Geophysical and Environmental Modeling
A.Y. 2021/2022
Learning objectives
To provide the students with a basic knowledge on some of the modeling methods used in geophysical and environmental problems. The main focus will be on providing the students with knowledge and skills for application of statistics and the theory of stochastic processes (including some techniques of data mining), for the numerical solution of partial differential equations (finite differences/finite volumes, finite elements/spectral methods), for the spectral analysis of geophysical data sets, and for model calibration via solution of inverse problems.
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
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
insegnamento non attivo (attivo nel 2022/23)
Lesson period
First semester
TEACHING METHODS
If required, on the basis of the restrictions intorduced to limit the pandemic spread, the Lectures will be given in synchronous telematic method, with the Zoom platform and will be recorded so that the video will be available through the Moodle site of the course unit from the web page https://labonline.ctu.unimi.it/
COURSE SYLLABUS AND BIBLIOGRAPHY
The syllabus and the study material will not be subject to any variation.
ASSESSMENT METHODS AND CRITERIA
The oral exam will be held in telematic way, through the MS Teams platform, which can be accessed by following the instructions available on the web portal of the University.
If required, on the basis of the restrictions intorduced to limit the pandemic spread, the Lectures will be given in synchronous telematic method, with the Zoom platform and will be recorded so that the video will be available through the Moodle site of the course unit from the web page https://labonline.ctu.unimi.it/
COURSE SYLLABUS AND BIBLIOGRAPHY
The syllabus and the study material will not be subject to any variation.
ASSESSMENT METHODS AND CRITERIA
The oral exam will be held in telematic way, through the MS Teams platform, which can be accessed by following the instructions available on the web portal of the University.
Course syllabus
1) Development and application of a model.
2) Prototypical equations: conservation principles and phenomenological laws; prototypical partial differential equations.
3) Finite differences and finite volume methods for the numerical solution of flow and transport equations. Accuracy and convergence; Von Neumann stability analysis; Courant-Friedrichs-Lewy condition); finite volume method (or integrated finite differences); staggered grids; methods of solution of large linear systems (Gaussian elimination; successive over relaxation method; preconditioned conjugate gradient); explicit, implicit and Crank-Nicolson schemes for parabolic equations; nested models.
4) Spectral analysis. Signals and systems; Fourier transform (representation of discrete-time signals and systems in the frequency domain; sampling); discrete Fourier transform (representation of periodic and finite-length discrete-time signals; power spectrum).
5) Basic properties of spectral and finite elements method for the solution of flow and transport equations: weighted residuals and variational approaches.
6) Basic statistic and theory of probability; basic theory of stochastic processes.
7) Modeling solute transport. Analytical solutions of transport equation. Lagrangian models: particle tracking method for convective transport (Runge-Kutta method for ordinary differential equations). Stochastic models (Monte Carlo methods for the advective-dispersive equation (Kolmogorov-Dmitriev theory of branching stochastic processes; discrete-time random walk).
8) Data mining and data analysis. Regression methods; multivariate analysis (Principal Component Analysis & Factor analysis); clustering algorithms; wavelets; applications of stochastic processes to geophysics and to environmental physics (Kriging; Kalman filter; Markov chains); artificial neural networks.
9) Model calibration by solution of inverse problems. General definition and properties of the discrete inverse problem; the null space; use of prior information and weighted least squares; Bayesian approach and the maximum likelihood method; gradient-based optimization algorithms (Newton's method; Levenberg-Marquardt's algorithm); global optimization methods (genetic algorithms; differential evolution; simulated annealing); sensitivity analysis (one-at-a-time approach; adjoint-state equation; first-order sensitivity).
Students' project. Each student will be asked to complete a project by developing original codes or by application of freely available software tools (e.g., Princeton Ocean Model, CALMET/CALPUFF/CALGRID package, MODFLOW/MODPATH package).
2) Prototypical equations: conservation principles and phenomenological laws; prototypical partial differential equations.
3) Finite differences and finite volume methods for the numerical solution of flow and transport equations. Accuracy and convergence; Von Neumann stability analysis; Courant-Friedrichs-Lewy condition); finite volume method (or integrated finite differences); staggered grids; methods of solution of large linear systems (Gaussian elimination; successive over relaxation method; preconditioned conjugate gradient); explicit, implicit and Crank-Nicolson schemes for parabolic equations; nested models.
4) Spectral analysis. Signals and systems; Fourier transform (representation of discrete-time signals and systems in the frequency domain; sampling); discrete Fourier transform (representation of periodic and finite-length discrete-time signals; power spectrum).
5) Basic properties of spectral and finite elements method for the solution of flow and transport equations: weighted residuals and variational approaches.
6) Basic statistic and theory of probability; basic theory of stochastic processes.
7) Modeling solute transport. Analytical solutions of transport equation. Lagrangian models: particle tracking method for convective transport (Runge-Kutta method for ordinary differential equations). Stochastic models (Monte Carlo methods for the advective-dispersive equation (Kolmogorov-Dmitriev theory of branching stochastic processes; discrete-time random walk).
8) Data mining and data analysis. Regression methods; multivariate analysis (Principal Component Analysis & Factor analysis); clustering algorithms; wavelets; applications of stochastic processes to geophysics and to environmental physics (Kriging; Kalman filter; Markov chains); artificial neural networks.
9) Model calibration by solution of inverse problems. General definition and properties of the discrete inverse problem; the null space; use of prior information and weighted least squares; Bayesian approach and the maximum likelihood method; gradient-based optimization algorithms (Newton's method; Levenberg-Marquardt's algorithm); global optimization methods (genetic algorithms; differential evolution; simulated annealing); sensitivity analysis (one-at-a-time approach; adjoint-state equation; first-order sensitivity).
Students' project. Each student will be asked to complete a project by developing original codes or by application of freely available software tools (e.g., Princeton Ocean Model, CALMET/CALPUFF/CALGRID package, MODFLOW/MODPATH package).
Prerequisites for admission
Good knowledge of differential and integral calculus and basic knowledge of statistics. Good knowledge of classical physics. Basic computer skills. Knowledge of a programming language is a useful, but not mandatory, prerequisite.
Teaching methods
Standard lectures. Fast quizzes (multiple-choice questions) will be proposed during lectures, whereas autonomous activities will be proposed as homework between successive lectures; these activities will be performed with telematic synchronous and/or asynchronous instruments.
Autonomous activity by students, through the development or the application of computer codes for a modeling exercise. At the end of this work, the student will write a report to describe the work done.
Autonomous activity by students, through the development or the application of computer codes for a modeling exercise. At the end of this work, the student will write a report to describe the work done.
Teaching Resources
The lecture notes can be downloaded from the Moodle site of the course unit, accessible through the link http://labonline.ctu.unimi.it/
These notes include useful references for appropriate detailed study.
These notes include useful references for appropriate detailed study.
Assessment methods and Criteria
Preparation of a written report related to the modeling project developed by each student.
Oral exam (discussion of the report and questions on the topics of the lectures) to verify the acquisition of knowledge about the topics taught during lectures.
Results of quizzes (multiple-choice questions) and homework (open-ended questions and exercises) performed during the semester will provide an additional, integrative assessment.
For the written report the assessment criteria are the ability to describe in a clear and rigorous way the results, the skill in the use of the specialistic lexicon and the ability to apply what has been taught during the lectures.
For the oral exam, the assessment criteria are the ability to organize the presentation of knowledge and the mastery of the results illustrated in the report and of the topics taught during the lectures.
The final evaluation is expressed with a mark in thirtieth and accounts for the assessment of the written report and of the oral exam; the assessment of the results of quizzes and homeworks can give an incremental, additional bonus for the final mark.
Oral exam (discussion of the report and questions on the topics of the lectures) to verify the acquisition of knowledge about the topics taught during lectures.
Results of quizzes (multiple-choice questions) and homework (open-ended questions and exercises) performed during the semester will provide an additional, integrative assessment.
For the written report the assessment criteria are the ability to describe in a clear and rigorous way the results, the skill in the use of the specialistic lexicon and the ability to apply what has been taught during the lectures.
For the oral exam, the assessment criteria are the ability to organize the presentation of knowledge and the mastery of the results illustrated in the report and of the topics taught during the lectures.
The final evaluation is expressed with a mark in thirtieth and accounts for the assessment of the written report and of the oral exam; the assessment of the results of quizzes and homeworks can give an incremental, additional bonus for the final mark.
GEO/12 - OCEANOGRAPHY AND PHYSICS OF THE ATMOSPHERE - University credits: 6
Lessons: 42 hours
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