Predictability of the monthly North Atlantic Oscillation index based on fractal analyses and dynamic system theory

M D Martínez,X Lana,C Serra,A Burgueño

doi:10.5194/npg-17-93-2010

M D Martínez, X Lana + Show 2 more

Open Access

https://doi.org/10.5194/npg-17-93-2010

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Abstract

Abstract. 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. Besides corroborating the complex time behaviour of the NAO index, present results suggest that random Cantor sets would be an interesting tool to model lacunarity and time evolution of the NAO index.

Highlights

The North Atlantic Oscillation, NAO, index can be defined as the difference between the normalized sea level atmospheric pressures at Gibraltar and South-West Iceland
The results show that the monthly NAO index behaves as a white-noise Gaussian process
Some comparisons can be made between the present results and those derived for the daily rainfall and dry spell regimes of the Iberian Peninsula (Martınez et al, 2007)

Summary

Introduction

The North Atlantic Oscillation, NAO, index can be defined as the difference between the normalized sea level atmospheric pressures at Gibraltar and South-West Iceland. Solid straight lines represent 69t16h8e5 loFgig-uloreg4ea.vCoolruretliaotionn oinfteCgra(lr, )C.(r), of the monthly NAO indices (dashed lines) for several reconstruction dimensions m ranging from 2 to 17, compared with a Gaussian white-noise series (open circles) for m equal to 2, 3, 4, 5, 10 and 15. The evolution of C(r) with r for the monthly NAO indices and the Gaussian white noise series at several reconstruction dimensions m (2, 3, 4, 5, 10, and 15). The evolution of the first three positive Lyapunov exponents when increasing dimension m (Fig. 5b) leads to stationary positive values of 0.13, 0.10, and 0.06 for λ1, λ2 and λ3, respectively, and reconstruction dimension m close to dE, certifying the predictive instability of monthly NAO indices. The embedding dimension should be at least equal to 15, and possibly higher according to the evolution of C(r) in Fig. 4a and the computation of κ

Findings

Discussion

Conclusions