集合资料同化方法的理论框架及其在海洋资料同化的研究展望

沈浙奇; 唐佑民; 高艳秋

doi:10.3969/j.issn.0253-4193.2016.03.001

集合资料同化方法的理论框架及其在海洋资料同化的研究展望

doi: 10.3969/j.issn.0253-4193.2016.03.001

1.
国家海洋局第二海洋研究所卫星海洋环境动力学国家重点实验室, 浙江杭州 310012
2.
国家海洋局第二海洋研究所卫星海洋环境动力学国家重点实验室, 浙江杭州 310012;北大不列颠哥伦比亚大学环境科学及工程系, 加拿大乔治王子城V2N 4Z9

基金项目: 国家自然科学基金项目(41276029,41321004);科技部国家基础科研项目(2013CB430302);卫星海洋环境动力学国家重点实验室自主课题(SOEDZZ1404,SOEDZZ1518)。

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出版历程
- 收稿日期: 2015-05-24
- 修回日期: 2015-08-07

The theoretical framework of the ensemble-based data assimilation method and its prospect in oceanic data assimilation

1.
State Key Laboratory of Satellite Ocean Environment Dynamics, Second Institute of Oceanography, State Oceanic Administration, Hangzhou 310012, China
2.
State Key Laboratory of Satellite Ocean Environment Dynamics, Second Institute of Oceanography, State Oceanic Administration, Hangzhou 310012, China;Environmental Science and Engineering, University of Northern British Columbia, Prince George V2N 4Z9, Canada

摘要

摘要: 在海洋动力系统的数值模拟中,海洋资料同化是一种能够有效融合多源海洋观测资料和数值模式的方法。它不仅可以显著地提高数值模拟的效果,构造海洋再分析资料场,还能有效减少海洋和气候预报时模式初始条件的不确定性。因此,海洋资料同化对于海洋研究和业务化应用具有非常重要的意义。资料同化方法的研究一直是大气、海洋科学的热门课题之一。其中,集合卡尔曼滤波器(EnKF)是一种有效的资料同化方法,自提出以来经过了20多年的发展和改进,已经在海洋资料同化中得到了广泛的研究和应用。近年来,随着动力模式的不断发展和计算能力的提高,粒子滤波器由于不受模型线性和误差高斯分布假设的约束,也逐渐成为了当前资料同化方法研究的热点。本文分析和总结了目前关于集合卡尔曼滤波器和粒子滤波器的一些最新理论研究结果,在贝叶斯滤波理论的框架下讨论了这两类算法的关联和区别,以及各自在资料同化实践中的优势和不足。在此基础上,我们探讨了粒子滤波器应用于海洋模式资料同化的主要困难和目前可行的一些解决方法,展望了集合资料同化方法研究的新趋势,为集合资料同化方法的进一步发展和应用提供理论基础。
- 资料同化 /
- 集合卡尔曼滤波器 /
- 粒子滤波器 /
- 非高斯噪声 /
- 贝叶斯滤波
Abstract: In the numerical simulation of the ocean dynamic system,data assimilation is able to use the limited observation data and numerical model to best estimate the ocean state,and effectively reduce the uncertainty from the initial conditions. Therefore,data assimilation plays an important role in the study of modern physical oceanography. The ensemble Kalman filter (EnKF) is an effective data assimilation method,which has attracted broad attention in oceanic data assimilation since it is proposed about twenty years ago. In recent years,the particle filter (PF) has become a hot research field,for it is not restricted by the linear and Gaussian assumption of the model. This paper analyzes and summarizes the current theories about the EnKF and PF,in the framework of Bayesian filtering theory. The EnKF and PF algorithms are proposed and compared. On this basis,we further discuss the major obstacle for applying the particle filter in oceanic data assimilaiton at present. Some feasible solutions are also introduced. This paper is expected to provide theoretical basis for further development and application of the ensemble-based data assimilation method in oceanic data assimilation.
- data assimilation /
- ensemble Kalman filter /
- particle filter /
- non-Gaussian noise /
- Bayesian filter

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参考文献(74)

Yan C,Zhu J,Xie J. An ocean reanalysis system for the joining area of Asia and Indian-Pacific ocean[J]. Atmos Oceanic Sci Lett,2010,3(2):81-86.

Han G,Li W,Zhang X,et al. A regional ocean reanalysis system for coastal waters of China and adjacent seas[J]. Advances in Atmospheric Sciences,2011,28(3):682-690.

马建文,秦思娴. 数据同化算法研究现状综述[J]. 地球科学进展,2012,27(7):747-757. Ma Jianwen,Qin Sixian. Recent advances and development of data assimilation algorithms[J]. Advances in Earth Science,2012,27(7):747-757.

李宏,许建平. 资料同化技术的发展及其在海洋科学中的应用[J]. 海洋通报,2011,30(4):463-472. Li Hong,Xu Jianpin. Development of data assimilation and its application in ocean science[J]. Marine Science Bulletin,2011,30(4):463-472.

Courtier P,Andersson E,Heckley W,et al. The ECMWF implementation of three-dimensional variational assimilation (3D-Var). I:Formulation[J]. Quarterly Journal of the Royal Meteorological Society,1998,124(550):1783-1807.

Le Dimet F X,Talagrand O. Variational algorithms for analysis and assimilation of meteorological observations:theoretical aspects[J]. Tellus A,1986,38(2):97-110.

Evensen G. Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics[J]. Journal of Geophysical Research:Oceans (1978-2012),1994,99(C5):10143-10162.

Gelb A. Applied optimal estimation[M]. Boston:The MIT Press,1974.

Evensen G. The ensemble Kalman filter:Theoretical formulation and practical implementation[J]. Ocean Dynamics,2003,53(4):343-367.

Kalnay E. Atmospheric modeling,data assimilation,and predictability[M]. Cambridge:Cambridge University Press,2003.

Park S K,Xu L. Data Assimilation for Atmospheric,Oceanic and Hydrologic Applications (Vol. Ⅱ)[M]. Berlin:Springer Science & Business Media,2013.

Burgers G,Van Leeuwen P J,Evensen G. Analysis scheme in the ensemble Kalman filter[J]. Monthly Weather Review,1998,126(6):1719-1724.

刘成思,薛纪善. 关于集合Kalman滤波的理论和方法的发展[J]. 热带气象学报,2005,21(6):628-633. Liu Chengsi,Xue Jishan. The ensemble Kalman filter theory and method development[J]. Journal of Tropical Meteorology,2005,21(6):628-633.

Gillijns S,Mendoza O B,Chandrasekar J,et al. What is the ensemble Kalman filter and how well does it work?[C]//Proceedings of the American Control Conference,2006. Minneapolis,Minnesota,USA,2006.

Bengtsson T,Snyder C,Nychka D. Toward a nonlinear ensemble filter for high-dimensional systems[J]. Journal of Geophysical Research,2003,108(D24):8775.

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(5):W05012.

毕海芸,马建文. 粒子滤波算法在数据同化中的应用研究进展[J]. 遥感技术与应用,2014,29(5):701-710. Bi Haiyun,Ma Jianwen. Advances in the study of partcile filter in data assimilation[J]. Remote Sensing Technology and Application,2014,29(5):701-710.

Kalman R E. A new approach to linear filtering and prediction problems[J]. Journal of basic Engineering,1960,82(1):35-45.

Bishop C H,Etherton B J,Majumdar S J. Adaptive sampling with the ensemble transform Kalman filter. Part Ⅰ:Theoretical aspects[J]. Monthly Weather Review,2001,129(3):420-436.

Anderson J L. An ensemble adjustment Kalman filter for data assimilation[J]. Monthly Weather Review,2001,129(12):2884-2903.

Tippett M K,Anderson J L,Bishop C H,et al. Ensemble square root filters[J]. Monthly Weather Review,2003,131(7):1485-1490.

Li H,Kalnay E,Miyoshi T. Simultaneous estimation of covariance inflation and observation errors within an ensemble Kalman filter[J]. Quarterly Journal of the Royal Meteorological Society,2009,135(639):523-533.

Miyoshi T. The Gaussian approach to adaptive covariance inflation and its implementation with the local ensemble transform Kalman filter[J]. Monthly Weather Review,2011,139(5):1519-1535.

Zheng X,Wu G,Zhang S,et al. Using analysis state to construct a forecast error covariance matrix in ensemble Kalman filter assimilation[J]. Advances in Atmospheric Sciences,2013,30(5):1303-1312.

Shu Y,Zhu J,Wang D,et al. Assimilating remote sensing and in situ observations into a coastal model of northern South China Sea using ensemble Kalman filter[J]. Continental Shelf Research,2011,31(6):S24-S36.

Hunt B R,Kostelich E J,Szunyogh I. Efficient data assimilation for spatiotemporal chaos:A local ensemble transform Kalman filter[J]. Physica D:Nonlinear Phenomena,2007,230(1):112-126.

Flowerdew J. Towards a theory of optimal localisation[J]. Tellus A,2015,67,25257.

Perianez A,Reich H,Potthast R. Optimal localization for ensemble Kalman filter systems[J]. 気象集誌第2輯,2014,92(6):585-597.

Houtekamer P L,Mitchell H L,Pellerin G,et al. Atmospheric data assimilation with an ensemble Kalman filter:Results with real observations[J]. Monthly Weather Review,2005,133(3):604-620.

Buehner M, Charette C, He B, et al. Intercomparison of 4-D Var and EnKF systems for operational deterministic NWP[R]. WWRP/THORPEX Workshop on 4D-VAR and Ensemble Kalman Filter Intercomparisons. Buenos Aires, 2008.

Samuelsen A,Bertino L,Hansen C. Impact of data assimilation of physical variables on the spring bloom from TOPAZ operational runs in the North Atlantic[J]. Ocean Science,2009,5(4):635-647.

Chassignet E P,Hurlburt H E,Metzger E J,et al. U.S. GODAE:Global Ocean Prediction With the HYbrid Coordinate Ocean Model (HYCOM)[J]. Oceanography,2009,22(2):64-75.

Bocquet M,Pires C A,Wu L. Beyond gaussian statistical modeling in geophysical data assimilation[J]. Monthly Weather Review,2010,138(8):2997-3023.

Han X,Li X. An evaluation of the nonlinear/non-Gaussian filters for the sequential data assimilation[J]. Remote Sensing of Environment,2008,112(4):1434-1449.

Van Leeuwen P J. A variance-minimizing filter for large-scale applications[J]. Monthly Weather Review,2003,131(9):2071-2084.

Van Leeuwen P J. Particle filtering in geophysical systems[J]. Monthly Weather Review,2009,137(12):4089-4114.

Hammersley J M,Handscomb D C. Monte carlo methods[M]. London:Methuen Publishing,1964.

Gordon N J,Salmond D J,Smith A F. Novel approach to nonlinear/non-Gaussian Bayesian state estimation[J]. Proceedings of the IEEE,1993,140(2):107-113.

Capp O,Godsill S J,Moulines E. An overview of existing methods and recent advances in sequential Monte Carlo[J]. Proceedings of the IEEE,2007,95(5):899-924.

Douc R,Capp O. Comparison of resampling schemes for particle filtering[C]//Proceedings of the 4th International Symposium on Image and Signal Processing and Analysis,ISPA05. Zagreb,Criatia,2005:64-69.

Kotecha J H,Djuric P M. Gaussian sum particle filtering[J]. Signal Processing,IEEE Transactions on,2003,51(10):2602-2612.

Kotecha J H,Djuric P M. Gaussian particle filtering[J]. Signal Processing,IEEE Transactions on,2003,51(10):2592-2601.

Xiong X,Navon I M,Uzunoglu B. A note on the particle filter with posterior Gaussian resampling[J]. Tellus A,2006,58(4):456-460.

Nakano S,Ueno G,Higuchi T. Merging particle filter for sequential data assimilation[J]. Nonlinear Processes in Geophysics,2007,14(4):395-408.

Snyder C,Bengtsson T,Bickel P,et al. Obstacles to high-dimensional particle filtering[J]. Monthly Weather Review,2008,136(12):4629-4640.

Daum F, Huang J. Curse of dimensionality and particle filters[C]//Proceedings of the Aerospace Conference,, IEEE. Newport, 2003.

Snyder C. Particle filters,the "optimal" proposal and high-dimensional systems[C]//Proceedings of the ECMWF Seminar on Data Assimilation for Atmosphere and Ocean,2011.

Diard J, Bessiere P, Mazer E. A survey of probabilistic models using the bayesian programming methodology as a unifying framework[C]//The Second International Conference on Computational Intelligence, Robotics and Autonomous Systems. France, 2003.

李新,摆玉龙. 顺序数据同化的Bayes滤波框架[J]. 地球科学进展,2010,25(5):515-522. Li Xin,Ba Yulong. A Bayesian filter framework for sequential data assimilation[J]. Advances in Earth Science,2010,25(5):515-522.

Chen Z. Bayesian filtering:From Kalman filters to particle filters,and beyond[J]. Statistics,2003,182(1):1-69.

Houtekamer P L,Mitchell H L. A sequential ensemble Kalman filter for atmospheric data assimilation[J]. Monthly Weather Review,2001,129(1):123-137.

Tang Y,Ambandan J,Chen D. Nonlinear measurement function in the ensemble Kalman filter[J]. Advances in Atmospheric Sciences,2014,31(3):551-558.

Yang C,Min J,Tang Y. Evaluation of two modified Kalman gain algorithms for radar data assimilation in the WRF model[J]. Tellus A,2015,67,25950.

Crisan D,Doucet A. A survey of convergence results on particle filtering methods for practitioners[J]. Signal Processing,IEEE Transactions on,2002,50(3):736-746.

Le Gland F,Monbet V,Tran V-D. Large sample asymptotics for the ensemble Kalman filter[M]//Crisan D. The Oxford Handbook of Nonlinear Filtering. Oxford:Oxford University Press,2009:598-634.

Anderson J L. Ensemble Kalman filters for large geophysical applications[J]. Control Systems,IEEE,2009,29(3):66-82.

Lorenz E N. Deterministic nonperiodic flow[J]. Journal of the Atmospheric Sciences,1963,20(2):130-141.

Lorenz E N. Predictability:A problem partly solved[C]//Proceedings of the Seminar on Predictability. UK,1996.

Morzfeld M,Tu X,Atkins E,et al. A random map implementation of implicit filters[J]. Journal of Computational Physics,2012,231(4):2049-2066.

Doucet A,Godsill S,Andrieu C. On sequential Monte Carlo sampling methods for Bayesian filtering[J]. Statistics and Computing,2000,10(3):197-208.

Papadakis N,M Min E,Cuzol A,et al. Data assimilation with the weighted ensemble Kalman filter[J]. Tellus A,2010,62(5):673-697.

Beyou S,Cuzol A,Gorthi S S,et al. Weighted ensemble transform kalman filter for image assimilation[J]. Tellus A,2013,65,18803.

Nakano S Y. Hybrid algorithm of ensemble transform and importance sampling for assimilation of non-Gaussian observations[J]. Tellus A,2014,66.

Frei M,Kunsch H R. Bridging the ensemble Kalman and particle filters[J]. Biometrika,2013,100(4):781-800.

Shen Z,Tang Y. A modified ensemble Kalman particle filter for non-Gaussian systems with nonlinear measurement functions[J]. Journal of Advances in Modeling Earth Systems,2015,7(1):50-66.

Van Leeuwen P J. Nonlinear data assimilation in geosciences:an extremely efficient particle filter[J]. Quarterly Journal of the Royal Meteorological Society,2010,136(653):1991-1999.

Ades M,Van Leeuwen P J. An exploration of the equivalent weights particle filter[J]. Quarterly Journal of the Royal Meteorological Society,2013,139(672):820-840.

Ades M,Van Leeuwen P J. The equivalent-weights particle filter in a high-dimensional system[J]. Quarterly Journal of the Royal Meteorological Society,2015,141(687):484-503.

Chorin A J,Morzfeld M,Tu X. Implicit particle filters for data assimilation[J]. Communications in Applied Mathematics and Computational Science,2010,5(2):221-240.

Luo X,Hoteit I. Efficient particle filtering through residual nudging[J]. Quarterly Journal of the Royal Meteorological Society,2014,140(679):557-572.

万莉颖. 集合同化方法在太平洋海洋高度计资料同化中的应用研究[D]. 北京:中国科学院大气物理研究所,2006. Wan Liying. Ensemble methods and applications to altimetry data assimilation in the Pacific[D]. Beijing:Institute of Atmospheric Physics,Chinese Academy of Science,2006.

Deng Z, Tang Y. The retrospective prediction of ENSO from 1881 to 2000 by a hybrid coupled model:(II) Interdecadal and decadal variations in predictability[J].Climate dynamics, 2009, 32(2/3):415-428.

Haugen V E,Evensen G. Assimilation of SLA and SST data into an OGCM for the Indian Ocean[J]. Ocean Dynamics,2002,52(3):133-151.

Arulampalam M S,Maskell S,Gordon N,et al. A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking[J]. Signal Processing,IEEE Transactions on,2002,50(2):174-188.

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