13 Jan 2021

13 Jan 2021

Review status: this preprint is currently under review for the journal ESD.

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

Tommaso Alberti1, Reik V. Donner2,3, and Stéphane Vannitsem4 Tommaso Alberti et al.
  • 1INAF-IAPS, via del Fosso del Cavaliere 100, 00133 Rome, Italy
  • 2Department of Water, Environment, Construction and Safety, Magdeburg–Stendal University of Applied Sciences, Breitscheidstraße 2, 39114 Magdeburg, Germany
  • 3Research Department IV – Complexity Science and Research Department I – Earth System Analysis, Potsdam Institute for Climate Impact Research (PIK) – Member of the Leibniz Association, Telegrafenberg A31, 14473 Potsdam, Germany
  • 4Royal Meteorological Institute of Belgium, Bruxelles, Belgium

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/multivariate generalized fractal dimensions. With these two 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 time scales. 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 topological and geometric features for different regions, being 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.

Tommaso Alberti et al.

Status: final response (author comments only)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on esd-2020-96', Anonymous Referee #1, 09 Feb 2021
    • AC1: 'Authors' short reply on RC1', Tommaso Alberti, 19 Feb 2021
  • RC2: 'Comment on esd-2020-96', Anonymous Referee #2, 01 Mar 2021
    • AC2: 'Reply on RC2', Tommaso Alberti, 15 Mar 2021

Tommaso Alberti et al.

Tommaso Alberti et al.


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