Aims of the module and acquired skills

Understanding inverse modelling methods for the determination of meteorological and geophysical parameters from measurements, gaining knowledge in major 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 judgment of model simulations and capacity of model development.

Contents of the module

• Basics: Inverse problems in geophysics and data assimilation in 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, Kalman filtering and 4d-var
• Applications: geoelectric and electromagnetic methods, gravity, magnetics, remote sensing of the atmosphere (humidity and temperature), weather forecasting

Type of module examinations

Written Examination (graded)