Dissertation Proposal - Sandra Babyale

Model Error Estimation for Weak Constraint Variational Data Assimilation

Presented by Sandra Babyale, Computing PhD Computational Math Science and Engineering emphasis

Hybrid presentation: Room update: City Center Plaza 358 or register to attend online via Zoom

Abstract

State estimates from weak constraint four-dimensional variational (4D-Var) data assimilation can vary significantly depending on the specified data and model error covariances. Consequently, the accuracy of these estimates relies on correctly defining these covariances. While observational data errors can often be inferred from measurement noise or instrument precision, estimating model errors is far more challenging. Model error covariances cannot be directly measured due to the complexity and variety of error sources, such as external forcing, boundary conditions, parameterization inaccuracies, and unresolved processes. As a result, their specification relies on assumptions, potentially introducing significant bias and uncertainty into the state estimates. The purpose of this dissertation is to develop a novel framework for estimating model error covariances using Tikhonov regularization parameter selection methods. By formulating the weak-constraint 4D-Var problem as a regularization inverse problem, this research develops three methods for covariance estimation based on the following regularization parameter selection techniques: the L-curve (or L-hypersurface), generalized cross-validation (GCV), and the χ2 method. These methods will be validated through numerical experiments simulating wildfire smoke transport using 1D and 2D transport equations. The validation process will assess the framework’s capability to manage varying levels of observational noise and model uncertainties, with the aim of enhancing the reliability and accuracy of the assimilation process. The expected contribution is a more accurate data assimilation approach that takes into account model and observational errors because we are developing a framework that accurately balances observational data and model dynamics in real-world environmental applications.

Committee

Dr. Jodi Mead (Chair), Dr. Donna Calhoun, Dr. Grady Wright, Dr. Mojitaba Sadegh