一种基于鲁棒集合滤波的资料同化方法
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摘要
在集合卡尔曼滤波方法中,根据预报集合的统计特性提供的预报误差协方差矩阵对资料同化起决定性作用。但协方差矩阵低估会引起资料同化滤波发散问题。通过将集合转换卡尔曼滤波方法和时间局地化的H_∞滤波方法相结合,提出一种基于鲁棒集合滤波思想的资料同化方法,放大转移矩阵的特征值,改善估计效果。主要思路是在集合滤波的框架下,按照鲁棒滤波的最小最大准则,实现同化系统性能的改进。利用非线性Lorenz-96混沌系统,考察集合时间局地化的H_∞滤波在系统参数变化时,对同化系统鲁棒性的影响。结果表明:集合时间局地化的H_∞滤波对系统参数变化具有很好的鲁棒性;与传统的滤波方法相比,鲁棒滤波方法提高了同化的效果。
The background error covariance matrix based on properties of the ensemble prediction statistics play an important role in the ensemble Kalman filter data assimilation. However,data assimilation divergence occurs from the inaccurate estimate of the covariance matrix and the limited ensembles. In this study,based on an ensemble time-local H-infinity filter which inflates the eigenvalues of the analysis error covariance matrix,a newdata assimilation filter method is proposed,referred to as the inflation transform matrix eigenvalues algorithm,in order to improve properties of the estimation. The properties of data assimilation is improved in the framework of ensemble filters according to the min-max criterion of robust filtering theory. Using the nonlinear Lorenz-96 chaos system,we investigate howthe ensemble time-local H-infinity filter methods impacts the robustness of the assimilation systems under the selected change conditions,such as initial background conditions,force parameters,and performance level coefficients. It is showthat the ensemble time-local H_∞ filter has good robustness to the change of above parameters. Compared with traditional filter methods,robust filter methods can improve the assimilation effect.
The background error covariance matrix based on properties of the ensemble prediction statistics play an important role in the ensemble Kalman filter data assimilation. However,data assimilation divergence occurs from the inaccurate estimate of the covariance matrix and the limited ensembles. In this study,based on an ensemble time-local H-infinity filter which inflates the eigenvalues of the analysis error covariance matrix,a newdata assimilation filter method is proposed,referred to as the inflation transform matrix eigenvalues algorithm,in order to improve properties of the estimation. The properties of data assimilation is improved in the framework of ensemble filters according to the min-max criterion of robust filtering theory. Using the nonlinear Lorenz-96 chaos system,we investigate howthe ensemble time-local H-infinity filter methods impacts the robustness of the assimilation systems under the selected change conditions,such as initial background conditions,force parameters,and performance level coefficients. It is showthat the ensemble time-local H_∞ filter has good robustness to the change of above parameters. Compared with traditional filter methods,robust filter methods can improve the assimilation effect.
引文
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胡春梅,陈道劲,于润玲.2010.BP神经网络和支持向量机在紫外线预报中的应用[J].高原气象,29(2):539-544.Hu Chunmei,Chen Daojin,Yu Runling.2010.Application of BP artificial neural netw ork and support vector machines to ultraviolet radiation prediction[J].Plateau M eteor,29(2):539-544.
李虎超,邵爱梅,何邓新,等.2015.BP神经网络在估算模式非系统性预报误差中的应用[J].高原气象,34(6):1751-1757.Li Huchao,Shao Aimei,He Dengxin,et al.2015.Application of back-propagation neural netw ork in predicting non-systematic error in numerical prediction model[J].Plateau M eteor,34(6):1751-1757.DOI:10.7522/j.issn.1000-0534.2014.00120.
刘亚亚,毛节泰,刘钧,等.2010.地基微波辐射计遥感大气廓线的BP神经网络反演方法研究[J].高原气象,29(6):1514-1523.Liu Yaya,M ao Jietai,Liu Jun,et al.2010.Research of BP neural netw ork for microw ave radiometer remote sensing retrieval of temperature,relative humidity,cloud liquid w ater profiles[J].Plateau M eteor,29(6):1514-1523.
邱晓滨,邱崇践.2009.混合误差协方差用于集合平方根滤波同化的试验[J].高原气象,28(6):1399-1407.Qiu Xiaobin,Qiu Chongjian.2009.The suitability test of Ensemble square root filter w ith hybrid background error covariance[J].Plateau M eteor,28(6):1399-1407.
邵爱梅,邱晓滨,邱崇践.2011.使用混合样本的集合四维变分同化试验研究[J].高原气象,30(3):583-593.Shao Aimei,Qiu Xiaobin,Qiu Chongjian.2011.Ensemble-based four-dimensional variational assimilation using hybrid samples[J].Plateau M eteor,30(3):583-593.
Anderson J D.1999.Aircraft Performance and Design[M].Boston:WCB/M c Graw Hill,406-453.
Bishop C H,Etherton B J,M ajumdar S J.2001.Adaptive sampling w ith the ensemble transform Kalman filter.Part I:Theoretical aspects[J].M on Wea Rev,129(3):420-436.
Bocquet M,Sakov P.2012.Combining inflation-free and iterative ensemble Kalman filters for strongly nonlinear systems[J].Nonlinear Processes in Geophysics,19(3):383-399.
Evensen G.2003.The ensemble Kalman filter:Theoretical formulation and practical implementation[J].Ocean Dyn,53(4):343-367.
Jaison T A,Youmin T.2009.Sigma-Point Kalman Filter Data Assimilation M ethods for Strongly Nonlinear Systems”[J].Atmos Sci,66:261-285.
Hamill T M.2001.An overview of ensemble forecasting and data assimilation[C]//conference on w eather analysis and forecasting.18:353-357.
Hoteit I,Pham D T,Blum J.2002.A simplified reduced order Kalman filtering and application to altimetric data assimilation in Tropical Pacific[J].Journal of M arine systems,36(1):101-127.
Julier S J.2003.The spherical simplex unscented transformation[C]//American Control Conference,2003.Proceedings of the 2003.IEEE,3:2430-2434.
Lorenz E N,Emanuel K A.1998.Optimal sites for supplementary w eather observations:Simulation w ith a small model[J].J Atmos Sci,55(3):399-414.
Luo X D,Hoteit I.2013.Covariance inflation in the ensemble Kalman filter:A residual nudging perspective and some implications[J].M on Wea Rev,141(10):3360-3368.
Luo X D,Hoteit I.2014.Ensemble Kalman filtering w ith residual nudging:An extension to state estimation problems w ith nonlinear observation operators[J].M on Wea Rev,142(10):3696-3712.
Luo X D,Hoteit I.2011.Robust ensemble filtering and its relation to covariance inflation in the ensemble Kalman filter[J].M on Wea Rev,139(12):3938-3953.
M iyoshi T,Bishop C,Kalnay E,et al.2011.FY2011 annual report of data assimilation and predictability studies for improving tropical cyclone intensity forecasts[R].M aryland Univ College Park Dept of Atmospheric and Oceanic Science.
Petersen G N,M ajumdar S J,Thorpe A J.2007.The properties of sensitive area predictions based on the ensemble transform Kalman filter(ETKF)[J].Quart J Roy M eteor Soc,133(624):697-710.
Qiu C,Shao A,Xu Q,et al.2007.Fitting model fields to observations by using singular value decomposition:An ensemble-based 4DVar approach[J].Geophys Res Atmos,112(D11):236-242.
Sakov P,Bertino L.2011.Relation betw een tw o common localisation methods for the En KF[J].Computational Geosciences,15(2):225-237.
Simon D.2006.Optimal state estimation:Kalman,H infinity,and nonlinear approaches[M].John Wiley&Sons.
Triantafyllou G,Hoteit I,Luo X,et al.2013.Assessing a robust ensemble-based Kalman filter for efficient ecosystem data assimilation of the Cretan Sea[J].Journal of M arine Systems,125:90-100.
Wang D,Cai X.2008.Robust data assimilation in hydrological modeling-A comparison of Kalman and H-infinity filters[J].Adv WaterResour,31(3):455-472.
Wang X,Bishop C H,Julier S J.2004.Which is better,an ensemble of positive-negative pairs or a centered spherical simplex ensemble?[J].Mon Wea Rev,132(7):1590.
Whitaker J S,Hamill T M.2002.Ensemble data assimilation w ithout perturbed observations[J].M on Wea Rev,130(7):1913-1924.
胡春梅,陈道劲,于润玲.2010.BP神经网络和支持向量机在紫外线预报中的应用[J].高原气象,29(2):539-544.Hu Chunmei,Chen Daojin,Yu Runling.2010.Application of BP artificial neural netw ork and support vector machines to ultraviolet radiation prediction[J].Plateau M eteor,29(2):539-544.
李虎超,邵爱梅,何邓新,等.2015.BP神经网络在估算模式非系统性预报误差中的应用[J].高原气象,34(6):1751-1757.Li Huchao,Shao Aimei,He Dengxin,et al.2015.Application of back-propagation neural netw ork in predicting non-systematic error in numerical prediction model[J].Plateau M eteor,34(6):1751-1757.DOI:10.7522/j.issn.1000-0534.2014.00120.
刘亚亚,毛节泰,刘钧,等.2010.地基微波辐射计遥感大气廓线的BP神经网络反演方法研究[J].高原气象,29(6):1514-1523.Liu Yaya,M ao Jietai,Liu Jun,et al.2010.Research of BP neural netw ork for microw ave radiometer remote sensing retrieval of temperature,relative humidity,cloud liquid w ater profiles[J].Plateau M eteor,29(6):1514-1523.
邱晓滨,邱崇践.2009.混合误差协方差用于集合平方根滤波同化的试验[J].高原气象,28(6):1399-1407.Qiu Xiaobin,Qiu Chongjian.2009.The suitability test of Ensemble square root filter w ith hybrid background error covariance[J].Plateau M eteor,28(6):1399-1407.
邵爱梅,邱晓滨,邱崇践.2011.使用混合样本的集合四维变分同化试验研究[J].高原气象,30(3):583-593.Shao Aimei,Qiu Xiaobin,Qiu Chongjian.2011.Ensemble-based four-dimensional variational assimilation using hybrid samples[J].Plateau M eteor,30(3):583-593.