Introduction to data assimilation

DATES: 15 May - 17 May 2017 (3 sessions)
TIME: 09:30 - 12:30 (a total of 9 hours)

Data assimilation has become an important component of modelling for a growing number of applications in geosciences and engineering sciences. This training course will provide introductive insights into data assimilation concepts and practical methods, with the following objectives:
- Introduce data assimilation from several viewpoints: basic concepts from statistical estimation theory, classical variational and Kalman filtering approaches to data assimilation
- Give an overview of the main families of methods and focus on the statistical approaches such as the ensemble Kalman filter
- Point out the main difficulties and current corresponding answers
The lectures will be complemented by presentations on specific applications at CERFACS in the geosciences (e.g., hydrodynamics, wildfire).
The lectures will be complemented by presentations on specific applications at CERFACS in the
geosciences (e.g., hydrodynamics, wildfire). 


PROGRAMME
Day 1 - Introduction to data assimilation, the science of compromises [M. Rochoux]
- Basic concepts of data assimilation 

- A daily example: numerical weather forecast 

- A simple example
o Least-squares approach 

o Reformulation in a probabilistic framework 

o Bayesian approach 

- The roles of covariance matrices 

- Main families of methods: variational approach vs. statistical approach
Day 2 - Focus on statistical approaches (part 1/2) [S. Ricci]
- Introduction to Kalman filters 

- Focus on the ensemble Kalman filter (Monte Carlo estimation) 

- Main methodological difficulties: nonlinearities, huge dimensions, poorly known error statistics, scientific computing issues (data management, code efficiency, parallelization)
Day 3 - Focus on statistical approaches (part 2/2) [50% M. Rochoux, 50 % S. Ricci]
- Introduction to uncertainty quantification methods to overcome the issues of Monte Carlo estimation in the standard ensemble Kalman filter 

- Combination of the ensemble Kalman filter and uncertainty quantification methods 

- Example #1: river hydrodynamics 

- Example #2: Wildfires 


PREREQUISITES
This training session is for engineers, physicists, computer scientists and numerical analysts wishing to learn the fundamentals of data assimilation and the numerical methods to develop data assimilation applications. A good knowledge of linear algebra and numerical analysis is required for this purpose.

REFERENCES
[1] Asch, M., M. Bocquet and M. Nodet, 2017: Data assimilation - Methods, Algorithms and Applications. SIAM. http://bookstore.siam.org/fa11/
[2] Bouttier F. and P. Courtier, 1999: Data assimilation, concepts and methods. Meteorological training course lecture series ECMWF, European Center for Medium range Weather Forecast, Reading, UK. http://www.ecmwf.int/sites/default/files/elibrary/2002/16928-data-assimilation- concepts-and-methods.pdf
[3] Cohn S., 1997: An introduction to estimation theory. Journal of the Meteorological Society of Japan, 75, 257-288.
[4] Daley R., 1993: Atmospheric data analysis. Cambridge University Press
[5] Evensen G., 2009: Data assimilation, the ensemble Kalman filter. Springer
[6] Kalnay E., 2003: Atmospheric modeling, data assimilation and predictability. Cambridge University Press
[7] Tarantola A., 2005: Inverse problem theory and methods for model parameter estimation. SIAM http://www.ipgp.fr/~tarantola/Files/Professional/Books/InverseProblemTheory.pdf

*Registration is free, but inscription is required before 10th May: So as to inscribe send an e-mail to roldan@bcamath.org. Student grants are available. Please, let us know if you need support for travel and accommodation expenses.

• BCAM Course ROCHOUX-RICCI