Abstract. 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 DansgaardOeschger (DO) events. The proposed method can be applied to a wide range of geophysical time series exhibiting bifurcations.

Abstract. 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.

A method for systematically deriving simple nonlinear dynamical models from ice-core data is proposed. It offers a tool to integrate models and theories with paleoclimatic data. The method is based on the unscented Kalman filter, a nonlinear extension of the conventional Kalman filter. Here, we adopt the abstract conceptual model of stochastically driven motion in a potential that allows for two distinctly different states. The parameters of the model, that is, the shape of the potential and the noise level are estimated from a North Greenland ice-core record. For the glacial period from 70 to 20 ky before present, a potential is derived that is asymmetric and almost degenerate. There is a deep well corresponding to a cold stadial state and a very shallow well corresponding to a warm interstadial state.

No abstract

Ensemble post-processing methods are used in operational weather forecasting to form probability distributions that represent forecast uncertainty. Several such methods have been proposed in the literature, including logistic regression, ensemble dressing, Bayesian model averaging and non-homogeneous Gaussian regression. We conduct an imperfect model experiment with the Lorenz 1996 model to investigate the performance of these methods, especially when forecasting the occurrence of rare extreme events. We show how flexible bias-correction schemes can be incorporated into these post-processing methods, and that allowing the bias correction to depend on the ensemble mean can yield considerable improvements in skill when forecasting extreme events. In the Lorenz 1996 setting, we find that ensemble dressing, Bayesian model averaging and non-homogeneous Gaussian regression perform similarly, while logistic regression performs less well.