Dual formulation of four‐dimensional variational assimilation

Quarterly Journal of the Royal Meteorological Society - Tập 123 Số 544 - Trang 2449-2461 - 1997
Philippe Courtier1
1European Centre for Medium‐Range Weather Forecasts, UK

Tóm tắt

AbstractA duality between two formulations of variational assimilation, three‐dimensionsal (3D‐Var) and the Physicalspace Statistical Analysis System (PSAS), is presented. It is shown that their conditioning is identical. the temporal extension of 3D‐Var leads to 4D‐Var. the temporal extension of PSAS, 4D‐PSAS, is achieved using an algorithm inspired by the representer technique but without the explicit computation of the representers. Assuming the model is perfect, both 4D‐Var and 4D‐PSAS are equivalent in terms of results produced and cost. Assuming the model is not perfect, the equivalence is preserved, but in 4D‐Var it is necessary to increase the size of the control variable while 4D‐PSAS remains almost unchanged. In duality, 4D‐Var remains almost unchanged by an increase in the number of observations used, whereas the size of the control variable in PSAS depends directly on this number.

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Tài liệu tham khảo

Amodei L., 1995, Solution approche pour un problème d'assimilation de donnes mtorologiques avec prise en compte de l'erreur de modèle, Comptes Rendus de l'Acadmie des Sciences, 321, 1087

10.1017/CBO9780511600807

10.1007/BF01029793

10.1007/BF01029698

Bensoussan A., 1971, Filtrage optimal des systèmes linaires

Courtier P., 1997, Variational methods, J. Meteorol. Soc. Japan

Courtier P., 1987, Variational assimilation of meteorological observations with the adjoint vorticity equation. II: Numerical results, Q. J. R. Meteorol. Soc., 113, 1329, 10.1002/qj.49711347813

10.3402/tellusa.v42i5.11896

Courtier P. Freydier C. Geleyn J.‐F. Rabier F.andRochas M. J.1991‘The Arpege project at Mto‐France’. pp.192–231in Proceedings of the ECMWF seminar on numerical methods in atmospheric models Shinfield Park Reading RG2 9AX UK 9‐13 September 1991 Vol. 2

Courtier P., 1993, Variational assimilation at ECMWF

Courtier P., 1993, Important literature on the use of adjoint, variational methods and the Kalman filter in meteorology, Tellus, 45, 342, 10.3402/tellusa.v45i5.14898

10.1002/qj.49712051912

Daley R., 1991, Atmospheric data analysis

Da Silva A. Pfaendtner J. Guo J. Sienkiewicz M.andCohn S.1995‘Assessing the effects of data selection with DAO's Physical‐space Statistical Analysis System’. pp.273–278in Proceedings of the second international WMO symposium on assimilation of observations in meteorology and oceanography Tokyo 13‐17 March 1995. WMO/TD 651

10.1175/1520-0493(1995)123<1128:OLEOEC>2.0.CO;2

10.1175/1520-0493(1987)115<0998:VFDAUQ>2.0.CO;2

10.1175/1520-0493(1989)117<2437:AVCAT>2.0.CO;2

Egbert G. D.andBennett A. F.1996‘Data assimilation methods for ocean tides’. InModern approaches to data assimilation in ocean modelling. Ed. P. Malanotte‐Rizzoli

10.1029/94JC01894

Fisher M., 1995, Estimating the covariance matrices of analysis and forecast error in variational data assimilation

10.1016/S0065-2687(08)60442-2

Hollingsworth A.1987Objective analysis for numerical weather prediction.Pp.11–60in Special volume J. Meteorol. Soc. Japan. “Short and Medium Range Numerical Weather Prediction”. E d. T Matsuno

Ide K., 1997, Unified notation for data assimilation: operational, sequential and variational, J. Meteorol. Soc. Japan

10.1111/j.1600-0870.1986.tb00459.x

10.1111/j.1600-0870.1985.tb00430.x

10.1002/qj.49711247414

10.1002/qj.49711447911

10.1175/1520-0469(1994)051<1037:ADAISN>2.0.CO;2

10.1175/1520-0493(1992)120<1433:VDAWAA>2.0.CO;2

10.1175/1520-0493(1992)120<1747:TNMCSS>2.0.CO;2

10.1002/qj.49711850604

Talagrand O., 1987, Variational assimilation of meteorological observations with the adjoint vorticity equation. I: Theory, Q. J. R. Meteorol. Soc., 113, 1321, 10.1002/qj.49711347812

10.1002/qj.49711750206

10.1256/smsqj.50906

Wergen W., 1992, The effect of model errors in variational assimilation, Tellus, 44, 297, 10.3402/tellusa.v44i4.14962

10.1175/1520-0493(1996)124<1000:ANHPMA>2.0.CO;2

10.1175/1520-0493(1993)121<2396:RFDVDA>2.0.CO;2