On the choice of an optimal localization radius in ensemble Kalman filter methods

Monthly Weather Review

Volumn 142, Issue 6, 2014, Pages 2165-2175

  Kirchgessner, Paul ^a   Nerger, Lars ^a   Bunse Gerstner, Angelika ^b  

^a ALFRED WEGENER INSTITUTE FOR POLAR AND MARINE RESEARCH   (Germany)

^b UNIVERSITY OF BREMEN   (Germany)

Author keywords

Data assimilation; Ensembles; Kalman filters; Ocean models

Indexed keywords

DEGREES OF FREEDOM (MECHANICS); EXPERIMENTS; KALMAN FILTERS; MECHANICS;

ADAPTIVE LOCALIZATIONS; DATA ASSIMILATION; ENSEMBLE KALMAN FILTER; ENSEMBLES; LOCALIZATION PARAMETERS; LOCALIZATION TECHNIQUE; OCEAN MODEL; SQUARE ROOT KALMAN FILTER;

QUALITY CONTROL;

DATA ASSIMILATION; ENSEMBLE FORECASTING; KALMAN FILTER; OPTIMIZATION; PARAMETERIZATION; PERFORMANCE ASSESSMENT; SHALLOW-WATER EQUATION; TWO-DIMENSIONAL MODELING; WEATHER FORECASTING;

EID: 84901594758     PISSN: 00270644     EISSN: 15200493     Source Type: Journal    
DOI: 10.1175/MWR-D-13-00246.1     Document Type: Article

References (36)

1. Anderson, J. L., 2007: Exploring the need for localization in ensemble data assimilation using a hierarchical ensemble filter. Physica D, 230, 99-111, doi: 10. 1016/j. physd. 2006. 02. 011.
2. Anderson, J. L., 2012: Localization and sampling error correction in ensemble Kalman filter data assimilation. Mon. Wea. Rev., 140, 2359-2371, doi: 10. 1175/MWR-D-11-00013. 1.
3. Bishop, C. H., and D. Hodyss, 2007: Flow-adaptive moderation of spurious ensemble correlations and its use in ensemble-based data assimilation. Quart. J. Roy. Meteor. Soc., 133, 2029-2044, doi: 10. 1002/qj. 169.
4. Bishop, C. H., and D. Hodyss, 2009: Ensemble covariances adaptively localized with ECO-RAP. Part 1: Tests on simple error models. Tellus, 61A, 84-96, doi: 10. 1111/j. 1600-0870. 2008. 00371. x.
5. Bishop, C. H., B. Etherton, and S. Majumdar, 2001: Adaptive sampling with the ensemble transform Kalman filter. Part I: Theoretical aspects. Mon. Wea. Rev., 129, 420-436, doi: 10. 1175/1520-0493(2001)129<0420: ASWTET>2. 0. CO;2.
6. Danilov, S., G. Kivman, and J. Schröter, 2004: A finite-element ocean model: Principles and evaluation. Ocean Modell., 6, 125-150, doi: 10. 1016/S1463-5003(02)00063-X.
7. Evensen, G., 1994: Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics. J. Geophys. Res., 99, 10 143-10 162, doi: 10. 1029/94JC00572.
8. Gaspari, G., and S. E. Cohn, 1999: Construction of correlation functions in two and three dimensions. Quart. J. Roy. Meteor. Soc., 125, 723-757, doi: 10. 1002/qj. 49712555417.
9. Greybush, S. J., E. Kalnay, T. Miyoshi, K. Ide, and B. R. Hunt, 2011: Balance and ensemble Kalman filter localization techniques. Mon. Wea. Rev., 139, 511-522, doi: 10. 1175/2010MWR3328. 1.
10. Houtekamer, P., and H. Mitchell, 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.
11. Houtekamer, P., and H. Mitchell, 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.
12. Hunt, B., E. Kostelich, and I. Szunyogh, 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.
13. Janjić, T., L. Nerger, A. Albertella, J. Schröter, and S. Skachko, 2011: On domain localization in ensemble-based Kalman filter algorithms. Mon. Wea. Rev., 139, 2046-2060, doi: 10. 1175/2011MWR3552. 1.
14. Janjić, T., J. Schröter, R. Savcenko, W. Bosch, A. Albertella, R. Rummel, and O. Klatt, 2012: Impact of combining GRACE and GOCE gravity data on ocean circulation estimates. Ocean Sci., 8, 65-79, doi: 10. 5194/os-8-65-2012.
15. Kang, J.-S., E. Kalnay, T. Miyoshi, J. Liu, and I. Fung, 2012: Estimation of surface carbon fluxes with an advanced data assimilationmethodology. J. Geophys. Res., 117, D24101, doi: 10. 1029/2012JD018259.
16. Krysta, M., E. Cosme, and J. Verron, 2011: A consistent hybrid variational-smoothing data assimilation method: Application to a simple shallow-water model of the turbulent midlatitude ocean. Mon. Wea. Rev., 139, 3333-3347, doi: 10. 1175/2011MWR3150. 1.
17. Lorenz, E., 1995: Predictability: A problem partly solved. Proc. Seminar on Predictability, Reading, United Kingdom, ECMWF, 1-18.
18. Losa, S. N., S. Danilov, J. Schröter, L. Nerger, S. Maßmann, and F. Janssen, 2012: Assimilating NOAA SST data into the BSH operational circulation model for the North and Baltic Seas: Inference about the data. J. Mar. Syst., 105-108, 152-162, doi: 10. 1016/j. jmarsys. 2012. 07. 008.
19. Migliorini, S., 2013: Information-based data selection for ensemble data assimilation. Quart. J. Roy. Meteor. Soc., 139, 2033-2054, doi: 10. 1002/qj. 2104.
20. Miyoshi, T., and S. Yamane, 2007: Local ensemble transform Kalman filtering with an AGCM at a T159/L48 resolution. Mon. Wea. Rev., 135, 3841-3861, doi: 10. 1175/2007MWR1873. 1.
21. Nerger, L., and W. Hiller, 2013: Software for ensemble-based data assimilation systems implementation strategies and scalability. Comput. Geosci., 55, 110-118, doi: 10. 1016/j. cageo. 2012. 03. 026.
22. Nerger, L., W. Hiller, and J. Schröter, 2005: PDAF-The parallel data assimilation framework: Experiences with Kalman filtering. Use of High Performance Computing in Meteorology-Proceedings of the 11th ECMWF Workshop, Reading, United Kingdom, ECMWF, 63-66.
23. Nerger, L., S. Danilov, W. Hiller, and J. Schröter, 2006: Using sea-level data to constrain a finite-element primitive-equation ocean model with a local SEIK filter. Ocean Dyn., 56, 634-649, doi: 10. 1007/s10236-006-0083-0.
24. Nerger, L., T. Janjic, J. Schroeter, and W. Hiller, 2012: A regulated localization scheme for ensemble-based Kalman filters. Quart. J. Roy. Meteor. Soc., 138, 802-812, doi: 10. 1002/qj. 945.
25. Otkin, J. A., 2012: Assessing the impact of the covariance localization radius when assimilating infrared brightness temperature observations using an ensemble Kalman filter. Mon. Wea. Rev., 140, 543-561, doi: 10. 1175/MWR-D-11-00084. 1.
26. Patil, D., B. Hunt, E. Kalnay, J. Yorke, and E. Ott, 2001: Local low dimensionality of atmospheric dynamics. Phys. Rev. Lett., 86, 5878-5881, doi: 10. 1103/PhysRevLett. 86. 5878.
27. Pham, D. T., 2001: Stochasticmethods for sequential data assimilation in strongly nonlinear systems. Mon. Wea. Rev., 129, 1194-1207, doi: 10. 1175/1520-0493(2001)129<1194: SMFSDA>2. 0. CO;2.
28. Robert, A. J., 1966: The integration of a low order spectral form of the primitive meteorological equations. J. Meteor. Soc. Japan, 44, 237-245.
29. Sadourny, R., 1975: The dynamics of finite-difference models of the shallow-water equations. J. Atmos. Sci., 32, 680-689, doi: 10. 1175/1520-0469(1975)032<0680: TDOFDM>2. 0. CO;2.
30. Sakov, P., and L. Bertino, 2011: Relation between two common localization methods for the EnKF. Comput. Geosci., 15, 225-237, doi: 10. 1007/s10596-010-9202-6.
31. Sakov, P., F. Counillon, L. Bertino, K. A. Lisæter, P. R. Oke, and A. Korablev, 2012: TOPAZ4: An ocean-sea ice data assimilation system for the North Atlantic and Arctic. Ocean Sci., 8, 633-656, doi: 10. 5194/os-8-633-2012.
32. Timmermann, R., S. Danilov, J. Schröter, C. Böning, D. Sidorenko, and K. Rollenhagen, 2009: Ocean circulation and sea ice distribution in a finite element global sea ice ocean model. Ocean Modell., 27, 114-129, doi: 10. 1016/j. ocemod. 2008. 10. 009.
33. Wang, Q., S. Danilov, and J. Schröter, 2008: Finite element ocean circulation model based on triangular prismatic elements, with application in studying the effect of topography representation. J. Geophys. Res., 113, C05015, doi: 10. 1029/2007JC004482.
34. Whitaker, J., and T. Hamill, 2002: Ensemble data assimilation without perturbed observations. Mon. Wea. Rev., 130, 1913-1924, doi: 10. 1175/1520-0493(2002)130<1913: EDAWPO>2. 0. CO;2.
35. Yoon, Y.-N., E. Ott, and I. Szunyogh, 2010: On the propagation of information and the use of localization in ensemble Kalman filtering. J. Atmos. Sci., 67, 3823-3834, doi: 10. 1175/2010JAS3452. 1.
36. Zupanski, D., A. S. Denning, M. Uliasz, M. Zupanski, A. E. Schuh, P. J. Rayner, W. Peters, and K. D. Corbin, 2007: Carbon flux bias estimation employing Maximum Likelihood Ensemble Filter (MLEF). J. Geophys. Res., 112, D17107, doi: 10. 1029/2006JD008371.