Multiscale fractal dimension analysis of a reduced order model of coupled ocean–atmosphere dynamics

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.

Multi-Time-Scale Analysis of Chaos and Predictability in vTEC

“…As the functions (Υ τ (t)) are calculated, each of them may undergo an embedding procedure applied to the whole vTEC time series reported in [9], as well as the subsequent calculation of D 2 and K 2 . The main difference here is that this analysis of "chaos degree" and predictability of the LIM is performed at each different time scale (τ) for each Υ τ (t) (see also [11,12]). The embedding procedure à la Grassberger-Procaccia [10], applied to the partial series (Υ τ (t)) determines a trajectory (Υ τ (t)) moving through an m(τ) dimensional real space:…”

“…This aspect is investigated starting from a 30 s resolution vTEC time series, followed by the construction of its single time-scale version via empirical mode decomposition (EMD), as illustrated in detail in Section 2. Once the τ reduction of the vTEC series is selected, the values of the elements of D are calculated using an embedding procedure applied to this τ version of the vTEC; this produces τ-dependent parameters m(τ), D 2 (τ) and K 2 (τ) (see also [11,12]). When different time scales are considered with respect to the LIM, completely different dynamics appear, in terms of phase-space topology.…”

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

“…Even though EMD and its 1D extension Ensemble EMD (EEMD; Wu and Huang 2009) have been applied in climate science in various applications, e.g., for smoothing, filtering, extracting trends, variability, and testing for red noise distribution of climate data (e.g., Duffy, 2004;Wu et al, 2007;Franzke, 2009;Lee and Ouarda, 2011;Qian et al, 2011;Franzke and Woollings, 2011;Franzke, 2012;Ezer and Corlett, 2012;Ezer et al, 2013;Wang and Ren, 2020), it has not been explicitly used for extracting quasi-periodic signals. Moreover, the MEMD has only been applied to an analysis of the atmosphere-ocean coupling strength (Alberti et al, 2021) in climate science, which was done in a more idealised setting from the present study. Therefore, we also perform extensive analysis of the method itself and compare it to the basic band-pass filtering (5th order Butterworth filter) and to Fourier transform analysis, to show that its results are consistent with other methods, but can also extract more information in an objective way (see below and Appendices A, B).…”

Local dimensionality and inverse persistence analysis of atmospheric turbulence in the stable boundary layer

“…For each scale , a pair of parameters (D (t) and θ (t)) can be obtained, enabling us to investigate the instantaneous scale-dependent features of the velocity field fluctuations. This method, first proposed in Alberti et al [72], has recently been applied to laboratory experiments on Von Kármán fluids, and represents an extension of a previous method based on generalized fractal dimensions [73,74]. The first parameter is the local dimension D (t), describing the geometry of the system's trajectory in a region of the PS around Û , and represents a measure of the active number of degrees of freedom.…”