A reduced-order Kalman filter for data assimilation in physical oceanography

SIAM Review

Volumn 49, Issue 3, 2007, Pages 449-465

  Rozier, David ^a   Birol, F ^b   Cosme, Emmanuel ^a   Brasseur, Pierre ^a   Brankart, J M ^a   Verron, Jacques Verron ^a  

^a CNRS   (France)

^b LEGOS   (France)

Author keywords

Data assimilation; Kalman filter; Numerical simulation; Physical oceanography

Indexed keywords

COMPUTER SIMULATION; DATA PROCESSING; KALMAN FILTERS; MATHEMATICAL MODELS; MATHEMATICAL TECHNIQUES;

DATA ASSIMILATION; OCEAN CIRCULATION; PHYSICAL OCEANOGRAPHY; REDUCED-ORDER KALMAN FILTER;

OCEANOGRAPHY;

EID: 34548487280     PISSN: 00361445     EISSN: None     Source Type: Journal    
DOI: 10.1137/050635717     Document Type: Article

References (44)

1. P. BAHUREL, MERCATOR OCEAN global to regional ocean monitoring and forecasting, in GODAE, an Integrated View of Oceanography: Ocean Weather Forecasting in the 21st Century, J. Verron and E. Chassignet, eds., Kluwer Academic, Dordrecht, The Netherlands, 2006, pp. 381-395.
2. J. M. BECKERS, Y. DESAUBIES, AND M. RIXEN, Marine Environmental Monitoring and Predictions, J. Marine Systems, 65 (2007). Special Issue dedicated to the 36th International Liège Colloquium on Ocean Dynamics.
3. R. BLECK, An oceanic general circulation model framed in hybrid isopycnic-Cartesian coordinates, Ocean Modelling, 37 (2002), pp. 55-88.
4. R. BLECK AND E. P. CHASSIGNET, Simulating the oceanic circulation with isopycnic-coordinate models, in The Oceans: Physical-Chemical Dynamics and Human Impact, S. K. Majumdar, E. W. Miller, G. S. Forbes, R. F. Schmalz, and A. A. Panah, eds., The Pennsylvania Academy of Science, 1994, pp. 17-39.
5. S. C. BLOOM, L. L. TAKACS, A. M. DASILVA, AND D. LEVINA, Data assimilation using incremental analysis updates, Monthly Weather Rev., 124 (1996), pp. 1256-1271.
6. A. F. BLUMBERG AND G. L. MELLOR, A description of a three-dimensional coastal ocean circulation model, in Three-Dimensional Coastal Ocean Models, N. S. Heaps, ed., American Geophysical Union, Washington, D.C., 1987, pp. 1-16.
7. J. M. BRANKART, C. E. TESTUT, P. BRASSEUR, AND J. VERRON, Implementation of a multivariate data assimilation scheme for isopycnic ocean models: Application to a 1993-1996 hindcast of the North Atlantic Ocean circulation, J. Geophys. Res., 108 (C3) (2003), pp. 1-20.
8. P. BRASSEUR, J. BALLABRERA-POY, AND J. VERRON, Assimilation of altimetric data in the mid-latitude oceans using the Singular Evolutive Extended Kalman filter with an eddy-resolving, primitive equation model, J. Marine Syst., 22 (1999), pp. 269-294.
9. P. BRASSEUR, P. BAHUREL, L. BERTINO, F. BIROL, J.-M. BRANKART, N. FERRY, S. LOSA, E. RÈMY, J. SCHRÖTER, S. SKACHKO, C.-E. TESTUT, B. TRANCHANT, P.-J. VAN LEUWEN, AND J. VERRON, Data assimilation for marine monitoring and prediction: The MERCATOR operational assimilation systems and the MERSEA developments, Quart. J. Roy. Meteor. Soc., 131 (2005), pp. 3561-3582.
10. M. A. CANE, A. KAPLAN, R. N. MILLER, B. TANG, E. C. HACKERT, AND A. J. BUSALACCHI, Mapping tropical Pacific sea level: Data assimilation via a reduced state space Kalman filter, J. Geophys. Res., 101 (C10) (1996), pp. 22599-22617.
11. Y. CAO, J. ZHU, Z. LUO, AND I. M. NAVON, Reduced order modeling of the upper tropical Pacific Ocean model using proper orthogonal decomposition, Comput. Math. Appl., 52 (2006), pp. 1373-1386.
12. Y. CAO, J. ZHU, I. M. NAVON, AND Z. LUO, A reduced order approach to four-dimensional variational data assimilation using proper orthogonal decomposition, Internat. J. Numer. Methods Fluids, 53 (2007), pp. 1571-1583.
13. E. P. CHASSIGNET AND J. VERRON, Ocean Modeling and Parameterization, NATO Sci. Ser. C Math. Phys. Sci. 516, Kluwer Academic, Dordrecht, The Netherlands, 1998.
14. E. P. CHASSIGNET, L. T. SMITH, G. R. HALLIWELL, AND R. BLECK, North Atlantic simulations with the Hybrid Coordinate Ocean Model (HYCOM): Impact of the vertical Coordinate choice, reference pressure, and thermobaricity, J. Phys. Oceanogr., 33 (2003), pp. 2504-2526.
15. S. E. COHN, An introduction to estimation theory, J. Meteor. Soc. Japan, 75 (1B) (1997), pp. 257-288.
16. S. E. COHN AND R. TODLING, Approximate Kalman filters for unstable dynamics, in Proceedings of the Second International Symposium on Assimilation of Observations in Meteorology and Oceanography, WMO, 1995, pp. 241-246.
17. S. E. COHN AND R. TODLING, Approximate Kalman filters for stable and unstable dynamics, J. Meteor. Soc. Japan, 74 (1996), pp. 63-75.
18. R. DALEY, Atmospheric Data Analysis, Cambridge University Press, Cambridge, UK, 1991.
19. D. P. DEE, An efficient algorithm for estimating noise covariances in distributed systems, IEEE Trans. Automat. Control, 30 (1985), pp. 1057-1065.
20. D. P. DEE, Simplification of the Kalman filter for meteorological data assimilation, Quart. J. Roy. Meteor. Soc., 117 (1991), pp. 365-384.
21. D. P. DEE, On-line estimation error covariance parameters for atmospheric data assimilation, Monthly Weather Rev., 123 (1995), pp. 1128-1145.
22. G. EVENSEN, Sequential data assimilation with a non linear quasigeostrophic model using Monte Carlo methods to forecast error statistics, J. Geophys. Res., 99 (C5) (1994), pp. 10143-10162.
23. B. F. FARRELL AND P. J. IOANNOU, State estimation using a reduced-order Kalman filter, J. Atmos. Sci., 58 (2001), pp. 3666-3680.
24. I. FUKUMORI, Assimilation of TOPEX sea level measurements with a reduced-gravity, shallow water model of the tropical Pacific Ocean, J. Geophys. Res., 100 (C12) (1995), pp. 25027-25039.
25. M. GHIL AND P. MALANOTTE-RIZZOLI, Data assimilation in meteorology and oceanography, Adv. Geophys., 33 (1991), pp. 141-266.
26. M. GHIL, K. IDE, A. BENNETT, P. COURTIER, M. KIMOTO, M. NAGATA, M. SAIKI, AND N. SATO, EDS., Data Assimilation in Meteorology and Oceanography: Theory and Practice, J. Meteor. Soc. Japan, special issue, 1997.
27. M. S. GREWAL AND A. P. ANDREWS, Kalman Filtering: Theory and Practice Using MATLAB, Wiley-Interscience, New York, 2001.
28. S. M. GRIFFIES, C. BÖNING, F. O. BRYAN, E. P. CHASSIGNET, R. GERDES, H. HASUMI, A. HIRST, A.-M. TREGUIER, AND D. WEBB, Developments in ocean climate modelling, Ocean Modelling, 2 (2000), pp. 123-192.
29. R. HALLBERG, HIM: The Hallberg Isopycnal Coordinate Primitive Equation Model, NOAA Geophysical Fluid Dynamics Laboratory, Tech. Report, Princeton University, Princeton, NJ, 1997.
30. P. L. HOUTEKAMER AND H. L. MITCHELL, Data assimilation using an ensemble Kalman filter technique, Monthly Weather Rev., 126 (1998 , pp. 796-811.
31. R. X. HUANG, Real freshwater flux as a natural boundary condition for salinity balance and thermohaline circulation forced by evaporation and precipitation, J. Phys. Oceanogr., 23 (1993), pp. 2428-2446.
32. A. H. JAZWINSKI, Stochastic Processes and Filtering Theory, Math. Sci. Engrg. 64, Academic Press, New York, 1970.
33. P. F. J. LERMUSIAUX AND A. R. ROBINSON, Data assimilation via error subspace statistical estimation. Part I: Theory and schemes, Monthly Weather Rev., 127 (1999), pp. 1385-1407.
34. A. LORENC, A global three-dimensional multivariate statistical interpolation scheme, Monthly Weather Rev., 109 (1981), pp. 701-721.
35. L. NERGER, W. HILLER, AND J. SCHRÖTER, A comparison of subspace Kalman filters, Tellus, 57A (2005), pp. 715-735.
36. Y. OURMIÈRES, J. M. BRANKART, L. BERLINE, J. VERRON, AND P. BRASSEUR, Incremental analysis update implementation into a sequential ocean data assimilation system, J. Atmospheric and Oceanic Technologies, 23 (2006), pp. 1729-1744.
37. D. F. PARRISH AND S. E. COHN, A Kalman Filter for a Two-Dimensional Shallow-Water Model: Formulation and Preliminary Experiments, Office Note 304, National Meteorological Center, Washington D.C., 1985.
38. T. PENDUFF, P. BRASSEUR, C.-E. TESTUT, B. BARNIER, AND J. VERRON, A four-year eddy-permitting assimilation of sea-surface temperature and altimetric data in the South Atlantic Ocean, J. Marine Res., 60 (2002), pp. 805-833.
39. D. PHAM, J. VERRON, AND M. ROUBAUD, A Singular Evolutive Extended Kalman filter for data assimilation in oceanography, J. Marine Syst., 16(3-4)(1998), pp. 323-340.
40. G. A. F. SEBER, Multivariate Observations, Wiley, New York, 1984.
41. C.-E. TESTUT, P. BRASSEUR, J.-M. BRANKART, AND J. VERRON, Assimilation of sea-surface temperature and altimetric observations during 1992-1993 into an eddy permitting primitive equation model of the North Atlantic Ocean, J. Marine Syst., 40-41 (2003), pp. 291-316.
42. R. TODLING AND S. E. COHN, Suboptimal schemes for atmospheric data assimilation based on the Kalman filter, Monthly Weather Rev., 122 (1994), pp. 2530-2557.
43. M. VERLAAN AND A. W. HEEMINK, Reduced rank square root filters for large scale data assimilation problem, in Proceedings of the Second International Symposium on Assimilation of Observations in Meteorology and Oceanography, WMO, 1995, pp. 247-252.
44. M. VERLAAN AND A. W. HEEMINK, Tidal flow forecasting using reduced-rank square root filter, Stochastic Hydro. Hydraul., 11 (1997), pp. 349-368.