PhD Thesis Defence | Yusuf Aydogdu, Reduced-Order Modeling and Data Assimilation of the El Niño–Southern Oscillation

Location

MC 5501

Candidate 

Yusuf Aydogdu | Applied Mathematics, University of Waterloo

Title

Reduced-Order Modeling and Data Assimilation of the El Niño–Southern Oscillation

Abstract

Simulations of complex fluid dynamics problems or climate models take weeks to complete even when run parallel in state-of-the-art supercomputers. Given computational resource constraints and the need for adaptable simulation settings, cost-efficient and accurate algorithms are essential. In this research, we explore stable, efficient, and accurate methodologies when applied to the El Niño–Southern Oscillation (ENSO), which integrates coupled atmosphere, ocean, and sea surface temperature (SST) mechanisms in the equatorial Pacific. ENSO is one of the most influential and complex climate phenomena, affecting weather patterns across the globe. Due to ENSO's inherent complexity and uncertainties, it is particularly suited for stochastic modeling. We first study the effects of stochastic perturbations on ENSO dynamics and introduce novel modeling and numerical schemes based on the Wiener Chaos Expansion (WCE). Our findings demonstrate that the simulation of the linear stochastic ENSO model driven by the Ornstein-Uhlenbeck process using WCE requires far less computational resources and gives more accurate results compared to Monte Carlo simulations. In the next stage of this research, we explore a reduced-order modeling (ROM) framework based on the POD-Galerkin method when applied to a nonlinear ENSO model. POD-Galerkin reduced order modeling aims to reduce the computational complexity and present high-dimensional problems (usually PDEs) with reduced-order equations (ODEs). By capturing the full-order ENSO (PDE) model with only four modes and four reduced-order equations, we achieve a substantial reduction in computational complexity without significant loss of accuracy. Due to the special properties of the model, we introduce a novel approach using different POD bases, but the same time coefficients for all model components. Moreover, we employ machine learning methods to explore different ROM and model discovery techniques in this part. The final part of this research focuses on the data assimilation of the nonlinear stochastic ENSO model, which forms the core results of this research. We employ particle filters and test the efficiency using different number of particles and ensembles. From novel ENSO modeling to uncertainty quantification, from reduced order modeling to nonlinear filtering, this work provides a promising approach for accurate and efficient predictions of ENSO-related climate variables.