Articles | Volume 12, issue 3
https://doi.org/10.5194/esd-12-837-2021
© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/esd-12-837-2021
© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
06 Aug 2021
Research article |
| 06 Aug 2021
| 06 Aug 2021
Multiscale fractal dimension analysis of a reduced order model of coupled ocean–atmosphere dynamics
INAF-IAPS, via del Fosso del Cavaliere 100, 00133 Rome, Italy
Reik V. Donner
Department of Water, Environment, Construction and Safety, Magdeburg–Stendal University of Applied Sciences, Breitscheidstraße 2, 39114 Magdeburg, Germany
Research 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
Stéphane Vannitsem
Royal Meteorological Institute of Belgium, Brussels, Belgium
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Jonathan Demaeyer, Jonas Bhend, Sebastian Lerch, Cristina Primo, Bert Van Schaeybroeck, Aitor Atencia, Zied Ben Bouallègue, Jieyu Chen, Markus Dabernig, Gavin Evans, Jana Faganeli Pucer, Ben Hooper, Nina Horat, David Jobst, Janko Merše, Peter Mlakar, Annette Möller, Olivier Mestre, Maxime Taillardat, and Stéphane Vannitsem
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Stéphane Vannitsem
Nonlin. Processes Geophys., 30, 1–12, https://doi.org/10.5194/npg-30-1-2023, https://doi.org/10.5194/npg-30-1-2023, 2023
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David Docquier, Stéphane Vannitsem, Alessio Bellucci, and Claude Frankignoul
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Preprint withdrawn
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Understanding whether variations in ocean heat content are driven by air-sea heat fluxes or by ocean dynamics is of crucial importance to enhance climate projections. We use a relatively novel causal method to quantify interactions between ocean heat budget terms based on climate models. We find that low-resolution models overestimate the influence of ocean dynamics in the upper ocean, and that changes in ocean heat content are dominated by air-sea fluxes at high resolution.
Nicolas Ghilain, Stéphane Vannitsem, Quentin Dalaiden, Hugues Goosse, Lesley De Cruz, and Wenguang Wei
Earth Syst. Sci. Data, 14, 1901–1916, https://doi.org/10.5194/essd-14-1901-2022, https://doi.org/10.5194/essd-14-1901-2022, 2022
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Modeling the climate at high resolution is crucial to represent the snowfall accumulation over the complex orography of the Antarctic coast. While ice cores provide a view constrained spatially but over centuries, climate models can give insight into its spatial distribution, either at high resolution over a short period or vice versa. We downscaled snowfall accumulation from climate model historical simulations (1850–present day) over Dronning Maud Land at 5.5 km using a statistical method.
Frederik Wolf, Aiko Voigt, and Reik V. Donner
Earth Syst. Dynam., 12, 353–366, https://doi.org/10.5194/esd-12-353-2021, https://doi.org/10.5194/esd-12-353-2021, 2021
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In our work, we employ complex networks to study the relation between the time mean position of the intertropical convergence zone (ITCZ) and sea surface temperature (SST) variability. We show that the information hidden in different spatial SST correlation patterns, which we access utilizing complex networks, is strongly correlated with the time mean position of the ITCZ. This research contributes to the ongoing discussion on drivers of the annual migration of the ITCZ.
Frederik Wolf, Ugur Ozturk, Kevin Cheung, and Reik V. Donner
Earth Syst. Dynam., 12, 295–312, https://doi.org/10.5194/esd-12-295-2021, https://doi.org/10.5194/esd-12-295-2021, 2021
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Motivated by a lacking onset prediction scheme, we examine the temporal evolution of synchronous heavy rainfall associated with the East Asian Monsoon System employing a network approach. We find, that the evolution of the Baiu front is associated with the formation of a spatially separated double band of synchronous rainfall. Furthermore, we identify the South Asian Anticyclone and the North Pacific Subtropical High as the main drivers, which have been assumed to be independent previously.
Stephan Hemri, Sebastian Lerch, Maxime Taillardat, Stéphane Vannitsem, and Daniel S. Wilks
Nonlin. Processes Geophys., 27, 519–521, https://doi.org/10.5194/npg-27-519-2020, https://doi.org/10.5194/npg-27-519-2020, 2020
Giorgia Di Capua, Jakob Runge, Reik V. Donner, Bart van den Hurk, Andrew G. Turner, Ramesh Vellore, Raghavan Krishnan, and Dim Coumou
Weather Clim. Dynam., 1, 519–539, https://doi.org/10.5194/wcd-1-519-2020, https://doi.org/10.5194/wcd-1-519-2020, 2020
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We study the interactions between the tropical convective activity and the mid-latitude circulation in the Northern Hemisphere during boreal summer. We identify two circumglobal wave patterns with phase shifts corresponding to the South Asian and the western North Pacific monsoon systems at an intra-seasonal timescale. These patterns show two-way interactions in a causal framework at a weekly timescale and assess how El Niño affects these interactions.
Cited articles
Alberti, T.: Multivariate empirical mode decomposition analysis of Swarm data, Nuovo Cimento C, 41, 1–10, 2018. a
Alberti, T., Giannattasio, F., De Michelis, P., and Consolini, G.: Linear Versus Nonlinear Methods for Detecting Magnetospheric and Ionospheric Current Systems Patterns, Earth Space Sci., 7, e2019EA000559, https://doi.org/10.1029/2019EA000559, 2020b. a
Alexander, M. A., Bladé, I., Newman, M., Lanzante, J. R., Lau, N.-C., and Scott, J. D.: The atmospheric bridge: The influence of ENSO teleconnections on air–sea interaction over the global oceans. J. Climate, 15, 2205–2231, 2002. a
Ambaum, M. H. P., Hoskins, B. J., and Stephenson, D. B.: Arctic Oscillation or North Atlantic Oscillation?, J. Climate, 14, 3495–3507, 2001. a
Badii, R. and Politi, A.: Hausdorff dimension and uniformity factor of strange attractors, Phys. Rev. Lett., 52, 1661–1664, 1984. a
D'Andrea, F., Czaja, A., and Marshall, J.: Impact of anomalous ocean heat transport on the North Atlantic Oscillation, J. Climate, 18, 4955–4969, 2005. a
De Boisséson, E., Balmaseda, M., and Mayer, M.: Ocean heat content variability in an ensemble of twentieth century ocean reanalyses, Clim. Dynam., 50, 3783–3798, https://doi.org/10.1007/s00382-017-3845-0, 2018. a, b
De Cruz, L., Demaeyer, J., and Vannitsem, S.: The Modular Arbitrary-Order
Ocean-Atmosphere Model: MAOOAM v1.0, Geosci. Model Dev., 9, 2793–2808,
https://doi.org/10.5194/gmd-9-2793-2016, 2016. a, b
De Cruz, L., Schubert, S., Demaeyer, J., Lucarini, V., and Vannitsem, S.: Exploring the Lyapunov instability properties of high-dimensional atmospheric and climate models, Nonlin. Processes Geophys., 25, 387–412, https://doi.org/10.5194/npg-25-387-2018, 2018. a
Del Rio Amador, L., and Lovejoy, S.: Predicting the global temperature with the Stochastic Seasonal to Interannual Prediction System (StocSIPS), Clim. Dynam., 53, 4373–4411, https://doi.org/10.1007/s00382-019-04791-4, 2019. a
Del Rio Amador, L. and Lovejoy, S.: Long-range forecasting as a past value problem: Untangling correlations and causality with scaling, Geophys. Res. Lett., 48, e2020GL092147, https://doi.org/10.1029/2020GL092147, 2021. a
Faranda, D., Messori, G., and Vannitsem, S.: Attractor dimension of time-averaged climate observables: insights from a low-order ocean-atmosphere model, Tellus A, 71:1, https://doi.org/10.1080/16000870.2018.1554413, 2019. a
Farmer, J. D., Ott, E., and Yorke, J. A.: The dimension of chaotic attractors, Physica D, 7, 153–180, 1983. a
Farneti, R.: Modelling interdecadal climate variability and the role of the ocean, WIREs Clim. Change, 8, e441, https://doi.org/10.1002/wcc.441, 2017. a
Feliks, Y., Ghil, M., and Robertson, A. W.: The atmospheric circulation over the North Atlantic as induced by the SST field, J. Climate, 24, 522–542, https://doi.org/10.1175/2010JCLI3859.1, 2011. a
Flandrin, P., Rilling, G., and Goncalves, P.: Empirical Mode Decomposition as a Filter Bank, IEEE Sign. Proc. Lett., 11, 112, https://doi.org/10.1109/LSP.2003.821662, 2004. a
Franzke, C. L. E., Barbosa, S., Blender, R., Fredriksen, H.-B., Laepple, T., Lambert, F., Nilsen, T., Rypdal, K., Rypdal, M., Scotto, M. G., Vannitsem, S., Watkins, N. W., Yang, L., and Yuan, N.: The Structure of Climate Variability Across Scales, Rev. Geophys., 58, e00657, https://doi.org/10.1029/2019RG000657, 2020. a, b
Gastineau, G., D'Andrea, F., and Frankignoul, C.: Atmospheric response to the North Atlantic Ocean variability on seasonal to decadal time scales, Clim. Dynam., 40, 2311–2330, https://doi.org/10.1007/s00382-012-1333-0, 2013. a
Huang, N. E. and Wu, Z.: A review on Hilbert-Huang transform: Method and its applications to geophysical studies, Rev. Geophys., 46, RG2006, https://doi.org/10.1029/2007RG000228, 2008. a, b
Huang, N. E., Shen, Z., Long, S. R., Wu, M. C., Shih, H. H., Zheng, Q., Yen, N.-C., Tung, C. C., and Liu, H. H.: The Empirical Mode Decomposition and the Hilbert Spectrum for Nonlinear and Nonstationary Time Series Analysis, Proc. R. Soc. Lon. Ser.-A, 454, 903, https://doi.org/10.1098/rspa.1998.0193, 1998. a, b, c, d, e, f, g, h, i, j, k
Jin, F.-F.: Tropical Ocean-Atmosphere interaction, the Pacific cold tongue, and the El-Niño-Southern Oscillation, Science, 274, 76–78, 1996. a
Kaplan, J. L. and Yorke, J. A.:
Chaotic behavior of multidimensional difference equations, in: Functional
Differential Equations and Approximation of Fixed Points, Lect. Notes Math.,
edited by: Peitgen, H.-O. and Walther, H.-O., 730, 204–227, Springer, Berlin, Heidelberg, https://doi.org/10.1007/BFb0064319, 1979. a
Kravtsov, S., Dewar, W. K., Berloff, P., Ghil, M. and McWilliams, J. C.: A highly nonlinear coupled mode of decadal variability in a mid-latitude ocean-atmosphere model, Dyn. Atmos. Oceans, 43, 123–150, 2007. a
Legras, B. and Ghil, M.: Persistent anomalies, blocking, and variations in atmospheric predictability, J. the Atmos. Sci., 42, 433–471, 1985. a
L'Hévéder, B., Codron, F., and Ghil, M.: Impact of anomalous northward oceanic heat transport on global climate in a slab-ocean setting, J. Climate, 28, 2650–2664, 2014. a
Lorenz, E. N.: Formulation of a low-order model of a moist general circulation, J. Atmos. Sci., 41, 1933–1945, 1984. a
Lovejoy, S.: The half-order energy balance equation – Part 1: The homogeneous HEBE and long memories, Earth Syst. Dynam., 12, 469–487, https://doi.org/10.5194/esd-12-469-2021, 2021. a
Lovejoy, S., Procyk, R., Hébert, R., and Del Rio Amador, L.: The fractional energy balance equation, Q. J. Roy. Meteorol. Soc., 147, 1964–1988, https://doi.org/10.1002/qj.4005, 2021. a
Mandelbrot, B.: How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension, Science, 156, 636–638, https://doi.org/10.1126/science.156.3775.636, 1967. a
Meehl, G. A., Arblaster, J. M., and Loschnigg, J.: Coupled Ocean–Atmosphere Dynamical Processes in the Tropical Indian and Pacific Oceans and the TBO, J. Climate, 16, 2138–2158, 2003. a
Mosedale, T. J., Stephenson, D. B., Collins, M., and Mills, T. C.: Granger Causality of Coupled Climate Processes: Ocean Feedback on the North Atlantic Oscillation, J. Climate, 19, 1182–1194, 2006. a
Neelin, J. D., Latif, M., and Jin, F.-F.: Dynamics of Coupled Ocean-Atmosphere Models: The Tropical Problem, Annu. Rev. Fluid Mech., 26:1, 617–659, 1994. a
Nese, J. M. and Dutton, J. A.: Quantifying predictability variations in a low-order ocean-atmosphere model: A dynamical system approach. J. Climate, 6, 185–203, 1993. a
Ott, E.: Chaos in Dynamical Systems – 2nd Edn., Cambridge University Press, Cambridge, 490 pp., https://doi.org/10.2277/0521811961, 2002. a, b, c
Pawelzik, K. and Schuster, H. G.: Generalized dimensions and entropies from a measured time series, Phys. Rev. A, 35, 481–484, 1987. a
Philander, S. G. H.: El Niño and the Southern Oscillation, Academic Press, New York, 1990. a
Poli, P., Hersbach, H., Tan, D. G. H., Dee, D. P., Thépaut, J.-N., Simmons, A., Peubey, C., Laloyaux, P., Komori, T., Berrisford, P., Dragani, R., Trémolet, Y., Hólm, E. V., Bonavita, M., Isaksen, L., and Fisher, M.: The data assimilation system and initial performance evaluation of the ECMWF pilot reanalysis of the 20th-century assimilating surface observations only, ERA report series, 14, European Centre for Medium-range Weather Forecasts, Reading, UK, 2015. a, b
Primavera, L. and
Florio, E.: Parallel Algorithms for Multifractal Analysis of River Networks,
in: Numerical Computations: Theory and
Algorithms, Lect. Notes Comput. Sc., edited by: Sergeyev Y. and Kvasov D. 11973, Springer, Cham, 2020. a
Roebber, P. J.: Climate variability in a low-order coupled atmosphere-ocean model, Tellus A, 47, 473–494, 1995. a
Steinhaus, H.: Length, shape and area, Colloq. Math., 3, 1–13, 1954. a
Timmermann, A., Jin, F.-F., and Abshagen, J.: A nonlinear theory for El Niño bursting, J. Atmos. Sci., 60, 152–165, 2003. a
Van der Avoird, E., Dijkstra, H. A., Nauw, J. J., and Schuurmans, C. J. E.: Nonlinearly induced low-frequency variability in a midlatitude coupled ocean-atmosphere model of intermediate complexity, Clim. Dynam., 19, 303–320, 2002. a
Vannitsem, S.: The role of the ocean mixed layer on the development of the North Atlantic Oscillation: A dynamical system's perspective, Geophys. Res. Lett., 42, 8615, https://doi.org/10.1002/2015GL065974, 2015. a, b, c
Vannitsem, S.: Predictability of large-scale atmospheric motions: Lyapunov exponents and error dynamics, Chaos, 27, 032101, https://doi.org/10.1063/1.4979042, 2017. a, b, c, d
Vannitsem, S.: Time series used in the manuscript “Causal dependences between the coupled ocean-atmosphere dynamics over the Tropical Pacific, the North Pacific and the North Atlantic” [Data set], Zenodo, https://doi.org/10.5281/zenodo.1135134, 2018. a
Vannitsem, S. and Ekelmans, P.: Causal dependences between the coupled ocean–atmosphere dynamics over the tropical Pacific, the North Pacific and the North Atlantic, Earth Syst. Dynam., 9, 1063–1083, https://doi.org/10.5194/esd-9-1063-2018, 2018. a, b, c, d
Vannitsem, S. and Ghil, M.: Evidence of coupling in ocean atmosphere dynamics over the North Atlantic, Geophys. Res. Lett., 44, 2016–2026, https://doi.org/10.1002/2016GL072229, 2017. a
Vannitsem, S., Demaeyer, J., and Ghil, M.: Extratropical low-frequency variability with ENSO forcing: A reduced-order coupled model study. J. Adv. Model. Earth Sy., 13, e2021MS002530, https://doi.org/10.1029/2021MS002530, 2021. a
Van Veen, L.: Overturning and wind driven circulation in a low-order ocean–atmosphere model, Dynam. Atmos. Oceans, 37, 197–221, 2003. a
Wang, C.: Three-ocean interactions and climate variability: a review and perspective, Clim. Dynam. 53, 5119–5136, 2019. a
Wunsch, C. and Ferrari, R.: Vertical mixing, energy, and the general circulation of the ocean, Annu. Rev. Fluid Mech., 36, 281–314, 2004. a
Xue, P., Malanotte Rizzoli, P., Wei, J., and Eltahir, E. A. B.: Coupled ocean atmosphere modeling over the Maritime Continent: A review, J. Geophys. Res.-Oceans, 125, e2019JC014978, https://doi.org/10.1029/2019JC014978, 2020. a, b
Short summary
We provide a novel approach to diagnose the strength of the ocean–atmosphere coupling by using both a reduced order model and reanalysis data. Our findings suggest the ocean–atmosphere dynamics presents a rich variety of features, moving from a chaotic to a coherent coupled dynamics, mainly attributed to the atmosphere and only marginally to the ocean. Our observations suggest further investigations in characterizing the occurrence and spatial dependency of the ocean–atmosphere coupling.
We provide a novel approach to diagnose the strength of the ocean–atmosphere coupling by using...
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