Data assimilation with a barotropically unstable shallow water system using representer algorithms

Liang Xu; Roger Daley

doi:10.3402/tellusa.v54i2.12135

Data assimilation with a barotropically unstable shallow water system using representer algorithms

Tellus

Volume 54 (2002): Issue 2

By: Liang Xu and Roger Daley

Open Access

|Jan 2002

Anderson , E. , Bai , Z. , Bischof , C. , Demmel , J. , Dongarra , J. , Du Croz , J. , Greenbaum , A. , Hammar-ling , S. , McKenney , A. , Ostrouchov , S. and Sorensen , D. 1995 . LAPACK users’ guide , 2nd edn . Society for Industrial and Applied Mathematics , Philadelphia . 325 pp.
Search in Google Scholar Back to article
Amodei , L. 1995 . Solution approchee pour un problem d’assimilation de donnees meteorologiques avec prise en compte de l’erreur de modele . C. R. Acad. Sci., Ser. ha 321 , 1087 – 1094 .
Search in Google Scholar Back to article
Bennett , A. F. 1997 . Inverse methods and data assimilation , 1997 Summer School Lecture Notes , Oregon State University , Corvallis, Oregon .
Search in Google Scholar Back to article
Bennett , A. F. and McIntosh , P. C. 1982 . Open ocean modeling as an inverse problem: tidal theory . J. Phys. Ocean . 12 , 1004 – 1018 .
Search in Google Scholar Back to article
Bennett , A. F. and Thorburn , M. A. 1992 . The generalized inverse of a nonlinear quasigeostrophic ocean circulation model . J. Phys. Ocean . 22 , 213 – 230 .
Search in Google Scholar Back to article
Chua , B. S. and Bennett , A. F. 2001 . An inverse ocean modeling system . Ocean Modeling 3 , 137 – 165 .
Search in Google Scholar Back to article
Cohn , S. E. and Parrish , F. P. 1991 . The behavior of forecast error covariance for a Kalman filter in two dimensions . Mon. Wea. Rev . 119 , 1757 – 1785 .
Search in Google Scholar Back to article
Courtier , P. 1998 . Dual formulation of four dimensional variational assimilation . Q. J. R. Meteorol. Soc . 123 , 2449 – 2461 .
Search in Google Scholar Back to article
Courtier , P. , Thepaut , J.-N. and Hollingsworth , A. 1994 . A strategy for operational implementation of 4D-Var using an incremental approach . Q. J. R. Meteorol. Soc . 120 , 1367 – 1387 .
Search in Google Scholar Back to article
Courtier , P. and Talagrand , O. 1990 . Variational assimilation of meteorological observations with the direct and adjoint shallow-water equations. Tellus 42A , 531 – 549 .
Search in Google Scholar Back to article
Daley , R. and Barker , E. 2000 . The NAVDAS source book , Defense Printing Office for the Naval Research Laboratory , Washington , DC . 217 pp .
Search in Google Scholar Back to article
Daley , R. and Barker , E. 2001 . NAVDAS — formulation and diagnostics . Mon. Wea. Rev . 129 , 869 – 883 .
Search in Google Scholar Back to article
Egbert , G. , Bennett , A. and Foreman , M. 1994 . TOPEX/POSEIDON tides estimated using a global inverse method. J. Geophys. Res . 99 , 24 , 821 – 24 , 852 .
Search in Google Scholar Back to article
Evensen , G. 1997 . Advanced data assimilation for strong nonlinear dynamics . Mon. Wea. Rev . 125 , 1342 – 1354 .
Search in Google Scholar Back to article
Evensen , G. and van Leeuwen , P. J. 2000 . An ensemble Kalman smoother for nonlinear dynamics . Mon. Wea. Rev . 128 , 1852 – 1867 .
Search in Google Scholar Back to article
Golub , G. H. and Van Loan , C. F. 1996 . Matrix computa-tions , 3rd edn . The Johns Hopkins Press , Baltimore and London . 694 pp.
Search in Google Scholar Back to article
Hodur , M. R. 1997 . The Naval Research Laboratory’s coupled ocean/atmosphere mesoscale prediction system (COAMPS) . Mon. Wea. Rev . 125 , 1414 – 1430 .
Search in Google Scholar Back to article
Hogan , T. and Rosmond , T. 1991 . The description of the Navy Operational Global Atmospheric Prediction System’s spectral forecast system . Mon. Wea. Rev . 119 , 1786 – 1815 .
Search in Google Scholar Back to article
Kuo , H. L. 1949 . Dynamic instability of two-dimensional nondivergent flow in a barotropic atmosphere . J. Meteorol . 6 , 105 – 122 .
Search in Google Scholar Back to article
Menard , R. 1994 . Kalman filtering of Burgers’ equation and its application to atmospheric data assimilation . Ph.D. Thesis , Department of Atmospheric and Ocean Sciences, McGill University, Montreal, Canada .
Search in Google Scholar Back to article
Reynolds , C. A. and Palmer , T. N. 1998 . Decaying singular vectors and their impact on analysis and forecast correction . J. Atmos. Sci . 55 , 3005 – 3023 .
Search in Google Scholar Back to article
Strang , G. 1986 . Introduction to applied mathematics . Wellesley-Cambridge Press , 758 pp.
Search in Google Scholar Back to article
Todling , R. and Ghil , M. 1994 . Tracking atmospheric instabilities with the Kalman filter. Part I: Methodology and one-layer results . Mon. Wea. Rev . 122 , 183 – 204 .
Search in Google Scholar Back to article
Xu , L. 1995 . The study of mesoscale land-air-sea inter-action processes using a nonhydrostatic model. Ph.D. Dissertation, North Carolina State University, Raleigh, 336 pp. (Available from Department of Marine, Earth and Atmospheric Sciences, North Carolina State University, Raleigh, NC).
Search in Google Scholar Back to article
Xu , L. and Daley , R. 2000 . Towards a true four dimensional data assimilation algorithm: application of a cycling representer algorithm to a simple transport problem . Tellus 52A , 109 – 128 .
Search in Google Scholar Back to article
Zupanski , D. 1997 . A general weak constraint applicable to operational 4DVAR data assimilation systems . Mon. Wea. Rev . 125 , 2274 – 2292 .
Search in Google Scholar Back to article