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MN-GM-IM

Study course:M.Sc. Physics of Earth and Atmosphere
Module:MN-GM-IM
TitleInverse Modelling (Inverse Modellierung)
Module NumberWorkload CP DurationSemester
MN-GM-IM180 h61 Semester ST
Person in Charge U. Löhnert and B. Tezkan
Offering DepartmentInstitute of Geophysics and Meteorology, University of Cologne
Applicability Course of StudyCategory Semester
M.Sc. Physics of Earth and Atmosphere Compulsory 2
Aims Understanding inverse modelling methods for the determination of meteorological and geophysical parameters from measurements, gaining knowledge in major spatial-temporal data assimilation methods
Skills 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
Content • Basics: Inverse problems in meteorology and geophysics, overview of methods and definitions
• Deterministic approaches: linear problems, general formulation, least-squares method, normal equations, generalised matrix inverse, 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, Jacobian matrix, information content, error assessment, data assimilation, optimum interpolation, 3d-var, Kalman filtering, 4d-var, adjoint and tangent-linear models
• Applications: geoelectric and electromagnetic methods, gravity, magnetics, remote sensing of the atmosphere (humidity and temperature)
Prerequisites Basics of mathematics, physics (mandatory)
Lectures Form, Theme Max. of Participants h/weekworkloadCP

Lecture

Exercise

20

2

2

90

120

2

4

ExaminationsForm of testing and examination Graded or not
Written examinationGraded
Requirements Successful participation in the exercises

Not graded

Miscellaneous Recommended Literature:

Aster, R.C., B. Borchers, C.H. Thurber, Parameter estimation and inverse problems, Elsevier, 2005.

Kalnay, E., Atmospheric Modelling, data assimilation and predictability, Cambridge Univ. Press, 2003,  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, 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.