Estimating the fractal dimension and the predictability of the atmosphere

Abstract

The fractal dimension, Lyapunov-exponent spectrum, Kolmogorov entropy, and predictability are analyzed for chaotic attractors in the atmosphere by analyzing the time series of daily surface temperature and pressure over several regions of the United States and the North Atlantic Ocean with different climatic signal-to-noise ratios. Though the total number of data points (from about 13 800 to about 36 500) is larger than those used in previous studies, it is still too small to obtain a reliable estimate of the Grassberger-Procaccia correlation dimension because of the limitations discussed by Ruelle. However, it can be shown that this dimension is greater than 8. Also, it is pointed out the most, if not all, of the previous estimates of low fractal dimensions in the atmosphere are spurious. -from Authors