An Ensemble-Based Four-Dimensional Variational Data Assimilation Scheme. Part I: Technical Formulation and Preliminary Test

Monthly Weather Review - Tập 136 Số 9 - Trang 3363-3373 - 2008
Chengsi Liu1, Qingnong Xiao2, Bin Wang3
1LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China, and NCAR*/ESSL/MMM, Boulder, Colorado
2NCAR*/ESSL/MMM, Boulder, Colorado
3LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China

Tóm tắt

Abstract Applying a flow-dependent background error covariance (𝗕 matrix) in variational data assimilation has been a topic of interest among researchers in recent years. In this paper, an ensemble-based four-dimensional variational (En4DVAR) algorithm, designed by the authors, is presented that uses a flow-dependent background error covariance matrix constructed by ensemble forecasts and performs 4DVAR optimization to produce a balanced analysis. A great advantage of this En4DVAR design over standard 4DVAR methods is that the tangent linear and adjoint models can be avoided in its formulation and implementation. In addition, it can be easily incorporated into variational data assimilation systems that are already in use at operational centers and among the research community. A one-dimensional shallow water model was used for preliminary tests of the En4DVAR scheme. Compared with standard 4DVAR, the En4DVAR converges well and can produce results that are as good as those with 4DVAR but with far less computation cost in its minimization. In addition, a comparison of the results from En4DVAR with those from other data assimilation schemes [e.g., 3DVAR and ensemble Kalman filter (EnKF)] is made. The results show that the En4DVAR yields an analysis that is comparable to the widely used variational or ensemble data assimilation schemes and can be a promising approach for real-time applications. In addition, experiments were carried out to test the sensitivities of EnKF and En4DVAR, whose background error covariance is estimated from the same ensemble forecasts. The experiments indicated that En4DVAR obtained reasonably sound analysis even with larger observation error, higher observation frequency, and more unbalanced background field.

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Tài liệu tham khảo

Anderson, 2001, An ensemble adjustment Kalman filter for data assimilation., Mon. Wea. Rev., 129, 2884, 10.1175/1520-0493(2001)129<2884:AEAKFF>2.0.CO;2

Anderson, 1999, A Monte Carlo implementation of the nonlinear filtering problem to produce ensemble assimilations and forecasts., Mon. Wea. Rev., 127, 2741, 10.1175/1520-0493(1999)127<2741:AMCIOT>2.0.CO;2

Bishop, 2001, Adaptive sampling with the ensemble transform Kalman filter. Part I: Theoretical aspects., Mon. Wea. Rev., 129, 420, 10.1175/1520-0493(2001)129<0420:ASWTET>2.0.CO;2

Bouttier, F., and P.Courtier, cited. 2007: Data assimilation concepts and methods. Meteorological Training Course Lecture Series, ECMWF, Reading, United Kingdom. [Available online at http://www.ecmwf.int/newsevents/training/rcourse_notes/DATA_ASSIMILATION/ASSIM_CONCEPTS/Assim_concepts.html.].

Buehner, 2005, Ensemble-derived stationary and flow-dependent background error covariances: Evaluation in a quasi-operation NWP setting., Quart. J. Roy. Meteor. Soc., 131, 1013, 10.1256/qj.04.15

Courtier, 1994, A strategy for operational implementation of 4DVAR, using an incremental approach., Quart. J. Roy. Meteor. Soc., 120, 1367, 10.1002/qj.49712051912

Daley, 1991, Atmospheric Data Analysis.

Dee, 1995, On-line estimation of error covariance parameters for atmospheric data assimilation., Mon. Wea. Rev., 123, 1128, 10.1175/1520-0493(1995)123<1128:OLEOEC>2.0.CO;2

Derber, 2003, Flow dependent Jb in a global grid-point 3D-var.

Evensen, 1994, Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics., J. Geophys. Res., 99, 143, 10.1029/94JC00572

Evensen, 2000, An ensemble Kalman smoother for nonlinear dynamics., Mon. Wea. Rev., 128, 1852, 10.1175/1520-0493(2000)128<1852:AEKSFN>2.0.CO;2

Fertig, 2007, A comparative study of 4D-VAR and a 4D ensemble filter: Perfect model simulations with Lorenz-96., Tellus, 59A, 96, 10.1111/j.1600-0870.2006.00205.x

Fisher, M. , 2003: Background error covariance modeling. Proc. Seminar on Recent Developments in Data Assimilation for Atmosphere and Ocean, Reading, United Kingdom, ECMWF, 45–63. [Available online http://www.ecmwf.int/newsevents/meetings/annual_seminar/seminar2003_presentations/Fisher.pdf.].

Gilbert, 1989, Some numerical experiments with variable storage quasi-Newton algorithms., Math. Programming, 45B, 407, 10.1007/BF01589113

Hamill, 2002, Ensemble-based data assimilation.

Hamill, 2001, A hybrid ensemble Kalman filter–3D variational analysis scheme., Mon. Wea. Rev., 128, 2905, 10.1175/1520-0493(2000)128<2905:AHEKFV>2.0.CO;2

Hayden, 1995, Recursive filter objective analysis of meteorological fields application to NESDIS operational processing., J. Appl. Meteor., 34, 3, 10.1175/1520-0450-34.1.3

Hollingsworth, 1986, The statistical structure of short-range forecast errors as determined from radiosonde data. Part I: The wind field., Tellus, 38A, 111, 10.1111/j.1600-0870.1986.tb00460.x

Houtekamer, 1998, Data assimilation using an ensemble Kalman filter technique., Mon. Wea. Rev., 126, 796, 10.1175/1520-0493(1998)126<0796:DAUAEK>2.0.CO;2

Houtekamer, 2001, A sequential ensemble Kalman filter for atmospheric data assimilation., Mon. Wea. Rev., 129, 123, 10.1175/1520-0493(2001)129<0123:ASEKFF>2.0.CO;2

Houtekamer, 2005, Ensemble Kalman filtering., Quart. J. Roy. Meteor. Soc., 131, 3269, 10.1256/qj.05.135

Hunt, 2004, Four-dimensional ensemble Kalman filtering., Tellus, 56A, 273, 10.3402/tellusa.v56i4.14424

Kalman, 1960, A new approach to linear filtering and prediction problems., Trans. ASME J. Basic Eng., 82D, 35, 10.1115/1.3662552

Li, 2001, Optimality of variational data assimilation and its relationship with the Kalman filter and smoother., Quart. J. Roy. Meteor. Soc., 127, 661, 10.1002/qj.49712757220

Lorenc, 1992, Iterative analysis using covariance functions and filters., Quart. J. Roy. Meteor. Soc., 118, 569

Lorenc, 2003, The potential of the ensemble Kalman filter for NWP: A comparison with 4D-VAR., Quart. J. Roy. Meteor. Soc., 129, 3183, 10.1256/qj.02.132

Mitchell, 2002, Ensemble size, and model-error representation in an ensemble Kalman filter., Mon. Wea. Rev., 130, 2791, 10.1175/1520-0493(2002)130<2791:ESBAME>2.0.CO;2

Parrish, 1992, The National Meteorological Center’s spectral statistical interpolation analysis system., Mon. Wea. Rev., 120, 1747, 10.1175/1520-0493(1992)120<1747:TNMCSS>2.0.CO;2

Simmons, 2002, Some aspects of the improvement in skill of numerical weather prediction., Quart. J. Roy. Meteor. Soc., 128, 647, 10.1256/003590002321042135

Snyder, 2003, Assimilation of simulated radar observations with an ensemble Kalman filter., Mon. Wea. Rev., 131, 1663, 10.1175//2555.1

Snyman, 2005, Practical Mathematical Optimization: An Introduction to Basic Optimization Theory and Classical and New Gradient-Based Algorithms.

Talagrand, 1987, Variational assimilation of meteorological observations with the adjoint vorticity equation. I: Theory., Quart. J. Roy. Meteor. Soc., 113, 1311, 10.1002/qj.49711347812

Whitaker, 2002, Ensemble data assimilation without perturbed observations., Mon. Wea. Rev., 130, 1913, 10.1175/1520-0493(2002)130<1913:EDAWPO>2.0.CO;2

Xiao, 2000, Initialization and simulation of a landfalling hurricane using a variational bogus data assimilation scheme., Mon. Wea. Rev., 128, 2252, 10.1175/1520-0493(2000)128<2252:IASOAL>2.0.CO;2

Xiao, 2002, Impact of GMS-5 and GOES-9 satellite-derived winds on the prediction of a NORPEX extratropical cyclone., Mon. Wea. Rev., 130, 507, 10.1175/1520-0493(2002)130<0507:IOGAGS>2.0.CO;2

Xu, 2001, Estimation of three-dimensional error covariances. Part II: Analysis of wind innovation vectors., Mon. Wea. Rev., 129, 2939, 10.1175/1520-0493(2001)129<2939:EOTDEC>2.0.CO;2

Xu, 2002, Estimation of three-dimensional error covariances. Part III: Height–wind forecast error correlation and related geostrophy., Mon. Wea. Rev., 130, 1052, 10.1175/1520-0493(2002)130<1052:EOTDEC>2.0.CO;2

Xu, 2001, Estimation of three-dimensional error covariances. Part I: Analysis of height innovation vectors., Mon. Wea. Rev., 129, 2126, 10.1175/1520-0493(2001)129<2126:EOTDEC>2.0.CO;2

Zou, 1996, Rainfall assimilation through an optimal control of initial and boundary conditions in a limited-area mesoscale model., Mon. Wea. Rev., 124, 2859, 10.1175/1520-0493(1996)124<2859:RATAOC>2.0.CO;2

Zupanski, 1993, Regional four-dimensional variational data assimilation in a quasi-operational forecasting environment., Mon. Wea. Rev., 121, 2396, 10.1175/1520-0493(1993)121<2396:RFDVDA>2.0.CO;2

Zupanski, 2005, Maximum likelihood ensemble filter: Theoretical aspects., Mon. Wea. Rev., 133, 1710, 10.1175/MWR2946.1

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Monthly Weather Review

Tập 136 Số 9

3363-3373

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