Bayesian Inference for Stochastic Predictions of Non-Gaussian Systems with Applications in Climate Change

TL;DR

This paper develops a Bayesian framework using advanced filtering techniques to improve stochastic climate predictions in non-Gaussian systems, addressing challenges like measurement noise and data limitations.

Contribution

It introduces a novel application of UKF, EnKF, and UPF in climate modeling, analyzing their effectiveness under various real-world conditions.

Findings

Selecting appropriate filtering methods is crucial for accurate predictions.

Increasing data alone does not significantly improve prediction accuracy.

The study highlights issues like information barriers and the curse of dimensionality in climate modeling.

Abstract

Climate change poses significant challenges for accurate climate modeling due to the complexity and variability of non-Gaussian climate systems. To address the complexities of non-Gaussian systems in climate modeling, this thesis proposes a Bayesian framework utilizing the Unscented Kalman Filter (UKF), Ensemble Kalman Filter (EnKF), and Unscented Particle Filter (UPF) for one-dimensional and two-dimensional stochastic climate models, evaluated with real-world temperature and sea level data. We study these methods under varying conditions, including measurement noise, sample sizes, and observed and hidden variables, to highlight their respective advantages and limitations. Our findings reveal that merely increasing data is insufficient for accurate predictions; instead, selecting appropriate methods is crucial. This research provides insights into issues related to information barrier, curse of dimensionality, prediction variability, and measurement noise quantification, thereby enhancing the application of these techniques in real-world climate scenarios.