## 留言板

 引用本文: 魏鸣, 刘国庆, 王成刚, 葛文忠, 许秦. 一类含有约束的变分问题中权重因子的最优选取[J]. 应用数学和力学, 2003, 24(8): 827-834.
WEI Ming, LIU Guo-qing, WANG Cheng-gang, GE Wen-zhong, XU Qin. Optimal Selection for the Weighted Coefficients of the Constrained Variational Problems[J]. Applied Mathematics and Mechanics, 2003, 24(8): 827-834.
 Citation: WEI Ming, LIU Guo-qing, WANG Cheng-gang, GE Wen-zhong, XU Qin. Optimal Selection for the Weighted Coefficients of the Constrained Variational Problems[J]. Applied Mathematics and Mechanics, 2003, 24(8): 827-834.

## 一类含有约束的变分问题中权重因子的最优选取

###### 作者简介:魏鸣(1957),女,天津人,博士(E-mail:b6531438@jlonline.com).
• 中图分类号: O177.92

## Optimal Selection for the Weighted Coefficients of the Constrained Variational Problems

• 摘要: 研究了一类含有线性对流约束的变分问题中权重因子的最优选取。在变分问题中,泛函权重因子选取的适当与否将影响数值计算的结果。针对目前权重因子选取的相对随意性,在对观测场和理想场合理假设的条件下,分别讨论了带有弱约束和强约束的变分问题,通过求解相应的Euler方程,运用矩阵理论和偏微分方程的差分方法,得到了在分析场与理想场之间方差最小意义下的客观权重因子。推证结果表明,若将带约束的变分问题的Euler方程离散成差分形式,且满足根据实际问题提出的合理假设以及差分方程稳定性条件,那么目标泛函中的权重因子在分析场与理想场的最小方差意义下存在最优选取。它们在理论上更客观可信,可以实现权重因子与数值模式、观测资料的整体协调以及各因子之间的相互协调。
•  [1] 丑纪范.四维同化的理论和新方法[A].见:廖洞贤,柳崇健主编.数值天气预报中的若干新技术[C].北京:气象出版社,1995,262-294. [2] 刘国庆.数值变分分析中的权重系数选取[J].南京化工大学学报,1995,17(1):74-76. [3] QIU Chong-jian,XU Qin.A simple adjoint method of wind analysis for single-doppler data[J].Journal of Atmospheric and Oceanic Technology,1992,9(5):588-598. [4] Sun J,Flicker D W,Lilly D K.Recovery of three-dimensional wind and temperature fields from single-doppler radar data[J].Journal of the Atmospheric Sciences,1991,48(6):876-890. [5] XU Qin,QIU Chong-Jian.Simple adjoint methods for single-doppler wind analysis with strong constraint of mass conservation[J].Journal of Atmospheric and Oceanic Technology,1994,11(2):289-298. [6] XU Qin,QIU Chong-jian.Adjoint-method retrievals of low-altitude wind fields from single-doppler reflectivity and radial-wind data[J].Journal of Atmospheric and Oceanic Technology,1995,12(5):1111-1119. [7] XU Qin,QIU Chong-jian,GU Hong-dao,et al.Simple adjoint retrievals of microburst winds from single-doppler radar data[J].Monthly Weather Review,1995.123(12):1822-1833. [8] Sasaki Y K.Some basic formulisms in numerical variational analysis[J].Monthly Weather Review,1970,98(6):875-883. [9] WEI Ming,DANG Ren-qing,GE Wen-zhong,et al.Retrieval single-doppler radar wind with variational assimilation method-Part Ⅰ:Objective selection of functional weighting factors[J].Advances in Atmospheric Sciences,1998,15(4):553-568.
##### 计量
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##### 出版历程
• 收稿日期:  2001-03-27
• 修回日期:  2003-05-02
• 刊出日期:  2003-08-15

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