We suggest a new nonlinear expansion of space-distributed observational time series. The expansion allows constructing principal nonlinear manifolds holding essential part of observed variability. It yields low-dimensional hidden time series interpreted as internal modes driving observed multivariate dynamics as well as their mapping to a geographic grid. Bayesian optimality is used for selecting relevant structure of nonlinear transformation, including both the number of principal modes and degree of nonlinearity. Furthermore, the optimal characteristic time scale of the reconstructed modes is also found. The technique is applied to monthly sea surface temperature (SST) time series having a duration of 33 years and covering the globe. Three dominant nonlinear modes were extracted from the time series: the first efficiently separates the annual cycle, the second is responsible for ENSO variability and combinations of the second and the third modes explain substantial parts of Pacific and Atlantic dynamics. A relation of the obtained modes to decadal natural climate variability including current hiatus in global warming is exhibited and discussed.

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.

We suggest a new method for building data-driven dynamical models from observed multidimensional time series. The method is based on a recurrent neural network with specific structure, which allows for the joint reconstruction of both a low-dimensional embedding for dynamical components in the data and an evolution operator. The key link of the method is a Bayesian optimization of both model structure and the hypothesis about the data generating law, which is needed for constructing the cost function for model learning. First, the performance of the method is successfully tested in the situation when a signal from a low-dimensional dynamical system is hidden in noisy multidimensional observations. Second, the method is used for building the data-driven model of the low frequency variability (LFV) in the quasigeostrophic model of the Earth’s midlatitude atmosphere—a high-dimensional chaotic system. It is demonstrated that the key regimes of the atmospheric LFV are reproduced correctly in data simulations by means of the obtained model.

Currently, causes of the middle Pleistocene transition (MPT) – the onset of large-amplitude glacial variability with 100 kyr time scale instead of regular 41 kyr cycles before – are a challenging puzzle in Paleoclimatology. Here we show how a Bayesian data analysis based on machine learning approaches can help to reveal the main mechanisms underlying the Pleistocene variability, which most likely explain proxy records and can be used for testing existing theories. We construct a Bayesian data-driven model from benthic δ¹⁸O records (LR04 stack) accounting for the main factors which may potentially impact climate of the Pleistocene: internal climate dynamics, gradual trends, variations of insolation, and millennial variability. In contrast to some theories, we uncover that under long-term trends in climate, the strong glacial cycles have appeared due to internal nonlinear oscillations induced by millennial noise. We find that while the orbital Milankovitch forcing does not matter for the MPT onset, the obliquity oscillation phase-locks the climate cycles through the meridional gradient of insolation.

The loss of autocorrelations of tropical sea surface temperatures (SST) during late spring, also called the spring predictability barrier (SPB), is a factor that strongly limits the predictability of El Nino Southern Oscillation (ENSO), and especially the statistical SST‐based ENSO forecasts starting from the winter‐spring season. Recent studies show that Pacific atmospheric circulation anomalies in winter‐spring may have a long‐term impact on the summer tropical climate via the SST footprint. Here, we infer an index based on sea level pressure (SLP) data from February to March in a single area surrounding Hawaii, and show that this area is the most informative part of the large SLP pattern initiating the SST footprinting mechanism. We then construct a statistically optimal linear model of the Nino 3.4 index taking this atmospheric index as a forcing. We find that this forcing efficiently lowers the SPB and provides significant improvements of interseasonal Niño 3.4 forecasts.