96843 - Numerical Laboratory of the Atmosphere and Ocean

Learning outcomes

Understanding the formulation of general circulation models and climate models. Knowledge of historical development and applications of General Circulation Models for the ocean and the atmosphere. Basic knowledge of the numerical algorithms used to solve the primitive equations. Ability to write numerical codes to integrate hyperbolic conservation laws in one and multiple dimensions. Basic knowledge of a UNIX-like shell and job submission in a HPC environment. Compiling and running a model, design and implementation of a numerical simulation. Interpretation and use of a self-describing, array-oriented data format. Expertise with analysis and post-processing of model outputs and simple strategies to handle large datasets. Interpretation of model results in view of governing equations.

Course contents

MODULE I

-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

- Introduction

Overview of the course, ocean general circulation models, ocean primitive equations.

- Numerical methods for Hyperbolic Equations

Hyperbolic conservation laws, method of characteristics, linear and non-linear hyperbolic equations, finite difference and finite volume methods, first and second order linear numerical schemes, Godunov’s theorem, non-linear numerial schemes, total variation diminishing (TVD) methods.

- Hands-on Session: Numerical Integration of the 1D linear advection equation and 1D non-linear Inviscid Burgers’ equation

Coding environment and introduction to data visualization in Python with Matplotlib, tutorial on the implementation of the program to solve the 1D linear advection equation and 1D inviscid Burger’s equation, comparison of the numerical solutions for several numerical schemes.

- Shallow water equations

Derivation of the shallow water equations, linearization and analytic solution of the shallow water equations.

- Hands-on Session: Numerical Integration of the 1D shallow water equations

Implementation of the program to solve the 1D inviscid Shallow water equations, comparison of the numerical solutions for several numerical schemes.

- Analysis and Applications of the NEMO ocean modelling code.

Analysis of the NEMO ocean modelling code, description of the simulation frameworks, bathymetry, numerical grids, surface and lateral boundary conditions, parametrization of subgrid scale processes, vertical mixing processes, estimation of the mixed layer depth, dynamical downscaling techniques.

- Hands-on Session: Implementation of 1D model of water column

Tutorial of the implementation of a 1D model of water column with NEMO-1D, comparison of the effects of different ocean vertical mixing schemes on the vertical structure of the water column.

- Hands-on Session: Implementation of a high-resolution limited area, nested ocean model

Implementation of a high-resolution nested ocean model, visualization, and analysis of the model results.

 

Readings/Bibliography

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

Free-surface flow shallow-water dynamics (Katopodes, Nikolaos D)

 

Teaching methods

Classroom lectures and hands-on sessions with numerical simulations.

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 with a qualitative 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 30 minutes. 

Teaching tools

Slide projector and laboratory.

Office hours

See the website of Paolo Ruggieri

See the website of Francesco Trotta