Climate of the Past www.clim-past.net 1814-9324 1814-9332 6 1 2010 10.5194/cp-6-77-2010 http://www.clim-past.net/6/77/2010/ http://www.clim-past.net/6/77/2010/cp-6-77-2010.html http://www.clim-past.net/6/77/2010/cp-6-77-2010.pdf 77 82 2010-02-17 Potential analysis reveals changing number of climate states during the last 60 kyr V. N. Livina v.livina@uea.ac.uk F. Kwasniok T. M. Lenton School of Environmental Sciences, University of East Anglia, Norwich, UK College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter, UK We develop and apply a new statistical method of potential analysis for detecting the number of states of a geophysical system, from its recorded time series. Estimation of the degree of a polynomial potential allows us to derive the number of potential wells in a system. The method correctly detects changes in the number of wells in artificial data. In ice-core proxy records of Greenland paleotemperature, a reduction in the number of climate states from two to one is detected sometime prior to the last glacial maximum (LGM), 23–19 kyr BP. This result is also found in analysis of Greenland Ca data. The bifurcation can be interpreted as loss of stability of the warm interstadial state of the Dansgaard-Oeschger (DO) events. The proposed method can be applied to a wide range of geophysical time series exhibiting bifurcations. Bond, G. Showers, W., Cheseby, M., Lotti, R., Almasi, P., de Menocal, P., Priore, P., Cullen, H., Hajdas, I., and Bonani, G.: A Pervasive Millennial-Scale Cycle in North Atlantic Holocene and Glacial Climates, Science, 278, 1257–1266, 1997. Colin de Verdiere, A., Ben Jelloul, M., and Sevellec, F.: Bifurcation structure of thermohaline millennial oscillations, J. Climate, 19, 5777–5795, 2006. Dansgaard, W., Johnson, S. J., Clausen, H. B., Dahljensen, D., Gundestrup, N. S., Hammer, C. U., Hvidberg, C. S., Steffensen, J. P., Sveinbjornsdottir, A. E., Jouzel, J., and Bond, G.: Evidence for general instability of past climate from a 250 kyr ice-core record, Nature, 364, 218–220, 1993. Ditlevsen, P D.: Observation of α-stable noise induced millennial climate changes from an ice-core record, Geophys Res Lett., 26(10), 1441–1444, 1999. Ditlevsen, P. D., Andersen, K. K., and Svensson, A.: The DO-climate events are probably noise induced: statistical investigation of the claimed 1470 years cycle, Clim. Past, 3, 129–134, 2007. Ganopolski, A. and Rahmstorf, S.: Rapid changes of glacial climate simulated in a coupled climate model, Nature, 409, 153–158, 2001. Gardiner, C. W.: Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences (Springer Series in Synergetics), Springer, 3rd~Edn., 415~pp., 2004. Ghil, M., Mullhaupt, A., and Pestiaux, P.: Deep water formation and Quaternary glaciations, Clim. Dynam., 2, 1–10, 1987. Kwasniok, F. and Lohmann, G.: Deriving dynamical models from paleoclimatic records: Application to glacial millennial-scale climate variability, Phys Rev E, 80, 066104, doi:10.1103/PhysRevE.80.066104, 2009. Kwasniok, F. and Lohmann, G.: A stochastic nonlinear oscillator model for glacial millennial-scale climate transitions derived from ice-core data, Nonl Proc Geophys., submitted, 2010. North Greenland Ice Core Project members: High-resolution record of Northern Hemisphere climate extending into the last interglacial period, Data are available at: http://www.iceandclimate.nbi.ku.dk/data/, Nature, 431, 147–151, 2004. Paillard, D.: Glacial cycles: toward a new paradigm, Rev. Geophys., 39(3), 325–346, 2001. Rahmstorf, S.: Bifurcation of the Atlantic thermohaline circulation in response to changes in the hydrological cycle, Nature, 378, 145–149, 1995. Rahmstorf, S.: Timing of abrupt climate change: A precise clock, Geophys Res Lett., 30(10), 1510, doi:10.1029/2003GL017115, 2003. Silverman, B. W.: Density estimation for statistics and data analysis, Chapman and Hall, 1986. Stommel, H.: Thermohaline convection with two stable regimes of flow, Tellus, XIII, 224–230, 1961. Svensson, A., Andersen, K. K., Bigler, M., Clausen, H. B., Dahl-Jensen, D., Davies, S. M., Johnsen, S. J., Muscheler, R., Parrenin, F., Rasmussen, S. O., Röthlisberger, R., Seierstad, I., Steffensen, J. P., and Vinther, B. M.: A 60 000 year Greenland stratigraphic ice core chronology, Clim. Past, 4, 47–57, 2008. Wang, Y. J., Cheng, H., Edwards, R. L., An, Z. S., Wu, J.Y., Shen, C. C., and Dorale, J. A.: A High-Resolution Absolute-Dated Late Pleistocene Monsoon Record from Hulu Cave, China, Science, 294, 2345–2348, 2001. Yokoyama Y., Lambeck, K., DeDekker, P., Johnston, P., and Fifield, L K.: Timing of the Last Glacial Maximum from observed sea-level minima, Nature, 406, 713–716, 2000.