Earth
Richard McGehee
The Mathematics of Climate Change Seminar
University of Minnesota
School of Mathematics

 

References

 

 
 
   
   
Suggested Reading
   
 

Kerry Emanuel, A simple model of multiple climate regimes, Journal of Geophysical Research 107, No. D9, 4077, doi:10.1029/2001JD001002, 2002. The full article is available online for subscribers only.

     A relatively simple model having multiple attractors is used to explain sudden changes in the Earth's climate.
        
 

V. N. Livina1 & T. M. Lenton, A modified method for detecting incipient bifurcations in a dynamical system, Geophysical Research Letters 34, L03712, doi:10.1029/2006GL028672, 2007. The full article is available online for subscribers only.

     Can impending bifurcations in the Earth's climate system be predicted from time series data?
 
September 23, 2008 Reference
        
 

Hogg, A. M. (2008), Glacial cycles and carbon dioxide: A conceptual model, Geophys. Res. Lett., 35, L01701, doi:10.1029/2007GL032071. The full article is available online for subscribers only.

 
April 16, 2008 Reference
        
 

James Hansen, Makiko Sato, Pushker Kharecha, David Beerling, Valerie Masson-Delmotte, Mark Pagani, Maureen Raymo, Dana Royer, and James C. Zachos, Target Atmospheric CO2: Where Should Humanity Aim?, preprint. Here is a cached copy.

 
J. Hansen, M. Sato, R. Ruedy, P. Kharecha, A. Lacis, R. Miller, L. Nazarenko, K. Lo, G. A. Schmidt, G. Russell, I. Aleinov, S. Bauer, E. Baum, B. Cairns, V. Canuto, M. Chandler, Y. Cheng, A. Cohen, A. Del Genio, G. Faluvegi, E. Fleming, A. Friend, T. Hall, C. Jackman, J. Jonas, M. Kelley, N. Y. Kiang, D. Koch, G. Labow, J. Lerner, S. Menon, T. Novakov, V. Oinas, Ja. Perlwitz, Ju. Perlwitz, D. Rind, A. Romanou, R. Schmunk, D. Shindell, P. Stone, S. Sun, D. Streets, N. Tausnev, D. Thresher, N. Unger, M. Yao, and S. Zhang, 2007, Dangerous human-made interference with climate: a GISS modelE study, Atmos. Chem. Phys. 7,#9, 2287-2312. Here is a cached copy.
 
James Hansen, Larissa Nazarenko, Reto Ruedy, Makiko Sato, Josh Willis, Anthony Del Genio, Dorothy Koch, Andrew Lacis, Ken Lo, Surabi Menon, Tica Novakov, Judith Perlwitz, Gary Russell, Gavin A. Schmidt, Nicholas Tausnev, “Earth’s Energy Imbalance: Confirmation and Implications,” Science 308, 1431-1435. The full article is available online for subscribers only.
 
April 2, 2008 References
        
 

J. D. Hays, John Imbrie & N. J. Shackleton (1976), Variations in the Earth's Orbit: Pacemaker of the Ice Ages, Science 194, #4270, 1121-1132. The full article is available online for subscribers only.

 
D. Rind, D. Peteet, and G. Kukla (1989), Can Milankovitch Orbital Variations Initiate the Growth of Ice Sheets in a General Circulation Model?, J. Geophys. Res., 94(D10), 12,851–12,871. The full article is available online for subscribers only.
 
James Zachos, Mark Pagani, Lisa Sloan, Ellen Thomas & Katharina Billups (2001), Trends, Rhythms, and Aberrations in Global Climate 65 Ma to Present, Science 292, 686-693. The full article is available online for subscribers only.
 
March 5, 2008 Reference
        
 

Samuel Shen & Gerald North, A Simple Proof of the Slope Stability Theorem for Energy Balance Climate Models, Canadian Applied Mathematics Quarterly 7 (1999) 203 –215. The full article is available online for subscribers only.

 
February 27, 2008 Reference
        
 

Eville Gorham, et al, Temporal and spatial aspects of peatland initiation following
deglaciation in North America
, Quaternary Science Reviews 26 (2007) 300–311. The full article is available online for subscribers only.

 
February 20, 2008 References
        
 

J.A. Whitehead, Multiple states in doubly driven flow, Physica D 97 (1996), 311–321. The full article is available online for subscribers only.

 
J. A. Whitehead, Multiple T-S States for Estuaries, Shelves, and Marginal Seas, Estuaries 21(1998), 281-293. The article is available online. Here is a cached copy.
 
February 13, 2008 References
        
 

Henry Stommel, Thermohaline Convection with Two Stable Regimes of Flow, Tellus XIII (1961), 224-230. The journal is not available online. Here is a scanned copy (pdf image file).

     Stommel describes a model containing only two cells, one corresponding to polar water and the other to equatorial water. Driven by differences in temperature and salinity, a transport arises between the cells. The model shows multiple steady states.
 
Jochem Marotzke, Lecture 10: Multiple Equilibria of the THC, 7 March, 2003. Here is a cached copy.
     This is a lecture from a course "Climate Dynamics," given at the University of Southampton in 2003. In this lecture the author discusses the Stommel model.
 
February 6, 2008 References
        
 

M. I. Budyko, The effect of solar radiation variations on the climate of the Earth, Tellus XXI (1969), 611-619. The journal is not available online. Here is a scanned copy (pdf image file).

 
K. K. Tung, Topics in Mathematical Modeling, Princeton University Press, 2007. Chapter 8 contains a discussion of Budyko's model.
 
December 5, 2007 Reference
        
 

Gerard H. Roe & Marica B. Baker, Why is Climate Sensitivity So Unpredictable? Science 318 (#5850), 26 Oct 2007, 629-632. The full article is available online for subscribers only.

     "Climate sensitivity" is defined as the increase in global mean temperature resulting from a doubling of the CO2 concentrations above pre-industrial levels. Recent papers treat climate sensitivity as a random variable rather than a physical constant. This paper defends the random variable approach and derives a probability distribution for climate sensitivity.
 
November 28 , 2007 Reference
        
 

Dijkstra, H.A., and W. Weijer, Stability of the Global Ocean Circulation: Basic Bifurcation Diagrams, J. Phys. Oceanogr. 35 (2005), 933–948. The full article is available online for subscribers only.

 
November 7 , 2007 References
        
 
Stefan Rahmstorf, et al, Recent Climate Observations Compared to Projections, Science 316 (4 May 2007), p.709. The full article is available online for subscribers only.
 
October 31, 2007 References
        
 
The following three references are all part of Climate Change 2007: The Physical Science Basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change [Susan Solomon, et al, (eds.)]. Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA. This report is available online from the IPCC. Here is the table of contents.
   
 
IPCC, 2007: Summary for Policymakers. This article is available online from the IPCC. Here is a cached copy.
   
 
Susan Solomon, et al, 2007: Technical Summary. This article is available online from the IPCC. Here is a cached copy.
   
 
Gerald A. Meehl, et al, 2007: Global Climate Projections. This article is available online from the IPCC. Here is a cached copy.
 
October 3, 2007 References
        
 
Svante Arrhenius, On the Influence of Carbonic Acid in the Air upon the Temperature of the Ground, The London, Edinburgh and Dublin philosophical magazine and journal of science 41 (1896), 237-276. An image in pdf is available online from Global Warming Art. Here is a cached copy. What appears to be an OCR version is available online from Campaign for a Hydrogen Economy. Here is a cached copy.
   
 
Joseph Fourier, Mémoires sur les temperatures du globe terrestre et des espaces planétarires, Mémoires de l'Académie des Sciences de l'Institut de France t. vii (1827), 569-604. An image in pdf is available online from Gallica (Bibliothèque Nationale de France). Here is a cached copy.
   
 
C. Lorius, et al, The ice-core record: climate sensitivity and future greenhouse warming, Nature 347 (1990), 139-145. The full article is available online for subscribers only.
   
 
J. R. Petit, et al, Climate and atmospheric history of the past 420,000 years from the Vostok ice core, Antarctica, Nature 399 (1999), 429-436. The full article is available online for subscribers only.
   
 
Gary Stix, A Climate Repair Manual, Scientific American September 2006, pp.46-49. The full article is available online for subscribers only.
   
 
Peter D. Ward, Impact from the Deep, Scientific American October 2006, pp.64-71. The full article is available online for subscribers only.
   
 
James Zachos, et al, Trends, Rhythms, and Aberrations in Global Climate 65 Ma to Present, Science 292 (2001), 686-693. The full article is available online for subscribers only.
 

Last update: September 17, 2008 ©2008 Richard McGehee