A Bayesian Filter Framework for Sequential Data Assimilation
Received date: 2009-07-31
Revised date: 2010-02-24
Online published: 2010-05-10
Supported by
李新（1969），男，甘肃酒泉人，博士，研究员，主要从事陆面数据同化、遥感和GIS在冰冻圈和水文水资源研究中的应用、流域集成研究.E-mail:lixin@lzb.ac.cn
Data assimilation is a method in which the observations can be merged with model states by taking advantage of consistent constraints from model physics. The Bayes theory can be considered as the very foundation for data assimilation. The purpose of this paper is to provide a unified theory and notation for the application of Bayesian filter in data assimilation. First, various methods of continuous and sequential data assimilation are classified. Secondly, the sequential data assimilation for nonlinear systems is generalized as a recursive Bayesian filter. Then, two typical sequential data assimilation methods, i.e., the particle filter and the ensemble Kalman filter are represented in the framework of Bayesian filter. The particle filters, in essence, is a Monte Carlo realization of recursive Bayesian filter, and the ensemble Kalman filter is equivalent to the particle filter with equal weights. The theory of Bayesian filter provides a generalized basis for the sequential data assimilation from a more fundamental mathematical viewpoint.
LI Xin . A Bayesian Filter Framework for Sequential Data Assimilation[J]. Advances in Earth Science, 2010 , 25(5) : 515 -522 . DOI: 10.11867/j.issn.1001-8166.2010.05.0515
[1] Li Xin, Huang Chunlin, Che Tao, et al. Development of a Chinese land data assimilation system: Its progress and prospects [J]. Progress in Natural Science,2007, 17(8): 881-892. [李新, 黄春林, 车涛, 等. 中国陆面数据同化系统研究的进展与前瞻 [J]. 自然科学进展, 2007, 17(2): 163-173.]
[2] Chou Jifan. Theory and New Method in Four Dimensional Data Assimilation [R]. Lanzhou: Department of Atmospheric Science, Lanzhou University, 1994. [丑纪范. 四维同化的理论和新方法 [R]. 兰州: 兰州大学大气科学系, 1994.]
[3] Daley R. Atmospheric Data Analysis [M]. New York: Cambridge University Press, 1991:457.
[4] Talagrand O. Assimilation of observations, an introduction [J]. Journal of the Meteorological Society of Japan,1997, 75(1B): 191-209.
[5] National Research Council, Panel on Model-Assimilated Data Sets for Atmospheric and Oceanic Research. Four Dimensional Model Assimilation of Data [M]. Washington DC: National Academy Press, 1991:78.
[6] Kalnay E. Atmospheric Modeling, Data Assimilation and Predictability[M].Cambridge:Cambridge University Press, 2002:512.
[7] Courtier P. Variational methods [J]. Journal of the Meteorological Society of Japan, 1997, 75(1B): 211-218.
[8] Li X, Koike T, Mahadevan P. A very fast simulated re-annealing (VFSA) approach for land data assimilation [J]. Computers and Geosciences, 2004, 30(3): 239-248.
[9] Yang K, Watanabe T, Koike T, et al. Auto-calibration system developed to assimilate AMSR-E data into a land surface model for estimating soil moisture and the surface energy budget [J]. Journal of the Meteorological Society of Japan, 2007, 85A: 229-242.
[10] Evensen G. The Ensemble Kalman Filter: Theoretical formulation and practical implementation [J]. Ocean Dynamics,2003, 53: 343-367.
[11] Evensen G. Data Assimilation, the Ensemble Kalman Filter [M]. Berlin, Heidelberg: Springer, 2007:279.
[12] Han X J, Li X. An evaluation of the nonlinear/non-Gaussian filters for the sequential data assimilation [J]. Remote Sensing of Environment,2008, 112(4): 1 434-1 449.
[13] Han Xujun, Li Xin. Review of nonlinear filters in the land data assimilation [J]. Advances in Earth Science, 2008, 23(8): 813-820. [韩旭军, 李新.非线性滤波方法与陆面数据同化[J]. 地球科学进展, 2008, 23(8): 813-820.]
[14] Huang Chunlin, Li Xin. Application of unscented Kalman filter for data assimilation [J]. Journal of Tropical Meteorology, 2007, 23(6): 617-622. [黄春林, 李新. UKF滤波算法在数据同化中的应用[J]. 热带气象学报, 2007, 23(6): 617-622.]
[15] Nakano S, Ueno G, Higuchi T. Merging particle filter for sequential data assimilation [J]. Nonlinear Processes in Geophysics,2007, 14(4): 395-408.
[16] Weerts A H, El Serafy G. Particle filtering and ensemble Kalman filtering for state updating with hydrological conceptual rainfall-runoff models [J]. Water Resources Research,2006, 42,W0940,doi:10.1029/2005WR004093.
[17] Ide K, Courtier P, Ghil M, et al. Unified notation for data assimilation: Operational, sequential and variational [J]. Journal of the Meteorological Society of Japan,- 1997, 75(1B): 181-189.
[18] Han Chongzhao, Zhu Hongyan, Duan Zhansheng. Multi-source Data Fusion [M]. Beijing: Tsinghua University Press, 2006:488.[韩崇昭, 朱洪艳, 段战胜. 多源信息融合[M]. 北京: 清华大学出版社, 2006:488.]
[19] Lorenc A C. Atmospheric Data Assimilation [R]. Scientific Paper No 34, Bracknell: Forecasting Research, Meteorological Office, 1995.
[20] Pham D T. Stochastic methods for sequential data assimilation in strongly nonlinear systems [J]. Monthly Weather Review,2001, 129(5): 1 194-1 207.
[21] Moradkhani H, Hsu K L, Gupta H, et al. Uncertainty assessment of hydrologic model states and parameters: Sequential data assimilation using the particle filter [J]. Water Resources Research, 2005, 41,W05012,doi:10.1029/2004WR003604.
[22] Anderson J L, Anderson S L. A Monte Carlo implementation of the nonlinear filtering problem to produce ensemble assimilations and forecasts [J]. Monthly Weather Review,1999, 127(12): 2 741-2 758.
[23] Gordon N J, Salmond D J, Smith A F M. Novel approach to nonlinear/non-Gaussian Bayesian state estimation [J]. IEEE Proceedings on Radar and Signal Processing, 1993, 140(2): 107-113.
[24] Isard M, Blake A. CONDENSATION-conditional density propagation for visual tracking[J]. International Journal of Computer Vision, 1998, 29(1): 5-28.
[25] Bergman N.Recursive Bayesian Estimation: Navigation and Tracking Applications[D]. Linköping, Sweden: Linköping University, 1999.
[26] Arulampalam M S, Maskell S, Gordon N, et al. A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking [J]. IEEE Transactions on Signal Processing,2002, 50(2): 174-188.
[27] van Leeuwen P J.A variance-minimizing filter for large-scale applications[J].Monthly Weather Review,2003,131(9):2 071-2 084.
[28] Evensen G. Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte-Carlo methods to forecast error statistics [J]. Journal of Geophysical Research,1994, 99(C5): 10 143-10 162.
[29] Burgers G, van Leeuwen P J, Evensen G. Analysis scheme in the ensemble Kalman filter [J]. Monthly Weather Review,1998, 126(6): 1 719-1 724.
[30] Evensen G. Sampling strategies and square root analysis schemes for the EnKF [J]. Ocean Dynamics,2004, 54(6): 539-560.
[31] Kalnay E, Li H, Miyoshi T, et al. 4D-Var or ensemble Kalman Filter? [J]. Tellus A, 2007, 59A(5): 758-773.
/
| 〈 |
|
〉 |
甘公网安备62010202000687
