Principles and Practice of Numerical Modelling
& Thomas Dubos
This course is shared with other OACOS specialities
Numerical models embody the best available knowledge of the mechanics
and physics of the atmosphere and oceans. In turn, since the advent of
numerical weather forecasting in the 1950s, models have become an
indispensable source of knowledge both for science and for
policy-making, in the short run of crisis management and in the long
run of infrastructure management or the regulation of the emissions of
pollutants. The aim of this course is to familiarize the students with
the fundamentals of numerical modelling of the atmosphere and oceans,
and to introduce them to the use of state-of-the art numerical models
to solve practical or scientific problems.
This module is organized as 3 lectures followed by 6 project-based
work sessions. The lectures present the essentials of the numerical
modelling process: quantitative understanding of elementary processes,
discrete formulation of resolved processes, parameterization of
subgrid-scale processes, computerized implementation. Lectures are
paired with computer classes where the students write from scratch
small models that expose them to important numerical issues, and to
some solutions adopted in realistic models.
Lecture 1: Fundamentals
Brief history and applications of numerical modelling of the atmosphere/ocean.
Fundamental budgets. Temporal and spatial scales. Hydrostatic vs non-hydrostatic.
Computer class 1: Temporal discretization
Accuracy vs stability. Courant-Friedrichs-Lewy criterion. Implicit schemes.
Lecture 2: Physical parameterizations
Turbulent mixing. Cloud microphysics. Convection schemes.
Computer class 2: Finite volume / finite difference methods.
Conservative transport. Positive transport. Numerical dispersion/dissipation.
Lecture 3: Deterministic chaos and predictability
Initialization of a forecast. Tangent and adjoint models.
The Lorentz model and its attractor. Predictability of weather.
Computer class 3: Inverse problems
Direct methods for linear problems. Iterative methods for linear and non-linear problems.
The second part of the course is devoted to projects based on
state-of-the art, realistic numerical models and data obtained from
local measurements or international databases. The goal of each project
is to answer a scientific or policy question through numerical
modelling of a natural phenomenon. The aim is to acquire the method
allowing exploiting the numerical tool while taking into account the
limitations and uncertainties inherent to the forecasting exercise.
Care is given to the design of the numerical experiment and to the
adequate analysis of its output.
Students are evaluated based on their project work presented at a final oral defense.
Examples of projects:
forecasting intense rain
dispersion of a polluting plume in the atmosphere/ocean
local impact of climate change
is Directeur de Recherche CNRS, Researcher and deputy director of the
Dynamic Meteorology Laboratory (LMD). Research interest: Climate
modelling for the Earth and planets.
Professor at Ecole Polytechnique and Researcher at the Dynamic
Meteorology Laboratory (LMD). My core research interests lie mainly in
geophysical turbulence, both in the form of synoptic-scale,
quasi-two-dimensional turbulence and small-scale, boundary-layer
turbulence. I try to combine theoretical approaches, numerical
simulations and observations (mostly ground-based) to make progress on
questions relating to: Stable Boundary-Layer (SBL) turbulence
-Organized Vortices - Dynamical Downscaling
The more theoretical part of my work often involves eventually the
numerical solution of an idealized problem. I tend to use in-house
tools for this, and have developed an interest in numerical methods,
mostly spectral and finite-element methods, and more recently
finite-difference and finite-volume methods, as well as Krylov methods
for algebraic and eigenvalue problems.
link to OACOS : http://master-oacos.lmd.jussieu.fr/m2/plans-des-cours/E6.pdf/