As obliquity and eccentricity vary around constant
values (23.32
for obliquity and 0.0287 for eccentricity),
these elements may be considered as a constant in a first
very rough approximation as compared to the variations
of climatic precession. As the amplitude of e sin e
o is modulated by eccentricity, the envelope of e sin e
o is given
exactly by e.
Because the length of the seasons varies in time
according to Kepler’s second law, the solstices and equinoxes occur at different calendar dates through time. The
meteorological seasons are therefore continuously shifting
through the astronomical ones and do not correspond to
the same configuration of the Earth relative to the Sun.
Bibliography
Adhémar, J. A., 1842. Re ´volution des mers, De ´luges pe ´riodiques.
Première édition: Carilian-Goeury et V. Dalmont, Paris. Seconde
édition: Lacroix-Comon, Hachette et Cie, Dalmont et Dunod,
Paris, 359 p.
Berger, A., 1973. The ´orie Astronomique des Pale ´oclimats. Dissertation doctorale, Belgium, Université catholique de Louvain,
2 Vol.
Berger, A., 1977. Long-term variations of the Earth’s orbital elements. Celestial Mechanics, 15, 53–74.
Berger, A., 1978. Long-term variations of daily insolation and Quaternary climatic changes. Journal of the Atmospheric Sciences,
35(12), 2362–2367.
Berger, A., 2012. A brief history of the astronomical theories of
paleoclimates. In Berger, A., Mesinger, F., and Sijacki,
D. (eds.), Climate change at the eve of the second decade of
the century. Inferences from Paleoclimates and regional
aspects. Proceedings of Milankovitch 130th Anniversary Symposium. Wien: Springer, pp. 107–129. doi:10.1007/978-3-70910973-1.
Berger, A., and Loutre, M. F., 1990. Origine des fréquences des éléments astronomiques intervenant dans le calcul de l’insolation.
Bulletin de la Classe des Sciences de l’Acade ´mie royale de Belgique, I(1–3), 45–106. 6ème série.
Berger, A., and Loutre, M. F., 1991. Insolation values for the climate
of the last 10 million years. Quaternary Science Review, 10(4),
297–317.
Berger, A., and Loutre, M. F., 1992. Astronomical solutions for
paleoclimate studies over the last 3 million years. Earth Planetary Science Letters, 111(2/4), 369–382.
Berger, A., and Loutre, M. F., 1994. Precession, eccentricity, obliquity, insolation and paleoclimates. In Duplessy, J. C., and
Spyridakis, M. T. (eds.), Long-Term Climatic Variations: Data
and Modling. Berlin: Springer. NATO ASI Series, Vol. I22,
pp. 107–151.
Berger, A., Loutre, M. F., and Mélice, J. L., 1998. Instability of the
astronomical periods from 1.5 Myr BP to 0.5 Myr
AP. Palaeoclimates Data and Modelling, 2(4), 239–280.
Berger, A., Mélice, J. L., and Loutre, M. F., 2005. On the origin of
the 100-kyr cycles in the astronomical forcing. Paleoceanography, 20, PA4019.
Bretagnon, P., 1974. Termes à longues périodes dans le système
solaire. Astronomy and Astrophysics, 30, 141–154.
Brouwer, D., and Van Woerkom, A. J. J., 1950. Secular variations of
the orbital elements of principal planets. Astronomical Papers
Prepared for American Ephemeris and Nautical Almanac, US
Naval Observatory, 13(2), 81–107.
Emiliani, C. R. W., 1955. Pleistocene temperatures. Journal of
Geology, 63(6), 538–578.
Hays, J. D., Imbrie, J., and Shackleton, N. J., 1976. Variations in the
Earth’s orbit: pacemaker of the ice ages. Sciences, 194,
1121–1132.
Laskar, J., 1988. Secular evolution of the solar system over 10 million years. Astronomy and Astrophysics, 198, 341–362.
Laskar, J., 1999. The limits of Earth orbital calculations for geological time scale use. In Shackleton, N. J., McCave, I. N., and
Weedon, G. P. (eds.), Astronomical (Milankovitch) Calibrations
of the Geological Time Scale. London: Philosophical Transactions of the Royal Society, Vol. 357, pp. 1735–1759.
Mélice, J. L., Coron, A., and Berger, A., 2001. Amplitude and frequency modulations of the Earth’s obliquity for the last million
years. Journal of Climate, 14(6), 1043–1054.
Milankovitch, M., 1920. The ´orie Mathe ´matique des Phe ´nomènes
Thermiques Produits par la Radiation Solaire. Acade ´mie
Yougoslave des Sciences et des Arts de Zagreb. Paris: Gauthier
Villars.
Vernekar, A. D., 1972. Long-period global variations of incoming
solar radiation. Meteorology Monographs, 12(34), 130.
Cross-references
Paleoceanography
Relative Sea-level (RSL) Cycle
AXIAL SUMMIT TROUGHS
Samuel Adam Soule
1 and Michael R. Perfit
2
1
Woods Hole Oceanographic Institution, Woods Hole,
MA, USA
2
Department of Geological Sciences, University of
Florida, Gainesville, FL, USA
Synonyms
Axial summit collapse trough; Axial summit graben; Cleft
Definition
An axial summit trough (AST) is a narrow trough or volcanically modified graben that develops at the crest of a
midocean ridge and typically is the locus of volcanic and
hydrothermal activity.
Introduction
At the summit of magmatically robust midocean ridges
(MORs), a narrow trough may develop that marks the
location of the divergent plate boundary and is the locus
of most magmatic and hydrothermal activity (Macdonald
and Fox, 1988). This axial summit trough (AST) is typically less than 500 m in width and 50 m in depth and
may be discontinuous along the ridge in terms of its width,
depth, strike, and continuity. ASTs are common along
fast- and intermediate-spreading rate ridges (e.g., East
Pacific Rise, Juan de Fuca Ridge, Galapagos Spreading
Center), and magma-rich, inflated portions of the slowspreading Mid-Atlantic Ridge and Lau Basin back-arc
spreading center.
AXIAL SUMMIT TROUGHS
33
values (23.32
for obliquity and 0.0287 for eccentricity),
these elements may be considered as a constant in a first
very rough approximation as compared to the variations
of climatic precession. As the amplitude of e sin e
o is modulated by eccentricity, the envelope of e sin e
o is given
exactly by e.
Because the length of the seasons varies in time
according to Kepler’s second law, the solstices and equinoxes occur at different calendar dates through time. The
meteorological seasons are therefore continuously shifting
through the astronomical ones and do not correspond to
the same configuration of the Earth relative to the Sun.
Bibliography
Adhémar, J. A., 1842. Re ´volution des mers, De ´luges pe ´riodiques.
Première édition: Carilian-Goeury et V. Dalmont, Paris. Seconde
édition: Lacroix-Comon, Hachette et Cie, Dalmont et Dunod,
Paris, 359 p.
Berger, A., 1973. The ´orie Astronomique des Pale ´oclimats. Dissertation doctorale, Belgium, Université catholique de Louvain,
2 Vol.
Berger, A., 1977. Long-term variations of the Earth’s orbital elements. Celestial Mechanics, 15, 53–74.
Berger, A., 1978. Long-term variations of daily insolation and Quaternary climatic changes. Journal of the Atmospheric Sciences,
35(12), 2362–2367.
Berger, A., 2012. A brief history of the astronomical theories of
paleoclimates. In Berger, A., Mesinger, F., and Sijacki,
D. (eds.), Climate change at the eve of the second decade of
the century. Inferences from Paleoclimates and regional
aspects. Proceedings of Milankovitch 130th Anniversary Symposium. Wien: Springer, pp. 107–129. doi:10.1007/978-3-70910973-1.
Berger, A., and Loutre, M. F., 1990. Origine des fréquences des éléments astronomiques intervenant dans le calcul de l’insolation.
Bulletin de la Classe des Sciences de l’Acade ´mie royale de Belgique, I(1–3), 45–106. 6ème série.
Berger, A., and Loutre, M. F., 1991. Insolation values for the climate
of the last 10 million years. Quaternary Science Review, 10(4),
297–317.
Berger, A., and Loutre, M. F., 1992. Astronomical solutions for
paleoclimate studies over the last 3 million years. Earth Planetary Science Letters, 111(2/4), 369–382.
Berger, A., and Loutre, M. F., 1994. Precession, eccentricity, obliquity, insolation and paleoclimates. In Duplessy, J. C., and
Spyridakis, M. T. (eds.), Long-Term Climatic Variations: Data
and Modling. Berlin: Springer. NATO ASI Series, Vol. I22,
pp. 107–151.
Berger, A., Loutre, M. F., and Mélice, J. L., 1998. Instability of the
astronomical periods from 1.5 Myr BP to 0.5 Myr
AP. Palaeoclimates Data and Modelling, 2(4), 239–280.
Berger, A., Mélice, J. L., and Loutre, M. F., 2005. On the origin of
the 100-kyr cycles in the astronomical forcing. Paleoceanography, 20, PA4019.
Bretagnon, P., 1974. Termes à longues périodes dans le système
solaire. Astronomy and Astrophysics, 30, 141–154.
Brouwer, D., and Van Woerkom, A. J. J., 1950. Secular variations of
the orbital elements of principal planets. Astronomical Papers
Prepared for American Ephemeris and Nautical Almanac, US
Naval Observatory, 13(2), 81–107.
Emiliani, C. R. W., 1955. Pleistocene temperatures. Journal of
Geology, 63(6), 538–578.
Hays, J. D., Imbrie, J., and Shackleton, N. J., 1976. Variations in the
Earth’s orbit: pacemaker of the ice ages. Sciences, 194,
1121–1132.
Laskar, J., 1988. Secular evolution of the solar system over 10 million years. Astronomy and Astrophysics, 198, 341–362.
Laskar, J., 1999. The limits of Earth orbital calculations for geological time scale use. In Shackleton, N. J., McCave, I. N., and
Weedon, G. P. (eds.), Astronomical (Milankovitch) Calibrations
of the Geological Time Scale. London: Philosophical Transactions of the Royal Society, Vol. 357, pp. 1735–1759.
Mélice, J. L., Coron, A., and Berger, A., 2001. Amplitude and frequency modulations of the Earth’s obliquity for the last million
years. Journal of Climate, 14(6), 1043–1054.
Milankovitch, M., 1920. The ´orie Mathe ´matique des Phe ´nomènes
Thermiques Produits par la Radiation Solaire. Acade ´mie
Yougoslave des Sciences et des Arts de Zagreb. Paris: Gauthier
Villars.
Vernekar, A. D., 1972. Long-period global variations of incoming
solar radiation. Meteorology Monographs, 12(34), 130.
Cross-references
Paleoceanography
Relative Sea-level (RSL) Cycle
AXIAL SUMMIT TROUGHS
Samuel Adam Soule
1 and Michael R. Perfit
2
1
Woods Hole Oceanographic Institution, Woods Hole,
MA, USA
2
Department of Geological Sciences, University of
Florida, Gainesville, FL, USA
Synonyms
Axial summit collapse trough; Axial summit graben; Cleft
Definition
An axial summit trough (AST) is a narrow trough or volcanically modified graben that develops at the crest of a
midocean ridge and typically is the locus of volcanic and
hydrothermal activity.
Introduction
At the summit of magmatically robust midocean ridges
(MORs), a narrow trough may develop that marks the
location of the divergent plate boundary and is the locus
of most magmatic and hydrothermal activity (Macdonald
and Fox, 1988). This axial summit trough (AST) is typically less than 500 m in width and 50 m in depth and
may be discontinuous along the ridge in terms of its width,
depth, strike, and continuity. ASTs are common along
fast- and intermediate-spreading rate ridges (e.g., East
Pacific Rise, Juan de Fuca Ridge, Galapagos Spreading
Center), and magma-rich, inflated portions of the slowspreading Mid-Atlantic Ridge and Lau Basin back-arc
spreading center.
AXIAL SUMMIT TROUGHS
33