Accounting for an imperfect model in 4D‐Var

Quarterly Journal of the Royal Meteorological Society - Tập 132 Số 621 - Trang 2483-2504 - 2006
Yannick Trémolet1
1European Centre for Medium-Range Weather Forecasts, Reading, UK

Tóm tắt

AbstractIn most operational implementations of four‐dimensional variational data assimilation (4D‐Var), it is assumed that the model used in the data assimilation process is perfect or, at least, that errors in the model can be neglected when compared to other errors in the system. In this paper, we study how model error could be accounted for in 4D‐Var.We present three approaches for the formulation of weak‐constraint 4D‐Var: estimating explicitly a model‐error forcing term, estimating a representation of model bias or, estimating a four‐dimensional model state as the control variable. The consequences of these approaches with respect to the implementation and the properties of 4D‐Var are discussed.We show that 4D‐Var with an additional model‐error representation as part of the control variable is essentially an initial‐value problem and that its characteristics are very similar to that of strong constraint 4D‐Var. Taking the four‐dimensional state as the control variable, however, leads to very different properties. In that case, weak‐constraint 4D‐Var can be interpreted as a coupling between successive strong‐constraint assimilation cycles. A possible extension towards long‐window 4D‐Var and possibilities for evolutions of the data assimilation system are presented. Copyright © 2006 Royal Meteorological Society

Từ khóa


Tài liệu tham khảo

10.1256/smsqj.56511

Andersson E. Cardinali C. Fisher M. Hólm E. Isaksen L. Trémolet Y.andHollingsworth A.2004‘Developments in ECMWF's 4D‐Var System’. From American Meteorological Society symposium on forecasting the weather and climate of the atmosphere and ocean.http://ams.confex.com/ams/84Annual/20WAF16NW

10.1007/BF01029793

10.1002/qj.49712051912

10.1256/qj.05.137

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

10.1175/1520-0493(1998)126<2287:TUOTCC>2.0.CO;2

Fisher M.1998‘Minimization algorithms for variational data assimilation’. Pp.364–385in Proceedings of seminar on recent developments in numerical methods for atmospheric modelling 7–11 September 1998. European Centre for Medium‐Range Weather Forecasts Shinfield Park Reading Berkshire RG2 9AX UK

2003‘Background error covariance modelling’. Pp.45–63in Workshop on recent developments in data assimilation for atmosphere and ocean 8–12 September 2003. European Centre for Medium‐Range Weather Forecasts Shinfield Park Reading Berkshire RG2 9AX UK

10.1256/qj.04.142

Griffith A., 1998, Numerical methods for fluid dynamics, 335

10.1016/S0076-5392(09)60368-4

10.5194/acpd-5-8879-2005

10.1002/qj.49712656417

10.1111/j.1600-0870.1986.tb00459.x

10.1002/qj.49711247414

McNally A.2003‘The assimilation of stratospheric satellite data at ECMWF’. Pp.103–106ECMWF/SPARC Workshop on modelling and assimilation for the stratosphere and tropopause. European Centre for Medium‐Range Weather Forecasts Shinfield Park Reading Berkshire RG2 9AX UK

10.1002/qj.49712656416

10.1002/qj.49712656415

10.1142/3171

10.1175/1520-0493(1970)098<0875:SBFINV>2.3.CO;2

Trémolet Y.2005Incremental 4D‐Var convergence study. ECMWF Technical Memorandum No. 469. European Centre for Medium‐Range Weather Forecasts Shinfield Park Reading Berkshire RG2 9AX UK

10.1016/0167-8191(96)00018-X

10.1111/j.1600-0870.2004.00057.x

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

10.1175/1520-0493(1997)125<2274:AGWCAT>2.0.CO;2

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

Thông tin
Thông tin xuất bản

Quarterly Journal of the Royal Meteorological Society

Tập 132 Số 621

2483-2504

Thông tin tác giả