On the consistency of the local ensemble square root Kalman filter perturbation update
By: Marc Bocquet and Alban Farchi
References
- Anderson
, J. L. 2001. An ensemble adjustment Kalman filter for data assimilation. Mon. Weather Rev., 2884– 2903. doi: 10.1175/1520-0493(2001)129<;2884:AEAKFF>2.0.CO;2 - Anderson
, J. L. 2003. A local least squares framework for ensemble filtering. Mon. Weather Rev., 634– 642. doi: 10.1175/1520-0493(2003)131<;0634:ALLSFF>2.0.CO;2 - Anderson
, J. L. 2012. Localization and sampling error correction in ensemble Kalman filter data assimilation. Mon. Weather Rev., 2359– 2371. doi: 10.1175/MWR-D-11-00013.1 - Anderson
, J. L.and Lei, L. 2013. Empirical localization of observation impact in ensemble Kalman filters. Mon. Weather Rev., 4140– 4153. doi: 10.1175/MWR-D-12-00330.1 - Asch
, M., Bocquet, M.and Nodet, M. 2016. : Data Assimilation: Methods, Algorithms, and Applications., Philadelphia, 324pp. - Bishop
, C. H., Etherton, B. J.and Majumdar, S. J. 2001. Adaptive sampling with the ensemble transform Kalman filter. Part I: Theoretical aspects. Mon. Weather Rev., 420– 436. doi: 10.1175/1520-0493(2001)129<;0420:ASWTET>2.0.CO;2 - Bishop
, C. H.and Hodyss, D. 2009. Ensemble covariances adaptively localized with ECO-RAP. Part 2: A strategy for the atmosphere. Tellus A, 97– 111. doi: 10.1111/j.1600-0870.2008.00372.x - Bishop
, C. H., Hodyss, D., Steinle, P., Sims, H., Clayton, A. M., and co-authors. 2011. Efficient ensemble covariance localization in variational data assimilation. Mon. Weather Rev., 573– 580. doi: 10.1175/2010MWR3405.1 - Bishop
, C. H., Whitaker, J. S.and Lei, L. 2017. Gain form of the Ensemble Transform Kalman Filter and its relevance to satellite data assimilation with model space ensemble covariance localization. Mon. Weather Rev., 4575– 4592. doi: 10.1175/MWR-D-17-0102.1 - Bocquet
, M. 2016. Localization and the iterative ensemble Kalman smoother. Q J R Meteorol. Soc., 1075– 1089. doi: 10.1002/qj.2711 - Bocquet
, M.and Carrassi, A. 2017. Four-dimensional ensemble variational data assimilation and the unstable subspace. Tellus A, 1304504. doi: 10.1080/16000870.2017.1304504 - Bocquet
, M., Raanes, P. N.and Hannart, A. 2015. Expanding the validity of the ensemble Kalman filter without the intrinsic need for inflation. Nonlin. Processes Geophys., 645– 662. doi: 10.5194/npg-22-645-2015 - Brankart
, J.-M., Cosme, E., Testut, C.-E., Brasseur, P.and Verron, J. 2011. Efficient local error parameterizations for square root or ensemble Kalman filters: Application to a basin-scale ocean turbulent flow. Mon. Weather Rev., 474– 493. doi: 10.1175/2010MWR3310.1 - Buehner
, M. 2005. Ensemble-derived stationary and flow-dependent background-error covariances: Evaluation in a quasi-operational NWP setting. Q J R Meteorol. Soc., 1013– 1043. doi: 10.1256/qj.04.15 - Buehner
, M.and Shlyaeva, A. 2015. Scale-dependent background-error covariance localisation. Tellus A, 28027. doi: 10.3402/tellusa.v67.28027 - Byrd
, R. H., Lu, P., Nocedal, J.and Zhu, C. 1995. A limited memory algorithm for bound constrained optimization. SIAM J. Sci. Comput., 1190– 1208. doi: 10.1137/0916069 - De La Chevrotière
, M.and Harlim, J. 2017. A data-driven method for improving the correlation estimation in serial ensemble Kalman filters. Mon. Weather Rev., 985– 1001. doi: 10.1175/MWR-D-16-0109.1 - Desroziers
, G., Arbogast, E.and Berre, L. 2016. Improving spatial localization in 4DEnVar. Q J R Meteorol. Soc., 3171– 3185. doi: 10.1002/qj.2898 - Desroziers
, G., Camino, J.-T.and Berre, L. 2014. 4DEnVar: Link with 4D state formulation of variational assimilation and different possible implementations. Q J R Meteorol. Soc., 2097– 2110. doi: 10.1002/qj.2325 - Evensen
, G. 2009. Data Assimilation: The Ensemble Kalman Filter. 2nd ed. Springer-Verlag, Berlin, 307pp. - Farchi
, A.and Bocquet, M. 2019. On the efficiency of covariance localisation of the ensemble Kalman filter using augmented ensembles. Front. Appl. Math. Stat., 3. doi: 10.3389/fams.2019.00003 - Gaspari
, G.and Cohn, S. E. 1999. Construction of correlation functions in two and three dimensions. Q J R Meteorol. Soc., 723– 757. doi: 10.1002/qj.49712555417 - Golub
, G. H.and van Loan, C. F. 2013. Matrix Computations. 4th ed. The John Hopkins University Press, Baltimore, MD, 784pp. - Greybush
, S. J., Kalnay, E., Miyoshi, T., Ide, K.and Hunt, B. R. 2011. Balance and ensemble Kalman filter localization techniques. Mon. Weather Rev., 511– 522. doi: 10.1175/2010MWR3328.1 - Hamill
, T. M., Whitaker, J. S.and Snyder, C. 2001. Distance-dependent filtering of background error covariance estimates in an ensemble Kalman filter. Mon. Weather Rev., 2776– 2790. doi: 10.1175/1520-0493(2001)129<;2776:DDFOBE>2.0.CO;2 - Hannart
, A.and Naveau, P. 2014. Estimating high dimensional covariance matrices: A new look at the Gaussian conjugate framework. J. Multivariate Anal., 149– 162. doi: 10.1016/j.jmva.2014.06.001 - Horn
, R. A.and Johnson, C. R. 2012. Matrix Analysis. Cambridge University Press, Cambridge, UK, 662pp. - Houtekamer
, P. L.and Mitchell, H. L. 2001. A sequential ensemble Kalman filter for atmospheric data assimilation. Mon. Weather Rev., 123– 137. doi: 10.1175/1520-0493(2001)129<;0123:ASEKFF>2.0.CO;2 - Houtekamer
, P. L., Mitchell, H. L., Pellerin, G., Buehner, M., Charron, M., Spacek, L.and Hansen, B. 2005. Atmospheric data assimilation with an ensemble Kalman filter: Results with real observations. Mon. Weather Rev., 604– 620. doi: 10.1175/MWR-2864.1 - Hunt
, B. R., Kostelich, E. J.and Szunyogh, I. 2007. Efficient data assimilation for spatiotemporal chaos: A local ensemble transform Kalman filter. Physica D, 112– 126. doi: 10.1016/j.physd.2006.11.008 - Kalnay
, E., Ota, Y., Miyoshi, T.and Liu, J. 2012. A simpler formulation of forecast sensitivity to observations: Application to ensemble Kalman filters. Tellus A, 18462. doi: 10.3402/tellusa.v64i0.18462 - Kassam
, A.-K.and Trefethen, L. N. 2005. Fourth-order time-stepping for stiff PDEs. Siam J. Sci. Comput., 1214– 1233. doi: 10.1137/S1064827502410633 - Kepert
, J. D. 2009. Covariance localisation and balance in an ensemble Kalman filter. Q J R Meteorol. Soc., 1157– 1176. doi: 10.1002/qj.443 - Kuramoto
, Y.and Tsuzuki, T. 1975. On the formation of dissipative structures in reaction-diffusion systems: Reductive perturbation approach. Progr. Theoret. Phys., 687– 699. doi: 10.1143/PTP.54.687 - Kuramoto
, Y.and Tsuzuki, T. 1976. Persistent propagation of concentration waves in dissipative media far from thermal equilibrium. Progr. Theoret. Phys., 356– 369. doi: 10.1143/PTP.55.356 - Livings
, D. M., Dance, S. L.and Nichols, N. K. 2008. Unbiased ensemble square root filters. Physica D, 1021– 1028. doi: 10.1016/j.physd.2008.01.005 - Lorenc
, A. C. 2003. The potential of the ensemble Kalman filter for NWP - a comparison with 4D-Var. Q J R Meteorol. Soc., 3183– 3203. doi: 10.1256/qj.02.132 - Lorenz
, E. N.and Emanuel, K. A. 1998. Optimal sites for supplementary weather observations: Simulation with a small model. J. Atmos. Sci., 399– 414. doi: 10.1175/1520-0469(1998)055<;0399:OSFSWO>2.0.CO;2 - Manton
, J. H., Mahony, R.and Hua, Y. 2003. The geometry of weighted low-rank approximations. IEEE Trans. Signal Process., 500– 514. doi: 10.1109/TSP.2002.807002 - Ménétrier
, B., Montmerle, T., Michel, Y.and Berre, L. 2015. Linear filtering of sample covariances for ensemble-based data assimilation. Part I: Optimality criteria and application to variance filtering and covariance localization. Mon. Weather Rev., 1622– 1643. doi: 10.1175/MWR-D-14-00157.1 - Nerger
, L.and Gregg, W. W. 2007. Assimilation of SeaWiFS data into a global ocean-biogeochemical model using a local SEIK filter. J. Marine Syst., 237– 254. doi: 10.1016/j.jmarsys.2006.11.009 - Ott
, E., Hunt, B. R., Szunyogh, I., Zimin, A. V., Kostelich, E. J., and co-authors. 2004. A local ensemble Kalman filter for atmospheric data assimilation. Tellus A, 415– 428. doi: 10.1111/j.1600-0870.2004.00076.x - Raanes
, P. N., Bocquet, M.and Carrassi, A. 2019. Adaptive covariance inflation in the ensemble Kalman filter by Gaussian scale mixtures. Q J R Meteorol. Soc., 53– 75. doi: 10.1002/qj.3386 - Sakov
, P.and Bertino, L. 2011. Relation between two common localisation methods for the EnKF. Comput. Geosci., 225– 237. doi: 10.1007/s10596-010-9202-6 - Sakov
, P., Counillon, F., Bertino, L., Lisaeter, K. A., Oke, P. R. and co-authors. 2012. TOPAZ4: An ocean-sea ice data assimilation system for the North Atlantic and Arctic. Ocean Sci., 633. doi: 10.5194/os-8-633-2012 - Sakov
, P.and Oke, P. R. 2008. A deterministic formulation of the ensemble Kalman filter: An alternative to ensemble square root filters. Tellus A, 361– 371. doi: 10.1111/j.1600-0870.2007.00299.x - Sakov
, P.and Oke, P. R. 2008. Implications of the form of the ensemble transformation in the ensemble square root filters. Mon. Weather Rev, 1042– 1053. doi: 10.1175/2007MWR2021.1 - Sivashinsky
, G. I. 1977. Nonlinear analysis of hydrodynamic instability in laminar flames-I. Derivation of basic equations. Acta Astronaut, 1177– 1206. doi: 10.1016/0094-5765(77)90096-0 - Srebro
, N.and Jaakkola, T. 2003. Weighted low-rank approximations. In: Proceedings of the 20th International Conference on Machine Learning (ICML-03), 720– 727. - Wang
, X., Snyder, C.and Hamill, T. M. 2007. On the theoretical equivalence of differently proposed ensemble-3DVAR hybrid analysis schemes. Mon. Weather Rev., 222– 227. doi: 10.1175/MWR3282.1 - Whitaker
, J. S.and Hamill, T. M. 2002. Ensemble data assimilation without perturbed observations. Mon. Weather Rev., 1913– 1924. doi: 10.1175/1520-0493(2002)130<;1913:EDAWPO>2.0.CO;2
DOI: https://doi.org/10.1080/16000870.2019.1613142 | Journal eISSN: 3035-9554
Language: English
Page range: 1613142 - 1613142
Published on: Jan 1, 2019
Published by: Stockholm University Press
In partnership with: Paradigm Publishing Services
Keywords:
© 2019 Marc Bocquet, Alban Farchi, published by Stockholm University Press
This work is licensed under the Creative Commons Attribution 4.0 License.