Skip to main content
Springer Nature Link
Log in

Perspectives of Parameter and State Estimation in Paleoclimatology

  • Conference paper
  • First Online:
Climate Change

  • 2960 Accesses

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

Notes

  1. 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

    Article  CAS  Google Scholar 

  • Berger AL (1978) Long term variations of daily insolation and Quaternary climatic changes. J Atmos Sci 35(12):2362–2367

    Article  Google Scholar 

  • Berger A (1988) Milankovitch theory and climate. Rev Geophys 26:624–657

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Errico RM (1997) What is an adjoint model? Bull Am Meteorol Soc 78(11):2577–2591

    Article  Google Scholar 

  • 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

    Chapter  Google Scholar 

  • Gilbert JC, Lemaréchal C (1989) Some numerical experiments with variable storage quasi-Newton algoritms. Math Program 45:407–435

    Article  Google Scholar 

  • Griewank A, Walther A (2008) Evaluating derivatives. Principles and techniques of algorithmic differentiation, vol 19, 2nd edn, Frontiers in Applied Mathematics. SIAM, Philadelphia

    Google Scholar 

  • Grubić A (2006) The astronomical theory of climatic changes of Milutin Milankovich. Episodes 29(3):197–203

    Google Scholar 

  • Hann JV (1915) Lehrbuch der Meteorologie, 3rd edn. C.H. Tauchnitz, Leipzig

    Google Scholar 

  • Hartmann DL (1994) Global physical climatology. Academic, San Diego

    Google Scholar 

  • Hartmann DL, Short DA (1979) On the role of zonal asymmetries in climate change. J Atmos Sci 36:519–528

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Google Scholar 

  • Joussaume S, Braconnot P (1997) Sensitivity of paleoclimate simulation results to season definitions. J Geophys Res 102(D2):1943–1956

    Article  Google Scholar 

  • 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

    Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Book  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Google Scholar 

  • Le Dimet F-X, Talagrand O (1986) Variational algorithms for analysis and assimilation of meteorological observations: Theoretical aspects. Tellus 38A(2):97–110

    Article  Google Scholar 

  • LeGrand P, Wunsch C (1995) Constraints from paleotracer data on the North Atlantic circulation during the last glacial maximum. Paleoceanography 6:1011–1045

    Article  Google Scholar 

  • Lorenz EN (1979) Forced and free variations of weather and climate. J Atmos Sci 36(8):1367–1376

    Article  Google Scholar 

  • Losch M, Wunsch C (2003) Bottom topography as a control parameter in an ocean circulation model. J Atmos Ocean Technol 20(11):1685–1696

    Article  Google Scholar 

  • Loutre MF (2003) Ice ages (Milankovitch theory). In: Holton JR, Curry JA, Pyle JA (eds) Encyclopedia of Atmospheric Sciences. Elsevier Ltd., pp 995–1003

    Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Google Scholar 

  • Milankovitch M (1920) Théorie Mathématique des Phénomène Thermique Produits par la Radiation Solaire. Gauther Villars, Paris

    Google Scholar 

  • 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

    Google Scholar 

  • Milankovitch M (1941) Kanon der Erdbestrahlung und seine Anwendung auf das Eiszeitenproblem. Acadèmie Royal Serbe, Belgrade

    Google Scholar 

  • 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

    Article  CAS  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Penck A, Brückner E (1901–1909) Die Alpen im Eiszeitalter. C. H. Tauchnitz, Leipzig

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Chapter  Google Scholar 

  • Rougier J (2008) Comment on article by Sansó et al. Bayesian Anal 3(1):45–56

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Article  Google Scholar 

  • Thacker W (1989) The role of the Hessian matrix in fitting models to measurements. J Geophys Res 94:6177–6196

    Article  Google Scholar 

  • Wessel P, Smith WHF (1998) New, improved version of Generic Mapping Tools released. EOS Trans Am Geophys Union 79:579

    Article  Google Scholar 

  • 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

    Chapter  Google Scholar 

  • Wunsch C (1996) The Ocean Circulation Inverse Problem. Cambridge University Press, New York

    Book  Google Scholar 

Download references

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

  1. MARUM – Center for Marine Environmental Sciences and Department of Geosciences, University of Bremen, 33 04 40, D-28334, Bremen, Germany

    André Paul

  2. Alfred Wegener Institute for Polar and Marine Research, Bremerhaven, Germany

    Martin Losch

Authors
  1. André Paul
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Martin Losch
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to André Paul .

Editor information

Editors and Affiliations

  1. Université Catholique de Louvain, Louvain-la-Neuve, 1348, Belgium

    André Berger

  2. University of Belgrade, Belgrade, 11120, Serbia

    Fedor Mesinger

  3. , Department of Physics, University of Belgrade, Belgrade, 11120, Serbia

    Djordje Sijacki

Rights and permissions

Reprints 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

Publish with us

Policies and ethics