Atmospheric Time Series Analysis Built on Underlying Nonlinear Dynamics

Abstract:

Two major sources to advance our understanding of atmospheric dynamics are the governing equations and the analysis of data from field observations. The equations, however, present enormous mathematical challenges, while observed records are commonly analyzed with models borrowed from traditional time series analysis. Such models typically involve unrealistic for atmospheric dynamics strong statistical assumptions, and their data generating mechanisms (DGMs) are noticeably different from the actual ones.

In contrast, discussed in the talk novel time series models (in the form of low-order nonlinear dynamical systems, extensions of the celebrated Lorenz model) are derived from the governing equations, whose fundamental properties they inherit. Simple enough to generate numerous long records, they are particularly suited for statistical studies of weather and climate, especially in topics such as extremes, where the estimators are exceedingly sensitive to properties of the DGMs.

This new approach to atmospheric time series analysis is motivated by recent progress in statistical properties of dynamical systems. It has been proved that the flow of the Lorenz model satisfies the central limit theorem of probability theory (i.e., series of observations on this model may exhibit statistics of sequences of random variables), and the extreme value theory has been extended from random phenomena to chaotic deterministic dynamical systems, the Lorenz model in particular.