Citation: | TENG Jia-jun, ZHANG Gui, HUANG Si-xun. Some Theoretical Problems on Variational Data Assimilation[J]. Applied Mathematics and Mechanics, 2007, 28(5): 581-591. |
[1] |
黄思训,韩威,伍荣生.结合反问题技巧对一维海温模式变分资料同化的理论分析及数值试验[J].中国科学D辑,2003,32(9):903-911.
|
[2] |
HUANG Si-xun,XIANG Jie,DU Hua-dong,et al.Inverse problems in atmospheric sciences and their application[J].Journal of Physics: Conference Series2005,12:45-57.
|
[3] |
黄思训,滕加俊,兰伟仁,等.利用正则化方法对三维风场的变分调整[J].力学学报,2005,37(4):399-407.
|
[4] |
Tikhonov A N,Arsenin V Y.Solutions of Ill-Posed Problems[M].Washington:Winston and Sons,1977.
|
[5] |
Wergen W.The effect of model errors in variational assimilation[J].Tellus,1992,44A:297-313.
|
[6] |
LU Chun-gu,Gerald L Browning.The impact of observational errors on objective analyses[J].Journal of the Atmospheric Sciences,1998,55(10):1791-1807. doi: 10.1175/1520-0469(1998)055<1791:TIOOEO>2.0.CO;2
|
[7] |
LU Chun-gu,Gerald L Browning.The impact of observational and model errors on the four-dimensional variational data assimilation[J].Journal of the Atmospheric Sciences,1998,55(6):995-1011. doi: 10.1175/1520-0469(1998)055<0995:TIOOAM>2.0.CO;2
|
[8] |
LU Chun-gu,Gerald L Browning. Discontinuous forcing generating rough initial conditions in 4DVAR data assimilation[J].Journal of the Atmospheric Sciences,2000,57(10):1646-1656. doi: 10.1175/1520-0469(2000)057<1646:DFGRIC>2.0.CO;2
|
[9] |
黄思训,伍荣生.大气科学中的数学物理问题[M].北京:气象出版社,2001.
|
[10] |
HUANG Si-xun,CAO Xiao-qun,DU Hua-dong,et al.Etrieval of atmospheric and oceanic parametersand the relevant numerical calculation[J].Advances in Atmospheric Sciences,2006,23(1):106-117. doi: 10.1007/s00376-006-0011-8
|
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[14] | You Yunxiang, Miao Guoping. On the Regularization Method of the First Kind Fredholm Integral Equation With a Complex Kernel and its Application[J]. Applied Mathematics and Mechanics, 1998, 19(1): 70-78. |
[15] | Liu Chuanhan. Fourth-Order Accurate Difference Method for the Singular Perturbation Problem[J]. Applied Mathematics and Mechanics, 1997, 18(10): 921-929. |
[16] | Zhao Yu-xiang, Gu Xiang-zhen, Song Xi-tai. Large Deformation Symmetrical Elasticity Problems Solved by the Variational Method[J]. Applied Mathematics and Mechanics, 1993, 14(8): 679-685. |
[17] | Ji Zhen-yi, Ye Kai-yuan. A High Convergent Precision Exact Analytic Method for Differential Equation with Variable Coefficients[J]. Applied Mathematics and Mechanics, 1993, 14(3): 189-194. |
[18] | Sun Guang-fu. Uniformly Higher Order Accurate Extrapolations to Solution of Uniformly Convergent Discretization Methods for Singularly Perturbed Problems[J]. Applied Mathematics and Mechanics, 1990, 11(3): 253-258. |
[19] | Dai Tian-min, Fu Ming-fu, Lin Zhong-xiang, Yang De-pin. Variational Methods for the Problems of Nonconservative Force Fields in the Micropolar Elastodynamics[J]. Applied Mathematics and Mechanics, 1987, 8(11): 943-952. |
[20] | Hsueh Dah-wei. A Method for Establishing Generalized Variational Principle[J]. Applied Mathematics and Mechanics, 1985, 6(6): 481-488. |