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Long-Term Variations of Caloric Insolation Resulting from the Earth's Orbital Elements1

Published online by Cambridge University Press:  20 January 2017

André L. Berger*
Institut d'Astronomie et de Géophysique, Université Catholique de Louvain, 2, chemin du Cyclotron, 1348 Louvain-la-Neuve, Belgium


A contribution to a global a priori model of climatic changes for the Quaternary Ice Age is tentatively proposed. Special emphases are put on the astronomical problem and on the insolation available in the assumption of a perfectly transparent atmosphere. It is shown that for these two steps an accurate solution can be obtained, limiting the cumulative effect of computational approximation and allowing input to a climatological model to be of real value. For the earth's orbital elements, the proposed solution includes terms dependent to the second degree on disturbing masses, to third degree on planetary eccentricities and inclinations and, for the obliquity and the annual general precession in longitude, also to the second degree on earth's eccentricity. Improvements introduced by this solution upon the insolation computed through the Milankovitch series are deduced from the differences between Vernekar's results and present ones. The relative agreement between results clearly shows that the new astronomical solution is probably close to the ideal one from a paleoclimatological point of view.

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University of Washington

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This paper is based on two communications presented by the author, respectively, at the WMO-IAMAP Symposium, “Long-Term Climatic Fluctuations and the Future of Our Climate,” held in Norwich, August 1975 (Berger, 1975b), and at the XVI General Assembly of the UGGI, Symposium 19, “Garp Second Objective: Climate Change,” held in Grenoble, September 1975.


Adam, D.P., 1973. Ice Ages and the thermal equilibrium of the earth. United States Geological Survey, Research. 1, 587 596.Google Scholar
Adam, D.P., 1975. Ice Ages and thermal equilibrium of the earth. Quaternary Research. 5, 161 171.CrossRefGoogle Scholar
Berger, A.L., 1973. La Théorie Astronomique des Paléoclimats. Doctoral dissertation. Université Catholique de Louvain, Louvain-la-Neuve, Belgium. Google Scholar
Berger, A.L., 1975. Détermination de l'irradiation solaire par les intégrales elliptiques. Annales Société Scientifique de Bruxelles. 89, 69 91.Google Scholar
Berger, A.L., 1975. The astronomical theory of paleoclimates: A cascade of accuracy. Proceedings of the WMO-IAMAP Symposium on Long-Term Climatic Fluctuations. WMO No. 421. World Meteorological Organization, Geneva, 65 72.Google Scholar
Berger, A.L., 1976. Obliquity and precession for the last 5,000,000 years. Astronomy and Astrophysics. 51, 127 135.Google Scholar
Berger, A.L., 1976. Long-term variations of daily and monthly insolation during the last Ice Age. Eos. 57, 254.Google Scholar
Berger, A.L., 1977. Power and limitation of an energy-balance climate model as applied to the astronomical theory of paleoclimates. Paleogeography, Climatology, and Ecology. 21, 227 235.CrossRefGoogle Scholar
Berger, A.L., 1977. Long-term variation of the earth's orbital elements. Celestial Mechanics. 15, 53 74.CrossRefGoogle Scholar
Berger, A.L., 1977. Support for the astronomical theory of climatic change. Nature (London). 269, 44 45.CrossRefGoogle Scholar
Bernard, E., 1962 Théorie Astronomique des Pluviaux et Interpluviaux du Quaternaire Africain. fasc 1, Acad. Roy. Sc. Outre-Mer. Cl. Sc. Nat. et Med, Bruxelles, Nouvelle série, XII.Google Scholar
Bowles, F.A., 1975. Paleomagnetic significance of quartz/illite variations in cores from the Eastern Equatorial North Atlantic. Quaternary Research. 5, 225 236.CrossRefGoogle Scholar
Bretagnon, P., 1974. Termes à longues périodes dans le système solaire. Astronomy and Astrophysics. 30, 141 154.Google Scholar
Broecker, W.S., 1968. In defense of the astronomical theory of glaciation. Meteorological Monographs. 8, 139 141.Google Scholar
Brouwer, D., van Woerkom, A.J.J., 1950. Secular variations of the orbital elements of principal planets. Astron. Papers Am. Ephemeris. 13, 81 107 part 2.Google Scholar
Brouwer, D., Clemence, G.M., 1961 Methods of Celestial Mechanics. Academic Press, New York and London. Google Scholar
Brumberg, 95.A., Evdikimova, L.S., Skripnichenko, 96.I., 1975. Secular perturbations in general planetary theory. Celestial Mechanics. 11, 131 138.CrossRefGoogle Scholar
Chyleck, P., Coakley, J.A., 1975. Analytical analysis of a Budyko type climate model. Journal of Atmospheric Science. 32, 675 679.2.0.CO;2>CrossRefGoogle Scholar
Climap Project Members 1976. The surface of the Ice-Age earth. Science. 191, 1131 1137.CrossRefGoogle Scholar
Cohen, C.J., Hubbard, E.C., Oesterwinter, C., 1973. Planetary elements for 10,000,000 years. Celestial Mechanics. 7, 438 448.CrossRefGoogle Scholar
Gates, W.L., 1976. Modeling the Ice-Age climate. Science. 191, 1138 1144.CrossRefGoogle ScholarPubMed
Gribbin, J., 1976. Mason develops Ice Age theory. Nature (London). 260, 396.CrossRefGoogle Scholar
Hays, J.D., Imbrie, J., Shackleton, N.J., 1976. Variations in the earth's orbit: Pacemaker of the Ice Ages. Science. 194, 1121 1132.CrossRefGoogle ScholarPubMed
Held, I.M., Suarez, M.J., 1974. Simple albedo feed back models of ice cap. Tellus. 26, 613 629.CrossRefGoogle Scholar
Imbrie, J., Kipp, N.G., 1971. A new micropaleontological method for quantitative paleoclimatology: Application to a Late Pleistocene Carribbean core. Turekian, K.K., Late Cenozoic glacial Ages. Yale University Press, New Haven and London, 71 182.Google Scholar
Johnson, R.G., McClure, B.T., 1976. A model for Northern Hemisphere continental ice sheet variation. Quaternary Research. 6, 325 353.CrossRefGoogle Scholar
Kovalevsky, J., 1963 Introduction à la Mécanique Céleste. Armand Colin, Paris. Google Scholar
Kukla, G.J., 1975. Missing link between Milanko-vitch and climate. Nature (London). 253, 600 603.CrossRefGoogle Scholar
Kukla, G.J., 1976. Revival of Milankovitch. Nature (London). 261, 11.CrossRefGoogle Scholar
Laubscher, R.E., 1972. A determination of the motion of the ecliptic. Astronomy and Astrophysics. 20, 407 414.Google Scholar
Mason, B.J., 1976. Towards the understanding and prediction of climatic variations. Quarterly Journal of the Royal Meteorological Society. 102, 473 499.CrossRefGoogle Scholar
Milankovitch, M.M., 1941 Canon of Insolation and the Ice-Age Problem. Königlich Serbische Akademie, Beograd, English translation by the israel Program for Scientific Translations and published for the U.S. Department of Commerce and the National Science Foundation, Washington, D.C..Google Scholar
Mitchell, J.M. Jr., 1976. An overview of climatic variability and its causal mechanisms. Quaternary Research. 6, 481 493.CrossRefGoogle Scholar
Newell, R.E., 1974. Changes in poleward energy flux by the atmosphere-ocean as a possible cause for Ice Ages. Quaternary Research. 4, 117 128.CrossRefGoogle Scholar
North, G.R., 1975. Theory of energy-balance climate models. Journal of Atmospheric Science. 32, 2033 2043.2.0.CO;2>CrossRefGoogle Scholar
Paltridge, G.W., 1975. Global dynamics and climate—A system of minimum entropy exchange. Quarterly Journal of the Royal Meterological Society. 429, 475 485.CrossRefGoogle Scholar
Peixoto, J.P., 1970. Water vapor balance of the atmosphere from 5 years of hemispheric data. Nordic Hydrology. 2, 120 138.CrossRefGoogle Scholar
Pisias, N.G., Heath, G.R., Moore, T.C. Jr., 1975. Lag times for oceanic responses to climatic change. Nature (London). 256, 716 717.CrossRefGoogle Scholar
Saltzman, B., Vernekar, A.D., 1975. A solution for the Northern Hemisphere climatic zonation during a glacial maximum. Quaternary Research. 5, 307 320.CrossRefGoogle Scholar
Sancetta, C., Imbrie, J., Kipp, N.G., 1973. Climatic record of the past 130,000 years in North Atlantic deep-sea core V23-82: Correlation with the terrestrial record. Quaternary Research. 3, 110 116.CrossRefGoogle Scholar
Sellers, W.D., 1969. A global climatic model based on the energy balance of the earth-atmosphere system. Journal of Applied Meteorology. 8, 392 400.2.0.CO;2>CrossRefGoogle Scholar
Sellers, W.D., 1976. A two-dimensional global climatic model. Monthly Weather Review. 104, 233 248.2.0.CO;2>CrossRefGoogle Scholar
Schneider, S.H., Dickinson, R.E., 1974. Climatic modeling. Reviews of Geophysics and Space Physics. 12, 447 493.CrossRefGoogle Scholar
Shackleton, N.J., 1975. The world climate record revealed in deep-sea sediments. Proceedings of the WMO-IAMAP Symposium on Long-Term Climatic Fluctuations. WMO no. 421. World Meteorological Organization, Geneva, 3.Google Scholar
Shackleton, N.J., Opdyke, N.D., 1973. Oxygen isotope and paleomagnetic stratigraphy of Equatorial Pacific core V28-238: Oxygen isotope temperature and ice volume on a 104 and 105 year scale. Quaternary Research. 3, 39 55.CrossRefGoogle Scholar
Sharaf, S.G., Boudnikova, N.A., 1967. Secular variations of elements of the earth's orbit which influence the climate of the geological past. Trudy Instituta Teoreticheskoi Astronomii. 11, 231 261 (in Russian).Google Scholar
Sharaf, S.G., Boudnikova, N.A., 1969. Secular perturbations in the elements of the earth's orbit and the astronomical theory of climate variations. Trudy Instituta Teoreticheskoi Astronomii. 14, 48 84 (in Russian).Google Scholar
Stidd, C.K., 1970. Meridional profiles of Northern Hemisphere water balance. Association International Hydrologie Scientifique. 93, 353 361.Google Scholar
Suarez, M.J., Held, I.M., 1976. Modeling Climatic response to orbital parameter variations. Nature (London). 263, 46 47.CrossRefGoogle Scholar
Tisserand, F., 1888 Traité de Mécanique Céleste. Gauthier-Villars, Paris, (nouveau tirage, 1960).Google Scholar
1974. U.S. Federal Council for Science and Technology, Interdepartmental Committee for Atmospheric Sciences. Report of the Ad Hoc panel on the Present Interglacial. ICAS Report 18b-FY 75.Google Scholar
Van Woerkom, A.J.J., 1953. Astronomical theory of climatic change. Shapley, H., Climatic Change. Harvard University Press, Cambridge, 147 157.Google Scholar
Vernekar, A.D., 1972. Long-period global variations of incoming solar radiation. Meteorological Monographs. 12, No. 34.Google Scholar
Weertman, J., 1976. Milankovitch solar radiation variations and Ice Age ice sheet sizes. Nature (London). 261, 17 20.CrossRefGoogle Scholar
Wetherald, R.T., Manabe, S., 1975. The effects of changing the solar constant on the climate of a general circulation model. Journal of Atmospheric Science. 32, 2044 2059.2.0.CO;2>CrossRefGoogle Scholar
Wigley, T.M.L., 1976. Spectral analysis and the astronomical theory of climatic change. Nature (London). 264, 629 631.CrossRefGoogle Scholar
Williams, J., Barry, R.G., Washington, N.M., 1974. Simulation of atmospheric circulation using NCAR global circulation model with Ice Age boundary conditions. Journal of Applied Meteorology. 13, 305 317.2.0.CO;2>CrossRefGoogle Scholar
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