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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 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 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 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 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 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 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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