Météo-France/CNRS Researcher member of the CNRM/GAME URA1357, French National Centre for Meteorological Research, Toulouse Associated member of the Laboratory of Statistics and Probability University of Toulouse III - Paul Sabatier

Office: CNRM-GMEI, B035 Postal address: Météo-France CNRM/GMEI 42 Avenue de Coriolis 31057 Toulouse cedex France Phone: +33 561 079 641 E-mail: christophe.baehr_{at}_meteo_{dot}_fr, christophe.baehr_{at}_math.univ-toulouse.fr .

Recherche / Research

Stochastic Filtering of Observations on Random Media. Application to Measurements of Turbulent Fluids

Stochastic Filters for Data Assimilation. Application to Atmospheric Data Assimilation

En quelques mots / In some words:
The filtering of experimental measurements carried out on a turbulent fluid was done until now by linear digital techniques. In order to turn to a non-linear filtering, we have developed stochastic modelings of measurement on a fluid. By studying the measurements made with a mobile sensor in a random medium, we have defined and give the properties of the acquisition process of a vector field along a random path. Then, we have deeply modified the Lagrangian models of fluids proposed by the physicists to make them compatible with the problem of filtering. These models initiated by S.B. Pope belong to the class of McKean-Vlasov equations with mean field. The closure of these equations was obtained by conditioning the Markovian dynamics to the observation and to the acquisition process along the sensor path.

For the stochastic filtering of the conditioned acquisition process, we have proposed new algorithms of non-linear filtering for mean-field processes and for some various types of laws. We prove the convergence of the particle approximation for each new algorithms of estimates we gave.

The resulted filtering algorithms are based on the dynamics of genealogical trees where the processes interact by genetic selections and by their mean-field law.

Finally, this innovative work allowed us to filter velocity measurements of a turbulent fluid. We present several applications of our methods by using some 1D, 2D or 3D measurements, simulated or real. Our techniques make it possible to obtain high frequency estimates of the fluid velocities as well as quantities characterizing turbulence, and we proceed to a systematic study on numerical errors produced by our methods of calculation.

The second part of our research is linked to data assimilation. We study different non-linear techniques used in stochastic engineering to suggest new algorithms appropriate to high dimensional problems occuring in atmospheric data assimilation. In the end, we study the mathematical properties of this new estimators.

ANR Research Projects 2009-2011 :

SESAR Joint Undertaking 2009-2016 :

Publications

• Publications
  
  • O. Pannekoucke and C. Baehr (2010) : Kalman filters family in geoscience and beyond chapter in Kalman Filtering. J.M. Gomez Ed. Nova Science Publishers, 2010
    
  • C. Baehr and O. Pannekoucke (2009) : Some issues and results on the EnKF and particle filters for meteorological models. chapter in Chaotic Systems: Theory and Applications. C. H. Skiadas and I. Dimotikalis Ed. World Scientific, 2010
    
  • M. Lei, P. Del Moral and C. Baehr (2009): Fisher Information Matrix-based Nonlinear System Conversion for State Estimation. Accepted for publication in IEEE transaction on Control and Automation ( preliminary version ).
    
  • M. Lei, P. Del Moral and C. Baehr (2009): Analysis of Approximated PCRLBs for Nonlinear Dynamics Using Different Moments of State Estimate. Accepted for publication in IEEE transaction on Control and Automation ( preliminary version ).
    
  • S. Rémy, O.Pannekoucke, T. Bergot and C. Baehr (2009): Adaptation of a particle filtering method for data assimilation in a 1D numerical model used for fog forecasting . Accepted with revision for publication in the QJRMS ( preliminary version )
    
  • C. Baehr (2009): Nonlinear Filtering for observations on a random vector field along a random path. Accepted for publication in M2AN - ESAIM ( preliminary version )
    
  • C. Baehr and François Le Gland (2009): Some Mean-Field Processes Filtering using Particles System Approximations. Application to turbulent fluids measurements. in prep
    
  • C. Baehr (2009): Stochastic modeling and filtering of discrete measurements for a turbulent field. application to measurements of atmospheric wind. Int. Journal Modern Phys. B, 23 (28-29), 5424-5433, DOI No: 10.1142/S0217979209063742 ( preliminary version )
    
  • C. Baehr (2008) Probabilistic models for atmospheric turbulence to filter measurements with particle approximations PhD. Thesis, pdf in french
    
  • C. Baehr et al. (1999) Dynamical Characterization of the FASTEX cyclogenesis cases. Quarterly Journal of the Royal Meteorological Society 125(561): 3469 online abstract
  • C. Baehr et al (1999) Effects of a low-level precursor and frontal stability on cyclogenesis during FASTEX IOP17. Quarterly Journal of the Royal Meteorological Society 125(561): 3415. online abstract

• Pre-publications
  

Workshop

• Workshop Organizer 2010 : 5èmes rencontres Météo/MathAppli : Air traffic modeling and meteorology, co-organisée avec la SMAI et la DSNA/DTI
  on 08th and 09th March 2010 at Météo-France Toulouse . Web link to the workshop (in French)

• Workshop Organizer 2009 : 4èmes rencontres Météo/MathAppli co-organisée avec la SMAI et l'IMT
  on 25th Mars 2009 at Paul Sabatier University of Toulouse and on 26th Mars at Météo-France Toulouse . Web link to the workshop (in French)

• Workshop Organizer 2008 : 3èmes rencontres Météo/MathAppli : Extrem Events + Ensemble Kalman Filter
  on 18th and 19th September at Météo-France Toulouse . Web link to the workshop (in French)

• Workshop Organizer 2007 : 2èmes rencontres Météo/MathAppli : Journée Méthodes Particulaires en Mécanique des fluides
  on Friday 16th March at Météo-France Toulouse . Web link to the workshop (in French)

• Workshop Organizer 2006 : 1ères rencontres Météo/MathAppli : PDF methods for fluids dynamics
  on 06th March 2006 at Météo-France Toulouse .

Talks

• Peer-reviewed proceedings of conference
  • 2nd Chaotic Modeling and Simulation International Conference - Chania Crete, Greece June 2009, 1-5, C. Baehr and O. Pannekoucke : Some issues and results on the EnKF and particle filters for meteorological models. ( Transparencies)
    
  • 18e congres francais de mecanique - Grenoble august 2007, 27-31, Filtrage par estimation particulaire des mesures de vitesses du fluide atmospherique turbulent. ( published proceeding) ( Transparencies)
    
  • Ateliers de modélisation de l'atmosphère 2008 - Toulouse january 2008, 22-24, Modélisation et Filtrage non-linéaire des mesures discrètes sur un fluide turbulent. Application au débruitage des mesures du vent atmosphérique. ( published proceeding) ( Transparencies)
    

• Talks and meetings in France
  • Paris, Décembre 2009. Talk at the Journée assimilation de données LEFE/ASSIM INRIA Paris. Filtrage stochastique non linéaire et approximation particulaire pour des modèles météorologiques.(pdf).
    
  • Toulouse, September 2008. Talk at the Séminaire de Probabilités of the Toulouse Mathematics Institute . Modélisation probabiliste des écoulements atmosphériques turbulents afin d'en filtrer la mesure par approche particulaire.(pdf).
    
  • Rennes, November 2007. Talk during the Turbulence Working Group at the CEMAGREF. Filtrage stochastique des mesures bruitées de vitesses d'un fluide turbulent.(pdf). Overview of the 3 days (in french) pdf
    
  • Rennes, January 2007. Talk at the IRISA., Filtrage des mesures de vitesse d'un fluide. Estimation particulaire par modèle markovien conditionnel vs modèle a priori.(pdf)
    
  • Toulouse, December 2006. Talk at the fluid mechanics work group of the laboratoire MIP;, Introduction au Filtrage non linéaire, application aux mesures de vitesses d'un fluide.
  • Nice, November 2006. Talk at the OMEGA work group of the INRIA Sophia Antipolis, Filtrage des mesures de vitesse d'un fluide en écoulements 2D et 3D.
  • Lille, September 2006. Talk at the Journées Modèles Aléatoires Spatiaux of the SMAI, Filtrage des mesures de vitesse d'un fluide par estimation particulaire.(pdf)
  • Nice, June 2006. Talk at the probability work group of the laboratoire Jean-Alexandre Dieudonné, Filtrage des mesures de vitesse d'un fluide par estimation particulaire.
  • Toulouse, March 2006. Talk at the "1ère Rencontre Météo/MathAppli", Méthodes PDF pour les fluides.
  • Toulouse, January 2006. Talk at the LSP Probability Work group, Inégalités fonctionnelles par semigroupes.
  • Toulouse, January 2005. Talk at the LSP Probability Work group, Caractère probabiliste de la Turbulence.

• Talks and meetings abroad
  • Roma, Italy, October 2004. CarboEurope Advanced Training Course.
    
  • Erice, Sicile, Italy, April/May 2008. Workshop modelling geophysical systems by statistical mechanics methods.
    
  • Xania, Crete, Greece, June 2009. Chaos 2009, the 2nd Chaotic Modeling and Simulation International Conference.
    

Lectures

• Master 2 Biostatistique et Modélisation
  
  • Traitement du Signal Aléatoire (Cours Magistral 12h, TD 16h )
  
  
• Master 1 Ecologie Aquatique
  
  • Introduction à l'étude des séries chronologiques (Cours Magistral 3h, TD 4h )
  
  
• Météo-France Cours Élève Ingénieur de la Météorologie
  
  • Traitement du Signal Déterministe et Aléatoire (Cours Magistral 18h - TD 4h)
  
  
• Météo-France Qualification Météo-Navigant
  
  • Introduction à  la dynamique des signaux (Cours Magistral 3h)(pdf)

Background

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