Abstract
Abstract. Atmosphere and ocean dynamics display many complex features and are characterized by a wide variety of processes and couplings across different timescales. Here we demonstrate the application of multivariate empirical mode decomposition (MEMD) to investigate the multivariate and multiscale properties of a reduced order model of the ocean–atmosphere coupled dynamics. MEMD provides a decomposition of the original multivariate time series into a series of oscillating patterns with time-dependent amplitude and phase by exploiting the local features of the data and without any a priori assumptions on the decomposition basis. Moreover, each oscillating pattern, usually named multivariate intrinsic mode function (MIMF), represents a local source of information that can be used to explore the behavior of fractal features at different scales by defining a sort of multiscale and multivariate generalized fractal dimensions. With these two complementary approaches, we show that the ocean–atmosphere dynamics presents a rich variety of features, with different multifractal properties for the ocean and the atmosphere at different timescales. For weak ocean–atmosphere coupling, the resulting dimensions of the two model components are very different, while for strong coupling for which coupled modes develop, the scaling properties are more similar especially at longer timescales. The latter result reflects the presence of a coherent coupled dynamics. Finally, we also compare our model results with those obtained from reanalysis data demonstrating that the latter exhibit a similar qualitative behavior in terms of multiscale dimensions and the existence of a scale dependency of the statistics of the phase-space density of points for different regions, which is related to the different drivers and processes occurring at different timescales in the coupled atmosphere–ocean system. Our approach can therefore be used to diagnose the strength of coupling in real applications.
Highlights
The atmosphere and the ocean form a complex system whose dynamical variability extends over a wide range of spatial and temporal scales (Liu, 2012; Xue et al, 2020)
We demonstrate the application of multivariate empirical mode decomposition (MEMD) to investigate the multivariate and multiscale properties of a reduced order model of the ocean–atmosphere coupled dynamics
The relation between the ocean mixed layer (OML) and the low-frequency variability (LFV) can be investigated from a dynamical system point of view by developing suitable reduced order ocean–atmosphere models dealing with the modeling of the coupling between the atmosphere and the underlying surface layer of the ocean
Summary
The atmosphere and the ocean form a complex system whose dynamical variability extends over a wide range of spatial and temporal scales (Liu, 2012; Xue et al, 2020). The tropical regions are markedly characterized by inter-/multi-annual processes like the El Niño–Southern Oscillation (ENSO) (Neelin et al, 1994; Meehl et al, 2003), while the North Atlantic Oscillation (NAO) affects extratropical northern hemispheric regions at seasonal and decadal timescales (Ambaum et al, 2001) The sources of these processes have been widely investigated by means of multiple data analysis methods and various types of modeling Other sources could be invoked to explain and to contribute to the development of LFV in the atmosphere, such as the long-range system memory as a consequence of the heat storage mechanism of the land–ocean–atmosphere system (e.g., Lovejoy, 2021; Lovejoy et al, 2021), the internal dynamics of the atmosphere itself (e.g., Legras and Ghil, 1985), or even the interaction between the tropical and extratropical regions (e.g., Alexander et al, 2002; Vannitsem et al, 2021), just to quote a few
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