IMA. Recent Developments in the Theory of Glacial Cycles. Math and Climate Seminar

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1 Mah and Climae Seminar IMA Recen Developmens in he Theory of Richard McGehee Join MCRN/IMA Mah and Climae Seminar Tuesdays 11:1 12:0 sreaming video available a Seminar on he Mahemaics of Climae IMA, MCRN, School of Mahemaics November, 201 Temperaures in he Cenozoic Era 18 O in Foraminifera Fossils During he Pas. Myr 2. Benhic Daa (δ18o) ime () Hansen, e al, Targe amospheric CO2: Where should humaniy aim? Open Amos. Sci. J. 2 (2008) Lisiecki, L. E., and M. E. Raymo (200), A Pliocene-Pleisocene sack of 7 globally disribued benhic d18o records, Paleoceanography,20, PA100, doi: /200pa O in Foraminifera Fossils During he Pas 1.0 Myr Recen (las 00 ) Temperaure Cycles Vosok Ice Core Daa 2. Benhic Daa (δ18o) ime () Lisiecki, L. E., and M. E. Raymo (200), A Pliocene-Pleisocene sack of 7 globally disribued benhic d18o records, Paleoceanography,20, PA100, doi: /200pa J.R. Pei, e al (1999) Climae and amospheric hisory of he pas 20,000 years from he Vosok ice core, Anarcica, Naure 99,

2 Wha Causes? Widely Acceped Hypohesis The glacial cycles are driven by he variaions in he Earh s orbi (Milankovich Cycles), causing a variaion in incoming solar radiaion (insolaion). This hypohesis is widely acceped, bu also widely regarded as insufficien o explain he observaions. The addiional hypohesis is ha here are feedback and riggering mechanisms ha amplify he Milankovich cycles. Wha hese mechanisms are and how hey work are no fully undersood. hp://en.wikipedia.org/wiki/milankovich_cycles Eccenriciy Obliquiy (degrees) Precession Index Summer Solsice 6 N index W/m ? 2

3 Climae Response, Hays, e al Hays wih Modern Daa d18o Three differen emperaure proxies from sea sedimen daa. Hays, e al, Science 19 (1976), p. 112 Milankovich vs. Climae Hays, e al, Summary Forcing Response? Increasing conribuion Hays explanaion is ha here are nonlinear feedbacks. Are here oher explanaions? Hays, e al, Science 19 (1976), p Cenozoic Era Temperaures in he Cenozoic Era Zachos, e al, Science 292 (2001), p. 689 Hansen, e al, Targe amospheric CO2: Where should humaniy aim? Open Amos. Sci. J. 2 (2008)

4 Climae Response (Zachos, e al) Zachos, e al, Summary Forcing Response Power specrum of climae for he las. Myr. Noe he peaks a 1 and 100. Increasing conribuion Nonlinear effecs? Oher explanaions? Zachos, e al, Science 292 (2001), p. 689 Zachos, e al, Science 292 (2001), p. 689 Why such a small conribuion? Zachos Summary (Revised) Incoming Solar Radiaion (Insolaion), averaged over he enire globe and over a full year, depends only on e, no on eiher or. Q0 Qe 2 1 e Insolaion as a funcion of laiude, averaged over a full year, depends on e and β, bu no. I Qesy, where s, 1 2 cossin cos sincos cosd 0 laiude If we assume ha glaciaion depends on annual average insolaion insead of insolaion a summer solsice, hen forcing and response are aligned. Increasing conribuion Forcing Response 18 O in Foraminifera Fossils During he Pas. Myr Las Million Years is Differen Lisiecki Raymo Sack daa power specrum power d18o ? A ransiion occurred abou one million years ago: he ampliude increased and he dominan period changed from 1 kyr o 100 kyr. - o 0 Myr - o -1 Myr power? frequency (1/) o 0 Myr frequency (1/) Lisiecki, L. E., and M. E. Raymo (200), A Pliocene-Pleisocene sack of 7 globally disribued benhic d18o records, Paleoceanography,20, PA100, doi: /200pa

5 Wha s up wih he Las Million Years? 100,000 Year Problem: Why did he signal become so dominan during he las million years? 00,000 Year Problem: If he las million years is dominaed by, wha happened o he 00,000 year cycle? 2. 1 kyr dominaes 100 kyr dominaes Benhic Daa (δ18o) ime () daa power? Wha s up wih he las million years? Did reasser iself? Or somehing else? frequency (1/) CO 2 as Feedback Hea Balance Pam Marin, Universiy of Chicago, 2010 Hisorical Overview of Climae Change Science, IPCC AR, p.96 hp://ipcc-wg1.ucar.edu/wg1/repor/arwg1_prin_ch01.pdf Hogg s Model Hogg s Model surface emperaure dt c S GCT, d amospheric carbon dc dt V W0 WC 1 Cmax Cmax,0. d d weahering volcanos CO2 ougassing 2 S S Si sin i i C GCG Aln C0 insolaion greenhouse forcing Andrew McC. Hogg, "Glacial cycles and carbon dioxide: A concepual model," Geophysical Research Leers (2008).

6 Hogg s Model Hogg s model shows how he carbon cycle can ac as a feedback amplifying and modifying he insolaion forcing, bu he forcing is somewha arificial, and he riggering mechanism is difficul o jusify. Wha if he 100,000 year glacial cycle is no driven by, bu is a naural oscillaion of he Earh s climae? Salzman and Maasch suggesed jus such a model. global ice mass amospheric CO 2 deep ocean emperaure X X Y um 2 2 Y pz ry sz Z Y Z qx Z Milankovich forcing Barry Salzman and Kirk A. Maasch, "A Low-Order Dynamical Model of Global Climaic Variabiliy Over he Full Pleisocene," Journal of Geophysical Research 9 (D2), (1990) unforced forced The Salzman-Maasch model shows how he carbon cycle and he ocean currens can inerac o produce unforced oscillaions wih periods of abou 100,000 years. The same model wih slighly differen parameers can exhibi saionary behavior. By forcing he model wih Milankovich cycles and by slowly varying he parameers over he las wo million years, hey can produce a bifurcaion from small oscillaions racking he Milankovich cycles o large oscillaions wih a dominan 100,000 year period. Seems like a nice idea, bu i is no widely acceped as he explanaion, and i has some problems. The Hopf bifurcaion explanaion seems o have wo serious problems ( cosmic coincidences ). 1. Why does he inrinsic period of he glacial cycles jus happen o have he same period as he cycles? 2. Why does he phase of he glacial cycles agree wih he phase of he and cycles? Ask Samanha. 6

7 Huybers Analysis of Deglaciaions Huybers Analysis of Deglaciaions V 1 if V T V 0 if V T T abc V : ice volume a ime T : hreshold variable : rae of increase of ice volume : normalized Unis and consans Red dos: deglaciaions. Peer Huybers, "Glacial variabiliy over he las wo million years: an exended deph-derived agemodel, coninuous pacing, and he Pleisocene progression," Quaernary Science Reviews 26, 7- (2007). : V : chosen so ha η = 1. θ : mean zero and variance one a = 0.0 b = 126 c = 20 Huybers Analysis of Deglaciaions Huybers Analysis of Deglaciaions Huybers model produces he decline in emperaure and he increase in period and ampliude of he glacial cycles, bu i depends heavily on an unspecified decline in he sensiiviy of he riggering mechanism over las wo million years. Revised in Huybers 2011 Analysis of Deglaciaions Huybers 2011 Analysis of Deglaciaions The deglaciaions are riggered by he following forcing funcion. F e sin( ) (1 ) where e angle and are parameers. V 1 if V T V 0 if V T T 110 2F V : ice volume a ime T : hreshold variable : rae of increase of ice volume F e sin( ) (1 )

8 Huybers 2011 Analysis of Deglaciaions Abe-Ouchi e al Ice Shee Model The larger he ice shee, he more unsable i becomes, and he more sensiive i is o insolaion. Once i begins o rerea, feedbacks cause a rapid pace. Ayako Abe-Ouchi, Fuyuki Saio, Kenji Kawamura, Maureen E. Raymo, Jun ichi Okuno, Kunio Takahashi & Heinz Blaer, Insolaion-driven 100,000-year glacial cycles and hyseresis of iceshee volume, Naure 00 (201), doi:10.108/naure127 black = climae daa grey = F red = simulaion Animaion available on Naure Web sie: hp:// ab/naure127_sv1.hml Mah and Climae Seminar IMA Quesions 1. Did play any role during he las million years? Is he apparen 100 kyr cycle an arifac (Huybers)? Is i an inrinsic cycle in he climae sysem ha coincidenally has a period of 100,000 years (Maasch and Salzman)? 2. Is he CO 2 feedback sufficien o explain he increasing ampliude and period of he glacial cycles during he las million years, i.e., is i he mechanism behind he Huybers model.. Where does he amospheric CO 2 go during he glacial maxima? The ocean? The land?. Wha will be he effec of he anhropogenic CO 2? Join MCRN/IMA Mah and Climae Seminar Tuesdays 11:1 12:0 sreaming video available a 8