On Nonlinear Time Series Analysis and Climate Variability

This paper aims to synthesize the underlying mathematical and physical principles that govern climate variability by examining the current body of research on nonlinear time series analysis. Thus, this paper hopes to be a primer for any reader new to the field.

Section 2 introduces foundational concepts that nonlinear time series analysis relies on, such as state space reconstruction and different mathematical characterization methods, such as Lyapunov exponents and attractors. Section 3 will discuss nonlinear techniques that help conduct analyses that are more robust. Section 4 discusses different analysis methods used to support climate variability studies. This section helps put in perspective some of the abstract concepts discussed in section 2. Some examples used in section 4 are models of the EN~SO phenomenon and the ozone layer. Section 5 discusses the predictive capabilities and limitations of nonlinear time series analysis. Section 6 suggests reading material for further exploration and poses some questions that still need examining. We conclude and offer some final remarks in section 7.