Notes and correspondence on ensemble-based three-dimensional variational filters

Hong-ze LENG; Jun-qiang SONG; Fu-kang YIN; Xiao-qun CAO

doi:10.1631/jzus.C1300024

Your Location：

Home >

Browse articles >

Notes and correspondence on ensemble-based three-dimensional variational filters

计算机与自动化 | Updated：2022-12-09

- Notes and correspondence on ensemble-based three-dimensional variational filters
- Notes and correspondence on ensemble-based three-dimensional variational filters
- 信息与电子工程前沿（英文） 2013年14卷第8期页码：634-641
- Affiliations：
  
  College of Computer, National University of Defense Technology, Changsha 410073, China
- Author bio：
  
  [ "Hong-ze LENG, hzleng@nudt.edu.cn" ]
- Funds：
  
  Project supported by the National Natural Science Foundation of China (No. 41105063) and the Special Fund for Meteorological Scientific Research in the Public Interest (No. GYHY20100615)
- DOI：10.1631/jzus.C1300024
  中图分类号： TP302.7;P409
- 收稿：2013-01-20，
  
  修回：2013-;7-12，
  
  纸质出版：2013-08
- Accepted：
Scan QR Code
Notes and correspondence on ensemble-based three-dimensional variational filters[J]. 信息与电子工程前沿（英文）, 2013,14(8):634-641.

Hong-ze LENG, Jun-qiang SONG, Fu-kang YIN, et al. Notes and correspondence on ensemble-based three-dimensional variational filters[J]. Frontiers of Information Technology & Electronic Engineering, 2013, 14(8): 634-641.
Notes and correspondence on ensemble-based three-dimensional variational filters[J]. 信息与电子工程前沿（英文）, 2013,14(8):634-641. DOI： 10.1631/jzus.C1300024.

Hong-ze LENG, Jun-qiang SONG, Fu-kang YIN, et al. Notes and correspondence on ensemble-based three-dimensional variational filters[J]. Frontiers of Information Technology & Electronic Engineering, 2013, 14(8): 634-641. DOI： 10.1631/jzus.C1300024.

摘要

Abstract

Several ensemble-based three-dimensional variational (3D-Var) filters are compared. These schemes replace the static background error covariance of the traditional 3D-Var with the ensemble forecast error covariance

but generate analysis ensemble anomalies (perturbations) in different ways. However

it is demonstrated in this paper that they are all theoretically equivalent to the ensemble transformation Kalman filter (ETKF). Furthermore

a new method named EnPSAS is presented. The analysis shows that EnPSAS has a small condition number and can apply covariance localization more easily than other ensemble-based 3D-Var methods.

关键词

Keywords

references

C.H. Bishop , , , B.J. Etherton , , , S.J. Majumdar . . Adaptive sampling with the ensemble transform Kalman filter. Part Ⅰ: theoretical aspects . . Mon. Wea. Rev. , , 2001 . . 129 ( ( 3 ): ): 420 - - 436 . . DOI: 10.1175/1520-0493(2001)129<0420:ASWTET>2.0.CO;2 http://doi.org/10.1175/1520-0493(2001)129<0420:ASWTET>2.0.CO;2 . .

M. Buehner . . Ensemble-derived stationary and flowdependent background-error covariances: evaluation in a quasi-operational NWP setting . . Q. J. R. Meteorol. Soc. , , 2005 . . 131 ( ( 607 ): ): 1013 - - 1043 . . DOI: 10.1256/qj.04.15 http://doi.org/10.1256/qj.04.15 . .

S.E. Cohn , , , A. da Silva , , , J. Guo , , , M. Sienkiewicz , , , D. Lamich . . Assessing the effects of data selection with the DAO physical-space statistical analysis system . . Mon. Wea. Rev. , , 1998 . . 126 ( ( 11 ): ): 2913 - - 2926 . . DOI: 10.1175/1520-0493(1998)126<2913:ATEODS>2.0.CO;2 http://doi.org/10.1175/1520-0493(1998)126<2913:ATEODS>2.0.CO;2 . .

G. Golub , , , C. van Loan . . Matrix Computations , , : : London The Johns Hopkins University Press , , 1996 . . .

N. Gustafsson , , , L. Berre , , , S. Hornquist , , , X.Y. Huang , , , M. Lindskog , , , B. Navascues , , , K.S. Mogensen , , , S. Thorsteinsson . . Three-dimensional variational data assimilation for a limited area model . . Tellus , , 2001 . . 53A 425 - - 446 . . . .

S.A. Haben , , , A.S. Lawless , , , N.K. Nichols . . Conditioning of incremental variational data assimilation, with application to the Met Office system . . Tellus , , 2011a . . 63A 782 - - 792 . . . .

S.A. Haben , , , A.S. Lawless , , , N.K. Nichols . . Conditioning and preconditioning of the variational data assimilation problem . . Comput. Fluids , , 2011b . . 46 ( ( 1 ): ): 252 - - 256 . . DOI: 10.1016/j.compfluid.2010.11.025 http://doi.org/10.1016/j.compfluid.2010.11.025 . .

T.M. Hamill , , , C. Snyder . . A hybrid ensemble Kalman filter-3D variational analysis scheme . . Mon. Wea. Rev. , , 2000 . . 128 ( ( 8 ): ): 2905 - - 2919 . . DOI: 10.1175/1520-0493(2000)128<2905:AHEKFV>2.0.CO;2 http://doi.org/10.1175/1520-0493(2000)128<2905:AHEKFV>2.0.CO;2 . .

T.M. Hamill , , , J.S. Whitaker , , , C. Snyder . . Distancedependent filtering of background error covariance estimates in an ensemble Kalman filter . . Mon. Wea. Rev. , , 2001 . . 129 ( ( 11 ): ): 2776 - - 2790 . . DOI: 10.1175/1520-0493(2001)129<2776:DDFOBE>2.0.CO;2 http://doi.org/10.1175/1520-0493(2001)129<2776:DDFOBE>2.0.CO;2 . .

B.R. Hunt , , , E.J. Kostelich , , , I. Szunyogh . . Efficient data assimilation for spatiotemporal chaos: a local ensemble transform Kalman filter . . Phys. D , , 2007 . . 230 ( ( 1-2 ): ): 112 - - 126 . . DOI: 10.1016/j.physd.2006.11.008 http://doi.org/10.1016/j.physd.2006.11.008 . .

T. Janjić , , , L. Nerger , , , A. Albertella , , , J. Schröter , , , S. Skachko . . On domain localization in ensemble-based Kalman filter algorithms . . Mon. Wea. Rev. , , 2011 . . 139 ( ( 7 ): ): 2046 - - 2060 . . DOI: 10.1175/2011MWR3552.1 http://doi.org/10.1175/2011MWR3552.1 . .

A.H. Jazwinski . . Stochastic Processes and Filtering Theory , , : : New York and London Academic Press , , 1970 . . .

C. Liu , , , Q. Xiao , , , B. Wang . . An ensemble-based fourdimensional variational data assimilation scheme. Part Ⅰ: technical formulation and preliminary test . . Mon. Wea. Rev. , , 2008 . . 136 ( ( 9 ): ): 3363 - - 3373 . . DOI: 10.1175/2008MWR2312.1 http://doi.org/10.1175/2008MWR2312.1 . .

C. Liu , , , Q. Xiao , , , B. Wang . . An ensemble-based fourdimensional variational data assimilation scheme. Part Ⅱ: observing system simulation experiments with advanced research WRF (ARW) . . Mon. Wea. Rev. , , 2009 . . 137 ( ( 5 ): ): 1687 - - 1704 . . DOI: 10.1175/2008MWR2699.1 http://doi.org/10.1175/2008MWR2699.1 . .

A.C. Lorenc . . Development of an operational variational assimilation scheme . . J. Meteorol. Soc. Jpn. , , 1997 . . 75 339 - - 346 . . . .

A.C. Lorenc . . The potential of the ensemble Kalman filter for NWP—A comparison with 4D-Var . . Q. J. R. Meteorol. Soc. , , 2003 . . 129 ( ( 595 ): ): 3183 - - 3203 . . DOI: 10.1256/qj.02.132 http://doi.org/10.1256/qj.02.132 . .

X. Pan , , , X. Tian , , , X. Li , , , Z. Xie , , , A. Shao , , , C. Lu . . Assimilating Doppler radar radial velocity and reflectivity observations in the weather research and forecasting model by a proper orthogonal-decomposition-based ensemble, three-dimensional variational assimilation method . . J. Geophys. Res. , , 2012 . . 117 ( ( D17113 ): ): DOI: 10.1029/2012JD017684 http://doi.org/10.1029/2012JD017684 . .

D.F. Parrish , , , J.C. Derber . . The national meteorological center's spectral statistical interpolation analysis system . . Mon. Wea. Rev. , , 1992 . . 120 ( ( 8 ): ): 1747 - - 1763 . . DOI: 10.1175/1520-0493(1992)120<1747:TNMCSS>2.0.CO;2 http://doi.org/10.1175/1520-0493(1992)120<1747:TNMCSS>2.0.CO;2 . .

X. Tian , , , Z. Xie , , , Q. Sun . . A POD-based ensemble four-dimensional variational assimilation method . . Tellus , , 2011 . . 63A 805 - - 816 . . . .

P.J. van Leeuwen , , , G. Evensen . . Data assimilation and inverse methods in terms of probabilistic formulation . . Mon. Wea. Rev. , , 1996 . . 124 ( ( 12 ): ): 2898 - - 2913 . . DOI: 10.1175/1520-0493(1996)124<2898:DAAIMI>2.0.CO;2 http://doi.org/10.1175/1520-0493(1996)124<2898:DAAIMI>2.0.CO;2 . .

X. Wang , , , C. Snyder , , , T.M. Hamill . . Notes and correspondence on the theoretical equivalence of differently proposed ensemble/3D-Var hybrid analysis schemes . . Mon. Wea. Rev. , , 2007 . . 135 ( ( 1 ): ): 222 - - 227 . . DOI: 10.1175/MWR3282.1 http://doi.org/10.1175/MWR3282.1 . .

X. Wang , , , D.M. Barker , , , C. Snyder , , , T.M. Hamill . . A hybrid ETKF-3DVAR data assimilation scheme for the WRF model. Part Ⅰ: observing system simulation experiment . . Mon. Wea. Rev. , , 2008 . . 136 ( ( 12 ): ): 5116 - - 5131 . . DOI: 10.1175/2008MWR2444.1 http://doi.org/10.1175/2008MWR2444.1 . .

S. Yang , , , E. Kalnay , , , B. Hunt , , , N.E. Bowler . . Weight interpolation for efficient data assimilation with the local ensemble transform Kalman filter . . Q. J. R. Meteorol. Soc. , , 2009 . . 135 ( ( 638 ): ): 251 - - 262 . . DOI: 10.1002/qj.353 http://doi.org/10.1002/qj.353 . .

M. Zupanski . . Maximum likelihood ensemble filter: theoretical aspects . . Mon. Wea. Rev. , , 2005 . . 133 ( ( 6 ): ): 1710 - - 1726 . . DOI: 10.1175/MWR2946.1 http://doi.org/10.1175/MWR2946.1 . .

M. Zupanski , , , I.M. Navon , , , D. Zupanski . . The maximum likelihood ensemble filter as a non-differentiable minimization algorithm . . Q. J. R. Meteorol. Soc. , , 2008 . . 134 ( ( 633 ): ): 1039 - - 1050 . . DOI: 10.1002/qj.251 http://doi.org/10.1002/qj.251 . .

浏览量

Downloads

CSCD

文章被引用时，请邮件提醒。

Submit

工具集

关联资源

暂无数据