Math 5490 9/29/2014 Glacial Cycles Math 5490 September 29, 2014 - PDF document

Math 5490 9/29/2014 Glacial Cycles Math 5490 September 29, 2014 The Big Picture Topics in Applied Mathematics: Introduction to the Mathematics of Climate Mondays and Wednesdays 2:30 – 3:45 http://www.math.umn.edu/~mcgehee/teaching/Math5490-2014-2Fall/ Streaming video is available at http://www.ima.umn.edu/videos/ Click on the link: "Live Streaming from 305 Lind Hall". Participation: https://umconnect.umn.edu/mathclimate http://www.snowballearth.org/when.html Math 5490 9/29/2014 Glacial Cycles Glacial Cycles Temperatures in the Cenozoic Era 18 O in Foraminifera Fossils During the Past 4.5 Myr 2.5 3 Benthic Data ( δ 18O) 3.5 4 4.5 5 5.5 ‐ 4500 ‐ 4000 ‐ 3500 ‐ 3000 ‐ 2500 ‐ 2000 ‐ 1500 ‐ 1000 ‐ 500 0 time (Kyr) Lisiecki, L. E., and M. E. Raymo (2005), A Pliocene-Pleistocene stack of 57 globally distributed benthic d18O records, Paleoceanography ,20, PA1003, doi:10.1029/2004PA001071. Hansen, et al, Target atmospheric CO2: Where should humanity aim? Open Atmos. Sci. J . 2 (2008) Math 5490 9/29/2014 Math 5490 9/29/2014 Glacial Cycles Glacial Cycles Recent (last 400 Kyr) Temperature Cycles 18 O in Foraminifera Fossils During the Past 1.0 Myr Vostok Ice Core Data 2.5 3 Benthic Data ( δ 18O) 3.5 4 4.5 5 5.5 ‐ 1000 ‐ 900 ‐ 800 ‐ 700 ‐ 600 ‐ 500 ‐ 400 ‐ 300 ‐ 200 ‐ 100 0 time (Kyr) J.R. Petit, et al (1999) Climate and atmospheric history of the past 420,000 years from the Vostok ice core, Lisiecki, L. E., and M. E. Raymo (2005), A Pliocene-Pleistocene stack of 57 globally distributed benthic Antarctica, Nature 399, 429-436. d18O records, Paleoceanography ,20, PA1003, doi:10.1029/2004PA001071. Math 5490 9/29/2014 Math 5490 9/29/2014 Richard McGehee, University of Minnesota 1

Math 5490 9/29/2014 Glacial Cycles Glacial Cycles Eccentricity Eccentricity 0.06 0.05 0.04 eccentricity 0.03 0.02 0.01 0.00 ‐ 1000 ‐ 900 ‐ 800 ‐ 700 ‐ 600 ‐ 500 ‐ 400 ‐ 300 ‐ 200 ‐ 100 0 time (Kyr) Note periods of about 100 kyr and 400 kyr. The effect due to eccentricity is more significant, but not that much: As e varies between 0 and 0.06, (1- e 2 ) -1/2 varies between 1 and 1.0018, or about 0.2%. (Twenty times the effect due to a .) J. Laskar, et al (2004) A long-term numerical solution for the insolation quantities of the Earth, Astronomy & John Imbrie & Katherine Palmer Imbrie, Ice Ages: Solving the Mystery, Harvard Univ. Press, 1979. Astrophysics 428 , 261–285. Math 5490 9/29/2014 Math 5490 9/29/2014 Glacial Cycles Glacial Cycles Obliquity Obliquity 24.5 24.0 obliquity (degrees) 23.5 23.0 22.5 22.0 ‐ 1000 ‐ 900 ‐ 800 ‐ 700 ‐ 600 ‐ 500 ‐ 400 ‐ 300 ‐ 200 ‐ 100 0 time (Kyr) Note period of about 41 Kyr. J. Laskar, et al (2004) A long-term numerical solution for the insolation quantities of the Earth, Astronomy & Astrophysics 428 , 261–285. http://upload.wikimedia.org/wikipedia/commons/6/61/AxialTiltObliquity.png Math 5490 9/29/2014 Math 5490 9/29/2014 Glacial Cycles Glacial Cycles Precession Precession Index 0.06 0.04 0.02 0.00 ‐ 0.02 ‐ 0.04 ‐ 0.06 ‐ 1000 ‐ 900 ‐ 800 ‐ 700 ‐ 600 ‐ 500 ‐ 400 ‐ 300 ‐ 200 ‐ 100 0 time (Kyr) index = e sin ρ , where e = eccentricity and ρ = precession angle (measured from spring equinox) Note period of about 23 Kyr. J. Laskar, et al (2004) A long-term numerical solution for the insolation quantities of the Earth, Astronomy & Astrophysics 428 , 261–285. http://earthobservatory.nasa.gov/Library/Giants/Milankovitch/milankovitch_2.html Math 5490 9/30/2014 Math 5490 9/30/2014 Richard McGehee, University of Minnesota 2

Math 5490 9/29/2014 Glacial Cycles Glacial Cycles Precession Daily Average Insolation at Summer Solstice at 65° N 580 560 540 520 W/m^2 500 480 460 440 420 ‐ 1000 ‐ 900 ‐ 800 ‐ 700 ‐ 600 ‐ 500 ‐ 400 ‐ 300 ‐ 200 ‐ 100 0 Kyr http://en.wikipedia.org/wiki/Zodiac Math 5490 9/29/2014 Math 5490 9/29/2014 Glacial Cycles Glacial Cycles Who was Milankovitch? Milutin Milankovitch was a Serbian mathematician and professor at the University of Belgrade. Milutin Milankovitch In 1920 he published his seminal work on 1879-1958 the relation between insolation and the Earth’s orbital parameters. In 1941 he published a book explaining his entire theory. His work was not fully accepted until 1976. http://en.wikipedia.org/wiki/Milankovitch_cycles Math 5490 9/29/2014 Math 5490 9/29/2014 Glacial Cycles Glacial Cycles Suggested Reading What happened in 1976? Hays, Imbrie, and Shackleton, “Variations in the Earth's Orbit: Pacemaker of the Ice Ages,” James D. Hays Science 194 , 10 December 1976. John Imbrie “It is concluded that changes in the earth's orbital geometry are the fundamental cause of the succession of Quaternary ice ages.” John Imbrie & Katherine Palmer Imbrie, Ice Ages: Solving the Mystery , Nicholas Shackleton H ARVARD U NIVERSITY P RESS , 1979 Math 5490 9/29/2014 Math 5490 9/29/2014 Richard McGehee, University of Minnesota 3

Math 5490 9/29/2014 Glacial Cycles Glacial Cycles History of Discovery Church of Saint Sulpice, Paris Agassiz announces glacial theory Evidence of multiple ice ages discovered in Illinois Magnetic reversals discovered 18 O theory developed climate fluctuations found in ocean cores Fourier paleomagnetic time scale developed Hays, et al 1800 1820 1840 1860 1880 1900 1920 1940 1960 1980 2000 Milankovitch explains glacial cycles Croll explains glacial cycles Humboldt debunks Adhemar Adhemar explains glacial cycles Math 5490 9/29/2014 Math 5490 9/29/2014 Glacial Cycles Glacial Cycles Church of Saint Sulpice, Paris Church of Saint Sulpice, Paris Math 5490 9/29/2014 Math 5490 9/29/2014 Glacial Cycles Glacial Cycles Church of Saint Sulpice, Paris Church of Saint Sulpice, Paris Math 5490 9/29/2014 Math 5490 9/29/2014 Richard McGehee, University of Minnesota 4

Math 5490 9/29/2014 Glacial Cycles Glacial Cycles Suggested Reading Milankovitch Theory, verified by Hays, et al: The glacial cycles are driven by the variations in the Earth’s orbit (Milankovitch Cycles), causing a variation in incoming solar radiation (insolation). We see the evidence for the existence of glacial cycles in the climate record. We can compute the Milankovitch cycles from classical physics and evidence has been gathered for thousands of years. What is the evidence for the connection between glacial cycles and Milankovitch cycles? Dan Brown, The Da Vinci Code , A NCHOR B OOKS , 2003 Math 5490 9/29/2014 Math 5490 9/29/2014 Glacial Cycles Glacial Cycles Example: Example: The ice ages occur about every 100,000 year, and the The ice ages occur about every 100,000 year, and the eccentricity of the Earth’s orbit cycles through changes eccentricity of the Earth’s orbit cycles through changes every 100,000 years. every 100,000 years. Can we quantify this observation? Can we quantify this observation? Fourier Transform (Power Spectrum) time series power spectrum Math 5490 9/29/2014 Math 5490 9/29/2014 Glacial Cycles Glacial Cycles Climate Response, Hays, et al Solar Forcing (Hays, et al) Three different temperature proxies from sea sediment data. Hays, et al , Science 194 (1976), p. 1125 Hays, et al , Science 194 (1976), p. 1125 Math 5490 9/29/2014 Math 5490 9/29/2014 Richard McGehee, University of Minnesota 5

Math 5490 9/29/2014 Glacial Cycles Glacial Cycles Eccentricity Obliquity 0.06 24.5 0.05 obliquity (degrees) 24.0 eccentricity 0.04 23.5 0.03 23.0 0.02 22.5 0.01 0 22.0 ‐ 5500 ‐ 5000 ‐ 4500 ‐ 4000 ‐ 3500 ‐ 3000 ‐ 2500 ‐ 2000 ‐ 1500 ‐ 1000 ‐ 500 0 ‐ 5500 ‐ 5000 ‐ 4500 ‐ 4000 ‐ 3500 ‐ 3000 ‐ 2500 ‐ 2000 ‐ 1500 ‐ 1000 ‐ 500 0 Kyr Kyr Math 5490 9/29/2014 Math 5490 9/29/2014 Glacial Cycles Glacial Cycles Precession Index Spectral Analysis of the Milankovitch cycles. 0.06 Laskar’s computations Spectra 0.04 precession index 0.06 0.02 0.05 eccentricity 0.04 0 Eccentricity 0.03 0.02 ‐ 0.02 0.01 ‐ 0.04 0 ‐ 5500 ‐ 5000 ‐ 4500 ‐ 4000 ‐ 3500 ‐ 3000 ‐ 2500 ‐ 2000 ‐ 1500 ‐ 1000 ‐ 500 0 ‐ 0.06 Kyr ‐ 5500 ‐ 5000 ‐ 4500 ‐ 4000 ‐ 3500 ‐ 3000 ‐ 2500 ‐ 2000 ‐ 1500 ‐ 1000 ‐ 500 0 24.5 obliquity (degrees) Kyr 24.0 23.5 Obliquity 23.0 22.5 22.0 ‐ 5500 ‐ 5000 ‐ 4500 ‐ 4000 ‐ 3500 ‐ 3000 ‐ 2500 ‐ 2000 ‐ 1500 ‐ 1000 ‐ 500 0 Kyr 0.06 0.04 precession index 0.02 Precession 0 ‐ 0.02 ‐ 0.04 ‐ 0.06 ‐ 2000 ‐ 1800 ‐ 1600 ‐ 1400 ‐ 1200 ‐ 1000 ‐ 800 ‐ 600 ‐ 400 ‐ 200 0 Kyr Math 5490 9/29/2014 Math 5490 9/29/2014 Glacial Cycles Glacial Cycles Summer Solstice 65 ° N Climate Response, Hays, et al 580 540 W/m 2 500 460 420 ‐ 5500 ‐ 5000 ‐ 4500 ‐ 4000 ‐ 3500 ‐ 3000 ‐ 2500 ‐ 2000 ‐ 1500 ‐ 1000 ‐ 500 0 Kyr precession obliquity eccentricity? Three different temperature proxies from sea sediment data. Hays, et al , Science 194 (1976), p. 1125 Math 5490 9/29/2014 Math 5490 9/29/2014 Richard McGehee, University of Minnesota 6