| We develop and apply a new statistical method for detecting the number of states and the shape of the potential 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 coefficients that determine the shape of the potential are then estimated using the unscented Kalman filter (UKF). The method correctly detects changes in the number of wells and shape of the potential in artificial time series. Applying the technique to GRIP and NGRIP ice-core proxy records of Greenland palaeotemperature, a reduction in the number of climate states from two to one (double-well potential transforming into single-well) is detected sometime prior to the last glacial maximum (LGM), 23-19 kyr BP. The changing shape of the potential reveals this as loss of stability of the warm interstadial state of the Dansgaard-Oeschger events in the interval 30-25 kyr BP. In data spanning the last glacial termination, up to four climate states are detected, plausibly representing the LGM, Bolling-Allerod warm interval, Younger Dryas cold interval, and the Holocene. The estimated number of system states returns to one when the data analysed spans only the last circa 10 kyr of the Holocene. The proposed method of potential analysis can be applied to a wide range of geophysical time series exhibiting a changing number of states (bifurcations). |
|