F10DA - Data Assimilation

Aims

The aims of this course are to develop techniques of data assimilation in a variety of contexts, such as in numerical weather prediction, climate change modelling, mathematical biology, ecology and medicine.

This will be achieved by a mixture of lectures on basic methodology, tutorial exercises, computer labs, case studies and a large group-based modelling, implementation and simulation project. We will introduce a number of data assimilation approaches that are widely used in applications such as numerical weather prediction, climate change modelling, mathematical biology, ecology and medicine, including basic regression analysis, variational approaches, Kalman filtering, extended and ensemble Kalman filtering and the Bayesian inference approach. The course will teach practical implementation of these data assimilation techniques in the context of computer simulations, which will be illustrated by prototype applications. These methodologies will form the basis for a series of modelling case studies as well as the group-based project component of the course.

Syllabus

1. Bivariate and joint probability models for data driven assimilation (1.1 Coverage of theory of probability models and distributions used for data assimilation and enhanced prediction.)

2. Multivariate distribution and probability models for data driven assimilation (2.1 Coverage of multivariate probability distributions and models for data assimilation and enhanced prediction.)

3. Bayesian inference for multivariate distributions (3.1 Theory and methodology of Bayesian inference and computational techniques for bivariate and multivariate distributions.)

4. Kalman filtering techniques (4.1 Theory and methodology for Kalman filtering techniques and its variations for real applications. Assessing the performance of these methodologies via computer codes and project assignments.)

5. Importance sampling and particle filtering techniques (5.1 Theory and methodology of importance sampling and particle filtering techniques in the case of non-normal data with illustrations of real applications. Assessing the performance of these methodologies via computer codes and project assignments.)