Gaussian approximations in filters and smoothers for data assimilation

References

• Anderson, J. L. 2010. A non-gaussian ensemble filter update for data assimilation. Mon. Wea. Rev. 138, 4186–4198. doi:10.1175/2010MWR3253.1
   Google Scholar
• Bardsley, J., Solonen, A., Haario, H. and Laine, M. 2014. Randomize-then-optimize: A method for sampling from posterior distributions in nonlinear inverse problems. SIAM J. Sci. Comput. 36, A1895–A1910. doi:10.1137/140964023
   Google Scholar
• Bengtsson, T., Bickel, P. and Li, B. 2008. Curse of dimensionality revisited: the collapse of importance sampling in very large scale systems. IMS Collect. 2, 316–334.
   Google Scholar
• Bickel, P., Bengtsson, T. and Anderson, J. 2008. Sharp failure rates for the bootstrap particle filter in high dimensions. IMS Collect. 3, 318–329.
   Google Scholar
• Bocquet, M. 2011. Ensemble Kalman filtering without the intrinsic need for inflation. Nonlin. Process. Geophys. 18, 735–750. doi:10.5194/npg-18-735-2011
   Google Scholar
• Bocquet, M. 2016. Localization and the iterative ensemble Kalman smoother. Q. J. Roy. Meteorol. Soc. 142, 1075–1089. doi:10.1002/qj.2711
   Google Scholar
• Bocquet, M. and Sakov, P. 2013. Joint state and parameter estimation with an iterative ensemble kalman smoother. Nonlin. Process. Geophys. 20, 803–818. doi:10.5194/npg-20-803-2013
   Google Scholar
• Bocquet, M. and Sakov, P. 2014. An iterative ensemble Kalman smoother. Q. J. Roy. Meteorol. Soc. 140, 1521–1535. doi:10.1002/qj.2236
   Google Scholar
• Bonavita, M., Isaksen, L. and Hólm, E. 2012. On the use of EDA background-error variances in the ECMWF 4D-Var. Q. J. Roy. Meteorol. Soc. 138, 1540–1559. doi:10.1002/qj.1899
   Google Scholar
• Buehner, M. 2005. Ensemble-derived stationary and flow-dependent background-error covariances: Evaluation in a quasi-operational NWP setting. Q. J. Roy. Meteorol. Soc. 131, 1013–1043. doi:10.1256/qj.04.15
   Google Scholar
• Doucet, A., de Freitas, N. and Gordon, N., eds. 2001. Sequential Monte Carlo Methods in Practice. Springer, New York.
   Google Scholar
• Evensen, G. 2006. Data Assimilation: The Ensemble Kalman Filter. Springer, Berlin Heidelberg.
   Google Scholar
• Evensen, G. 2018. Analysis of iterative ensemble smoothers for solving inverse problems. Comput. Geosci. 22, 885–908. doi:10.1007/s10596-018-9731-y
   Google Scholar
• Farchi, A., and Bocquet, M. 2018. Review article: Comparison of local particle filters and new implementations. Nonlinear Process. Geophys. Discuss. 1–63. doi:10.5194/npg-2018-15
   Google Scholar
• Hamill, T. M., Whitaker, J. and Snyder, C. 2001. Distance-dependent filtering of background covariance estimates in an ensemble Kalman filter. Mon. Wea. Rev. 129, 2776–2790. doi:10.1175/1520-0493(2001)129<2776:DDFOBE>2.0.CO;2
   Google Scholar
• Hodyss, D. and Campbell, W. 2013. Square root and perturbed observation ensemble generation techniques in kalman and quadratic ensemble filtering algorithms. Mon. Wea. Rev. 141, 2561–2573. doi:10.1175/MWR-D-12-00117.1
   Google Scholar
• Hodyss, D. and Nathan, T. 2007. The role of forcing in the local stability of stationary long waves. Part 1. Linear dynamics. J. Fluid Mech. 576, 349–376. doi:10.1017/S0022112006004307
   Google Scholar
• Hodyss, D. and Nathan, T. R. 2006. Instability of variable media to long waves with odd dispersion relations. Commun. Math. Sci. 4, 669–676. doi:10.4310/CMS.2006.v4.n3.a10
   Google Scholar
• Hodyss, D., Campbell, W. F. and Whitaker, J. S. 2016. Observation-dependent posterior inflation for the ensemble kalman filter. Mon. Wea. Rev. 144, 2667–2684. doi:10.1175/MWR-D-15-0329.1
   Google Scholar
• Houtekamer, P. and Mitchell, H. 2001. A sequential ensemble Kalman filter for atmospheric data assimilation. Mon. Wea. Rev. 129, 123–136. doi:10.1175/1520-0493(2001)129<0123:ASEKFF>2.0.CO;2
   Google Scholar
• Hunt, B. R., Kostelich, E. J. and Szunyogh, I. 2007. Efficient data assimilation for spatiotemporal chaos: A local ensemble transform kalman filter. Phys. D 230, 112–126. doi:10.1016/j.physd.2006.11.008
   Google Scholar
• Kuhl, D., Rosmond, T., Bishop, C., McLay, J. and Baker, N. 2013. Comparison of hybrid ensemble/4DVar and 4DVar within the NAVDAS-AR data assimilation framework. Mon. Wea. Rev. 141, 2740–2758. doi:10.1175/MWR-D-12-00182.1
   Google Scholar
• Lawson, W. and Hansen, J. 2004. Implications of stochastic and deterministic filters as ensemble-based data assimilation methods in varying regimes of error growth. Mon. Wea. Rev. 136, 1966–1981.
   Google Scholar
• Lee, Y. and Majda, A. 2016. State estimation and prediction using clustered particle filters. Proc. Natl. Acad. Sci. USA. 113, 14609–14614. doi:10.1073/pnas.1617398113
   Google Scholar
• Lei, J. and Bickel, P. 2011. A moment matching ensemble filter for nonlinear non-Gaussian data assimilation. Mon. Wea. Rev. 139, 3964–3973. doi:10.1175/2011MWR3553.1
   Google Scholar
• Liu, C., Xiao, Q. and Wang, B. 2008. An ensemble-based four-dimensional variational data assimilation scheme. Part I: Technical formulation and preliminary test. Mon. Wea. Rev. 136, 3363–3373. doi:10.1175/2008MWR2312.1
   Google Scholar
• Lorenc, A., Bowler, N., Clayton, A., Pring, S. and Fairbairn, D. 2015. Comparison of hybrid-4DEnVar and hybrid-4DVar data assimilation methods for global NWP. Mon. Wea. Rev. 143, 212–229. doi:10.1175/MWR-D-14-00195.1
   Google Scholar
• Lorenz, E. 1963. Deterministic nonperiodic flow. J. Atmos. Sci. 20, 130–141. doi:10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2
   Google Scholar
• Lorenz, E. N. 1996. Predictability: A problem partly solved, Vol. 1. In: Proceedings of the ECMWF Seminar on predictability, Reading, United Kingdom, 1–18.
   Google Scholar
• Mandel, J., Cobb, L. and Beezley, J. 2011. On the convergence of the ensemble Kalman filter. Appl. Math. (Prague) 56, 533–541. doi:10.1007/s10492-011-0031-2
   Google Scholar
• Metref, S., Cosme, E., Snyder, C. and Brasseur, P. 2014. A non-gaussian analysis scheme using rank histograms for ensemble data assimilation. Nonlin. Process. Geophys. 21, 869–885. doi:10.5194/npg-21-869-2014
   Google Scholar
• Morzfeld, M., Hodyss, D. and Poterjoy, J. 2018. Variational particle smoothers and their localization. Q. J. Roy. Meteor. Soc. 144, 806–825. doi:10.1002/qj.3256
   Google Scholar
• Morzfeld, M., Hodyss, D. and Snyder, C. 2017. What the collapse of the ensemble Kalman filter tells us about particle filters. Tellus A 69, 1283809. doi:10.1080/16000870.2017.1283809
   Google Scholar
• Penny, S. and Miyoshi, T. 2015. A local particle filter for high dimensional geophysical systems. Nonlinear Process. Geophys. 2, 1631–1658. doi:10.5194/npgd-2-1631-2015
   Google Scholar
• Posselt, D., Hodyss, D. and Bishop, C. 2014. Errors in ensemble Kalman smoother estimates of cloud microphysical parameters. Mon. Wea. Rev. 142, 1631–1654. doi:10.1175/MWR-D-13-00290.1
   Google Scholar
• Poterjoy, J. 2016. A localized particle filter for high-dimensional nonlinear systems. Mon. Wea. Rev. 144, 59–76. doi:10.1175/MWR-D-15-0163.1
   Google Scholar
• Poterjoy, J. and Anderson, J. 2016. Efficient assimilation of simulated observations in a high-dimensional geophysical system using a localized particle filter. Mon. Wea. Rev. 144, 2007–2020. doi:10.1175/MWR-D-15-0322.1
   Google Scholar
• Poterjoy, J. and Zhang, F. 2015. Systematic comparison of four-dimensional data assimilation methods with and without the tangent linear model using hybrid background error covariance: E4DVar versus 4DEnVar. Mon. Wea. Rev. 143, 1601–1621. doi:10.1175/MWR-D-14-00224.1
   Google Scholar
• Poterjoy, J., Sobash, R. and Anderson, J. 2017. Convective-scale data assimilation for the weather research and forecasting model using the local particle filter. Mon. Wea. Rev. 145, 1897–1918. doi:10.1175/MWR-D-16-0298.1
   Google Scholar
• Poterjoy, J., Wicker, L. and Buehner, M. 2018. Progress toward the application of a localized particle filter for numerical weather prediction. Mon. Wea. Rev.
   Google Scholar
• Potthast, R., Walter, A. and Rhodin, A. 2018. A localised adaptive particle filter within an operational NWP framework. Mon. Wea. Rev.
   Google Scholar
• Reich, S. 2013. A nonparametric ensemble transform method for Bayesian inference. Mon. Wea. Rev. 35, 1337–1367.
   Google Scholar
• Robert, S. and Künsch, H. R. 2017. Localizing the ensemble Kalman particle filter. Tellus A 69, 1282016. doi:10.1080/16000870.2017.1282016
   Google Scholar
• Sakov, P., Oliver, D. S. and Bertino, L. 2012. An iterative EnKF for strongly nonlinear systems. Mon. Wea. Rev. 140, 1988–2004. doi:10.1175/MWR-D-11-00176.1
   Google Scholar
• Snyder, C. 2011. Particle filters, the “optimal” proposal and high-dimensional systems. Proceedings of the ECMWF Seminar on Data Assimilation for Atmosphere and Ocean, Reading, UK, 1–10.
   Google Scholar
• Snyder, C., Bengtsson, T., Bickel, P. and Anderson, J. 2008. Obstacles to high-dimensional particle filtering. Mon. Wea. Rev. 136, 4629–4640. doi:10.1175/2008MWR2529.1
   Google Scholar
• Snyder, C., Bengtsson, T. and Morzfeld, M. 2015. Performance bounds for particle filters using the optimal proposal. Mon. Wea. Rev. 143, 4750–4761. doi:10.1175/MWR-D-15-0144.1
   Google Scholar
• Talagrand, O. and Courtier, P. 1987. Variational assimilation of meteorological observations with the adjoint vorticity equation. I: Theory. Q. J. Roy. Meteor. Soc. 113, 1311–1328. doi:10.1002/qj.49711347812
   Google Scholar
• Tippet, M., Anderson, J., Bishop, C., Hamill, T. and Whitaker, J. 2003. Ensemble square root filters. Mon. Wea. Rev. 131, 1485–1490. doi:10.1175/1520-0493(2003)131<1485:ESRF>2.0.CO;2
   Google Scholar
• Tödter, J. and Ahrens, B. 2015. A second-order exact ensemble square root filter for nonlinear data assimilation. Mon. Wea. Rev. 143, 1337–1367.
   Google Scholar
• Weir, B., Miller, R. N. and Spitz, Y. H. 2013. A potential implicit particle method for high-dimensional systems. Nonlin. Process. Geophys. 20, 1047–1060. doi:10.5194/npg-20-1047-2013
   Google Scholar