Statistics and Its Interface

Volume 4 (2011)

Number 4

Quantifying the predictability of noisy space-time dynamical processes

Pages: 535 – 549



Barbara A. Bailey (Department of Mathematics and Statistics, San Diego State University, San Diego, Calif., U.S.A.)


Many environmental processes are complex space-time dynamical systems and the predictability of the system is an important feature of its dynamics. The extension of local Lyapunov exponents, the quantity that measures the shortterm growth of a perturbation in time to include implicit spatial dependence is developed in this paper. A nonlinear modeling approach using flexible neural network models is used to describe the space-time dynamics and quantify the predictability of data from nonlinear stochastic systems. This allows for estimation of dynamical system quantities from data, along with measures of uncertainty for these estimates. The evolution of cloud cover over time and its space-time relationship to other climate variables is an interesting dynamical system that is very important in climate modeling. In the spirit of a cloud parameterization, a nonlinear nearest-neighbor model to describe grid cell relationships is fit to data. The estimation of the spacetime local Lyapunov exponents are used to quantifying the stability and predictability of the space-time cloud process.


nonlinear time series, neural network models, local Lyapunov exponents

2010 Mathematics Subject Classification

Primary 37M25. Secondary 62M45.

Accepted 21 September 2011

Published 17 November 2011