Spectral analysis of climate dynamics with operator-theoretic approaches

Abstract

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.

Identifying quasi-periodic variability using multivariate empirical mode decomposition: a case of the tropical Pacific

“…In fact, we find ∼4 modes with average timescales ranging from ∼1.5 to ∼15 years that can reproduce the majority of ENSO variability (not shown), but the rest of these modes are consistent with red noise. (e.g., 1908-11), whereas strong Niño3 events generally show a constructive interference or mode-combination (e.g., 1997, a super-El Niño event), which is consistent with, e.g., Slawinska and Giannakis (2017); Jajcay et al (2018); Wang and Ren (2020); Froyland et al (2021).…”

“…3), who used EEMD on Niño3.4 index. IMF13 is also similar to Froyland et al (2021) 4-year mode (their Fig. 10), who used operator-theoretic approach.…”

“…However, ENSO has many flavours and can, for example, occur in the Eastern or Central Pacific (EP and CP ENSO, respectively; e.g., Kao and Yu 2009;Singh and Delcroix 2013;Zhang et al 2019), and can also occur on different timescales, e.g. : (i) a quasi-biennial (QB) ENSO with a ∼2 year timescale and (ii) a low-frequency/quasi-quadrennial (LF/QQ) ENSO with a ∼4-year timescale (e.g., Jiang et al, 1995;Allan, 2000;Kim et al, 2003;Keenlyside et al, 2007;Bejarano and Jin, 2008;Jajcay et al, 2018;Froyland et al, 2021).…”

Forecasting commodity returns by exploiting climate model forecasts of the El Niño Southern Oscillation

“…The neutral phase is topologically similar to La Niña, but with less extreme anomalous temperature, winds, convection, and precipitation. There is also evidence for a greater variety of transitional phases (Froyland et al, 2021). Due to climate teleconnections, ENSO can affect rainfall and temperature to more distant nonlocal regions of the Earth, with the strongest influences in the tropics.…”

Natural Exponential and Three‐Dimensional Chaotic System

“…As for the chaotic system complexity, stability analysis and mutational control, [27] in contrast with the traditional multiple time scale and Laplace transform, [28] various entropy-based methods [29][30][31] are reported and proved to be effective in intrinsic law mining for a chaotic time series. [32] Chaotic system and method can be applied to weak signal detection, [33] security of digital image, [34] climate change, [35] and biomedicine monitoring, [36] hardware design and optimization, [37,38] time series prediction [39] in amplitude and frequency domain. [40] Various improved and optimization methods are proposed to enhance the recognition accuracy and prediction precision from the perspective of parameter selection and adaptive adjustment, but they are limited to specific application scenarios.…”