Perspectives of Parameter and State Estimation in Paleoclimatology
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 ene
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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.
Introduction Milankovitch is mainly renowned for his computation of the incoming solar radiation (insolation) at the top of the atmosphere over the past 600,000 years for different latitudes and seasons (Milankovitch 1920, 1930, 1941). Yet he also formulated one of the early “climate models”: He used the energy balance as implied by the planetary albedo and the outgoing longwave radiation according to the Stefan–Boltzmann law to infer the solar temperatures on the Earth’s surface if it were covered uniformly by land and the atmosphere
A. Paul (*) MARUM – Center for Marine Environmental Sciences and Department of Geosciences, University of Bremen, PO Box 33 04 40, D-28334 Bremen, Germany e-mail: [email protected]
and ocean were at rest (Milankovitch 1920, p. 200); he compared these solar temperatures to then-current observations by Hann (1915). Furthermore, he computed the fluctuations in the extent of the polar ice caps in response to the fluctuations in insolation, even taking into account the feedback of the increasing albedo and surface height of a growing ice cap on temperature (Milankovitch 1941). Finally, he related the predictions of his climate model to geological data published by Penck and Br€uckner (1909). Thus, he could associate four minima of his famous radiation curves, expressed in terms of equivalent latitudes, with the European ice ages as they were known at the time (for more detailed accounts of Milankovitch’s achievements, see Berger 1988; Petrovic´ 2002; Loutre 2003; Grubic´ 2006). Formulating a climate model, then solving it either analytically or numerically, calibrating it against
A. Berger et al. (eds.), Climate Change, DOI 10.1007/978-3-7091-0973-1_7, # Springer-Verlag Wien 2012
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current observations, applying it to past conditions, and relating its predictions to geological data—this is the traditional or “forward” method of paleoclimate modeling that Milankovitch pioneered in the first half of the last century. So-called “st
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