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Estimating climate response to observed and projected increases in atmospheric greenhouse gases usually requires averaging among multiple independent simulations of computationally expensive global climate models to filter out the internal climate variability. Studies have shown that advanced pattern recognition methods allow one to obtain accurate estimates of the forced climate signal from just a handful of such climate realizations. The accuracy of these methods for a fixed ensemble size, however, decreases with an increasing magnitude of the low-frequency, decadal and longer internal climate variability. Here we generalize a previously developed Bayesian methodology of Linear Dynamical Mode (LDM) decomposition for spatially extended time series to enable joint identification and analysis of forced signal and internal variability in ensembles of climate simulations, a methodology dubbed here an ensemble LDM, or ELDM. The new ELDM method is shown to outperform its pattern-recognition competitors by more accurately isolating the forced signal in small ensembles of both toy- and state-of-the-art climate-model simulations. It is able to do so by explicitly recognizing a non-random structure of the internal variability, identified by the ELDM algorithm alongside the optimal forced-signal estimate, which allows one to study possible dynamical connections between the two types of variability. The optimal ELDM filtering provides a unique opportunity for objective intercomparison of decadal and longer climate variability across different global climate models—a task that proved difficult due to uncertainties associated with the noisy character and limited length of historical climate simulations combined with parameter uncertainties of alternative signal-detection methods. [ABSTRACT FROM AUTHOR]

It is well-known that the upper ocean heat content (OHC) variability in the tropical Pacific contains valuable information about dynamics of El Niño–Southern Oscillation (ENSO). Here we combine sea surface temperature (SST) and OHC indices derived from the gridded datasets to construct a phase space for data-driven ENSO models. Using a Bayesian optimization method, we construct linear as well as nonlinear models for these indices. We find that the joint SST-OHC optimal models yield significant benefits in predicting both the SST and OHC as compared with the separate SST or OHC models. It is shown that these models substantially reduce seasonal predictability barriers in each variable—the spring barrier in the SST index and the winter barrier in the OHC index. We also reveal the significant nonlinear relationships between the ENSO variables manifesting on interannual scales, which opens prospects for improving yearly ENSO forecasting. [ABSTRACT FROM AUTHOR]

A new data-driven model for analysis and prediction of spatially distributed time series is proposed. The model is based on a linear dynamical mode (LDM) decomposition of the observed data which is derived from a recently developed nonlinear dimensionality reduction approach. The key point of this approach is its ability to take into account simple dynamical properties of the observed system by means of revealing the system's dominant time scales. The LDMs are used as new variables for empirical construction of a nonlinear stochastic evolution operator. The method is applied to the sea surface temperature anomaly field in the tropical belt where the El Nino Southern Oscillation (ENSO) is the main mode of variability. The advantage of LDMs versus traditionally used empirical orthogonal function decomposition is demonstrated for this data. Specifically, it is shown that the new model has a competitive ENSO forecast skill in comparison with the other existing ENSO models. [ABSTRACT FROM AUTHOR]

A nonlinear decomposition method is applied to the analysis of global sea surface temperature (SST) time series in different epochs related to the Pacific Decadal Oscillation (PDO) since the end of 19th century to present time. This method allows one to extract an optimal (small) number of global nonlinear teleconnection patterns associated with distinct dominant time scales from the original high-dimensional spatially extended data set. In particular, it enables us to reveal ENSO teleconnection patterns corresponding to different PDO cycles during the last 145 years, to uncover four climate shifts connected with PDO phase changes and to reconstruct the corresponding global PDO patterns. We find that SST teleconnections between the ENSO region, extra-tropical Pacific regions and the Indian ocean became fundamentally nonlinear since the second half of 20th century. [ABSTRACT FROM AUTHOR]