99521 - NUMERICAL LABORATORY OF THE ATMOSPHERE AND THE OCEAN

Learning outcomes

The student will understanding the formulation of general circulation models and climate models. The student will acquire knowledge of historical development and applications of General Circulation Models for the ocean and the atmosphere. The student will be able to use basic knowledge of the numerical algorithms used to solve the primitive equations. At the end of the course , the student will acquire ability to write numerical codes to integrate hyperbolic conservation laws in one and multiple dimensions. The student will have basic knowledge of a UNIX-like shell and job submission in a HPC environment; he/she will be able to compile and run a model, design and implement a numerical simulation. The student will be able to interpret and use of a self-describing, array-oriented data format.The student will be equipped with expertise with analysis and post-processing of model outputs and simple strategies to handle large datasets.

Course contents

Module I (Atmosphere)

This module provides a comprehensive introduction weather climate modeling, covering both their theoretical foundations and practical applications. Students will explore the mathematical and physical principles underlying atmospheric models, from dynamical cores to parameterization schemes. Through hands-on exercises ranging from chaotic systems and ensemble forecasting to state-of-the-art climate simulations, participants will gain direct experience with modern tools used in weather and climate research.

Theoretical introduction: Overview of the course, history and development of climate models and numerical weather predictions. Classification of PDEs, consistency and stability analysis, semi-lagrangian schemes, spectral methods, grids. Vertical coordinates in AGCMs, subgrid-scale processes, overview of model dynamical core and parameterizations.

Hands-on Session 1 is devoted to chaos and ensemble techniques. The student will work autonomously and will perform a numerical Integration of the Lorenz 63 system and a conceptual example of an ensemble forecast.

In the hands-on Session 2 is recreation of the pioneering numerical weather prediction made by Charney, Fjörtoff and von Neumann. The student will work in group to perform the numerical integration of the barotropic vorticity equation and discuss the results.

Hands-on Session 3 is based on a simulation and analysis with a General Circulation Model, computation of the model climatology, a sensitivity simulation. AI techniques for the analysis of model output will be employed. The student will work in group and will prepare a group presentation.

MODULE II (Ocean)

Introduction: The governing equations and a short history about ocean models. Here we review the equation of state, the Navier-Stokes equation, the approximations (Hydrostatic, Boussinesq), and consequences to derive the Primitive Equations. Brief history of oceanographic modelling. Review and classification of different ocean models

Lecture 2: Finite difference Method. Taylor series and finite difference. How to find solution for 1st and 2nd derivatives. Low order and high orders schemes. Overview of the different possibilities and implications (Backward, centered and forward). Examples applied to the heat equation.

Lecture 3: Numerical dispersion and diffusivity. Overview of the advection schemes.

Lecture 4: SGS processes. Horizontal and vertical diffusion & viscosity. Lateral Open boundary conditions and nested grids (time-permitting).

Hands-on Session: Introduction to the NEMO code. Preparing the environment. Getting familiar with bash/Fortran. Overview of the code, its structure, the modules. Modularity and choices to be done.

Hands-on Session: Available options for the momentum equation (flux vs vorticity / baroclinic and barotropic). Surface and lateral boundary conditions. Execute the code (pre-defined test cases). Check results and diagnostic files.

Hands-on Session: Create your own model configuration: Definition of the problem. Run the Experiments. Study and understand the model results and output.

Hands-on Session: Sensitivity tests. Study and understand the model results and output (comparison).

Readings/Bibliography

Lecture notes and slides

Atmospheric Modeling, Data Assimilation and Predictability, E. Kalnay, Cambridge university press

Haidvogel and Beckmann, Numerical Ocean Circulation Modeling, Imperial College Press, 1999

Benoit Cushman-Roisin and Jean-Marie Becker. Introduction to Geophysical Fluid Dynamics. Physical and Numerical Aspects. Academic Press

F. Mesinger, A. Arakawa, Numerical Methods Used in Atmospheric Models, GARP Publ. Ser. No. 17, vol. 1, WMO, Geneva, 1976

Teaching methods

Classroom lectures and hands-on sessions with numerical simulations.

Mandatory Lab safety training to be completed in advance: Moduli 1 e 2 di formazione sulla sicurezza nei luoghi di studio, [https://elearning-sicurezza.unibo.it/] are required (E-Learning).

Assessment methods

Module I.

Reports developed during the course are evaluated but do not directly influence the final mark. The final mark is determined with an oral examination focused on the theoretical part of the lectures and on the discussion of the reports. The duration of the exam is about 35 minutes.

Module II

Students will present and interpret the results of a user-defined numerical ocean experiment. The presentation is followed by an oral examination focused on the theoretical part of the lectures. The duration of the exam is approximately 35 minutes.

Teaching tools

Slide projector and computer laboratory.

Students with Specific Learning Disabilities (SLD) or temporary or permanent disabilities are advised to contact the relative University Office (https://site.unibo.it/studenti-con-disabilita-e-dsa/en). The office will be responsible for proposing any necessary accommodations for the students concerned. These adaptations must be submitted to the teacher at least 15 days in advance for approval, who will evaluate their appropriateness, also in relation to the learning objectives of the course.

Office hours

See the website of Paolo Oddo

See the website of Paolo Ruggieri