Recent Developments in the Theory of Glacial Cycles

Transcription

1 Recent Developments in the Theory of Richard McGehee Seminar on the Mathematics of Climate Change School of Mathematics October 6, 010 Hansen, et al, Target atmospheric CO: Where should humanity aim? Open Atmos. Sci. J. (008) O in Foraminifera Fossils During the Past. Myr O in Foraminifera Fossils During the Past 1.0 Myr.. Benthic Data (δ 8O).. Benthic Data (δo O) Lisiecki, L. E., and M. E. Raymo (00), A Pliocene-Pleistocene stack of 7 globally distributed benthic do records, Paleoceanography,0, PA100, doi:10.109/00pa Lisiecki, L. E., and M. E. Raymo (00), A Pliocene-Pleistocene stack of 7 globally distributed benthic do records, Paleoceanography,0, PA100, doi:10.109/00pa Recent (last 00 Kyr) Temperature Cycles Vostok Ice Core Data What Causes? Widely Accepted Hypothesis The glacial cycles are driven by the variations in the Earth s orbit (Milankovitch it Cycles), causing a variation in incoming i solar radiation (insolation). This hypothesis is widely accepted, but also widely regarded as insufficient to explain the observations. The additional hypothesis is that there are feedback mechanisms that amplify the Milankovitch cycles. What these feedbacks are and how they work is not fully understood. J.R. Petit, et al (1999) Climate and atmospheric history of the past 0,000 years from the Vostok ice core, Antarctica, Nature 99,

2 Eccentricity Obliquity Precession Index Climate, Hays, et al Hays Summary Three different temperature proxies from sea sediment data. Hays, et al, Science 19 (1976), p. 117 The explanation is that there are nonlinear feedbacks. Is there another explanation? Hays, et al, Science 19 (1976), p. 117

3 Cenozoic Era Hansen, et al, Target atmospheric CO: Where should humanity aim? Open Atmos. Sci. J. (008) Climate (Zachos, et al) O in Foraminifera Fossils During the Past. Myr. Benthic Data (δ 8O).. Power spectrum of climate for the last. Myr. Note the peaks at 1Kyr and 100 Kyr Lisiecki, L. E., and M. E. Raymo (00), A Pliocene-Pleistocene stack of 7 globally distributed benthic do records, Paleoceanography,0, PA100, doi:10.109/00pa Zachos Summary Energy Balance Nonlinear effects? is defined as the maximum insolation at latitude 6 N. Is there another definition of forcing? Global annual average insolation Q0 Q Q e 1 e Distribution ib ti of annual average insolation with latitude, 1 1 sin cos cos s y s y y y d 0 e = β = Note that Q depends only on, s(y) depends only on, and nothing depends on.

4 Climate (Zachos, et al) Energy Balance If we assume that glaciation depends on annual average insolation instead of insolation at summer solstice, then forcing and response are aligned. Power spectrum of climate for the last. Myr. Note the peaks at 1Kyr and 100 Kyr. Climate (Zachos, et al) Power spectrum of climate for the period Myr. Note the peak at 00. Hansen, et al, Target atmospheric CO: Where should humanity aim? Open Atmos. Sci. J. (008) Eccentricity Zachos 0 Myr ago Maybe 6 N at summer solstice isn t the right forcing.

5 Heat Balance Ice Albedo Feedback Model T R Qs y 1 y, A BT C T T t insolation albedo outward radiation y = sine of latitude T(y) = annual mean temperature Qs(y) = annual mean insolation Q = global annual mean insolation heat transport This equation has a stable equilibrium consisting of polar ice caps. The latitude of the equilibrium ice boundary and the equilibrium global annual mean temperature are functions of the parameters. Historical Overview of Climate Change Science, IPCC AR, p.96 K.K. Tung, Topics in Mathematical Modeling, Princeton (007), Chapt ice-albedo model Power ice-albedo model GMT ( C) Power Spectra Note dominance of the signal. data Insolation at 6 N at summer solstice Power Power frequency 1/Kyr frequency 1/Kyr frequency 1/Kyr Annual Global Mean Temperature The data are not duplicated by either method, but note the spectral similarities. data Insolation at 6 N at summer solstice Benthic Data (δ δo) Q day (W/m ) Ice Albedo Feedback Model T R Qs y 1 y, A BT C T T t insolation albedo outward radiation heat transport If the albedo is constant (i.e., independent of latitude, then the global mean temperature depends only on, not. Prediction: Analysis of the climate 0-0 Myr ago should show increased signal (00 and 100 Kyr) and reduced signal (1 Kyr). (current research) Hansen, et al, Target atmospheric CO: Where should humanity aim? Open Atmos. Sci. J. (008)

6 . O in Foraminifera Fossils During the Past. Myr Recent (last 00 Kyr) Temperature Cycles Vostok Ice Core Data Benthic Data (δ 8O) Lisiecki, L. E., and M. E. Raymo (00), A Pliocene-Pleistocene stack of 7 globally distributed benthic do records, Paleoceanography,0, PA100, doi:10.109/00pa J.R. Petit, et al (1999) Climate and atmospheric history of the past 0,000 years from the Vostok ice core, Antarctica, Nature 99, 9-6. Triggering Mechanism CO as Feedback Idea (Huybers, Paillard): The glaciers tend to grow. From time-totime, the reaches a critical value triggering a melt-down. Peter Huybers, Quaternary Science Reviews 6 (007) Pam Martin, University of Chicago, 010 Greenhouse Gas Feedback Model Greenhouse Gas Feedback Model dt c S t G C T, dt dc dt V W0 WC 1 Cmax C max,0. dt dt weathering volcanos CO outgassing t S t S Si sin i i C G C G Aln C0 insolation greenhouse forcing Andrew Hogg, Geophysical Research Letters (008) Andrew Hogg, Geophysical Research Letters (008) 6

7 Questions 1. Did play any role during the last million years, or is the apparent 100 Kyr cycle an artifact (Huybers).. Is the CO feedback sufficient to explain the increasing amplitude and period of the glacial cycles during the last million years, i.e., is it the mechanism behind the Huyber model.. Where does the atmospheric CO go during the glacial maxima? The ocean? The land?. What will be the effect of the anthropogenic CO? 7