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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union
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Nonlin. Processes Geophys., 19, 611-621, 2012
https://doi.org/10.5194/npg-19-611-2012
© Author(s) 2012. This work is distributed under
the Creative Commons Attribution 3.0 License.
Research article
12 Nov 2012
Complete synchronization of chaotic atmospheric models by connecting only a subset of state space
P. H. Hiemstra1, N. Fujiwara2, F. M. Selten1, and J. Kurths2 1Royal Netherlands Meteorological Institute (KNMI), P.O. Box 201, 3730 AE, De Bilt, The Netherlands
2Potsdam Institute for Climate Impact Research (PIK), P.O. Box 60 12 03, 14412 Potsdam, Germany
Abstract. Connected chaotic systems can, under some circumstances, synchronize their states with an exchange of matter and energy between the systems. This is the case for toy models like the Lorenz 63, and more complex models. In this study we perform synchronization experiments with two connected quasi-geostrophic (QG) models of the atmosphere with 1449 degrees of freedom. The purpose is to determine whether connecting only a subset of the model state space can still lead to complete synchronization (CS). In addition, we evaluated whether empirical orthogonal functions (EOF) form efficient basis functions for synchronization in order to limit the number of connections. In this paper, we show that only the intermediate spectral wavenumbers (5–12) need to be connected in order to achieve CS. In addition, the minimum connection timescale needed for CS is 7.3 days. Both the connection subset and the connection timescale, or strength, are consistent with the time and spatial scales of the baroclinic instabilities in the model. This is in line with the fact that the baroclinic instabilities are the largest source of divergence between the two connected models. Using the Lorenz 63 model, we show that EOFs are nearly optimal basis functions for synchronization. The QG model results show that the minimum number of EOFs that need to be connected for CS is a factor of three smaller than when connecting the original state variables.

Citation: Hiemstra, P. H., Fujiwara, N., Selten, F. M., and Kurths, J.: Complete synchronization of chaotic atmospheric models by connecting only a subset of state space, Nonlin. Processes Geophys., 19, 611-621, https://doi.org/10.5194/npg-19-611-2012, 2012.
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