A new empirical approach is proposed for predicting critical transitions in the climate system based on a time series alone. This approach relies on nonlinear stochastic modeling of the system's time-dependent evolution operator by the analysis of observed behavior. Empirical models that take the form of a discrete random dynamical system are constructed using artificial neural networks; these models include statedependent stochastic components. To demonstrate the usefulness of such models in predicting critical climate transitions, they are applied here to time series generated by a number of delay-differential equation (DDE) models of sea surface temperature anomalies. These DDE models take into account the main conceptual elements responsible for the El Niño-Southern Oscillation phenomenon. The DDE models used here have been modified to include slow trends in the control parameters in such a way that critical transitions occur beyond the learning interval in the time series. Numerical results suggest that the empirical models proposed herein are able to forecast sequences of critical transitions that manifest themselves in future abrupt changes of the climate system's statistics.

The present paper is the second part of a two-part study on empirical modeling and prediction of climate variability. This paper deals with spatially distributed data, as opposed to the univariate data of Part I. The choice of a basis for effective data compression becomes of the essence. In many applications, it is the set of spatial empirical orthogonal functions that provides the uncorrelated time series of principal components (PCs) used in the learning set. In this paper, the basis of the learning set is obtained instead by applying multichannel singular-spectrum analysis to climatic time series and using the leading spatiotemporal PCs to construct a reduced stochastic model. The effectiveness of this approach is illustrated by predicting the behavior of the Jin-Neelin-Ghil (JNG) hybrid seasonally forced coupled ocean-atmosphere model of El Niño- Southern Oscillation. The JNG model produces spatially distributed and weakly nonstationary time series to which the model reduction and prediction methodology is applied. Critical transitions in the hybrid periodically forced coupled model are successfully predicted on time scales that are substantially longer than the duration of the learning sample.