Abstract
Past climates provide a means for evaluating the response of the climate system to large perturbations. Our ultimate goal is to constrain climate models rigorously by paleoclimate data. For illustration, we used a conceptual climate model (a classical energy balance model) and applied the so-called “adjoint method” to minimize the misfit between our model and sea-surface temperature data for the Last Glacial Maximum (LGM, between 19,000 and 23,000 years before present). The “adjoint model” (derivative code) was generated by an “adjoint compiler.” We optimized parameters controlling the thermal diffusion and the sensitivity of the outgoing longwave radiation to changes in the zonal-mean surface temperature and the atmospheric CO2 concentration. As a result, we estimated that an equilibrium climate sensitivity between 2.2 °C and 2.5 °C was consistent with the reconstructed glacial cooling, and we were able to infer structural deficits of the simple model where the fit to current observations and paleo data was not successful.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Notes
- 1.
The code of the one-dimensional energy balance–climate model and its adjoint Ebm1D is available upon request from apaul@marum.de.
References
Annan JD, Hargreaves JC (2007) Efficient estimation and ensemble generation in climate modelling. Philos Trans R Soc A 365(1857):2077–2088
Berger AL (1978) Long term variations of daily insolation and Quaternary climatic changes. J Atmos Sci 35(12):2362–2367
Berger A (1988) Milankovitch theory and climate. Rev Geophys 26:624–657
Edwards TL, Crucifix M, Harrison SP (2007) Using the past to constrain the future: how the palaeorecord can improve estimates of global warming. Prog Phys Geogr 31:481–500. doi:10.1177/0309133307083295
Errico RM (1997) What is an adjoint model? Bull Am Meteorol Soc 78(11):2577–2591
Giering R (2000) Tangent linear and adjoint biogeochemical models. In: Kasibhatla P, Heimann M, Rayner P, Mahowald N, Prinn RG, Hartley DE (eds) Inverse Methods in Global Biogeochemical Cycles, vol 114, Geophysical Monograph Series. AGU, Washington, DC, pp 33–48
Gilbert JC, Lemaréchal C (1989) Some numerical experiments with variable storage quasi-Newton algoritms. Math Program 45:407–435
Griewank A, Walther A (2008) Evaluating derivatives. Principles and techniques of algorithmic differentiation, vol 19, 2nd edn, Frontiers in Applied Mathematics. SIAM, Philadelphia
Grubić A (2006) The astronomical theory of climatic changes of Milutin Milankovich. Episodes 29(3):197–203
Hann JV (1915) Lehrbuch der Meteorologie, 3rd edn. C.H. Tauchnitz, Leipzig
Hartmann DL (1994) Global physical climatology. Academic, San Diego
Hartmann DL, Short DA (1979) On the role of zonal asymmetries in climate change. J Atmos Sci 36:519–528
Holden PB, Edwards NR, Oliver KIC, Lenton TM, Wilkinson RD (2010) A probabilistic calibration of climate sensitivity and terrestrial carbon change in GENIE-1. Clim Dyn 35:785–806. doi:10.1007/s00382-009-0630-8
Jentsch V (1987) Cloud-ice-vapor feedbacks in a global climate model. In: Nicolis C, Nicolis G (eds) Irreversible Phenomena and Dynamical Systems Analysis in Geosciences. D. Reidel, Boston, pp 417–437
Joussaume S, Braconnot P (1997) Sensitivity of paleoclimate simulation results to season definitions. J Geophys Res 102(D2):1943–1956
Joussaume S, Taylor K (1995) Status of the Paleoclimate Modeling Intercomparison Project. In: Proceedings of the first international AMIP scientific conference, WCRP-92, Monterey, CA, 15–19 May 1995, 532 pp (pp 425–430). Geneva, Switzerland: WMO/TD-No. 732
Kalnay E, Kanamitsu M, Kistler R, Collins W, Deaven D, Gandin L, Iredell M, Saha S, White G, Woolen J, Zhu Y, Chelliah M, Ebisuzaki W, Higgins W, Janowiak J, Mo KC, Ropelewski C, Leetmaa A, Reynolds R, Jenne R (1996) The NCEP/NCAR reanalysis project. Bull Am Meteorol Soc 77:437–471
Kasibhatla P, Heimann M, Rayner P, Mahowald N, Prinn RG, Hartley DE (2000) Inverse Methods in Global Biogeochemical Cycles, vol 114, Geophysical monograph series. AGU, Washington, DC
Kucera M, Rosell-Melé A, Schneider R, Waelbroeck C, Weinelt M (2005) Multiproxy approach for the reconstruction of the glacial ocean surface (MARGO). Quat Sci Rev 24:813–819
Larson VE, Golaz JC, Hansen J, Schanen DP, Griffin BM (2008) Diagnosing structural errors in climate model parameterizations. In: Extended Abstracts, 20th Conference on Climate Variability and Change, 88th Annual Meeting of the American Meteorological Society, New Orleans, LA
Le Dimet F-X, Talagrand O (1986) Variational algorithms for analysis and assimilation of meteorological observations: Theoretical aspects. Tellus 38A(2):97–110
LeGrand P, Wunsch C (1995) Constraints from paleotracer data on the North Atlantic circulation during the last glacial maximum. Paleoceanography 6:1011–1045
Lorenz EN (1979) Forced and free variations of weather and climate. J Atmos Sci 36(8):1367–1376
Losch M, Wunsch C (2003) Bottom topography as a control parameter in an ocean circulation model. J Atmos Ocean Technol 20(11):1685–1696
Loutre MF (2003) Ice ages (Milankovitch theory). In: Holton JR, Curry JA, Pyle JA (eds) Encyclopedia of Atmospheric Sciences. Elsevier Ltd., pp 995–1003
MARGO Project Members (2009) Constraints on the magnitude and patterns of ocean cooling at the Last Glacial Maximum. Nat Geosci 2:127–132. doi:10.1039/NGEO411
Meehl GA, Stocker TF, Collins WD, Friedlingstein P, Gaye AT, Gregory JM, Kitoh A, Knutti R, Murphy JM, Noda A, Raper SCB, Watterson IG, Weaver AJ, Zhao Z-C (2007) Global climate projections. In Solomon S, Qin D, Manning M, Chen M, Marquis Z, Averyt K, Tignor M, Miller H (eds) Climate Change 2007: The Physical Science Basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change. Cambridge University Press, Cambridge, pp 747–845
Milankovitch M (1920) Théorie Mathématique des Phénomène Thermique Produits par la Radiation Solaire. Gauther Villars, Paris
Milankovitch M (1930) Mathematische Klimalehre und Astronomische Theorie der Klimaschwankungen. Volume I, part A of Handbuch der Klimatologie. Verlag von Gebrüder Borntraeger, Berlin, pp A1–A176
Milankovitch M (1941) Kanon der Erdbestrahlung und seine Anwendung auf das Eiszeitenproblem. Acadèmie Royal Serbe, Belgrade
Myhre G, Highwood EJ, Shine KP, Stordal F (1998) New estimates of radiative forcing due to well mixed greenhouse gases. Geophys Res Lett 25(14):2715–2718
North GR, Mengel JG, Short DA (1983) Simple energy balance model resolving the seasons and the continents: Application to the astronomical theory of the ice ages. J Geophys Res 88(C11):6576–6586
Paul A, Schäfer-Neth C (2005) How to combine sparse proxy data and coupled climate models. Quat Sci Rev 23:1095–1107. doi:10.1016/j.quascirev.2004.05.010
Penck A, Brückner E (1901–1909) Die Alpen im Eiszeitalter. C. H. Tauchnitz, Leipzig
Petrović A (2002) Insolation and climate. Milutin Milanković and the mathematical theory of climate changes. Technical report, Ministry for Protection of Natural Resources and Environment of the Republic of Serbia in collaboration with Serbian Society of History of Science
Rayner PJ, Giering R, Kaminski T, Ménard R, Todling R, Trudinger CM (2000) Exercises. In: Kasibhatla P, Heimann M, Rayner P, Mahowald N, Prinn RG, Hartley DE (eds) Inverse Methods in Glogal Biogeochemical Cycles, vol 114, Geophysical Monograph Series. AGU, Washington, DC, pp 81–106
Rougier J (2008) Comment on article by Sansó et al. Bayesian Anal 3(1):45–56
Sarnthein M, Gersonde R, Niebler S, Pflaumann U, Spielhagen R, Thiede J, Wefer G, Weinelt M (2003) Overview of Glacial Atlantic Ocean Mapping (GLAMAP 2000). Paleoceanography 18. doi:10:1029/2002PA00769
Schäfer-Neth C, Paul A (2004) The Atlantic Ocean at the Last Glacial Maximum: 1. Objective mapping of the GLAMAP sea-surface conditions. In: Wefer G, Mulitza S, Ratmeyer V (eds) The South Atlantic in the Late Quaternary: Reconstruction of Material Budgets and Current Systems. Springer, Berlin, pp 531–548
Schneider von Deimling T, Held H, Ganopolski A, Rahmstorf S (2006) Climate sensitivity estimated from ensemble simulations of glacial climate. Clim Dyn 27:149–163. doi:10.1007/s00382-006-0126-8
Thacker W (1989) The role of the Hessian matrix in fitting models to measurements. J Geophys Res 94:6177–6196
Wessel P, Smith WHF (1998) New, improved version of Generic Mapping Tools released. EOS Trans Am Geophys Union 79:579
Winguth AME, Archer D, Maier-Reimer E, Mikolajewicz U (2000) Paleonutrient data analysis of the glacial Atlantic using an adjoint ocean general circulation model. In: Kasibhatla P, Heimann M, Rayner P, Mahowald N, Prinn RG, Hartley DE (eds) Inverse Methods in Global Biogeochemical Cycles, vol 114, Geophysical Monograph Series. AGU, Washington, DC, pp 171–183
Wunsch C (1996) The Ocean Circulation Inverse Problem. Cambridge University Press, New York
Acknowledgments
AP expresses his sincere gratitude to the organizers of the “Milutin Milankovitch 130th Anniversary Symposium” (Belgrade, 22–25 September 2009), who made this conference a very memorable and inspiring experience. We acknowledge the helpful discussions with Takasumi Kurahashi-Nakamura, as well as the instructive comments by Michel Crucifix and an anonymous reviewer. All graphs were drawn with the Generic Mapping Tools (Wessel and Smith 1998). This research was funded by the DFG-Research Center/Center of Excellence MARUM—“The Ocean in the Earth System.”
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Wien
About this paper
Cite this paper
Paul, A., Losch, M. (2012). Perspectives of Parameter and State Estimation in Paleoclimatology. In: Berger, A., Mesinger, F., Sijacki, D. (eds) Climate Change. Springer, Vienna. https://doi.org/10.1007/978-3-7091-0973-1_7
Download citation
DOI: https://doi.org/10.1007/978-3-7091-0973-1_7
Published:
Publisher Name: Springer, Vienna
Print ISBN: 978-3-7091-0972-4
Online ISBN: 978-3-7091-0973-1
eBook Packages: Earth and Environmental ScienceEarth and Environmental Science (R0)