Abstract

Simple conceptual nonlinear dynamical models are derived from ice-core data, thus integrating models and theories with palaeoclimatic records. The method is based on parameter estimation using the unscented Kalman filter, a nonlinear extension of the Kalman filter. Unlike the conventional linear Kalman filter and the widely used extended Kalman filter, the unscented Kalman filter keeps the full system dynamics rather than linearising it, leading to a superior treatment of nonlinearities. The unscented Kalman filter truncates the filter probability density to a Gaussian in each iteration by only propagating first and second moments but neglecting higher-order moments. The method is applicable to both deterministic and stochastic models. It offers a practical and computationally cheap alternative to more complete but also considerably more cumbersome approaches like particle filters or Markov chain Monte Carlo methods.

Two different conceptual models for glacial millennial-scale climate transitions (the so-called Dansgaard-Oeschger events) are considered and their parameters estimated from a North Greenland ice-core record. Firstly, we adopt the model of stochastically driven motion in a potential that allows for two distinctly different states. The shape of the potential and the noise strength are determined from the data. The data reveal that during glacial times the potential is asymmetric and degenerate. There is one stable cold stadial state and one indifferently stable warm interstadial state. Secondly, a damped stochastically forced nonlinear oscillator is considered. The restoring force is given by a bistable potential. The temporal asymmetry of the Dansgaard-Oeschger events is modelled by an asymmetric damping mechanism. The shape of the potential, the damping coefficient and the noise level are estimated from the data.