Purpose of Review
This review summarizes the inverse methods used to estimate the net aerosol forcing inferred from the historical climate change records for the Earth.
The available methods are similar in design while differing in their assumptions. Primary differences are (a) the complexity of the earth system model used for forward simulations of the historical period (~ 1850 to the present), (b) the uncertainty sampling methodology, and (c) the representation of internal climate variability in the statistical approach. All methods, in some fashion, include the net aerosol radiative forcing as a residual forcing that is scaled to find simulations that match the observed records of surface air and deep ocean temperatures. Inverse methods also require sampling the model response uncertainty in the equilibrium climate sensitivity and the transient climate response (i.e., the delay due to mixing heat into the deep ocean), and therefore, a joint probability distribution is estimated that includes uncertainty across multiple components.
The resulting estimates of the net aerosol forcing and its uncertainty are, by construction, necessarily linked to the earth system model, its response characteristics, and the estimates of the internal chaotic variability. Summary results indicate that the net aerosol forcing during the late twentieth century was − 0.77 Wm−2 with a 5–95% range of − 1.15 to − 0.31 Wm−2 based on 19 results from simple- to full-complexity climate system models.
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We note that ECBMs and EMICs are already an emulator of the true climate system, and thus, a statistical emulator is similar to these. The ability to capture the critical dynamics and feedbacks by the ECBMs and EMICs can set them apart from simple statistical emulators. As statistical models become more complicated, their computational efficiency will also eventually limit their abilities.
Aldrin M, Holden M, Guttorp P, Skeie R, Myhre G, Berntsen T. Bayesian estimation of climate sensitivity based on a simple climate model fitted to observations of hemispheric temperatures and global ocean heat content. Environmetrics. 2012;23(3):253–71. https://doi.org/10.1002/env.2140.
Allen M, Tett S. Checking for model consistency in optimal fingerprinting. Clim Dyn. 1999;15(6):419–34. https://doi.org/10.1007/s003820050291.
Allen M, Gillett N, Kettleborough J, Hegerl G, Schnur R, Stott P, et al. Quantifying anthropogenic influence on recent near-surface temperature change. Surv Geophys. 2006;27(5):491–544. https://doi.org/10.1007/s10712-006-9011-6.
Andronova N, Schlesinger M. Objective estimation of the probability density function for climate sensitivity. J Geophys Res D: Atmos. 2001;106(D19):22,605–12. https://doi.org/10.1029/2000JD000259.
Armour K. Energy budget constraints on climate sensitivity in light of inconstant climate feedbacks. Nat Clim Chang. 2017;7(5):331–5. https://doi.org/10.1038/nclimate3278.
Bindoff N, Stott P, AchutaRao K, Allen M, Gillett N, Gutzler D, et al. Detection and attribution of climate change: from global to regional. In: Stocker TF, Qin D, Plattner G-K, Tignor M, Allen SK, Boschung J, Nauels A, Xia Y, Bex V, Midgley PM, editors. Climate Change 2013: the physical science basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change. Cambridge: Cambridge University Press; 2013. p. 867–952.
Boucher O, Randall D, Artaxo P, Bretherton C, Feingold G, Forster P, et al. Clouds and aerosols. In: Stocker TF, Qin D, Plattner G-K, Tignor M, Allen SK, Boschung J, Nauels A, Xia Y, Bex V, Midgley PM, editors. Climate Change 2013: the physical science basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change. Cambridge: Cambridge University Press; 2013. p. 571–658.
Domingues C, Church J, White N, Gleckler P, Wijffels S, Barker P, et al. Improved estimates of upper–ocean warming and multi-decadal sea-level rise. Nature. 2008;453(7198):1090–3. https://doi.org/10.1038/nature07080.
Flato G, Marotzke J, Abiodun B, Braconnot P, Chou S, Collins W, et al. Evaluation of climate models. In: Stocker TF, Qin D, Plattner G-K, Tignor M, Allen SK, Boschung J, Nauels A, Xia Y, Bex V, Midgley PM, editors. Climate Change 2013: the physical science basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change. Cambridge: Cambridge University Press; 2013. p. 741–866.
Forest C, Allen M, Stone P, Sokolov A. Constraining uncertainties in climate models using climate change detection methods. Geophys Res Lett. 2000;27(4):569–72. https://doi.org/10.1029/1999GL010859.
Forest C, Stone P, Sokolov A, Allen M, Webster M. Quantifying uncertainties in climate system properties with the use of recent climate observations. Science. 2002;295(5552):113–7. https://doi.org/10.1126/science.1064419.
Forest C, Stone P, Sokolov A (2006) Estimated PDFs of climate system properties including natural and anthropogenic forcings. Geophys Res Lett (L01705):doi:https://doi.org/10.1029/2005GL023,977.
Forest C, Stone P, Sokolov A. Constraining climate model parameters from observed 20th century changes. Tellus Series A-Dynamic Meteorology and Oceanography. 2008;60A(5):911–20.
Gelfand A, Smith A (1990) Sampling-based approaches to calculating marginal densities. J Am Stat Assoc 85(410):398–409, https://doi.org/10.1080/01621459.1990.10476213, URL http://amstat.tandfonline.com/doi/abs/10.1080/01621459.1990.10476213.
Gleckler P, Durack P, Stouffer R, Johnson G, Forest C. Industrial-era global ocean heat uptake doubles in recent decades. Nat Clim Chang. 2016;6(4):394–8. https://doi.org/10.1038/nclimate2915.
Hansen J, Russell G, Rind D, Stone P, Lacis A, Lebedeff S, et al. Efficient three-dimensional global models for climate studies: models I and II. Mon Weather Rev. 1983;111(4):609–62. https://doi.org/10.1175/1520-0493(1983)111<0609:ETDGMF>2.0.CO;2.
Hansen J, Sato M, Ruedy R, Nazarenko L, Lacis A, Schmidt G, et al. Efficacy of climate forcings. J Geophys Res-Atmos. 2005;110(D18):D18,104. https://doi.org/10.1029/2005JD005776.
Hansen J, Ruedy R, Sato M, Lo K (2010) Global surface temperature change. Rev Geophys 48(RG4004), https://doi.org/10.1029/2010RG000345.
Hastings WK. Monte carlo sampling methods using Markov chains and their applications. Biometrika. 1970;57(1):97–109. https://doi.org/10.1093/biomet/57.1.97.
Hegerl G, von Storch H, Hasselmann K, Santer B, Cubasch U, Jones P. Detecting greenhouse gas induced climate change with an optimal fingerprint method. J Clim. 1996;9(10):2281–306. https://doi.org/10.1175/1520-0442(1996)009<2281:DGGICC>2.0.CO;2.
Iman R (2008) Latin hypercube sampling. Encyclopedia of quantitative risk analysis and assessment.
Iman R, Davenport J, Zeigler D (1980) Latin hypercube sampling (program user’s guide). [LHC, in FORTRAN]. Tech. Rep. SAND-79-1473, Sandia Labs.
IPCC. Summary for policymakers. In: Houghton JT, Ding Y, Griggs DJ, Noguer M, van der Linden PJ, Dai X, Maskell K, Johnson CA, editors. Climate Change 2001: the scientific basis. Contribution of Working Group I to the Third Assessment Report of the Intergovernmental Panel on Climate Change. Cambridge: Cambridge University Press; 2001. p. 1–20.
IPCC. Summary for policymakers. In: Solomon S, Qin D, Manning M, Chen Z, Marquis M, Averyt KB, Tignor M, Miller HL, editors. Climate Change 2007: the physical science basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change. Cambridge: Cambridge University Press; 2007. p. 1–18.
IPCC. Summary for policymakers. In: Stocker TF, Qin D, Plattner G-K, Tignor M, Allen SK, Boschung J, Nauels A, Xia Y, Bex V, Midgley PM, editors. Climate Change 2013: the physical science basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change. Cambridge: Cambridge University Press; 2013. p. 1–30.
Ishii M, Kimoto M. Reevaluation of historical ocean heat content variations with time-varying XBT and MBT depth bias corrections. J Oceanogr. 2009;65(3):287–99. https://doi.org/10.1007/s10872-009-0027-7.
Kennedy J, Rayner N, Smith R, Parker D, Saunby M (2011a) Reassessing biases and other uncertainties in sea surface temperature observations measured in situ since 1850: 1. Measurement and sampling uncertainties. J Geophys Res Atmos 116(D14).
Kennedy J, Rayner N, Smith R, Parker D, Saunby M (2011b) Reassessing biases and other uncertainties in sea surface temperature observations measured in situ since 1850: 2. Biases and homogenization. J Geophys Res Atmos 116(D14).
Knutti R, Tomassini L (2008) Constraints on the transient climate response from observed global temperature and ocean heat uptake. Geophys Res Lett 35(L09701):doi:https://doi.org/10.1029/2007GL032,904.
Knutti R, Stocker T, Joos F, Plattner G. Constraints on radiative forcing and future climate change from observations and climate model ensembles. Nature. 2002;416(6882):719–23. https://doi.org/10.1038/416719a.
Levitus S, Antonov J, Boyer T, Stephens C. Warming of the world ocean. Science. 2000;287(5461):2225–9. https://doi.org/10.1126/science.287.5461.2225.
Levitus S, Antonov J, Boyer T, Baranova O, Garcia H, Locarnini R, Mishonov A, Reagan J, Seidov D, Yarosh E, et al (2012) World ocean heat content and thermosteric sea level change (0–2000 m), 1955–2010. Geophys Res Lett 39(10).
Lewis N. An objective Bayesian improved approach for applying optimal fingerprint techniques to climate sensitivity. J Clim. 2013;26(19):7414–29. https://doi.org/10.1175/JCLI-D-12-00473.1.
Libardoni A, Forest C (2011) Sensitivity of distributions of climate system properties to the surface temperature dataset. Geophys Res Lett 38(L22705):doi:https://doi.org/10.1029/2011GL049,431.
Libardoni A, Forest C (2013) Correction to “sensitivity of distributions of climate system properties to the surface temperature data set”. Geophys Res Lett 40:doi:https://doi.org/10.1002/grl.50,480.
McGuffie K, Henderson-Sellers A (2005) A climate modelling primer. John Wiley & Sons.
Meinshausen M, Meinshausen N, Hare W, Raper S, Frieler K, Knutti R, et al. Greenhouse-gas emission targets for limiting global warming to 2 degrees C. Nature. 2009;458(7242):1158–62. https://doi.org/10.1038/nature08017.
Metropolis N, Rosenbluth A, Rosenbluth M, Teller A, Teller E. Equation of state calculations by fast computing machines. J Chem Phys. 1953;21(6):1087–92. https://doi.org/10.1063/1.1699114.
Mitchell JFB, Johns TC. On modification of global warming by sulfate aerosols. J Clim. 1997;10(2):245–67. https://doi.org/10.1175/1520-0442(1997)010<0245:OMOGWB>2.0.CO;2.
Mitchell JFB, Johns TC, Gregory JM, Tett SFB. Climate response to increasing levels of greenhouse gases and sulfate aerosols. Nature. 1994;376:504.
Monier E, Scott JR, Sokolov AP, Forest CE, Schlosser CA. An integrated assessment modeling framework for uncertainty studies in global and regional climate change: the MIT IGSM-CAM (version1.0). Geosci Model Dev. 2013;6(6):2063–85. https://doi.org/10.5194/gmd-6-2063-2013.
Morice C, Kennedy J, Rayner N, Jones P. Quantifying uncertainties in global and regional temperature change using an ensemble of observational estimates: the HADCRUT4 data set. Journal of Geophysical Research: Atmospheres. 2012;117(D8) https://doi.org/10.1029/2011JD017187.
Myhre G, Shindell D, Brãcon FM, Collins W, Fuglestvedt J, Huang J, et al. Anthropogenic and natural radiative forcing. In: Stocker TF, Qin D, Plattner G-K, Tignor M, Allen SK, Boschung J, Nauels A, Xia Y, Bex V, Midgley PM, editors. Climate Change 2013: the physical science basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change. Cambridge: Cambridge University Press; 2013. p. 659–740.
National Academies of Sciences, Engineering, and Medicine. Valuing climate damages: updating estimation of the social cost of carbon dioxide. Washington, D.C.: National Academies Press; 2017. https://doi.org/10.17226/24651.
Olson R, Sriver R, Chang W, Haran M, Urban N, Keller K. What is the effect of unresolved internal climate variability on climate sensitivity estimates? J Geophys Res D: Atmos. 2013;118(10):4348–58.
Purkey S, Johnson G. Warming of global abyssal and deep southern ocean waters between the 1990s and 2000s: contributions to global heat and sea level rise budgets. J Clim. 2010;23(23):6336–51. https://doi.org/10.1175/2010JCLI3682.1.
Rohde R, Muller R, Jacobsen R, Perlmutter S, Rosenfeld A, Wurtele J, Curry J, Wickhams C, Mosher S (2013) Berkeley earth temperature averaging process, geoinfor. geostat.: an overview 1:2. of 1:1–13, https://doi.org/10.4172/gigs.1000103.
Sansó B, Forest C. Statistical calibration of climate system properties. Journal of the Royal Statistical Society Series C-Applied Statistics. 2009;58(4):485–503. https://doi.org/10.1111/j.1467-9876.2009.00669.x.
Santer B, Brüggemann W, Cubasch U, Hasselmann K, Höck H, Maier-Reimer E, et al. Signal-to-noise analysis of time-dependent greenhouse warming experiments. Clim Dyn. 1994;9(6):267–85. https://doi.org/10.1007/BF00204743.
Santer B, Taylor K, Wigley T, Johns T, Jones P, Karoly D, et al. A search for human influences on the thermal structure of the atmosphere. Nature. 1996;382(6586):39–45. https://doi.org/10.1038/382039a0.
Senior CA, Mitchell JFB. The time-dependence of climate sensitivity. Geophys Res Let. 2000;27(17):2685–8. https://doi.org/10.1029/2000GL011373.
Shindell D, Faluvegi G. Climate response to regional radiative forcing during the twentieth century. Nat Geosci. 2009;2(4):294–300. https://doi.org/10.1038/ngeo473.
Shindell D, Faluvegi G, Koch D, Schmidt G, Unger N, Bauer S. Improved attribution of climate forcing to emissions. Science. 2009;326(5953):716–8. https://doi.org/10.1126/science.1174760.
Skeie R, 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 System Dynamics. 2014;5(1):139–75. https://doi.org/10.5194/esd-5-139-2014.
Smith T, Reynolds R, Peterson T, Lawrimore J. Improvements to NOAA’s historical merged land–ocean surface temperature analysis (1880–2006). J Clim. 2008;21(10):2283–96. https://doi.org/10.1175/2007JCLI2100.1.
Sobol I (2001) Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Math Comput Simul 55(1–3):271–280, https://doi.org/10.1016/S0378-4754(00)00270-6, URL http://www.sciencedirect.com/science/article/pii/S0378475400002706, the second IMACS seminar on Monte Carlo methods.
Sokolov A, Stone P. A flexible climate model for use in integrated assessments. Clim Dyn. 1998;14(4):291–303. https://doi.org/10.1007/s003820050224.
Sokolov A, Forest C, Stone P. Comparing oceanic heat uptake in AOGCM transient climate change experiments. J Clim. 2003;16(10):1573–82. https://doi.org/10.1175/1520-0442-16.10.1573.
Sokolov A, Stone P, Forest C, Prinn R, Sarofim M, Webster M, et al. Probabilistic forecast for twenty-first-century climate based on uncertainties in emissions (without policy) and climate parameters. J Clim. 2009;22(19):5175–204. https://doi.org/10.1175/2009JCLI2863.1.
Sokolov A, Forest C, Stone P. Sensitivity of climate change projections to uncertainties in the estimates of observed changes in deep-ocean heat content. Clim Dyn. 2010;34(5):735–45. https://doi.org/10.1007/s00382-009-0556-1.
Solow A. Bootstrapping correlated data. Math Geol. 1985;17(7):769–75. https://doi.org/10.1007/BF01031616.
Stott P, Mitchell J, Allen M, Delworth T, Gregory J, Meehl G, et al. Observational constraints on past attributable warming and predictions of future global warming. J Clim. 2006;19(13):3055–69. https://doi.org/10.1175/JCLI3802.1.
Tomassini L, Reichert P, Knutti R, Stocker T, Borsuk M. Robust bayesian uncertainty analysis of climate system properties using Markov chain Monte Carlo methods. J Clim. 2007;20(7):1239–54. https://doi.org/10.1175/JCLI4064.1.
Vose R, Arndt D, Banzon V, Easterling D, Gleason B, Huang B, et al. NOAA’s merged land–ocean surface temperature analysis. Bull Am Meteorol Soc. 2012;93(11):1677–85. https://doi.org/10.1175/BAMS-D-11-00241.1.
The author would like to thank A.G. Libardoni and A.P. Sokolov for their comments, O. Boucher for his patience and helpful review suggestions, and the two anonymous reviewers.
This work was supported in part by the Office of Science (BER), the U.S. Department of Energy Grant No. DE-FG02-94ER61937, and the National Science Foundation through the Network for Sustainable Climate Risk Management (SCRiM) under NSF cooperative agreement GEO-1240507.
Conflict of Interest
On behalf of myself, the corresponding author states that there is no conflict of interest.
This article is part of the Topical Collection on Aerosols and Climate
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Appendix. Uncertainty Sampling Strategies for EMICs
Appendix. Uncertainty Sampling Strategies for EMICs
Because the MIT IGSM  is the only model to include similar atmospheric physics to full AOGCMs, it is significantly different from the other models in its representation of the feedbacks and processes in the model equations. The IGSM is based on the GISS Model II atmospheric general circulation model  and solves the zonal mean atmospheric geophysical fluid dynamics equations, which includes zonal mean representations of radiative transfer, convection, clouds, land surface fluxes, sea-ice, snow-cover, and others. While having a more complex atmospheric component, in contrast with both the UVIC and BERN2.5 models, the model does not account for changes in ocean circulation that can occur on multi-century timescales related to glacial and interglacial climate states.
For this review, there are several differences from the other models that are relevant for comparing results with other estimates of net aerosol forcing. By including the relevant atmospheric physics components, the MIT IGSM does not specify the radiative forcings, but the model is forced directly by the concentrations of the long-lived and short-lived greenhouse gases and other climate forcing agents . Thus, both the radiative forcing and the feedbacks are modeled explicitly rather than being specified as done in the ECBMs as well as in the UVIC and BERN 2.5 EMICs. A similar issue is that the IGSM does not specify the equilibrium climate sensitivity (Seq) to CO2 concentrations. Instead, the model uses a temperature-dependent adjustment to the cloud fraction used in the radiative transfer equations, which, in turn, changes the model’s “cloud feedbacks” while the other feedbacks (e.g., water vapor, lapse rate, Planck, and albedo feedbacks) are left to the model physics. As such, the net feedback, often called λ, corresponding to Seq, can be varied by the cloud feedback term in the IGSM.
In all models, the rate of ocean heat uptake is typically altered by changing an ocean thermal diffusion coefficient within the model and, for a given Seq, this will also adjust the transient climate response (TCR) estimated as the global mean surface temperature change from equilibrium at the time of doubling for a 1% increasing CO2 concentration scenario. Overall, these adjustments (for Seq, TCR, and the net aerosol forcing) allow for changes in the net forcing and the net response that are required in the inverse methods as discussed in this paper. For the IGSM, the thermal diffusion coefficient is for diffusion of heat anomalies. For UVIC and BERN 2.5, the models vary an explicit thermal diffusion equation within the GFD equations. For the energy balance models with an upwelling-diffusion ocean component, the vertical diffusivity of heat is specified and downward heat flux is compensated by an advective upwelling term.
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Forest, C.E. Inferred Net Aerosol Forcing Based on Historical Climate Changes: a Review. Curr Clim Change Rep 4, 11–22 (2018). https://doi.org/10.1007/s40641-018-0085-2
- Anthropogenic radiative forcing
- Net aerosol radiative forcing
- Inverse methods
- Observed historical climate change
- Intermediate complexity earth system models
- Internal climate variability
- Joint probability distributions