Master WAPE Courses

Principles and Practice of Numerical Modelling

Frédéric Hourdin & 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

Frédéric Hourdin is Directeur de Recherche CNRS, Researcher and deputy director of the Dynamic Meteorology Laboratory (LMD). Research interest: Climate modelling for the Earth and planets.

Thomas Dubos is Assistant 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.

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