An anisotropic formulation of the parametric Kalman filter assimilation
References
- Belo Pereira, M. and Berre, L. 2006. The use of an ensemble approach to study the background error covariances in a global NWP model. Mon. Weather Rev. 134 , 2466–2489. doi:10.1175/MWR3189.1
- Berre, L. O. , Pannekoucke, G. , Desroziers, S. , Stefanescu, S. E. , Chapnik, B. and Raynaud, L. 2007. A variational assimilation ensemble and the spatial filtering of its error covariances: increase of sample size by local spatial averaging. In ECMWF Workshop on Flow-Dependent Aspects of Data Assimilation, 11–13 June 2007. Reading, UK, pp. 151–168.
- Bocquet, M. , Raanes, P. and Hannart, A. 2015. Expanding the validity of the ensemble Kalman filter without the intrinsic need for inflation. Nonlin. Processes Geophys. 22 , 645–662. doi:10.5194/npg-22-645-2015
- Bonavita, M. , Isaksen, L. and Hólm, E. 2012. On the use of eda background-error variances in the ecmwf 4d-var. Q. J. R. Meteorol. Soc. 138 , 1540–1559. doi:10.1002/qj.1899
- Bormann, N. , Saarinen, S. , Kelly, G. and Thépaut, J.-N. 2003. The spatial structure of observation errors in atmospheric motion vectors from geostationary satellite data. Mon. Wea. Rev. 131 , 706–718. doi:10.1175/1520-0493(2003)131<;0706:TSSOOE>2.0.CO;2
- Bouttier, F. 1994. A dynamical estimation of error covariances in an assimilation system. Mon. Wea. Rev. 122 , 2376–2390. doi:10.1175/1520-0493(1994)122<;2376:ADEOFE>2.0.CO;2
- Cohn, S. 1993. Dynamics of short-term univariate forecast error covariances. Mon. Wea. Rev. 121 , 3123–3149. doi:10.1175/1520-0493(1993)121<;3123:DOSTUF>2.0.CO;2
- Coman, A. , Foret, G. , Beekmann, M. , Eremenko, M. , Dufour, G. et al. 2012. Assimilation of IASI partial tropospheric columns with an ensemble Kalman filter over Europe. Atmos. Chem. Phys. 12 , 2513–2532. doi:10.5194/acp-12-2513-2012
- Daley, R. 1991. : Atmospheric Data Analysis . New York, USA: Cambridge University Press, 472pp.
- Derber, J. and Bouttier, F. 1999. A reformulation of the background error covariance in the ecmwf global data assimilation system. Tellus A 51 , 195–221. doi:10.3402/tellusa.v51i2.12316
- Evensen, G. 2009. : Data Assimilation: The Ensemble Kalman Filter . Springer-Verlag Berlin Heidelberg: Springer, 332 pp.
- Fisher, M. 2003. Background error covariance modelling. In Proceedings of ECMWF Seminar on Recent Developments in Data Assimilation for Atmosphere and Ocean, Reading, UK, pp. 45–63.
- Gaspari, G. and Cohn, S. 1999. Construction of correlation functions in two and three dimensions. QJ. Royal Met. Soc. 125 , 723–757. doi:10.1002/qj.49712555417
- Houtekamer, P. L. and Mitchell, H. 1998. Data assimilation using an ensemble Kalman filter technique. Mon. Wea. Rev. 126 , 796–811. doi:10.1175/1520-0493(1998)126<;0796:DAUAEK>2.0.CO;2
- Houtekamer, P. and Mitchell, H. 2001. A sequential ensemble Kalman filter for atmospheric data assimilation. Mon. Wea. Rev. 129 , 123–137. doi:10.1175/1520-0493(2001)129<;0123:ASEKFF>2.0.CO;2
- Houtekamer, P. , Mitchell, H. L. , Pellerin, G. , Buehner, M. , Charron, M. , et al. 2005. Atmospheric data assimilation with an ensemble Kalman filter: results with real observations. Mon. Wea. Rev. 133 , 604–620. doi:10.1175/MWR-2864.1
- Hristopulos, D. 2002. New anisotropic covariance models and estimation of anisotropic parameters based on the covariance tensor identity. Stoch. Environ. Res. Risk Assess. 16 , 43–62. doi:10.1007/s00477-001-0084-y
- Hunt, B. R. , Kostelich, E. J. and Szunyogh, I. 2007. Efficient data assimilation for spatiotemporal chaos: a local ensemble transform Kalman filter. Physica D 230 , 112–126. doi:10.1016/j.physd.2006.11.008
- Kalman, R. E. 1960. A new approach to linear filtering and prediction problems. J. Basic Eng. 82 , 35–45. doi:10.1115/1.3662552
- Massart, S. , Piacentini, A. and Pannekoucke, O. 2012. Importance of using ensemble estimated background error covariances for the quality of atmospheric ozone analyses. Qjr. Meteorol. Soc. 138 , 889–905. doi:10.1002/qj.971
- Ménard, R. and L.-P. Chang , 2000. Assimilation of stratospheric chemical tracer observations using a Kalman filter. Part II: chi-2-validated results and analysis of variance and correlation dynamics. Mon. Wea. Rev. 128 , 2672–2686. AOSCTO⟩2.0.CO;2. doi:10.1175/1520-0493(2000)128<;2672:AOSCTO>2.0.CO;2
- Ménard, R. , Cohn, S. , Chang, L.-P. and Lyster, P. M. 2000. Assimilation of stratospheric chemical tracer observations using a Kalman filter. Part I: Formulation. Mon. Wea. Rev. 128 , 2654–2671. doi:10.1175/1520-0493(2000)128<;2654:AOSCTO>2.0.CO;2
- Mirouze, I. and Weaver, A. T. 2010. Representation of correlation functions in variational assimilation using an implicit diffusion operator. Q. J. R. Meteorol. Soc. 136 , 1421–1443. doi:10.1002/qj.643
- Paciorek, C. and Schervish, M. 2004. Nonstationary covariance functions for gaussian process regression. Adv. Neural Inf. Process. Syst. 16 , 273–280.
- Pannekoucke, O. and Massart, S. 2008. Estimation of the local diffusion tensor and normalization for heterogeneous correlation modelling using a diffusion equation. Qjr. Meteorol. Soc. 134 , 1425–1438. doi:10.1002/qj.288
- Pannekoucke, O. and Fablet, R. 2020. PDE-NetGen 1.0: from symbolic partial differential equation (PDE) representations of physical processes to trainable neural network representations. Geosci. Model Dev. 13 , 3373–3382. doi:10.5194/gmd-13-3373-2020
- Pannekoucke, O. , Emili, E. and Thual, O. 2014. Modeling of local length-scale dynamics and isotropizing deformations. Qjr. Meteorol. Soc. 140 , 1387–1398. doi:10.1002/qj.2204
- Pannekoucke, O. , Ricci, S. , Barthelemy, S. , Ménard, R. and Thual, O. 2016. Parametric Kalman filter for chemical transport model. Tellus 68 , 31547. doi:10.3402/tellusa.v68.31547
- Pannekoucke, O. , Bocquet, M. and Ménard, R. 2018a. Parametric covariance dynamics for the nonlinear diffusive burgers’ equation. Nonlinear Process. Geophys. 2018 , 1–21.. https://www.nonlin-processes-geophys-discuss.net/npg-2018-10/.
- Pannekoucke, O. , Ricci, S. , Barthelemy, S. , Ménard, R. and Thual, O. 2018b. Parametric Kalman filter for chemical transport models - corrigendum. Tellus A: Dynamic Meteorology and Oceanography 70 , 1–2.
- Pannekoucke, O. , Ménard, R. , Aabaribaoune, M. E. and Plu, M. 2020. A methodology to obtain model-error covariances due to the discretization scheme from the parametric Kalman filter perspective. Nonlinear Process. Geophys. 28, 1–22.
- Purser, R. , Wu, W.-S. , Parrish, D. and Roberts, N. 2003. Numerical aspects of the application of recursive filters to variational statistical analysis. Part II: Spatially inhomogeneous and anisotropic general covariances. Mon. Weather Rev. 131 , 1536–1548. doi:10.1175//2543.1
- Sakov, P. and Sandery, P. A. 2015. Comparison of EnOI and EnKF regional ocean reanalysis systems. Ocean Modell. 89 , 45–60. doi:10.1016/j.ocemod.2015.02.003
- Warming, R. and Hyett, B. 1974. The modified equation approach to the stability and accuracy analysis of finite-difference methods. Comput. Phys. 14 , 159–179. doi:10.1016/0021-9991(74)90011-4
- Weaver, A. and Courtier, P. 2001. Correlation modelling on the sphere using a generalized diffusion equation (Tech. Memo. ECMWF, num. 306). Q. J. R. Meteorol. Soc. 127 , 1815–1846. doi:10.1002/qj.49712757518
- Weaver, A. T. and Mirouze, I. 2013. On the diffusion equation and its application to isotropic and anisotropic correlation modelling in variational assimilation. Qjr. Meteorol. Soc. 139 , 242–260. doi:10.1002/qj.1955
- Weaver, A. , Deltel, C. , Machu, E. , Ricci, S. and Daget, N. 2005. A multivariate balance operator for variational ocean data assimilation. Q J. R Meteorol. Soc. 131 , 3605–3625. doi:10.1256/qj.05.119
- Wu, W.-S. , Purser, R. J. and Parrish, D. F. 2002. Three-dimensional variational analysis with spatially inhomogeneous covariances. Mon. Wea. Rev. 130 , 2905–2916. doi:10.1175/1520-0493(2002)130<;2905:TDVAWS>2.0.CO;2
DOI: https://doi.org/10.1080/16000870.2021.1926660 | Journal eISSN: 3035-9554
Language: English
Page range: 1926660 - 1926660
Published on: Jan 1, 2021
Published by: Stockholm University Press
In partnership with: Paradigm Publishing Services
© 2021 Olivier Pannekoucke, published by Stockholm University Press
This work is licensed under the Creative Commons Attribution 4.0 License.