Objectifs :
Data assimilation is often presented as the art of combining various sources of information (most often, measurements and numerical models) to estimate the state of a partially observed dynamical system. In geophysics, it is now a research topic per se. It is mainly used to:
• define as precisely as possible a physical state (atmosphere, ocean, ...) of a system to predict its temporal evolution;
• optimally estimate a system state over a period of time for example, to study its variabilities;
• identify systematic errors in models;
• optimize the design of observation networks;
• extrapolate values of non observed variables;
• estimate parameters in physical laws.
The course aims at introducing the theoretical concepts and practical implementation aspects of modern data assimilation with a peculiar focus on high dimensional, non linear systems, as usually met in geosciences.

Programme :
Part 1: Data assimilation based on estimation theory

1. Introduction to ensemble data assimilation
2. Notions in estimation theory
3. Particle filtering
5. Ensemble Kalman filters

Part 2: Data assimilation based on control theory
1. Introduction to variational data assimilation
2. Variational data assimilation for time-independent problems
3. The adjoint method
4. Variational Data assimilation : Practical aspect
5. Adjoint coding

Pré-requis :
Necessary background for the course

- Basic notions in probability and statistics (Expectation, variance, covariance matrix)
- Basic notions in linear algebra
- Basic notions in differential calculus

Equipe pédagogique :
Emmanuel COSME, UGA/UFR PHITEM, Laboratoire de Glaciologie et Géophysique Institut des Géosciences de l'Environnement (IGE)

La formation participe à l'objectif suivant :être directement utile pour la réalisation des travaux personnels de recherche