Nonlinear Processes in Geophysics www.nonlin-processes-geophys.net 1023-5809 1607-7946 17 2 2010 10.5194/npg-17-93-2010 http://www.nonlin-processes-geophys.net/17/93/2010/ http://www.nonlin-processes-geophys.net/17/93/2010/npg-17-93-2010.html http://www.nonlin-processes-geophys.net/17/93/2010/npg-17-93-2010.pdf 93 101 2010-03-05 Predictability of the monthly North Atlantic Oscillation index based on fractal analyses and dynamic system theory M. D. Martínez dolors.martinez@upc.edu X. Lana A. Burgueño C. Serra Dept. de Física Aplicada, Universitat Politècnica de Catalunya, Av. Diagonal 649, 08028 Barcelona, Spain Dept. de Física i Enginyeria Nuclear, Universitat Politècnica de Catalunya, Av. Diagonal 647, 08028 Barcelona, Spain Dept. d'Astronomia i Meteorologia, Universitat de Barcelona, C./ Martí Franquès 1, 08028 Barcelona, Spain The predictability of the monthly North Atlantic Oscillation, NAO, index is analysed from the point of view of different fractal concepts and dynamic system theory such as lacunarity, rescaled analysis (Hurst exponent) and reconstruction theorem (embedding and correlation dimensions, Kolmogorov entropy and Lyapunov exponents). The main results point out evident signs of randomness and the necessity of stochastic models to represent time evolution of the NAO index. The results also show that the monthly NAO index behaves as a white-noise Gaussian process. The high minimum number of nonlinear equations needed to describe the physical process governing the NAO index fluctuations is evidence of its complexity. A notable predictive instability is indicated by the positive Lyapunov exponents. 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