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Complex dynamical processes occurring in the earth’s climate system are strongly nonlinear and exhibit wave-like oscillations within broad time-space spectrum. One way to imitate essential features of such processes is using a coupled nonlinear dynamical system, obtained by coupling two versions of the well-known Lorenz (1963) model with distinct time scales that differ by a certain time-scale factor. This dynamical system is frequently applied for studying various aspects of atmospheric and climate dynamics, as well as for estimating the effectiveness of numerical algorithms and techniques used in numerical weather prediction, data assimilation, and climate simulation. This paper examines basic dynamic, correlative, and spectral properties of this system and quantifies the influence of the coupling strength on power spectrum densities, spectrograms, and autocorrelation functions

Correlation and Spectral Properties of a Coupled Nonlinear Dynamical System in the Context of Numerical Weather Prediction and Climate Modeling