El Niño-Southern Oscillation frequency cascade

Revealing trends and persistent cycles of non-autonomous systems with autonomous operator-theoretic techniques

An important problem in modern applied science is to characterize the behavior of systems with complex internal dynamics subjected to external forcings. Many existing approaches rely on ensembles to generate information from the external forcings, making them unsuitable to study natural systems where only a single realization is observed. A prominent example is climate dynamics, where an objective identification of signals in the observational record attributable to natural variability and climate change is crucial for making climate projections for the coming decades. Here, we show that operator-theoretic techniques previously developed to identify slowly decorrelating observables of autonomous dynamical systems provide a powerful means for identifying nonlinear trends and persistent cycles of non-autonomous systems using data from a single trajectory of the system. We apply our framework to real-world examples from climate dynamics: Variability of sea surface temperature over the industrial era and the mid-Pleistocene transition of Quaternary glaciation cycles.

Spectral analysis of climate dynamics with operator-theoretic approaches

The Earth's climate system is a classical example of a multiscale, multiphysics dynamical system with an extremely large number of active degrees of freedom, exhibiting variability on scales ranging from micrometers and seconds in cloud microphysics, to thousands of kilometers and centuries in ocean dynamics. Yet, despite this dynamical complexity, climate dynamics is known to exhibit coherent modes of variability. A primary example is the El Niño Southern Oscillation (ENSO), the dominant mode of interannual (3-5 yr) variability in the climate system. The objective and robust characterization of this and other important phenomena presents a long-standing challenge in Earth system science, the resolution of which would lead to improved scientific understanding and prediction of climate dynamics, as well as assessment of their impacts on human and natural systems. Here, we show that the spectral theory of dynamical systems, combined with techniques from data science, provides an effective means for extracting coherent modes of climate variability from high-dimensional model and observational data, requiring no frequency prefiltering, but recovering multiple timescales and their interactions. Lifecycle composites of ENSO are shown to improve upon results from conventional indices in terms of dynamical consistency and physical interpretability. In addition, the role of combination modes between ENSO and the annual cycle in ENSO diversity is elucidated.

Explicit Granger causality in kernel Hilbert spaces

Granger causality (GC) is undoubtedly the most widely used method to infer cause-effect relations from observational time series. Several nonlinear alternatives to GC have been proposed based on kernel methods. We generalize kernel Granger causality by considering the variables' cross-relations explicitly in Hilbert spaces. The framework is shown to generalize the linear and kernel GC methods and comes with tighter bounds of performance based on Rademacher complexity. We successfully evaluate its performance in standard dynamical systems, as well as to identify the arrow of time in coupled Rössler systems, and it is exploited to disclose the El Niño-Southern Oscillation phenomenon footprints on soil moisture globally.

Revisiting the Pacific Meridional Mode

Numerous studies demonstrated that the Pacific Meridional Mode (PMM) can excite Central Pacific (CP) El Niño-Southern Oscillation (ENSO) events and that the PMM is mostly a stochastic phenomenon associated with mid-latitude atmospheric variability and wind-evaporation-SST feedback. Here we show that CP sea surface temperature (SST) variability exhibits high instantaneous correlations both on interannual (ENSO-related) and decadal (Pacific Decadal Oscillation (PDO)-related) timescales with the PMM. By prescribing an idealized interannual equatorial CP ENSO SST forcing in a partially-coupled atmosphere/slab ocean model we are able to generate a realistic instantaneous PMM response consistent with the observed statistical ENSO/PMM relationship. This means that CP ENSO and the PMM can excite each other respectively on interannual timescales, strongly suggesting that a fast positive feedback exists between the two phenomena. Thus, we argue that they cannot be considered two independent dynamical entities. Additionally, we show that the interannual CP ENSO SST forcing generates atmospheric circulation variability that projects strongly on the Aleutian Low and North Pacific SST anomalies that exhibit the characteristic PDO pattern.

Dynamic Regimes of El Niño Southern Oscillation and Influenza Pandemic Timing

El Niño southern oscillation (ENSO) dynamics has been shown to drive seasonal influenza dynamics. Severe seasonal influenza epidemics and the 2009-2010 pandemic were coincident with chaotic regime of ENSO dynamics. ENSO dynamics from 1876 to 2016 were characterized to determine if influenza pandemics are coupled to chaotic regimes. Time-varying spectra of southern oscillation index (SOI) and sea surface temperature (SST) were compared. SOI and SST were decomposed to components using the algorithm of noise-assisted multivariate empirical mode decomposition. The components were Hilbert transformed to generate instantaneous amplitudes and phases. The trajectories and attractors of components were characterized in polar coordinates and state space. Influenza pandemics were mapped to dynamic regimes of SOI and SST joint recurrence of annual components. State space geometry of El Niños lagged by influenza pandemics were characterized and compared with other El Niños. Timescales of SOI and SST components ranged from sub-annual to multidecadal. The trajectories of SOI and SST components and the joint recurrence of annual components were dissipative toward chaotic attractors. Periodic, quasi-periodic, and chaotic regimes were present in the recurrence of trajectories, but chaos-chaos transitions dominated. Influenza pandemics occurred during chaotic regimes of significantly low transitivity dimension (p < 0.0001). El Niños lagged by influenza pandemics had distinct state space geometry (p < 0.0001). Chaotic dynamics explains the aperiodic timing, and varying duration and strength of El Niños. Coupling of all influenza pandemics of the past 140 years to chaotic regimes of low transitivity indicate that ENSO dynamics drives influenza pandemic dynamics. Forecasts models from ENSO dynamics should compliment surveillance for novel influenza viruses.

Strong sub-seasonal wintertime cooling over East Asia and Northern Europe associated with super El Niño events

East Asia experienced a record-breaking cold event during the 2015/16 boreal winter, with pronounced impacts on livelihood in the region. We find that this large-scale cold spell can be attributed to the concurrent super El Niño event in the tropical Pacific. Our analysis reveals that all super El Niño winters (1982/83, 1997/98, and 2015/16) were accompanied by a rapid sub-seasonal North Atlantic Oscillation (NAO)/Arctic Oscillation (AO) phase reversal from a positive to a negative state during early January, which was largely caused by the interaction of these super El Niño events with the subtropical jet annual cycle. The NAO/AO phase transition leads to a rapidly strengthened Siberian High, which favors southward intrusions of cold air to East Asia and thus causes severe local cooling. Similar cold spells can also be detected over Northern Europe associated with the fast sub-seasonal NAO/AO phase reversal. Due to the weaker amplitude of the ENSO forcing, these sub-seasonal atmospheric responses cannot be detected for moderate El Niño events. The super El Niño associated sub-seasonal signal of the East Asian and Northern Europe wintertime temperature responses carries important implications for future predictability of regional extreme events.