Modelling background error correlations with spatial deformations: a case study

References

• Bannister R. N . A review of forecast error covariance statistics in atmospheric variational data assimilation. II: modelling the forecast error covariance statistics. Q. J. Roy. Meteorol. Soc. 2008; 134(637): 1971–1996.
   Web of Science ®Google Scholar
• Benjamin S. G . An isentropic meso α-scale analysis system and its sensitivity to aircraft and surface observations. Mon. Weather Rev. 1989; 117(7): 1586–1603.
   Web of Science ®Google Scholar
• Berre L . Estimation of synoptic and mesoscale forecast error covariances in a limited-area model. Mon. Weather Rev. 2000; 128: 644–667.
   Web of Science ®Google Scholar
• Berre L. , Desroziers G . Filtering of background error variances and correlations by local spatial averaging: a review. Mon. Weather Rev. 2010; 138(10): 3693–3720.
   Web of Science ®Google Scholar
• Bouttier F . The dynamics of error covariances in a barotropic model. Tellus A. 1993; 45(5): 408–423.
   Google Scholar
• Bouttier F . A dynamical estimation of forecast error covariances in an assimilation system. Mon. Weather Rev. 1994; 122: 2376–2390.
   Web of Science ®Google Scholar
• Chaboureau J.-P. , Nuissier O. , Claud C . Verification of ensemble forecasts of Mediterranean high-impact weather events against satellite observations. Nat. Hazards Earth Syst. Sci. 2012; 12(8): 2449–2462.
   Web of Science ®Google Scholar
• Clerc M. , Mallat S . The texture gradient equation for recovering shape from texture. IEEE Trans. Pattern Anal. Mach. Intell. 2002; 24(4): 536–549.
   Web of Science ®Google Scholar
• Courtier P. , Andersson E. , Heckley W. , Vasiljevic D. , Hamrud M. , co-authors . The ECMWF implementation of three-dimensional variational assimilation (3D-Var). I: formulation. Q. J. Roy. Meteorol. Soc. 1998; 124(550): 1783–1807.
   Web of Science ®Google Scholar
• Deckmyn A. , Berre L . A wavelet approach to representing background error covariances in a limited-area model. Mon. Weather Rev. 2005; 133: 1279–1294.
   Web of Science ®Google Scholar
• Derber J. , Bouttier F . A reformulation of the background error covariance in the ECMWF global data assimilation system. Tellus A. 1999; 51(2): 195–221.
   Google Scholar
• Desroziers G . A coordinate change for data assimilation in spherical geometry of frontal structures. Mon. Weather Rev. 1997; 125(11): 3030–3038.
   Web of Science ®Google Scholar
• Ducrocq V. , Belamari S. , Boudevillain B. , Bousquet O. , Cocquerez P. , co-authors . HyMeX, les campagnes de mesures: focus sur les événements extrêmes en Méditerranée. La Météorologie. 2013; 80: 37–47.
   Google Scholar
• Fisher M . Generalized frames on the sphere, with application to the background error covariance modelling. Proceedings of ECMWF Seminar on Developments in Numerical Methods for Atmospheric and Ocean Modelling. 2004; UK: Reading. 87–101.
   Google Scholar
• Hamill T. M. , Snyder C. , Morss R. E . Analysis-error statistics of a quasi geostrophic model using three-dimensional variational assimilation. Mon. Weather Rev. 2002; 130(11): 2777–2790.
   Web of Science ®Google Scholar
• Hoskins B. J . The geostrophic momentum approximation and the semi-geostrophic equations. J. Atmos. Sci. 1975; 32(2): 233–242.
   Web of Science ®Google Scholar
• Hoskins B. J. , Bretherton F. P . Atmospheric frontogenesis models: mathematical formulation and solution. J. Atmos. Sci. 1972; 29(1): 11–37.
   Web of Science ®Google Scholar
• Mallat S . A Wavelet Tour of Signal Processing: The Sparse Way. 2008; Burlington, MA: Academic Press, Elsevier.
   Google Scholar
• Ménétrier B. , Montmerle T. , Berre L. , Michel Y . Estimation and diagnosis of heterogeneous flow-dependent background error covariances at convective scale using either large or small ensembles. Q. J. Roy. Meteorol. Soc. 2014; 140: 2050–2061.
   Web of Science ®Google Scholar
• Michel Y . Estimating deformations of random processes for correlation modelling in a limited area model. Q. J. Roy. Meteorol. Soc. 2013a; 139: 534–547.
   Web of Science ®Google Scholar
• Michel Y . Estimating deformations of random processes for correlation modelling: methodology and the one-dimensional case. Q. J. Roy. Meteorol. Soc. 2013b; 139: 771–783.
   Web of Science ®Google Scholar
• Nordeng T. E . A Simple and Efficient Method to Obtain Flow Dependent Structure Functions for Objective Analysis of Weather Elements. 1998. HIRLAM4, Technical Report, no. 36, August 1998, c/o Met Éireann, Glasnevin Hill, Dublin 9, Ireland.
   Google Scholar
• Pailleux J. , Geleyn J.-F. , Legrand E . La prévision numérique du temps avec les modèles ARPÈGE et ALADIN-Bilan et perspectives. La Météorologie. 2000; 30: 32–60.
   Google Scholar
• Pereira M. B. , Berre L . The use of an ensemble approach to study the background error covariances in a global NWP model. Mon. Weather Rev. 2006; 134(9): 2466–2489.
   Web of Science ®Google Scholar
• Perrin O. , Senoussi R . Reducing non-stationary stochastic processes to stationarity by a time deformation. Stat. Probab. Lett. 1999; 43: 393–397.
   Web of Science ®Google Scholar
• Purser R. J. , Wu W.-S. , Parrish D. F. , Roberts N. M . Numerical aspects of the application of recursive filters to variational statistical analysis. Part I: spatially homogeneous and isotropic Gaussian covariances. Mon. Weather Rev. 2003a; 131(8): 1524–1535.
   Web of Science ®Google Scholar
• Purser R. J. , Wu W.-S. , Parrish D. F. , Roberts N. M . Numerical aspects of the application of recursive filters to variational statistical analysis. Part II: spatially inhomogeneous and anisotropic general covariances. Mon. Weather Rev. 2003b; 131(8): 1536–1548.
   Web of Science ®Google Scholar
• Raynaud L. , Berre L. , Desroziers G . An extended specification of flow-dependent background error variances in the Météo-France global 4D-Var system. Q. J. Roy. Meteorol. Soc. 2011; 137(656): 607–619.
   Web of Science ®Google Scholar
• Raynaud L. , Berre L. , Desroziers G . Accounting for model error in the Météo-France ensemble data assimilation system. Q. J. Roy. Meteorol. Soc. 2012; 138(662): 249–262.
   Web of Science ®Google Scholar
• Semple A . A Meteorological Assessment of the Geostrophic Co-ordinate Transform and Error Breeding System When used in 3D Variational Data Assimilation. 2001; NWP Tech Rep, UK. 357.
   Google Scholar
• Snyder C. , Hamill T. M. , Trier S. B . Linear evolution of error covariances in a quasigeostrophic model. Mon. Weather Rev. 2003; 131(1): 189–205.
   Web of Science ®Google Scholar
• Varella H. , Berre L. , Desroziers G . Diagnostic and impact studies of a wavelet formulation of background-error correlations in a global model. Q. J. Roy. Meteorol. Soc. 2011; 137(658): 1369–1379.
   Web of Science ®Google Scholar