L. Bengtsson, M. Ghil, and E. Källén, Dynamic Meteorology: Data Assimilation Methods, Applied 632 Mathematical Sciences, vol.36, 1981.

X. Luo, T. Bhakta, M. Jakobsen, and G. Navdal, Efficient big data assimilation through sparse representation: 634 A 3d benchmark case study in petroleum engineering, PLoS One, vol.13, p.198586, 2018.

A. Hutt, W. Stannat, and R. Potthast, Data Assimilation and Control: Theory and Applications, p.637

, Life Sciences (Frontiers Media, 2019.

S. J. Schiff, Neural Control Engineering, 2011.

G. Nakamura, R. I. Potthast, and . Modeling, , pp.2053-2563, 2015.

M. Asch, M. Bocquet, and M. Nodet, Data Assimilation: Methods, Algorithms, and Applications, vol.642, 2016.

B. Hunt, E. Kostelich, and I. Szunyoghc, Efficient data assimilation for spatiotemporal chaos: A local 644 ensemble transform Kalman filter, Physica D, vol.230, pp.112-126, 2007.

C. Schraff, H. Reich, A. Rhodin, A. Schomburg, K. Stephan et al., Kilometre-scale ensemble 646 data assimilation for the cosmo model (kenda). Q, J. R. Meteorol. Soc, vol.142, pp.1453-1472, 2016.

A. Schomburg, C. Schraff, and R. Potthast, A concept for the assimilation of satellite cloud information 649 in an ensemble Kalman filter: single-observation experiments, Q. J. R. Meteorol. Soc, vol.141, pp.893-908, 2015.

T. Miyoshi and Y. Sato, Assimilating satellite radiances with a local ensemble transform Kalman filter 652 (letkf) applied to the jma global model (gsm), SOLA, vol.3, pp.37-40, 2007.

F. Kurzrock, S. Cros, F. Ming, J. Otkin, A. Hutt et al., A review of the use of geostationary 654 satellite observations in regional-scale models for short-term cloud forecasting, Meteorologische, vol.655, pp.277-298, 2018.

E. J. Fertig, B. R. Hunt, E. Ott, and I. Szunyogh, Assimilating non-local observations with a local ensemble 657

. Kalman-filter, Tellus A, vol.59, pp.719-730, 2007.

A. Hutt, C. Schraff, H. Anlauf, L. Bach, M. Baldauf et al., Assimilation of SEVIRI 659 water vapour channels with an ensemble Kalman filter on the convective scale, Front. Earth Sci, vol.8, p.70, 2019.

R. Furrer and T. Bengtsson, Estimation of high-dimensional prior and posterior covariance matrices in 662

, Kalman filter variants. J. Multivar. Ana, vol.98, pp.227-255, 2007.

J. L. Anderson, An ensemble adjustment Kalman filter for data assimiliation, Mon. Wea. Rev, vol.129, pp.2884-2903, 2001.

T. M. Hamill, J. S. Whitaker, and C. Snyder, Distance-dependent filtering of background error covariance 666 estimates in an ensemble Kalman filter, Mon. Wea. Rev, vol.129, pp.1520-0493, 2001.

X. T. Tong, A. Majda, and D. Kelly, Nonlinear stability and ergodicity of ensemble based Kalman filters

, Nonlinearity, vol.29, pp.657-691, 2016.

X. T. Tong, A. Majda, and D. Kelly, Nonlinear stability of ensemble Kalman filters with adaptive covariance 671 inflation, Commun. Math. Sci, vol.14, pp.1283-1313, 2016.

G. Gottwald and A. J. Majda, A mechanism for catastrophic filter divergence in data assimilation for sparse 673 observation networks, Nonlin. Processes Geophys, vol.20, pp.705-712, 2013.

D. Kelly, A. Majda, and X. T. Tong, Concrete ensemble Kalman filters with rigorous catastrophic filter 675 divergence, Proc. Natl. Acad. Sci. USA, vol.112, pp.10589-10594, 2015.

A. Majda and J. Harlim, Catastrophic filter divergence in filtering nonlinear dissipative systems, Comm

, Math. Sci, vol.8, pp.27-43, 2008.

S. Migliorini and B. Candy, All-sky satellite data assimilation of microwave temperature sounding channels 679 at the met office, Quart. J. Roy. Meteor. Soc, vol.145, pp.867-883, 2019.

E. N. Lorenz and K. A. Emanuel, Optimal sites for supplementary weather observations: Simulations 681 with a small model, J. Atmos. Sci, vol.555, pp.399-414, 1998.

C. H. Bishop, J. S. Whitaker, and L. Lei, Gain form of the Ensemble Transform Kalman Filter and its relevance 684 to satellite data assimilation with model space ensemble covariance localization, Mon. Wea. Rev, vol.145, pp.4575-4592, 2017.

J. A. Waller, S. L. Dance, A. S. Lawless, and N. K. Nichols, Estimating correlated observation error statistics 687 using an ensemble transform Kalman filter, Tellus A, vol.66, p.23294, 2014.

P. L. Houtekamer and F. Zhang, Review of the ensemble Kalman filter for atmospheric data assimilation

. Mon, Wea. Rev, vol.144, pp.4489-4532, 2016.

A. Perianez, H. Reich, and R. Potthast, Optimal localization for ensemble Kalman filter systems, J. Met

, Soc. Japan, vol.92, pp.585-597, 2014.

S. J. Greybush, E. Kalnay, T. Miyoshi, K. Ide, and B. R. Hunt, Balance and ensemble Kalman filter localization 693 techniques, Mon. Wea. Rev, vol.139, pp.511-522, 2011.

G. Gaspari, S. J. Cohn, and . Meteo, Construction of correlation functions in two and three dimensions

, Soc, vol.125, pp.723-757, 1999.

A. Nadeem and R. Potthast, Transformed and generalized localization for ensemble methods in data 697 assimilation, Math. Meth. Appl. Sci, vol.39, pp.619-634, 2016.

C. H. Bishop and D. Hodyss, Ensemble covariances adaptively localized with eco-rap. part 2: a strategy for 699 the atmosphere, Tellus, vol.61, pp.97-111, 2009.

H. Leng, J. Song, F. Lu, and X. Cao, A new data assimilation scheme: the space-expanded ensemble 701 localization Kalman filter, Adv. Meteorol, vol.2013, p.410812, 2013.

T. Miyoshi and S. Yamane, Local Ensemble Transform Kalman Filtering with an AGCM at a T159/L48 703 resolution, Mon. Wea. Rev, vol.135, pp.3841-3861, 2007.

A. Farchi and M. Boquet, On the efficiency of covariance localisation of the ensemble Kalman filter using 705 augmented ensembles, Front. Appl. Math. Stat, vol.5, p.3, 2019.

L. Lei and J. S. Whitaker, Model space localization is not always better than observation space 707 localization for assimilation of satellite radiances, Mon. Wea. Rev, vol.143, 2015.

W. F. Campbell, C. H. Bishop, and D. Hodyss, Vertical covariance localization for satellite radiances in 710 ensemble Kalman filters, Mon. Wea. Rev, vol.138, pp.282-290, 2010.

P. L. Houtekamer, H. Mitchell, G. Pellerin, M. Buehner, M. Charron et al., Atmospheric data 712 assimilation with an ensemble Kalman filter: Results with real observations, Mon. Wea. Rev, vol.133, pp.604-620, 2005.

N. J. Higham, Accuracy and stability of numerical algorithms (SIAM), 2002.

J. L. Anderson and S. L. Anderson, A monte carlo implementation of the nonlinear filtering problem to 716 produce ensemble assimilations and forecasts, Mon. Wea. Rev, vol.127, pp.1520-0493, 1999.

X. Luo and I. Hoteit, Covariance inflation in the ensemble Kalman filter: A residual nudging perspective 719 and some implications, Mon. Weath. Rev, vol.141, pp.3360-3368, 2013.

T. M. Hamill and J. S. Whitaker, What constrains spread growth in forecasts initialized from ensemble 721 Kalman filters ? Mon, Wea. Rev, vol.139, pp.117-131, 2011.

H. L. Mitchell and P. L. Houtekamer, An adaptive ensemble Kalman filter, Mon. Weath. Rev, vol.128, pp.416-433, 2000.

M. S. Grewal and A. P. Andrews, Kalman filtering: Theory and practice useing MATLAB, 2001.

B. Marx and R. Potthast, On instabilities in data assimilation algorithms, Mathematics, vol.8, 2012.

W. A. Lahoz and P. Schneider, Data assimilation: making sense of earth observation. Front, Environ. Sci, vol.2, p.16, 2014.

X. T. Tong, Performance analysis of local ensemble Kalman filter, J. Nonlinear. Sci, vol.28, pp.731-1397, 2018.

Y. Ying, F. Zhang, and J. Anderson, On the selection of localization radius in ensemble filtering for multiscale 733 quasigeostrophic dynamics, Mon. Wea. Rev, vol.146, pp.543-560, 2018.

T. Miyoshi and K. Kondo, A multi-scale localization approach to an ensemble Kalman filter, SOLA, vol.9, pp.170-173, 2013.

S. Migliorini, Information-based data selection for ensemble data assimilation, Quart. J. Roy. Meteor

, Soc, vol.139, pp.2033-2054, 2013.

P. Kirchgessner, L. Nerger, and A. Bunse-gerstner, On the choice of an optimal localization radius 739 in Ensemble Kalman Filter methods, Mon. Wea. Rev, vol.142, pp.2165-2175, 2014.

C. H. Bishop, J. S. Whitaker, and L. Lei, Commentary: On the efficiency of covariance localisation of the 742 ensemble Kalman filter using augmented ensembles by alban farchi and marc bocquet, Front. Appl

L. Lei, J. S. Whitaker, and C. Bishop, Improving assimilation of radiance observations by implementing model 745 space localization in an ensemble Kalman filter, J. Adv. Model. Earth Syst, vol.10, pp.3221-3232, 2018.

G. Ng, D. Mclaughlin, D. Entekhabi, and A. Ahanin, The role of model dynamics in ensemble Kalman 748 filter performance for chaotic systems, Tellus A, vol.63, pp.958-977, 2011.

Y. Zhen and F. Zhang, A probabilistic approach to adaptive covariance localization for serial ensemble 750 square root filters, Mon. Wea. Rev, vol.142, pp.4499-4518, 2014.

J. Flowerdew, Towards a theory of optimal localisation, Tellus A, vol.67, p.25257, 2015.

Y. Lee, A. J. Majda, and D. Qi, Preventing catastrophic filter divergence using adaptive additive inflation for 753 baroclinic turbulence, Mon. Wea. Rev, vol.145, pp.669-682, 2017.

T. Miyoshi, The gaussian approach to adaptive covariance inflation and its implementation with 755 the local ensemble transform Kalman filter, Mon. Wea. Rev, vol.139, pp.1519-1535, 2011.