海洋数值建模中伴随方法的研究
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摘要
本项研究旨在探讨数据同化方法在物理海洋学中的应用,重点对伴随方法进行了深入、细致的研究,作了以下工作:
1.伴随方法中的根本问题是如何得到代价函数关于控制变量的梯度。对于伴随法应用的有关问题提出了新的观点:(1)得到代价函数关于控制变量梯度的方法不能仅局限于差分方程的伴随。(2)反向积分伴随方程的时间可以缩短。本项研究认为前人强调差分方程的伴随而排斥微分方程的伴随是有疑问的,所作的大量数值模拟实验表明微分方程的伴随应该受到足够的重视。
2.所作的孪生数值模拟实验表明,如果只有表层和次表层的观测资料,借助于变分优化控制技术将其同化到海洋的埃克曼层流模型中,也可以将未知的风应力拖曳系数和垂向涡动粘性系数的分布同时反演出来。
3.采用伴随法,由渤海沿岸19个验潮站的潮汐调和常数来反演渤海海域的开边界条件和底摩擦系数,以实现渤海m1和M 2潮波的数值模拟。数值模拟结果正确地反映了渤海m1和M 2潮波的基本特征。
4.采用伴随方法,根据渤海海域内M 2潮汐调和常数的实测值:验潮站资料和高度计资料或者两者之一,来反演开边界处的潮汐调和常数,同时也对给定的底摩擦系数进行订正并对水深进行微调。实验结果较好地体现了渤海M 2潮波的特征。
Application of Data Assimilation in Physical Oceanography was studied in this report. Much attention was paid to the adjoint method. The main results are summarized as follows:
1. The elementary problem of adjoint method is how to obtain the gradient of cost function with respect to the control variables. Some new points were proposed in applying adjoint to problems in physical oceanography: (1) The method to obtain the gradient of cost function with respect to the control variables can’t be limited to the adjoint of model. (2) The time to integrate adjoint equations can be shortened. According to our study, it is not reasonable that one can only use the adjoint of the finite difference equation in data assimilation. The simulated numerical experiments show that the adjoint of the differential equation should attract much attention.
2. A variational optimal control technique is used to assimilate both meteorological and oceanographic (sea surface current and subsurface current) observations into an oceanic Ekman layer model. An identical twin experiment is discussed. By fitting the model results to the data, the unknown boundary condition (the wind stress drag coefficient) and the unknown vertical eddy viscosity distribution are deduced simultaneously from the data.
3. To simulate m1 and M 2 tides in the Bohai Sea, adjoint method was used to deduce the open boundary conditions and the bottom friction coefficients of the Bohai Sea by using the harmonic constants at 19 tide stations in the interior of the region. The results in the numerical simulation coincide with m1 and M 2 tides observed in the Bohai Sea. 4. Adjoint method was used to deduce M 2 tidal harmonic constants on the open boundary of the Bohai Sea by using M 2 tidal harmonic constants in the interior region: harmonic constants at 19 tidal stations and at some points on the T/P Satellite Tracks, Both of them or one of them. To improve the results of numerical simulation, both the prescribed bottom friction coefficients and the water depths were also adjusted by adjoint assimilation. The results in the experiments coincide with the observed M 2 tide in the Bohai Sea fairly well.
1.伴随方法中的根本问题是如何得到代价函数关于控制变量的梯度。对于伴随法应用的有关问题提出了新的观点:(1)得到代价函数关于控制变量梯度的方法不能仅局限于差分方程的伴随。(2)反向积分伴随方程的时间可以缩短。本项研究认为前人强调差分方程的伴随而排斥微分方程的伴随是有疑问的,所作的大量数值模拟实验表明微分方程的伴随应该受到足够的重视。
2.所作的孪生数值模拟实验表明,如果只有表层和次表层的观测资料,借助于变分优化控制技术将其同化到海洋的埃克曼层流模型中,也可以将未知的风应力拖曳系数和垂向涡动粘性系数的分布同时反演出来。
3.采用伴随法,由渤海沿岸19个验潮站的潮汐调和常数来反演渤海海域的开边界条件和底摩擦系数,以实现渤海m1和M 2潮波的数值模拟。数值模拟结果正确地反映了渤海m1和M 2潮波的基本特征。
4.采用伴随方法,根据渤海海域内M 2潮汐调和常数的实测值:验潮站资料和高度计资料或者两者之一,来反演开边界处的潮汐调和常数,同时也对给定的底摩擦系数进行订正并对水深进行微调。实验结果较好地体现了渤海M 2潮波的特征。
Application of Data Assimilation in Physical Oceanography was studied in this report. Much attention was paid to the adjoint method. The main results are summarized as follows:
1. The elementary problem of adjoint method is how to obtain the gradient of cost function with respect to the control variables. Some new points were proposed in applying adjoint to problems in physical oceanography: (1) The method to obtain the gradient of cost function with respect to the control variables can’t be limited to the adjoint of model. (2) The time to integrate adjoint equations can be shortened. According to our study, it is not reasonable that one can only use the adjoint of the finite difference equation in data assimilation. The simulated numerical experiments show that the adjoint of the differential equation should attract much attention.
2. A variational optimal control technique is used to assimilate both meteorological and oceanographic (sea surface current and subsurface current) observations into an oceanic Ekman layer model. An identical twin experiment is discussed. By fitting the model results to the data, the unknown boundary condition (the wind stress drag coefficient) and the unknown vertical eddy viscosity distribution are deduced simultaneously from the data.
3. To simulate m1 and M 2 tides in the Bohai Sea, adjoint method was used to deduce the open boundary conditions and the bottom friction coefficients of the Bohai Sea by using the harmonic constants at 19 tide stations in the interior of the region. The results in the numerical simulation coincide with m1 and M 2 tides observed in the Bohai Sea. 4. Adjoint method was used to deduce M 2 tidal harmonic constants on the open boundary of the Bohai Sea by using M 2 tidal harmonic constants in the interior region: harmonic constants at 19 tidal stations and at some points on the T/P Satellite Tracks, Both of them or one of them. To improve the results of numerical simulation, both the prescribed bottom friction coefficients and the water depths were also adjusted by adjoint assimilation. The results in the experiments coincide with the observed M 2 tide in the Bohai Sea fairly well.
引文
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[2] 万振文,乔方利,袁业立,渤、黄、东海三维潮波运动数值模拟。海洋与湖沼,1998,29(6):611-616。
[3] 方国洪,杨景飞,渤海潮波运动的一个二维数值模型。海洋与湖沼,1985,16(5):337-346。
[4] 王东哓,兰健,吴国雄,朱江,一个海洋环流模式伴随同化系统的初步试验。自然科学进展,1999,9(9):824-833。
[5] 王东哓,吴国雄,朱江,兰健,大洋风生环流观测优化的伴随分析。中国科学(D 辑),2000,30(1):97-106。
[6] 王凯,方国洪,冯士筰,渤海、黄海、东海 M 2潮汐潮流的三维数值模拟。海洋学报,1999,21(4):1-13。
[7] 叶安乐,梅丽明,渤黄东海潮波数值模拟。海洋与湖沼,1995,26(1):63-69。
[8] 朱江,曾庆存,郭冬建,刘卓,IAP 正压模式的伴随模式和二阶伴随模式的构造。中国科学(D 辑),1997,27(3):277-283。
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