Glacial Cycles: the 100,000-Year Problem Glacial Cycles: The

Home , Milankovitch cycles

Glacial Cycles: Glacial Cycles: the 100,000-Year Problem the 100,000-Year Problem

Richard McGehee

Seminar on the Mathematics of Climate Change School of Mathematics April 13, 2011

http://www.tqnyc.org/NYC052141/beginningpage.html

Ice-Albedo Feedback Glacial Cycles

Climate in the Cenozoic Era Climate During the Past 4.5 Myr

2.5

3 O)

8 353.5 1 δ (

4 Data

4.5 Benthic

5.5 ‐4500 ‐4000 ‐3500 ‐3000 ‐2500 ‐2000 ‐1500 ‐1000 ‐500 0

time (Kyr)

Myr

Lisiecki, L. E., and M. E. Raymo (2005), A Pliocene-Pleistocene stack of 57 globally distributed benthic d18O Hansen, et al, Target atmospheric CO2: Where should humanity aim? Open Atmos. Sci. J. 2 (2008) records, Paleoceanography,20, PA1003, doi:10.1029/2004PA001071.

Glacial Cycles Glacial Cycles

Climate During the Past 1.0 Myr Recent (last 400 Kyr) Temperature Cycles Vostok Ice Core Data

2.5

3 ) O 3.5 18 δ (

4 Data

4.5 Benthic

5.5 ‐1000 ‐900 ‐800 ‐700 ‐600 ‐500 ‐400 ‐300 ‐200 ‐100 0

time (Kyr)

Lisiecki, L. E., and M. E. Raymo (2005), A Pliocene-Pleistocene stack of 57 globally distributed benthic d18O J.R. Petit, et al (1999) Climate and atmospheric history of the past 420,000 years from the Vostok ice core, records, Paleoceanography,20, PA1003, doi:10.1029/2004PA001071. Antarctica, Nature 399, 429-436.

1 Glacial Cycles Glacial Cycles

Heat Balance What Causes Glacial Cycles?

Widely Accepted Hypothesis

The glacial cycles are driven by the variations in the Earth’s orbit (Milank ovit ch C ycl es) , causi ng a vari ati on i n i ncomi ng sol ar 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 are not fully understood.

Historical Overview of Climate Change Science, IPCC AR4, p.96 http://ipcc-wg1.ucar.edu/wg1/Report/AR4WG1_Print_CH01.pdf

Glacial Cycles Glacial Cycles

Obliquity Eccentricity

http://www.crrel.usace.army.mil/permafrosttunnel/Ice_Age_Earth_Orbit.jpg http://upload.wikimedia.org/wikipedia/commons/6/61/AxialTiltObliquity.png

Glacial Cycles Glacial Cycles

Precession Eccentricity

0.06

0.05

0.04

0.03 eccentricity 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.

J. Laskar, et al (2004) A long-term numerical solution for the insolation quantities of the Earth, http://earthobservatory.nasa.gov/Library/Giants/Milankovitch/milankovitch_2.html Astronomy & Astrophysics 428, 261–285.

2 Glacial Cycles Glacial Cycles

Obliquity Precession Index

24.5 0.06

0.04 24.0 0.02

23.5 0.00 (degrees)

23.0 ‐0.02 liquity b o ‐0.04 22.5 ‐0.06 ‐1000 ‐900 ‐800 ‐700 ‐600 ‐500 ‐400 ‐300 ‐200 ‐100 0 22.0 ‐1000 ‐900 ‐800 ‐700 ‐600 ‐500 ‐400 ‐300 ‐200 ‐100 0 time (Kyr)

time (Kyr) index = e sinρ, where e = eccentricity and ρ = precession angle (measured from spring equinox) Note period of about 41 Kyr. Note period of about 23 Kyr.

J. Laskar, et al (2004) A long-term numerical solution for the insolation quantities of the Earth, J. Laskar, et al (2004) A long-term numerical solution for the insolation quantities of the Earth, Astronomy & Astrophysics 428, 261–285. Astronomy & Astrophysics 428, 261–285.

Glacial Cycles Glacial Cycles

Eccentricity Power Spectrum Obliquity Power Spectrum

Glacial Cycles Glacial Cycles

Precession Index Power Spectrum Lisiecki–Raymo δ18O Stack

Lisiecki Data 2.5

3.5 O

18 4  4.5

5.5 ‐5000 ‐4000 ‐3000 ‐2000 ‐1000 0

Kyr

0 0 0.010.020.030.040.050.06

eccentricity obliquity precession

3 Glacial Cycles Glacial Cycles

Why obliquity and eccentricity? Why obliquity over eccentricity?

Incoming Solar Radiation (Insolation), averaged over the entire globe and over a full year, depends only on eccentricity e , not on Possible explanation: Ice-albedo feedback either obliquity or precession. Q Ice reflects more energy than land or water. Qe 0 1 e2 more ice → less energy → colder → more ice liless ice → more energy → warmer → liless ice Insolation as a function of latitude, averaged over a full year, depends on eccentricity e and obliquity β , but not precession.

IQesy ,   where

2 2 2  2 s yyyd,11sincoscos   2      0 y  sin latitude

Glacial Cycles Glacial Cycles

Budyko-Sellers Model Heat Balance T R  Qs y1,  y   A BT C T T t insolation albedo re-radiation transport

TTyt  , : annual mean surface temperature y sin latitude yy0 0, 1 Q : global annual mean insolation 1 st: relative annual mean insolation s ydy 1   0 y  : ice boundary

1,,y  y,  albedo 2 ,.y 

1 Tt Tytdy ,  : global annual mean temperature 0 Historical Overview of Climate Change Science, IPCC AR4, p.96 http://ipcc-wg1.ucar.edu/wg1/Report/AR4WG1_Print_CH01.pdf

Glacial Cycles Glacial Cycles

Budyko-Sellers Model

Solve for equilibrium solution T*(y) . T Set right hand side = 0. R  Qs y1,  y   A BT C T T t equilibrium temperature profiles

30 Note that the equilibrium solution T*(y) depends on Q and s(y) , which depend on the eccentricity e and the obliquity β . Two equilibrium solutions: 20 Therefore,,q the equilibrium location of the ice boundary and 10 η small cap: stable the equilibrium global mean temperature (GMT) depend on the large cap: unstable 0 eccentricity and the obliquity. -10 We can use the computed values of eccentricity and obliquity to Not equilbria: -20 compute the ice boundary and GMT over the glacial cycles. ice free temperature (ºC) -30 snowball Q -40 Qe 0 2 -50 1 e 0.00.20.40.60.81.0 2 sin(latitude) 2 2  2 s yyyd,11sincoscos   2    ice free snowball small cap big cap   0

4 Glacial Cycles Glacial Cycles

Budyko-Sellers Model power spectra

Model output: ice boundary ice boundary

Model output: global mean temperature

20 global mean Climate data 15 temperature 10 5

0 0 0.01 0.02 0.03 0.04 0.05 0.06

eccentricity obliquity precession

Glacial Cycles Glacial Cycles

The ice-albedo feedback model correctly predicts the dominance of obliquity, but it fails to explain most of the 41 Kyr dominates 100 Kyr dominates other features of the climate data.

2.5 2.5

3 3

3.5 18O)

δ 3.5 ( 18O)

δ (

4 Data Climate data ta hic a

t 4

4.5 D

Ben

5 4.5 Benthic 5.5 ‐4500 ‐4000 ‐3500 ‐3000 ‐2500 ‐2000 ‐1500 ‐1000 ‐500 0 5 time (Kyr) 5.5 ‐4500 ‐4000 ‐3500 ‐3000 ‐2500 ‐2000 ‐1500 ‐1000 ‐500 0

time (Kyr)

Model output 100,000 Year Problem: What’s up with the last million years? Did eccentricity reassert itself? Or something else?

Glacial Cycles Glacial Cycles

Huyber’s Analysis of Deglaciations Huyber’s Analysis of Deglaciations

The deglaciations are triggered by obliquity cycles, but sometimes they don’t trigger. When cycles are skipped, the deggpyyy,laciations can be separated by 80 Kyr or 120 Kyr, creating the appearance of 100 Kyr cycles.

Red dots: deglaciations.

Peter Huybers, "Glacial variability over the last two million years: an extended depth-derived agemodel, continuous obliquity pacing, and the Pleistocene progression," Quaternary Science Reviews 26, 37-55 (2007).

5 Glacial Cycles Glacial Cycles

Huyber’s Triggering Model Huyber’s Triggering Model

Vtt : ice volume at time VVTttt1  if Vt   Tt : threshold variable  0if VTtt  : rate of increase of ice volume Tatbctt t: normalized obliquity

Units and constants

t : Kyr V : chosen so that η = 1. θ’: mean zero and variance one a = 0.05 b = 126 c = 20 black: model red: data

Glacial Cycles Glacial Cycles

Huyber’s Triggering Model Vostok Core Sample Data Petit, et al, Nature 399 (June 3 1999), pp.429-436

Huyber’s model produces the decline in temperature and the increase kiloyear bp in period and amplitude of the glacial cycles, but it depends heavily on 450 400 350 300 250 200 150 100 50 0 4 an unspecified decline in the sensitivity of the triggering mechanism 2 over last two million years. 0 ture

-2 a -4 What about greenhouse gases and the carbon cycle? -6 temper -8 Andrew Hogg suggested a model incorporating the carbon cycle. -10

300

250

200 atmos CO2 ppm 150 450 400 350 300 250 200 150 100 50 0 kiloyear bp

Glacial Cycles Glacial Cycles

Hogg’s Model Hogg’s Model

dT cStGCT    4 , dt dC dT VWWCC01   max  Cmax  , 0 . dt dt

weathering CO2 outgassing volcanos

2t St S Si sininsolation i i C GC G Aln  greenhouse forcing C0

Andrew McC. Hogg, "Glacial cycles and carbon dioxide: A conceptual model," Geophysical Research Letters 35 (2008).

6 Glacial Cycles Glacial Cycles

Salzman-Maasch Model Hogg’s Model

Hogg’s model shows how the carbon cycle can act as a feedback Milankovitch forcing amplifying and modifying the insolation forcing, but the forcing is somewhat artificial, and the triggering mechanism is difficult to justify.  Also, it does not solve the 100,000-year problem. global ice mass XXYuMt    atmospheric CO  22 What if the 100,000 year glacial cycle is not driven by 2 YpZrYsZZY   eccentricity, but is a natural oscillation of the Earth’s climate? deep ocean temperature ZqXZ   Saltzman and Maasch suggested just such a model.

Barry Salzman and Kirk A. Maasch, "A Low-Order Dynamical Model of Global Climatic Variability Over the Full Pleistocene," Journal of Geophysical Research 95 (D2), 1955-1963 (1990)

Glacial Cycles Glacial Cycles

Salzman-Maasch Model Salzman-Maasch Model unforced forced

Glacial Cycles Glacial Cycles

Salzman-Maasch Model Current Project

The Salzman-Maasch model shows how the carbon cycle and the The Mathematics and Climate Research Network (MCRN) has a ocean currents can interact to produce unforced oscillations with Webinar working group developing a model incorporating ice-albedo periods of about 100,000 years. The same model with slightly feedback with the carbon cycle. different parameters can exhibit stationary behavior. By forcing the Local expert: Samantha Oestriecher mode l w ith Milan kov itc h cyc les an d by s low ly vary ing the parame ters over the last two million years, they can produce a bifurcation from small oscillations tracking the Milankovitch cycles to large oscillations with a dominant 100,000 year period. Seems like a nice idea, but it is not widely accepted as the explanation.

7 Glacial Cycles

The 100,000-Year Problem Summary

100 Kyr cycles during the last million years, but 41 Kyr cycles before that. Why? Huybers: Obliquity rules, but glaciers started skipping beats. Alternating 80 Kyr and 120 Kyr looks like 100 Kyr Saltzman & Maasch: Under some conditions, the climate naturally oscillates at 100 Kyr. Those conditions arose 1 Myr ago. Before that, the climate tracked Milankovitch. Other ... ?