To provide the students with a basic knowledge on some of the modeling methods used in geophysical and environmental problems. The focus will be on statistical methods, on applications of the theory of stochastic processes, on numerical methods for the solution of partial differential equations (finite differences, finite elements), on spectral analysis, on model calibration.
Expected learning outcomes
The students will be able to:
1)read and understand scientific papers and books to expand their knowledge on the topics presented during the lectures;
2)read and critically analyze technical reports where simulation models or data processing tools are described and applied to environmental and geophysical problems;
3) set up in a proper way the modeling of phenomena relevant in the environmental and geophysical fields.
Lesson period: First semester
(In case of multiple editions, please check the period, as it may vary)
Fundamentals of probability theory, statistics and stochastic processes; applications to geophysics and environmental physics (regression methods; multivariate analysis, principal component and factor analysis; geostatistical interpolation; Kalman filter; Markov chains). Numerical solution of flow and transport partial differential equations: prototypical equations (equations of motion of geophysical fluids, convective-dispersive transport equations for air, water and soils); finite difference modeling; finite element modeling; analytical solutions of transport equations; particle tracking. Spectral or Fourier analysis: signals and systems, Fourier transform (representation of signals and systems at discrete time and of the sampling in the frequency domain), discrete Fourier transform (representation of periodic and of finite-length signals, power spectrum). Development of a model: structure of the model; model calibration (examples, inverse problems, null space, use of prior information and weighted least squares, maximum likelihood method).