UC Irvine

We were motivated by the two major limitations of the current research approaches on the North Atlantic Oscillation (NAO) based on empirical orthogonal functions (EOF) analysis: (i) long-term stationary assumptions; (ii) lack of measures of uncertainty, and proposed and developed a time-varying low-dimensional representation for spatio-temporal data in this thesis.

The low-dimensional representation is based on a structured spatial covariance matrix using a certain number of structured basis functions with certain parametric forms. Initially, we developed the Parametric Basis Function (PBF) spatial covariance model in a stationary scenario and provided the statistical inference in both maximum likelihood and Bayesian analysis frameworks.

We further extended the model by introducing time-varying parameters to develop the time-varying parametric basis function (TV-PBF) model in the state space model framework. The Bayesian approach with MCMC techniques was used to make inference for the TV-PBF model. The model is able to provide smoothly changing patterns of the 1st EOFs NAO over time which can serve as an alternative representation for the spatio-temporal NAO data.