Dmitry Mukhin

Principal nonlinear dynamical modes of climate variability.

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.

Predicting Critical Transitions in ENSO models. Part II: Spatially Dependent Models

AbstractThe 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 Nino–Southern Oscillation. The JNG model produces spatially distributed and weakly nonstationary time series to which the model reduction and prediction m...

Method for reconstructing nonlinear modes with adaptive structure from multidimensional data

We present a detailed description of a new approach for the extraction of principal nonlinear dynamical modes (NDMs) from high-dimensional data. The method of NDMs allows the joint reconstruction of hidden scalar time series underlying the observational variability together with a transformation mapping these time series to the physical space. Special Bayesian prior restrictions on the solution properties provide an efficient recognition of spatial patterns evolving in time and characterized by clearly separated time scales. In particular, we focus on adaptive properties of the NDMs and demonstrate for model examples of different complexities that, depending on the data properties, the obtained NDMs may have either substantially nonlinear or linear structures. It is shown that even linear NDMs give us more information about the internal system dynamics than the traditional empirical orthogonal function decomposition. The performance of the method is demonstrated on two examples. First, this approach is successfully tested on a low-dimensional problem to decode a chaotic signal from nonlinearly entangled time series with noise. Then, it is applied to the analysis of 250-year preindustrial control run of the INMCM4.0 global climate model. There, a set of principal modes of different nonlinearities is found capturing the internal model variability on the time scales from annual to multidecadal.

Predicting Critical Transitions in ENSO Models. Part I: Methodology and Simple Models with Memory

AbstractA 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 state-dependent 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 Nino–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 ...

Nonlinear reconstruction of global climate leading modes on decadal scales

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.

Linear dynamical modes as new variables for data-driven ENSO forecast

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.

An approach of the space-time empirical modes to the nonlinear phenomena in lasers with low-q cavities

Highly nonlinear spatial-temporal patterns are inevitable features of lasing in the low-Q (bad) cavities where a photon lifetime, TE, is less than a polarization relaxation time (a lifetime of the optical dipole oscillations), T2, of the individual active centers excited by pumping [1]. A theoretical analysis of the spatial-temporal dynamics of the field and its spectral and correlation features in such lasers, known as the superradiant lasers, cannot be based on a standard decomposition on neither ‘cold’ no ‘hot’ modes which have fixed spatial profiles and are defined, respectively, by a cavity without or with taking into account the active medium. A progress in modern technologies, especially in the field of semiconductor heterostructures, leaves no doubts about near fabrication of these lasers and their applications in the optical information processing, the wideband dynamical spectroscopy, and diagnostics of many-particle systems in condensed active media.