This thesis analyzes the effectiveness of bias-aware filtering techniques, particularly the ColKF, in addressing parameter and bias estimation in data assimilation problems. The research explores the ability of this method to differentiate between the impacts of bias and parameter uncertainty, focusing on how the concept of feedback within the filtering process influences the estimation of both bias and parameters.

The study uses the Lorenz-96 model to conduct twin experiments, investigating various scenarios involving parameter estimation, bias estimation, and combined parameter and bias estimation. The experiments reveal that in a feedback filter configuration, where the bias directly influences the ODE system, the forcing parameter F of the Lorenz-96 model becomes indistinguishable from the bias. Conversely, a non-feedback filter configuration allows for the independent estimation of both the parameter and the bias.

In addition, the research highlights the challenges and considerations in implementing a flexible data assimilation framework, particularly in managing state augmentation, stochastic updates, and bias representation. It emphasizes the importance of carefully considering the feedback mechanism in bias-aware filtering, as it significantly impacts the estimation of parameters and bias.

The findings of this thesis offer valuable insights into the application of bias-aware filtering techniques in the presence of parameter uncertainty and provide a foundation for future research in developing robust and versatile data assimilation frameworks. The study encourages further exploration of these methods in real-world applications and with more complex bias structures to advance our understanding and ability to address uncertainties in dynamic systems effectively.