Local dimension and finite time prediction in spatiotemporal chaotic systems

We show how a recently introduced statistic [Patil , Phys. Rev. Lett. 81, 5878 (2001)] provides a direct relationship between dimension and predictability in spatiotemporal chaotic systems. Regions of low dimension are identified as having high predictability and vice versa. This conclusion is reached by using methods from dynamical systems theory and Bayesian modeling. In this work we emphasize on the consequences for short time forecasting and examine the relevance for factor analysis. Although we concentrate on coupled map lattices and coupled nonlinear oscillators for convenience, any other spatially distributed system could be used instead, such as turbulent fluid flows.