Phase Space Structure, Attractor Dimension, Lyapunov Exponent and Nonlinear Prediction from Earth’s Atmospheric Angular Momentum Time Series

Abstract

—On a short time scale, Atmospheric Angular Momentum (AAM) has been demonstrated to be essentially the sole excitation source of LOD variations. The LOD variation, therefore, merely reflects the AAM variation (LOD as proxy for AAM). The study of the nonlinear nature of AAM variability (e.g., its orbital complexity, dimensionality and extreme sensitivity to the initial conditions) may provide a physical premise for theoretical modelling of the earth-atmosphere-ocean system. Analysis of the high quality of detailed daily LOD/AAM variations time series, spanning the period of 1962–1992, reveals a non-zero and low positive Lyapunov exponent value which suggests possible evidence of deterministic chaos in the underlying dynamics. Application of modern nonlinear prediction techniques capable of distinguishing chaos and random fractals to the data set, further support the above findings and render a predictive time limit of approximately 12–15 days. A low dimensional strange attractor and a low average Lyapunov exponent suggest a low level of unpredictability and stability in the system dynamics. It is argued here that a possible source of the raised entropy in LOD/AAM systems possibly stems from a conceivable nonlinear interaction between the seasonal cycle and inter- or intra-annual fluctuations due to thermodynamics properties of the atmosphere-ocean system.