. 38, L14708 (2011).

  147. 147.

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

  148. 148.

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

  149. 149.

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

  150. 150.

    , , & Earth's energy imbalance and implications. Atmos. Chem. Phys. 11, 13421–13449 (2011).

  151. 151.

    , & Nonlinearities in patterns of long-term ocean warming. Geophys. Res. Lett. 43, 3380–3388 (2016).

  152. 152.

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

  153. 153.

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

  154. 154.

    & 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).

  155. 155.

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

  156. 156.

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

  157. 157.

    , & Timescales in energy balance climate models. 1: The limiting case solutions. J. Geophys. Res. 99, 3631–3641 (1994).

  158. 158.

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

  159. 159.

    , & Atmosphere response time scales estimated from AOGCM experiments. J. Clim. 25, 7956–7972 (2012).

  160. 160.

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

  161. 161.

    , & Probabilistic estimates of transient climate sensitivity subject to uncertainty in forcing and natural variability. J. Clim. 24, 5521–5537 (2011).

  162. 162.

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

  163. 163.

    , , & Alternatives to stabilization scenarios. Geophys. Res. Lett. 33, L14707 (2006).

  164. 164.

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

  165. 165.

    & Climate commitment in an uncertain world. Geophys. Res. Lett. 38, L01707 (2011).

  166. 166.

    , & How much more global warming and sea level rise? Science 307, 1769–1773 (2005).

  167. 167.

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

  168. 168.

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

  169. 169.

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

  170. 170.

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

  171. 171.

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

  172. 172.

    , , & Transient climate response to increasing atmospheric carbon dioxide. Science 215, 56 (1982).

  173. 173.

    , , & New estimates of radiative forcing due to well mixed greenhouse gases. Geophys. Res. Lett. 25, 2715–2718 (1998).

  174. 174.

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

  175. 175.

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

  176. 176.

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

  177. 177.

    & Why is climate sensitivity so unpredictable? Science 318, 629–632 (2007).

  178. 178.

    , & Why climate sensitivity may not be so unpredictable. Geophys. Res. Lett. 36, L16707 (2009).

  179. 179.

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

  180. 180.

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

  181. 181.

    , , & Constraints on radiative forcing and future climate change from observations and climate model ensembles. Nature 416, 719–723 (2002).

  182. 182.

    , , & Probabilistic climate change projections using neural networks. Clim. Dyn. 21, 257–272 (2003).

  183. 183.

    , , , & Quantifying uncertainties in climate system properties with the use of recent climate observations. Science 295, 113–117 (2002).

  184. 184.

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

  185. 185.

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

  186. 186.

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

  187. 187.

    & Climate forcings and climate sensitivities diagnosed from coupled climate model integrations. J. Clim. 19, 6181–6194 (2006).

  188. 188.

    , , , & An observationally based estimate of the climate sensitivity. J. Clim. 15, 3117–3121 (2002).

  189. 189.

    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).

  190. 190.

    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).

  191. 191.

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

  192. 192.

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

  193. 193.

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

  194. 194.

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

  195. 195.

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

  196. 196.

    , & Inferring climate system properties using a computer model. Bayesian Anal. 3, 1–37 (2008).

  197. 197.

    , & Constraining climate model parameters from observed 20th century changes. Tellus A 60, 911–920 (2008).

  198. 198.

    , & Estimated PDFs of climate system properties including natural and anthropogenic forcings. Geophys. Res. Lett. 33, L01705 (2006).

  199. 199.

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

  200. 200.

    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).

  201. 201.

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

  202. 202.

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

  203. 203.

    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).

  204. 204.

    , , & Earth's climate sensitivity: apparent inconsistencies in recent assessments. Earth's Future 2, 601–605 (2014).

  205. 205.

    , , , & Disentangling greenhouse warming and aerosol cooling to reveal Earth's climate sensitivity. Nat. Geosci. 9, 286–289 (2016).

  206. 206.

    , , & Insufficient forcing uncertainty underestimates the risk of high climate sensitivity. Geophys. Res. Lett. 36, L16709 (2009).

  207. 207.

    & Correlation between climate sensitivity and aerosol forcing and its implication for the 'climate trap'. Clim. Change 109, 815–825 (2011).

  208. 208.

    & Complementary observational constraints on climate sensitivity. Geophys. Res. Lett. 36, L04708 (2009).

  209. 209.

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

  210. 210.

    & Simultaneously constraining climate sensitivity and aerosol radiative forcing. J. Clim. 15, 2837–2861 (2002).

  211. 211.

    , & Strong present-day aerosol cooling implies a hot future. Nature 435, 1187–1190 (2005).

  212. 212.

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

  213. 213.

    & Objectively combining AR5 instrumental period and paleoclimate climate sensitivity evidence. Clim. Dyn. (2017).

  214. 214.

    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).

  215. 215.

    & Impact of the Atlantic Multidecadal Oscillation (AMO) on deriving anthropogenic warming rates from the instrumental temperature record. Earth Syst. Dyn. 5, 375–382 (2014).

  216. 216.

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

  217. 217.

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

  218. 218.

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

  219. 219.

    , , & Observed climate change constrains the likelihood of extreme future global warming. Tellus B 60B, 76–81 (2008).

  220. 220.

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

  221. 221.

    , , , & Improved constraints on 21st-century warming derived using 160 years of temperature observations. Geophys. Res. Lett. 39, L01704 (2012).

  222. 222.

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

  223. 223.

    , , & Constraining the ratio of global warming to cumulative CO2 emissions using CMIP5 simulations. J. Clim. 26, 6844–6858 (2013).

  224. 224.

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

  225. 225.

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

  226. 226.

    , & Inferring aerosol cooling from hydrological sensitivity. J. Clim. 29, 6167–6178 (2016).

  227. 227.

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

  228. 228.

    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).

  229. 229.

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

  230. 230.

    , , & Atmospheric CO2: principal control knob governing Earth's temperature. Science 330, 356–359 (2010).

  231. 231.

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

  232. 232.

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

  233. 233.

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

  234. 234.

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

  235. 235.

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

  236. 236.

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

  237. 237.

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

  238. 238.

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

  239. 239.

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

  240. 240.

    & Tracking Earth's energy: from El Niño to global warming. Surv. Geophys. 33, 413–426 (2011).

  241. 241.

    , & Earth's energy imbalance. J. Clim. 27, 3129–3144 (2014).

  242. 242.

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

  243. 243.

    , , , & Transient climate sensitivity depends on base climate ocean circulation. J. Clim. 30, 1493–1504 (2017).

  244. 244.

    , , , & Transient climate response in coupled atmospheric–ocean general circulation models. J. Atmos. Sci. 70, 1291–1296 (2013).

  245. 245.

    , , , & Large-scale ocean circulation–cloud interactions reduce the pace of transient climate change. Geophys. Res. Lett. 43, 3935–3943 (2016).

  246. 246.

    , , & Constraining uncertainties in climate models using climate change detection techniques. Geophys. Res. Lett. 27, 569–572 (2000).

  247. 247.

    , & Uncertainty in continental-scale temperature predictions. Geophys. Res. Lett. 33, L02708 (2006).

  248. 248.

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

  249. 249.

    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).

  250. 250.

    , & Sensitivity of climate change projections to uncertainties in the estimates of observed changes in deep-ocean heat content. Clim. Dyn. 34, 735–745 (2010).

  251. 251.

    , & Uncertainties in the attribution of greenhouse gas warming and implications for climate prediction. J. Geophys. Res. Atmos. 121, 6969–6992 (2016).

  252. 252.

    & Cointegration analysis of hemispheric temperature relations. J. Geophys. Res. 107, D000174 (2002).

  253. 253.

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

  254. 254.

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

  255. 255.

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

  256. 256.

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

  257. 257.

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

  258. 258.

    & Climate sensitivity via a nonparametric fluctuation–dissipation theorem. J. Atmos. Sci. 68, 937–953 (2011).

  259. 259.

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

  260. 260.

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

  261. 261.

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

  262. 262.

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

  263. 263.

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

  264. 264.

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

  265. 265.

    , , & The relationship between interannual and long-term cloud feedbacks. Geophys. Res. Lett. 42, 10463–10469 (2015).

  266. 266.

    , & Water-vapor climate feedback inferred from climate fluctuations, 2003–2008. Geophys. Res. Lett. 35, L20704 (2008).

  267. 267.

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

  268. 268.

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

  269. 269.

    , & Distinct energy budgets for anthropogenic and natural changes during global warming hiatus. Nat. Geosci. 9, 29–33 (2016).

  270. 270.

    , , & 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).

  271. 271.

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

  272. 272.

    , , , & 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).

  273. 273.

    , , & Climate variability and relationships between top-of-atmosphere radiation and temperatures on Earth. J. Geophys. Res. Atmos. 120, 3642–3659 (2015).

  274. 274.

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

  275. 275.

    , & Issues in establishing climate sensitivity in recent studies. Remote Sens. 3, 2051–2056 (2011).

  276. 276.

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

  277. 277.

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

  278. 278.

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

  279. 279.

    , , , & Misdiagnosis of Earth climate sensitivity based on energy balance model results. Sci. Bull. 60, 1370–1377 (2015).

  280. 280.

    & On the determination of climate feedbacks from ERBE data. Geophys. Res. Lett. 36, L16705 (2009).

  281. 281.

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

  282. 282.

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

  283. 283.

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

  284. 284.

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

  285. 285.

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

  286. 286.

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

  287. 287.

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

  288. 288.

    , & Revisiting the determination of climate sensitivity from relationships between surface temperature and radiative fluxes. Geophys. Res. Lett. 37, L10703 (2010).

  289. 289.

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

  290. 290.

    , , & Why models run hot: results from an irreducibly simple climate model. Sci. Bull. 60, 122–135 (2015).

  291. 291.

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

  292. 292.

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

  293. 293.

    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).

  294. 294.

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

  295. 295.

    , , & Comment on 'Heat capacity, time constant, and sensitivity of Earth's climate system' by S. E. Schwartz. J. Geophys. Res. 113, D15102 (2008).

  296. 296.

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

  297. 297.

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

  298. 298.

    , , & Relationships between tropical sea surface temperature and top-of-atmosphere radiation. Geophys. Res. Lett. 37, L03702 (2010).

  299. 299.

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

  300. 300.

    , , , & On a minimal model for estimating climate sensitivity. Ecol. Modell. 297, 20–25 (2015).

  301. 301.

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

  302. 302.

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

  303. 303.

    , & Response to the eruption of Mount Pinatubo in relation to climate sensitivity in the CMIP3 models. Clim. Dyn. 35, 875–886 (2010).

  304. 304.

    , , , & Constraining transient climate sensitivity using coupled climate model simulations of volcanic eruptions. J. Clim. 27, 7781–7795 (2014).

  305. 305.

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

  306. 306.

    , & Inferring climate sensitivity from volcanic events. Clim. Dyn. 28, 481–502 (2007).

  307. 307.

    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).

  308. 308.

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

  309. 309.

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

  310. 310.

    , , , & The importance of ENSO phase during volcanic eruptions for detection and attribution. Geophys. Res. Lett. 43, 2851–2858 (2016).

  311. 311.

    , , & Thermocline flux exchange during the Pinatubo event. Geophys. Res. Lett. 33, L19711 (2006).

  312. 312.

    , & Constraining model transient climate response using independent observations of solar-cycle forcing and response. Geophys. Res. Lett. 35, L17707 (2008).

  313. 313.

    , & The role of climate sensitivity and ocean heat uptake on AOGCM transient temperature response. J. Clim. 15, 124–130 (2002).

  314. 314.

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

  315. 315.

    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).

  316. 316.

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

  317. 317.

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

  318. 318.

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

  319. 319.

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

  320. 320.

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

  321. 321.

    , , & Assessment of the use of current climate patterns to evaluate regional enhanced greenhouse response patterns of climate models. Geophys. Res. Lett. 34, L14701 (2007).

  322. 322.

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

  323. 323.

    , , , & Challenges in combining projections from multiple climate models. J. Clim. 23, 2739–2758 (2010).

  324. 324.

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

  325. 325.

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

  326. 326.

    , , & Constraining climate sensitivity from the seasonal cycle in surface temperature. J. Clim. 19, 4224–4233 (2006).

  327. 327.

    & How well do coupled models simulate today's climate? Bull. Am. Meteorol. Soc. 89, 303 (2008).

  328. 328.

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

  329. 329.

    & On the interpretation of constrained climate model ensembles. Geophys. Res. Lett. 39, L16708 (2012).

  330. 330.

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

  331. 331.

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

  332. 332.

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

  333. 333.

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

  334. 334.

    , , , & Towards constraining climate sensitivity by linear analysis of feedback patterns in thousands of perturbed-physics GCM simulations. Clim. Dyn. 30, 175–190 (2008).

  335. 335.

    , , & Constraints on climate change from a multi-thousand member ensemble of simulations. Geophys. Res. Lett. 32, L23825 (2005).

  336. 336.

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

  337. 337.

    , , , & Constraints on climate sensitivity from radiation patterns in climate models. J. Clim. 24, 1034–1052 (2011).

  338. 338.

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

  339. 339.

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

  340. 340.

    , , , & Climate model fidelity and projections of climate change. Geophys. Res. Lett. 33, L07702 (2006).

  341. 341.

    , , & Can top-of-atmosphere radiation measurements constrain climate predictions? Part II: Climate sensitivity. J. Clim. 26, 9367–9383 (2013).

  342. 342.

    , , , & Can top-of-atmosphere radiation measurements constrain climate predictions? Part I: Tuning. J. Clim. 26, 9348–9366 (2013).

  343. 343.

    , & Spread in model climate sensitivity traced to atmospheric convective mixing. Nature 505, 37–42 (2014).

  344. 344.

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

  345. 345.

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

  346. 346.

    , & Observational constraints on mixed-phase clouds imply higher climate sensitivity. Science 352, 224–227 (2016).

  347. 347.

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

  348. 348.

    , , & Recent progress toward reducing the uncertainty in tropical low cloud feedback and climate sensitivity: a review. Geosci. Lett. 3, 1–10 (2016).

  349. 349.

    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).

  350. 350.

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

  351. 351.

    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).

  352. 352.

    , & Present-day springtime high-latitude surface albedo as a predictor of simulated climate sensitivity. Geophys. Res. Lett. 34, L17703 (2007).

  353. 353.

    , & Radiative damping of annual variation in global mean surface temperature: comparison between observed and simulated feedback. Clim. Dyn. 24, 591–597 (2005).

  354. 354.

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

  355. 355.

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

  356. 356.

    , & Variability in modeled cloud feedback tied to differences in the climatological spatial pattern of clouds. Clim. Dyn. (2017).

  357. 357.

    & Low-cloud optical depth feedback in climate models. J. Geophys. Res. Atmos. 119, 6052–6065 (2014).

  358. 358.

    & Processes responsible for cloud feedback. Curr. Clim. Change Rep. 2, 179–189 (2016).

  359. 359.

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

  360. 360.

    , & Observational and model evidence for positive low-level cloud feedback. Science 325, 460–464 (2009).

  361. 361.

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

  362. 362.

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

  363. 363.

    et al. Practice and philosophy of climate model tuning across six U. S. modeling centers. Geosci. Model Dev. Discuss. (2017).

  364. 364.

    , & Reexamining the relationship between climate sensitivity and the Southern Hemisphere radiation budget in CMIP models. J. Clim. 28, 9298–9312 (2015).

  365. 365.

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

  366. 366.

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

  367. 367.

    , & Climate feedbacks determined using radiative kernels in a multi-thousand member ensemble of AOGCMs. Clim. Dyn. 35, 1219–1236 (2009).

  368. 368.

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

  369. 369.

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

  370. 370.

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

  371. 371.

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

  372. 372.

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

  373. 373.

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

  374. 374.

    , , & On the spread of changes in marine low cloud cover in climate model simulations of the 21st century. Clim. Dyn. 42, 2603–2626 (2014).

  375. 375.

    , & Origins of differences in climate sensitivity, forcing and feedback in climate models. Clim. Dyn. 40, 677–707 (2013).

  376. 376.

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

  377. 377.

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

  378. 378.

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

  379. 379.

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

  380. 380.

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

  381. 381.

    , , , & Evaluating the present-day simulation of clouds, precipitation, and radiation in climate models. J. Geophys. Res. 113, D14209 (2008).

  382. 382.

    , & Performance metrics for climate models. J. Geophys. Res. 113, D06104 (2008).

  383. 383.

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

  384. 384.

    , , & Selecting global climate models for regional climate change studies. Proc. Natl Acad. Sci. USA 106, 8441–8446 (2009).

  385. 385.

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

  386. 386.

    , , & Constraining future summer austral jet stream positions in the CMIP5 Ensemble by process-oriented multiple diagnostic regression. J. Clim. 29, 673–687 (2016).

  387. 387.

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

  388. 388.

    , & A representative democracy to reduce interdependency in a multimodel ensemble. J. Clim. 28, 5171–5194 (2015).

  389. 389.

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

  390. 390.

    , & Skill and independence weighting for multi-model assessments. Geosci. Model Dev. 10, 2379–2395 (2017).

  391. 391.

    & Climate model genealogy. Geophys. Res. Lett. 38, L08703 (2011).

  392. 392.

    , & Local eigenvalue analysis of CMIP3 climate model errors. Tellus A 60, 992–1000 (2008).

  393. 393.

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

  394. 394.

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

  395. 395.

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

  396. 396.

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

  397. 397.

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

  398. 398.

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

  399. 399.

    , , & Risks of model weighting in multimodel climate projections. J. Clim. 23, 4175–4191 (2010).

  400. 400.

    , & Using the past to constrain the future: how the palaeorecord can improve estimates of global warming. Prog. Phys. Geogr. 31, 481–500 (2007).

  401. 401.

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

  402. 402.

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

  403. 403.

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

  404. 404.

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

  405. 405.

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

  406. 406.

    , , & Climate sensitivity estimated from ensemble simulations of glacial climate. Clim. Dyn. 27, 149–163 (2006).

  407. 407.

    , & Linking glacial and future climates through an ensemble of GCM simulations. Clim. Past 3, 77–87 (2007).

  408. 408.

    , , & Can the Last Glacial Maximum constrain climate sensitivity? Geophys. Res. Lett. 39, L24702 (2012).

  409. 409.

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

  410. 410.

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

  411. 411.

    , , , & Efficiently constraining climate sensitivity with ensembles of paleoclimate simulations. SOLA 1, 181–184 (2005).

  412. 412.

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

  413. 413.

    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).

  414. 414.

    , , , & Nonlinear climate sensitivity and its implications for future greenhouse warming. Sci. Adv. 2, e1501923 (2016).

  415. 415.

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

  416. 416.

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

  417. 417.

    , , , & A probabilistic calibration of climate sensitivity and terrestrial carbon change in GENIE-1. Clim. Dyn. 35, 785–806 (2010).

  418. 418.

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

  419. 419.

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

  420. 420.

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

  421. 421.

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

  422. 422.

    & 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).

  423. 423.

    & 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).

  424. 424.

    & 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).

  425. 425.

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

  426. 426.

    , , , & Sea surface and high-latitude temperature sensitivity to radiative forcing of climate over several glacial cycles. J. Clim. 25, 1635–1656 (2012).

  427. 427.

    , , & Deep time evidence for climate sensitivity increase with warming. Geophys. Res. Lett. 43, 6538–6545 (2016).

  428. 428.

    , , & The dependence of equilibrium climate sensitivity on climate state: applications to studies of climates colder than present. Geophys. Res. Lett. 40, 3721–3726 (2013).

  429. 429.

    , , , & On the state dependency of the equilibrium climate sensitivity during the last 5 million years. Clim. Past 11, 1801–1823 (2015).

  430. 430.

    , & Geobiological constraints on Earth system sensitivity to CO2 during the Cretaceous and Cenozoic. Geobiology 10, 298–310 (2012).

  431. 431.

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

  432. 432.

    , & Climate sensitivity constrained by CO2 concentrations over the past 420 million years. Nature 446, 530–532 (2007).

  433. 433.

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

  434. 434.

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

  435. 435.

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

  436. 436.

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

  437. 437.

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

  438. 438.

    , , & High Earth-system climate sensitivity determined from Pliocene carbon dioxide concentrations. Nat. Geosci. 3, 27–30 (2010).

  439. 439.

    , , & Climate sensitivity, sea level and atmospheric carbon dioxide. Philos. Trans. A 371, 20120294 (2013).

  440. 440.

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

  441. 441.

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

  442. 442.

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

  443. 443.

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

  444. 444.

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

  445. 445.

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

  446. 446.

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

  447. 447.

    & Subjective judgements by climate experts. Environ. Sci. Technol. 29, 468–476 (1995).

  448. 448.

    , , & Expert judgments about transient climate response to alternative future trajectories of radiative forcing. Proc. Natl Acad. Sci. USA 107, 12451–12456 (2010).

  449. 449.

    , , & Do probabilistic expert elicitations capture scientists' uncertainty about climate change? Clim. Change 116, 427–436 (2013).

  450. 450.

    , & Expert judgement and uncertainty quantification for climate change. Nat. Clim. Change 6, 445–451 (2016).

  451. 451.

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

  452. 452.

    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).

  453. 453.

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

  454. 454.

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

  455. 455.

    , & On the proportionality between global temperature change and cumulative CO2 emissions during periods of net negative CO2 emissions. Environ. Res. Lett. 11, 55006 (2016).

  456. 456.

    , , & The proportionality of global warming to cumulative carbon emissions. Nature 459, 829–832 (2009).

  457. 457.

    , , & Setting cumulative emissions targets to reduce the risk of dangerous climate change. Proc. Natl Acad. Sci. USA 106, 16129–16134 (2009).

  458. 458.

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

  459. 459.

    , , & Quantifying carbon cycle feedbacks. J. Clim. 22, 5232–5250 (2009).

  460. 460.

    , & Allowable carbon emissions lowered by multiple climate targets. Nature 499, 197–201 (2013).

  461. 461.

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

  462. 462.

    , , , & The climate response to five trillion tonnes of carbon. Nat. Clim. Change 6, 851–855 (2016).

  463. 463.

    , , & A framework to understand the transient climate response to emissions. Environ. Res. Lett. 11, 15003 (2016).

  464. 464.

    , & Continued global warming after CO2 emissions stoppage. Nat. Clim. Change 4, 40–44 (2013).

  465. 465.

    , , , & Ongoing climate change following a complete cessation of carbon dioxide emissions. Nat. Geosci. 4, 83–87 (2011).

  466. 466.

    , , & Irreversible climate change due to carbon dioxide emissions. Proc. Natl Acad. Sci. USA 106, 1704–1709 (2009).

  467. 467.

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

  468. 468.

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

  469. 469.

    , & Is the climate response to CO2 emissions path dependent? Geophys. Res. Lett. 39, L05703 (2012).

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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.

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Affiliations

  1. Institute for Atmospheric and Climate Science, ETH Zurich, CH-8092 Zurich, Switzerland

    • Reto Knutti
    •  & Maria A. A. Rugenstein
  2. National Center for Atmospheric Research, Boulder, Colorado 80307, USA

    • Reto Knutti
  3. School of Geosciences, University of Edinburgh, Edinburgh EH9 3FE, UK

    • Gabriele C. Hegerl

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Contributions

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

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to Reto Knutti.

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