Principal nonlinear dynamical modes of climate variability.

Dmitry Mukhin,Alexander Feigin,Andrey Gavrilov,Juergen Kurths,Evgeny Loskutov

doi:10.1038/srep15510

Dmitry Mukhin, Alexander Feigin + Show 3 more

Open Access

https://doi.org/10.1038/srep15510

Copy DOI

Abstract

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.

Highlights

We suggest a new nonlinear expansion of space-distributed observational time series
Three dominant nonlinear modes were extracted from the time series: the first efficiently separates the annual cycle, the second is responsible for El-Niño Southern Oscillation (ENSO) variability, and combinations of the second and the third modes explain substantial parts of Pacific and Atlantic dynamics
We have 44,219 sea surface temperature (SST) signals in different grid points and our aim is to describe them by a moderate number of principal nonlinear dynamical modes (NDMs) p – the set of scalar time series capturing the more the better part of observed variability

Summary

Introduction

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. The suggested approach is based on a direct analysis of the data without any prior knowledge about first-principal models This is a nonlinear generalization of EOF decomposition: instead of constructing linear constraints in the data space, we try to resolve NDMs as most principal nonlinear manifolds (curves) and project data on them. It is a sort of construction of principal curves[23] allowing an expansion of vector time series X(t) ∈D (e.g. discretized climatic spatial field) into the set of dominant parametrically defined curves

Objectives

Methods

Results

Conclusion