Glacial Cycles. Glacial Cycles. Glacial Cycles. Glacial Cycles. Glacial Cycles. Glacial Cycles. What Causes Glacial Cycles?

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1 : he 1,-Year Problem : he 1,-Year Problem Richard McGehee Seminar on he Mahemaics of Climae Change School of Mahemaics April 1, 11 hp:// Ice-Albedo Feedback Climae in he Cenozoic Era Climae During he Pas. Myr. Benhic Daa (δ18 8O) Myr Hansen, e al, Targe amospheric CO: Where should humaniy aim? Open Amos. Sci. J. (8) Lisiecki, L. E., and M. E. Raymo (), A Pliocene-Pleisocene sack of 7 globally disribued benhic d18o records, Paleoceanography,, PA1, doi:1.19/pa171.. Climae During he Pas 1. Myr Recen (las Kyr) Temperaure Cycles Vosok Ice Core Daa Benhic Daa (δ18o O) Lisiecki, L. E., and M. E. Raymo (), A Pliocene-Pleisocene sack of 7 globally disribued benhic d18o records, Paleoceanography,, PA1, doi:1.19/pa171. J.R. Pei, e al (1999) Climae and amospheric hisory of he pas, years from he Vosok ice core, Anarcica, Naure 99,

2 Wha Causes? Hea Balance Widely Acceped Hypohesis The glacial cycles are driven by he variaions in he Earh s orbi (Milankovich i Cycles), causing a variaion in incoming i 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 mechanisms ha amplify he Milankovich cycles. Wha hese feedbacks are and how hey work are no fully undersood. Hisorical Overview of Climae Change Science, IPCC AR, p.96 hp://ipcc-wg1.ucar.edu/wg1/repor/arwg1_prin_ch1.pdf Eccenriciy Obliquiy hp:// hp://upload.wikimedia.org/wikipedia/commons/6/61/axialtilobliquiy.png Precession Eccenriciy.6.. eccenriciy Noe periods of abou 1 Kyr and Kyr. hp://earhobservaory.nasa.gov/library/gians/milankovich/milankovich_.hml J. Laskar, e al () A long-erm numerical soluion for he insolaion quaniies of he Earh, Asronomy & Asrophysics 8, 61 8.

3 Obliquiy Precession Index..6 ob bliquiy (degrees) Noe period of abou 1 Kyr. J. Laskar, e al () A long-erm numerical soluion for he insolaion quaniies of he Earh, Asronomy & Asrophysics 8, index = e sinρ, where e = eccenriciy and ρ = precession angle (measured from spring equinox) Noe period of abou Kyr. J. Laskar, e al () A long-erm numerical soluion for he insolaion quaniies of he Earh, Asronomy & Asrophysics 8, Eccenriciy Power Specrum Obliquiy Power Specrum Precession Index Power Specrum Lisiecki Raymo δ 18 O Sack. Lisiecki Daa. 18 O.. 1 Kyr eccenriciy obliquiy precession

4 Why obliquiy and eccenriciy? Incoming Solar Radiaion (Insolaion), averaged over he enire globe and over a full year, depends only on eccenriciy e, no on eiher obliquiy or precession. Q Qe 1 e Insolaion as a funcion of laiude, averaged over a full year, depends on eccenriciy e and obliquiy β, bu no precession. I Qesy, where, 1 1 sin cos cos s y y y d y sin laiude Why obliquiy over eccenriciy? Possible explanaion: Ice-albedo feedback Ice reflecs more energy han land or waer. more ice less energy colder more ice less ice more energy warmer less ice Hea Balance Hisorical Overview of Climae Change Science, IPCC AR, p.96 hp://ipcc-wg1.ucar.edu/wg1/repor/arwg1_prin_ch1.pdf Budyko-Sellers Model T R Qs y1 y, A BT C T T insolaion albedo re-radiaion ranspor T T y, : annual mean surface emperaure y sin laiude y,1 Q : global annual mean insolaion 1 s : relaive annual mean insolaion s ydy 1 y : ice boundary 1, y, y, albedo, y. 1 T Ty, dy: global annual mean emperaure Two equilibrium soluions: small cap: sable large cap: unsable No equilbria: ice free snowball Solve for equilibrium soluion T*(y). Se righ hand side =. emperaure (ºC) equilibrium emperaure profiles sin(laiude) ice free snowball small cap big cap Budyko-Sellers Model T R Qs y1 y, A BT C T T Noe ha he equilibrium soluion T*(y) depends on Q and s(y), which depend on he eccenriciy e and he obliquiy β. Therefore, he equilibrium locaion η of he ice boundary and he equilibrium global mean emperaure (GMT) depend on he eccenriciy and he obliquiy. We can use he compued values of eccenriciy and obliquiy o compue he ice boundary and GMT over he glacial cycles. Q Qe 1 e, 1 1 sin cos cos s y y y d

5 Budyko-Sellers Model power specra Model oupu: ice boundary ice boundary Model oupu: global mean emperaure global mean emperaure Climae daa eccenriciy obliquiy precession The ice-albedo feedback model correcly predics he dominance of obliquiy, bu i fails o explain mos of he oher feaures of he climae daa. 1 Kyr dominaes 1 Kyr dominaes.. Climae daa Ben hic Daa (δ18o).. Benhic Da aa (δ18o) Model oupu 1, Year Problem: Wha s up wih he las million years? Did eccenriciy reasser iself? Or somehing else? Huyber s Analysis of Deglaciaions Huyber s Analysis of Deglaciaions The deglaciaions are riggered by obliquiy cycles, bu someimes hey don rigger. When cycles are skipped, he deglaciaions can be separaed by 8 Kyr or 1 Kyr, creaing he appearance of 1 Kyr cycles. Red dos: deglaciaions. Peer Huybers, "Glacial variabiliy over he las wo million years: an exended deph-derived agemodel, coninuous obliquiy pacing, and he Pleisocene progression," Quaernary Science Reviews 6, 7- (7).

6 Huyber s Triggering Model Huyber s Triggering Model V 1 if V T V if V T T abc V : ice volume a ime T : hreshold variable : rae of increase of ice volume : normalized obliquiy Unis and consans : Kyr V : chosen so ha η = 1. θ : mean zero and variance one a =. b = 16 c = black: model red: daa Huyber s Triggering Model Vosok Core Sample Daa Pei, e al, Naure 99 (June 1999), pp.9-6 Huyber s 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. Wha abou greenhouse gases and he carbon cycle? Andrew Hogg suggesed a model incorporaing he carbon cycle. kiloyear bp empera aure amos CO ppm kiloyear bp Hogg s Model Hogg s Model dt c S GCT, d dc dt V W WC 1 Cmax Cmax,. d d weahering volcanos CO ougassing S S Si sin i i C GCG Aln C insolaion greenhouse forcing Andrew McC. Hogg, "Glacial cycles and carbon dioxide: A concepual model," Geophysical Research Leers (8). 6

7 Hogg s Model Salzman-Maasch 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. Also, i does no solve he 1,-year problem. Wha if he 1, year glacial cycle is no driven by eccenriciy, bu is a naural oscillaion of he Earh s climae? Salzman and Maasch suggesed jus such a model. global ice mass amospheric CO deep ocean emperaure X X Y um 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 (D), (199) Salzman-Maasch Model unforced Salzman-Maasch Model forced Salzman-Maasch Model Curren Projec The Salzman-Maasch model shows how he carbon cycle and he ocean currens can inerac o produce unforced oscillaions wih periods of abou 1, years. The same model wih slighly differen parameers can exhibi saionary behavior. By forcing he model wih Milankovich i cycles and by slowly l 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 1, year period. Seems like a nice idea, bu i is no widely acceped as he explanaion. The Mahemaics and Climae Research Nework (MCRN) has a Webinar working group developing a model incorporaing ice-albedo feedback wih he carbon cycle. Local exper: Samanha Oesriecher 7

8 The 1,-Year Problem Summary 1 Kyr cycles during he las million years, bu 1 Kyr cycles before ha. Why? Huybers: Obliquiy rules, bu glaciers sared skipping beas. Alernaing 8 Kyr and 1 Kyr looks like 1 Kyr Salzman & Maasch: Under some condiions, he climae naurally oscillaes a 1 Kyr. Those condiions arose 1 Myr ago. Before ha, he climae racked Milankovich. Oher...? 8