| Summary: | 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 bifurcation can be interpreted as loss of stability of the warm interstadial state of the Dansgaard-Oeschger events. In data spanning the last glacial termination, up to four climate states are detected, plausibly representing the LGM, Bolling-Allerod, Younger Dryas, and the Holocene. The proposed method can be applied to a wide range of geophysical time series exhibiting bifurcations.
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