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经典四维变分同化(four dimensional variational data assimilation,简称4dvar)中认为模式是完美的, 而实际数值模式中存在的模式误差将对变分同化效果产生直接影响, 弱约束4dvar的提出为4dvar中考虑模式误差的影响提供了一种可行途径. 研究了基于模式误差控制变量的弱约束4dvar基本理论, 并在一维浅水方程组中对其同化效果及估计模式误差的有效性进行相关数值实验研究. 结果表明,在模式误差不可忽略的情况下,模式误差弱约束4dvar在整个区间 (包括同化区间和预报区间)上预报误差均比传统4dvar小, 在模式误差相对较大时改进效果更明显,具有明显优越性; 并且,模式误差弱约束4dvar能有效估计模式误差大小及分布形式.In the traditional implementations of four-dimensional variational data assimilation (4dvar for short), it is assumed that the model used is perfect. However the model error in the model can directly affect the accuracy of data assimilation. The weak constraint 4dvar is an effective way of correcting and estimating the model error in 4dvar. In this paper, an approach to weak constraint 4dvar with model error forcing control variable is studied and implemented in the one-dimensional shallow water equations. The results show that when the model error cannot be ignored, the prediction error with the weak constraint 4dvar is smaller than with the traditional 4dvar in both the assimilation window and the prediction period, and the improvement with weak constraint 4dvar is more obvious in the condition with large model error. Also, the weak constraint 4dvar approach to estimating model error captures some basic features of model error including the magnitude and the characteristic of distribution.
[1] Zhao Y L, Huang S X, Du H D, Zhong J Q 2011 Acta Phys. Sin. 60 079202 (in Chinese) [赵延来, 黄思训, 杜华栋, 仲跻芹 2011 物理学报 60 079202]
[2] Cao X Q, Huang S X, Du H D 2008 Acta Phys. Sin. 57 1984 (in Chinese) [曹小群, 黄思训, 杜华栋 2008 物理学报 57 1984]
[3] Wang S C, Zhang W M, Cao X Q 2011 Acta Phys. Sin. 60 099203 (in Chinese) [王舒畅, 张卫民, 曹小群 2011 物理学报 60 099203]
[4] Zhong J, Huang S X, Fei J F, Du H D 2011 Chinese Journal of Atmospheric Sciences 35 1169 (in Chinese) [钟剑, 黄思训, 费建芳, 杜华栋 2011 大气科学 35 1169]
[5] Wang S C 2008 Study on Weak Constrain in Four Dimension Variational Data Assimilation (Nanjing: PLA university of Science and Techonology) pp113-121 (in Chinese) [王舒畅 2008 四维变分同化中弱约束研究(南京:解放军理工大学) 第113—121页]
[6] Sasaki Y 1970 Mon. Wea. Rev. 98 875
[7] Derber J 1989 Mon. Wea. Rev. 117 2437
[8] Zupanski D 1997 Mon. Wea. Rev. 125 2274
[9] Griffith A K, Nichols N K 2001 Flow Turb. Comb. 65 469
[10] Vidard P A, Piacentini A, Le Dimet F X 2004 Tellus 56A 177
[11] Tremolet Y 2006 Q. J. R. Meteorol. Soc. 132 2483
[12] Lan W R, Zhu J, Xue M, Lei T, Gao J D 2010 Chinese J. Atmospheric Sciences 34 737 (in Chinese) [兰伟仁, 朱江, Ming Xue, 雷霆, Jidong Gao 2010 大气科学 34 737]
[13] Zhuang Z R, Xue J S, Li X L, Zhang L H 2010 Chinese Journal of Atmospheric Sciences 34 591 (in Chinese) [庄照荣, 薛纪善, 李兴良, 张利红 2010 大气科学 34 591]
[14] Tremolet Y 2007 Q. J. R. Meteorol. Soc. 133 1267
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[1] Zhao Y L, Huang S X, Du H D, Zhong J Q 2011 Acta Phys. Sin. 60 079202 (in Chinese) [赵延来, 黄思训, 杜华栋, 仲跻芹 2011 物理学报 60 079202]
[2] Cao X Q, Huang S X, Du H D 2008 Acta Phys. Sin. 57 1984 (in Chinese) [曹小群, 黄思训, 杜华栋 2008 物理学报 57 1984]
[3] Wang S C, Zhang W M, Cao X Q 2011 Acta Phys. Sin. 60 099203 (in Chinese) [王舒畅, 张卫民, 曹小群 2011 物理学报 60 099203]
[4] Zhong J, Huang S X, Fei J F, Du H D 2011 Chinese Journal of Atmospheric Sciences 35 1169 (in Chinese) [钟剑, 黄思训, 费建芳, 杜华栋 2011 大气科学 35 1169]
[5] Wang S C 2008 Study on Weak Constrain in Four Dimension Variational Data Assimilation (Nanjing: PLA university of Science and Techonology) pp113-121 (in Chinese) [王舒畅 2008 四维变分同化中弱约束研究(南京:解放军理工大学) 第113—121页]
[6] Sasaki Y 1970 Mon. Wea. Rev. 98 875
[7] Derber J 1989 Mon. Wea. Rev. 117 2437
[8] Zupanski D 1997 Mon. Wea. Rev. 125 2274
[9] Griffith A K, Nichols N K 2001 Flow Turb. Comb. 65 469
[10] Vidard P A, Piacentini A, Le Dimet F X 2004 Tellus 56A 177
[11] Tremolet Y 2006 Q. J. R. Meteorol. Soc. 132 2483
[12] Lan W R, Zhu J, Xue M, Lei T, Gao J D 2010 Chinese J. Atmospheric Sciences 34 737 (in Chinese) [兰伟仁, 朱江, Ming Xue, 雷霆, Jidong Gao 2010 大气科学 34 737]
[13] Zhuang Z R, Xue J S, Li X L, Zhang L H 2010 Chinese Journal of Atmospheric Sciences 34 591 (in Chinese) [庄照荣, 薛纪善, 李兴良, 张利红 2010 大气科学 34 591]
[14] Tremolet Y 2007 Q. J. R. Meteorol. Soc. 133 1267
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