Handbook

Real-world physical systems, like the ocean and atmosphere, are immensely complicated, and understanding and predicting the future behaviour of these systems is crucial for weather forecasting, marine operations, and climate science. However, our knowledge of the real world sits upon two shaky pillars: imperfect observations and incomplete models (both mathematical and computational). The mathematical discipline for merging observations and models, plus their relative uncertainties, to form a best guess estimate for the true state of a system is called inverse modelling.

This course aims to provide an overview of the mathematical foundations of inverse modelling and prediction and their application to real-world systems, primarily the ocean and the atmosphere. The course covers topics in forward and inverse modelling, well-posed and overdetermined problems, calculus of variations, the generalised inverse, optimal interpolation, Bayesian data assimilation, the Kalman filter, principal component analysis, and ensemble and particle filters. Course materials will be explored in detail in lectures and reinforced via practical hands-on computer labs and tutorials.