Abstract
Variational data assimilation consists in estimating control parameters of a numerical model in order to minimize the misfit between the forecast values and some actual observations. The gradient based minimization methods require the multiplication of the transpose jacobian matrix (adjoint model), which is of huge dimension, with the derivative vector of the cost function at the observation points. We present a method based on a modular graph concept and two algorithms to avoid these expensive multiplications. The first step of the method is a propagation algorithm on the graph that allows computing the output of the numerical model and its linear tangent, the second is a backpropagation on the graph that allows the computation of the adjoint model. The YAO software implements these two steps using appropriate algorithms. We present a brief description of YAO functionalities.
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References
Data Assimilation, Concepts and Methods. In: Training Course Notes of ECMWF, European Center for Medium-range Weather Forecasts. vol. 53, UK (1997)
Le Dimet, F.-X., Talagrand, O.: Variational Algorithms for Analysis and Assimilation of Meteorological Observations: Theoretical Aspects. J. Tellus, Series A, Dynamic Meteorology and Oceanography 38(2) (1986)
Louvel, S.: Etude d’un Algorithme d’Assimilation Variationnelle de Données à Contrainte Faible. Mise en Oeuvre sur le Modèle Océanique aux Equations Primitives MICOM (in French). PhD, Université de Toulouse III, France (1999)
Sportisse, B., Quélo, D.: Assimilation de Données. 1ère Partie: Eléments Théoriques (in French). Technical report, CEREA (2004)
Talagrand, O.: The Use of Adjoint Equations in Numerical Modelling of the Atmospheric Circulation. In: Griewank, A., Corliss, G. (eds.) Workshop of Automatic, Differentiation of Algorithms: Theory, Implementation and Applications, Breckenridge, Colorado, USA (1991)
Talagrand, O.: Assimilation of Observations, an Introduction. J. Meteorological Society Japan 75, 191–209 (1997)
Hascoët, L., Pascual, V.: TAPENADE 2.1 User’s Guide. Technical report, INRIA, France (2004), http://www-sop.inria.fr/tropics/papers/Hascoet2004T2u.html
Naumann, U., Utke, J., Wunsch, C., Hill, C., Heimbach, P., Fagan, M., Tallent, N., Strout, M.: Adjoint Code by Source Transformation with OpenAD/F. In: Wesseling, P., Périaux, J., Oñate, E. (eds.) Proceedings of the European Conference on Computational Fluid Dynamics (ECCOMAS CFD 2006), TU Delft (2006), http://proceedings.fyper.com/eccomascfd2006/documents/35.pdf
Giering, R., Kaminski, T.: Recipes for Adjoint Code Construction. ACM Transactions on Mathematical Software 24(4), 437–474 (1998), http://www.FastOpt.com/papers/racc.pdf
Fouilloux, A., Piacentini, A.: The PALM Project: MPMD Paradigm for an Oceanic Data Assimilation Software. In: Amestoy, P.R., Berger, P., Daydé, M., Duff, I.S., Frayssé, V., Giraud, L., Ruiz, D. (eds.) Euro-Par 1999. LNCS, vol. 1685, p. 1423. Springer, Heidelberg (1999)
Ide, K., Courtier, P., Ghil, M., Lorenc, A.: Unified Notation for Data Assimilation: Operational, Sequential and Variational. Special Issue J. Meteorological Society Japan, Data Assimilation in Meteorology and Oceanography: Theory and Practice 75, 181–189 (1997)
Fletcher, R.: Practical Methods of Optimization, 2nd edn. John Wiley, New York (1987)
Courtier, P., Thépaut, J., Hollingsworth, A.: A Strategy for Operational Implementation of 4D-VAR Using an Incremental Approach. Q. J. R. Meteorological Society 120, 1367–1387 (1994)
Louvel, S.: Implementation of a Dual Variational Algorithm for Assimilation of Synthetic Altimeter Data in the Oceanic Primitive Equation Model micom. J. Geophys. Res. 106(C5), 9199–9212 (2001)
Weaver, A., Deltel, C., Machu, E., Ricci, S., Daget, N.: A Multivariate Balance Operator for Variational Ocean Data Assimilation. Q. J. Royal Meteorological Society (2005)
Gilbert, J., Lemaréchal, C.: Some Numerical Experiments with Variable-storage Quasi-newton Algorithms. Mathematical Programming 45, 407–435 (1989), http://www-rocq.inria.fr/estime/modulopt/optimization-routines/m1qn3/m1qn3.html
Brajard, J., Jamet, C., Moulin, C., Thiria, S.: Use of a Neuro-variational Inversion for Retrieving Oceanic and Atmospheric Constituents from Satellite Ocean Colour Sensor: Application to Absorbing Aerosols. Neural Networks 19(2), 178–185 (2006)
Badran, F., Berrada, M., Brajard, J., Crépon, M., Sorror, C., Thiria, S., Hermand, J.P., Meyer, M., Perichon, L., Asch, M.: Inversion of Satellite Ocean Colour Imagery and Geoacoustic Characterization of Seabed Properties: Variational Data Inversion Using a Semi-automatic Adjoint Approach. J. of Marine Systems 69, 126–136 (2008)
Hermand, J.P., Meyer, M., Asch, M., Berrada, M.: Adjoint-based Acoustic Inversion for the Physical Characterization of a Shallow Water Environment. J. Acoust. Soc. Am. 119(6), 3860–3871 (2006)
Kane, A., Thiria, S., Moulin, C.: Développement d’une Méthode d’Assimilation de Données in Situ dans une Version 1D du Modèle de Biogeochimie Marine PISCES (in French). Master’s thesis, LSCE/IPSL, CEA-CNRS-UVSQ laboratories, France (2006)
YAO: Home Page, http://www.locean-ipsl.upmc.fr/~yao/
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Nardi, L., Sorror, C., Badran, F., Thiria, S. (2009). YAO: A Software for Variational Data Assimilation Using Numerical Models. In: Gervasi, O., Taniar, D., Murgante, B., Laganà, A., Mun, Y., Gavrilova, M.L. (eds) Computational Science and Its Applications – ICCSA 2009. ICCSA 2009. Lecture Notes in Computer Science, vol 5593. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02457-3_53
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DOI: https://doi.org/10.1007/978-3-642-02457-3_53
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