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)

-Introduction
Overview of the course, History and development of Atmospheric General Circulation Models, global and mesoscale numerical weather predictions, climate models.

-Numerical Methods I
Classification of PDEs, consistency and stability analysis,
semi-lagrangian schemes, spectral methods, grids

-Hands-on Session: Numerical Integration of the Lorenz 63 system
Deriving the Lorenz system, the coding environment, writing the code for the integration, exercises on fundamentals of chaotic systems, conceptual example of an ensemble forecast.

-Hands-on Session: Numerical integration of the barotropic vorticity equation
Implementation of a code to solve the barotropic vorticity equation, filtering approximations, recreation of the
pioneering numerical weather prediction made by Charney, Fjörtoff and von Neumann.

-Hands-on Session: Simulations with an atmospheric General Circulation Model
Vertical coordinates in AGCMs, subgrid-scale processes, overview of model dynamical core and parameterizations. Computation of the model climatology, a sensitivity simulation.
What is a weather forecast system, the example of the ECMWF Integrated Forecast System, forecast and discussion of a case study.

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 1^st and 2^nd 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

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 examination is done with 3 questions and at least 1 question per module. 

The duration of the exam is about 35 minutes.

Teaching tools

Slide projector and computer laboratory.

Office hours

See the website of Paolo Ruggieri

See the website of Paolo Oddo