The aims of this course are to develop techniques of data assimilation in numerical weather prediction and climate change modelling. 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 to numerical weather prediction and climate change modelling, 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.
1. Background/Review (1.1 Data sets, statistics, re-analysis; polynomial interpolation Legendre, Chebychev, etc and errors; Fourier Transform and Fast Fourier Transform theory and practical implementation.)
2. Variational Approach (2.1 Cost functions; regression analysis review least squares, linear and nonlinear models; Optimal Interpolation, 3DVar and 4DVar approaches, applications to Numerical Weather Prediction.)
3. Kalman Filtering (3.1 Basic ideas filtering/smoothing of Kalman Filter; Extended Kalman Filter nonlinear; Ensemble Kalman Filter sequential MC methods, numerical implementation, Case study on the ensemble Kalman filter applied to the Lorenz system.)
4. Bayesian Inference Approach (4.1 Basic ideas, Bayes Theorem, prior and posterior distributions selection and interpretation; implementation: acceptance-rejection sampling, MCMC approach to target distributions Metropolis-Hastings, examples from diffusion problems, wave equation, fluid mechanics, geophysics and molecular dynamics. Discussion of general Inverse Problems, Uncertainty Quantification and Extreme Events.)
5. Modelling, Data Assimilation and Simulation Project (5.1 Group-based work on an extended project related to biology, climate change or finance, including the modelling and subsequent direct numerical implementation of one or more of the data assimilation approaches above. The project includes a background literature search, development of the underlying model, assessment of the data and appropriate data assimilation techniques that can be applied, hands-on simulation of one or more of these techniques, a group-based presentation and a written report.)
By the end of the course, students should be able to do the following:
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SCQF Level: 11
Credits: 15