Many processes in atmosphere-ocean science develop multiscale temporal and spatial patterns, with complex underlying dynamics and time-dependent external forcings. Because of the possible advances in our understanding and prediction of climate phenomena, extracting that variability empirically from incomplete observations is a problem of wide contemporary interest. Here, we present a technique for analyzing climatic time series that exploits the geometrical relationships between the observed data points to recover features characteristic of strongly nonlinear dynamics (such as intermittency), which are not accessible to classical Singular Spectrum Analysis (SSA). The method utilizes Laplacian eigenmaps, evaluated after suitable time-lagged embedding, to produce a reduced representation of the observed samples, where standard tools of matrix algebra can be used to perform truncated Singular Value Decomposition despite the nonlinear manifold structure of the data set. As an application, we study the variability of the upper-ocean temperature in the North Pacific sector of a 700-year equilibrated integration of the CCSM3 model. Imposing no a priori assumptions (such as periodicity in the statistics), our machine-learning technique recovers three distinct types of temporal processes: (1) periodic processes, including annual and semiannual cycles; (2) decadal-scale variability with spatial patterns resembling the Pacific Decadal Oscillation; (3) intermittent processes associated with the Kuroshio extension and variations in the strength of the subtropical and subpolar gyres. The latter carry little variance (and are therefore not captured by SSA), yet their dynamical role is expected to be significant.

Dimitris Giannakis @VideoLectures.net