MN-GM-IM

Core Module: Inverse Modelling (IM)
Identification number MN-GM-IM		Workload 180 h	Credits 6	Term 2nd (or 1st) semester	Offered every year	Start Summer term	Duration 1 semester
1	Course types a) Lecture b) Exercise			Contact time 30 h 30 h		Private study 60 h 60 h
2	Module objectives and skills to be acquired Understanding inverse modelling methods for the determination of meteorological and geophysical parameters from measurements, gaining knowledge in relevant spatial-temporal data assimilation methods. Acquired skills are the mathematical foundation of linear and non-linear inverse problems, formulation of inverse problems, assessment of statistical prerequisites and numerical complexity, assessment of inverse solutions, practical limitation of current assimilation methods, critical judgement of model simulations and capacity of model development.
3	Module content Basics: Inverse problems and data assimilation in geophysics and meteorology, overview of methods and definitions Deterministic approaches: linear problems, general formulation, least-squares method, normal equations, Jacobian matrix, generalised matrix inverse, adjoint and tangent-linear models, SVD decomposition, data and model gain matrices, data and model covariance matrices (data error and model assessment), nonlinear problems, Jacobian matrix, iterative conjugate gradient and Gauss-Newton methods, regularisation (Occam, Levenberg-Marquardt) Stochastic approaches, general formulation, Bayes theorem, optimal estimation, information content, error assessment Data assimilation: optimum interpolation, 3D-Var, 4D-Var, Kalman filtering Applications: geoelectric and electromagnetic methods, gravity, magnetics, remote sensing of the atmosphere (humidity and temperature), weather forecasting Literature: Aster, R.C., B. Borchers, C.H. Thurber, Parameter estimation and inverse problems, Elsevier, 2005. Benner, A. F., 2005. Inverse Modeling of the Ocean and Atmosphere. Cambridge University Press, ISBN: 9780521021579. Evensen, G., 2009. Data Assimilation: the Ensemble Kalman Filter. Springer, SBN 978-3-642-03711-5 Kalnay, E., 2003. Atmospheric Modelling, data assimilation and predictability, Cambridge Univ. Press, 342 pp. Meju, M.A., 1994. Geophysical data analysis: Understanding inverse problems, Theory and practice, Society of Exploration Geophysicists. Rodgers, C. D., 2000. Inverse methods for atmospheric sounding: Theory and practice. World Scientific, 238 pp. Menke, W., 2012. Geophysical Data Analysis: Discrete Inverse Theory – 3rd Ed., Elsevier. Oliver et al., 2008, Inverse Theory for Petroleum Reservoir Characterization and History Matching, Cambridge Univ. Press. Tarantola, A., 2005. Inverse Problem Theory and Methods for Model Parameter Estimation. SIAM. ISBN 978-0-89871-572-9.
4	Teaching methods Lectures and exercises
5	Prerequisites (for the module) Formal: None The content of the course requires the undergraduate knowledge of mathematics, physics, and programming.
6	Type of examination At the beginning of the lecture-free period, there is a 120 to 180-minute written examination, the content of which is the material from the lecture and exercises. Successful completion of the exercises is required for admission to the examination; for this, the acquisition of 50% of the points to be achieved is sufficient. A repeat examination is offered before or at the beginning of the following semester. The examination grade is the module grade. In the case of two passed examinations (see § 20 paragraph 10 examination regulations), the better grade is the module grade.
7	Credits awarded The module is passed, and the credit points will be awarded, if the written examination is passed.
8	Compatibility with other Curricula N/A
9	Proportion of final grade Weight of the module grade in the overall grade: 6/150 (4 %)
10	Module coordinator Ulrich Löhnert, Bülent Tezkan
11	Further information Version: 2023-03-28