NPG Nonlinear Processes in Geophysics NPG Nonlin. Processes Geophys. 1607-7946 Copernicus Publications Göttingen, Germany 10.5194/npg-20-793-2013 A variational formulation for translation and assimilation of coherent structures Plu M. https://orcid.org/0000-0002-5374-1895 1 Laboratoire de l'Atmosphère et des Cyclones, UMR8105, Unité mixte CNRS/Météo-France/Université de La Réunion, and CNRM-GAME, Météo-France/CNRS, Toulouse, France 17 10 2013 20 5 793 801 Copyright: © 2013 M. Plu 2013 This work is licensed under the Creative Commons Attribution 3.0 Unported License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/3.0/ This article is available from https://npg.copernicus.org/articles/20/793/2013/npg-20-793-2013.html The full text article is available as a PDF file from https://npg.copernicus.org/articles/20/793/2013/npg-20-793-2013.pdf

The assimilation of observations from teledetected images in geophysical models requires one to develop algorithms that would account for the existence of coherent structures. In the context of variational data assimilation, a method is proposed to allow the background to be translated so as to fit structure positions deduced from images. Translation occurs as a first step before assimilating all the observations using a classical assimilation procedure with specific covariances for the translated background. A simple validation is proposed using a dynamical system based on the one-dimensional complex Ginzburg–Landau equation in a regime prone to phase and amplitude errors. Assimilation of observations after background translation leads to better scores and a better representation of extremas than the method without translation.

 References Beezley, J. D. and Mandel, J.: Morphing ensemble Kalman filters, Tellus, 60A, 131–140, 2008. Chen, Y. and Snyder, C.: Assimilating vortex position with an ensemble Kalman filter, Mon. Weather Rev., 135, 1828–1845, 2007. Deckmyn, A. and Berre, L.: A wavelet approach to representing background error covariances in a limited-area model, Mon. Weather Rev., 133, 1279–1294, 2005. Derber, J. and Bouttier, F.: A reformulation of the background error covariance in the ECMWF global data assimilation system, Tellus, 51A, 195–222, 1999. Gilbert, J. C. and Lemaréchal, C.: Some numerical experiments with variable-storage quasi-Newton algorithms, Math. Programm., 45, 407–435, 1989. Heming, J. T., Chan, J. C., and Radford, A. M.: A new scheme for the initialisation of tropical cyclones in the UK Meteorological Office global model, Meteor. Appl., 2, 171–184, 1995. Hoffman, R. N., Liu, Z., Louis, J.-F., and Grassoti, C.: Distortion representation of forecast errors, Mon. Weather Rev., 123, 2758–2770, 1995. Kalman, R. E.: A new approach to linear filtering and prediction problems, J. Basic Eng., 82D, 35–45, 1960. Le Dimet, F.-X. and Talagrand, O.: Variational algorithm for analysis and assimilation of meteorological observations: theoretical aspects, Tellus, 38A, 97–110, 1986. Michel, Y.: Displacing potential vorticity structures by the assimilation of pseudo-observations, Mon. Weather Rev., 139, 549–565, 2011. Montroty, R., Rabier, F., Westrelin, S., Faure, G., and Viltard, N.: Impact of wind bogus and cloud and rain affected SSM/I data on tropical cyclones analyses and forecasts, Q. J. R. Meteorol. Soc., 134, 1673–1699, 2008. Parrish, D. F. and Derber, J. C.: The National Meteorological Center's spectral statistical interpolation analysis system, Mon. Weather Rev., 120, 1747–1763, 1992. Pereira, M. B. and Berre, L.: The use of an ensemble approach to study the background error covariances in a global NWP model, Mon. Weather Rev., 134, 2466–2489, 2006. Plu, M., Arbogast, P., and Joly, A.: A wavelet representation of synoptic-scale coherent structures, J. Atmos. Sci., 65, 3116–3138, 2008. Ravela, S., Emanuel, K., and McLaughlin, D.: Data assimilation by field alignment, Physica D, 230, 127–145, 2007. Talagrand, O.: Assimilation of observations, an introduction, J. Meteor. Soc. Japan, 75, 191–209, 1997. Talagrand, O. and Courtier, P.: Variational assimilation of meteorological observations with the adjoint vorticity equation, I: Theory, Q. J. R. Meteorol. Soc., 113, 1311–1328, 1987. Titaud, O., Vidard, A., Souopgui, I., and Le Dimet, F.-X.: Assimilation of image sequences in numerical models, Tellus, 62A, 30–47, 2010. Weber, A., Kramer, L., Aranson, I. S., and Aranson, L.: Stability limits of traveling waves and the transition to spatiotemporal chaos in the complex Ginzburg-Landau equation, Physica D, 61, 279–283, 1992.