【作者】 张继才；

【导师】 吕咸青；

【作者基本信息】 中国海洋大学 ， 物理海洋， 2008， 博士

【摘要】 潮汐潮流运动是海洋中的基本运动之一,它是动力海洋学研究的重要组成部分,对它的研究直接影响着波浪、风暴潮、环流、水团等其他海洋现象的研究,在大陆架浅海海洋中,对潮汐潮流的研究更具重要性.伴随同化方法是建立在严格的数学基础之上的一种有效的四维变分同化技术,它将变分原理与最优控制理论相结合,以海洋动力模型作为约束条件,通过同化可观测到的海洋要素优化控制变量,达到反演无法观测到的海洋要素的目的.潮汐潮流数值模拟中最大的难点莫过于开边界条件和底摩擦系数的确定,在数学物理反问题的框架下,伴随同化方法可以把开边界条件和底摩擦系数的确定变成依赖于区域内部观测资料的数值迭代过程,实现了调试控制参数的自动化和最优化.本文对伴随同化方法在潮汐潮流数值模拟中的应用进行了深入研究.本文建立了一个球坐标系下的二维非线性潮波伴随同化模型,并基于渤、黄、东海M2分潮的数值模拟,对空间分布底摩擦系数处理方法进行了伴随法反演研究.孪生实验结果表明,空间分布底摩擦系数与伴随同化方法相结合,可以成功反演出给定的空间结构非常复杂的底摩擦系数分布,这是传统的处理方法所不能做到的.底摩擦效应由海底地形决定,本文尝试了根据海底地形的空间分布特征选取独立底摩擦系数的做法;数值实验结果表明,与均匀选取相比,根据底地形的空间分布特征选取独立参数,能在减少独立变量个数的情况下提高模拟精度.通过同化T/P高度计资料,本文数值模拟了渤、黄、东海的M2潮波;实验结果表明,与传统的底摩擦系数处理方法相比,空间分布的底摩擦系数能有效提高模拟精度,实验结果准确体现了渤、黄、东海M2潮波的分布特征.使用上述二维非线性潮波伴随同化模型,考虑分潮间的非线性相互作用,本文通过同化T/P高度计资料,优化模式开边界条件及空间分布的底摩擦系数,数值模拟了渤、黄、东海的M2、S2、K1、O1四个主要分潮,模拟结果与验潮站资料(独立资料)之间的绝均差分别为(5 .7cm ,5.2)、(3 .2cm ,6.9)、( 2.6cm ,6.3)和( 2.1cm ,8.5).实验所得同潮图准确体现了渤、黄、东海四个主要分潮的潮位分布特征,半日分潮共有三个无潮点和一个退化型无潮点,全日分潮有三个无潮点,分别位于渤海海峡、南黄海和对马海峡.基于内外模态分离技术,本文建立了一个三维正压非线性潮汐潮流模型,外模态采用ADI方法离散,时间步长不受CFL条件的限制;内模态的时间步长则可以远大于外模态时间步长,从而显著提高计算效率.将上述模型作为正向模型,本文建立了其伴随模型.此三维伴随模式建立之后,运算过程中开边界条件、底摩擦系数和垂向涡动粘性系数等控制参数的选取、数值模式和观测结果的有机结合等问题就可迎刃而解.与前人的有关三维潮汐潮流伴随同化模型的工作不同,本模式将底应力项设置为底层流速的函数,从而在物理上更加合理.在数学物理反问题的框架下,本文设计孪生实验研究了三维正压潮汐潮流模型中开边界条件、空间分布底摩擦系数和垂向混合涡动粘性系数的伴随法反演问题,以验证伴随模型的有效性和正确性.同时,本文分别讨论了参数的不同类型分布、参数初值、观测误差以及观测数量对参数估计反问题的影响,对反问题适定性进行了初步研究.更多还原

【Abstract】 The research on the tide and tidal current, which has close relation to those of the wind wave, ocean circulation, storm surge and other ocean phenomenon, is very important for the understanding of the dynamics of the ocean, especially in the continental marginal seas. Among all the data assimilation methods, four-dimensional variational (4DVAR) data assimilation is one of the most effective and powerful approaches. It is an advanced data assimilation method which involves the adjoint method and has the advantage of directly assimilating various observations distributed in time and space into numerical models while maintaining dynamical and physical consistency with the model. The major difficulties faced by numerical models of tidal flow concern the treatment of open boundary conditions (OBC) and bottom friction coefficients (BFC). By assimilating the data in the interior region, the adjoint method can optimize the OBC and BFC automatically and reach a global optimization of the model parameters. This paper researches the application of adjoint assimilation method in the numerical simulation of tides and tidal currents in-depth.This paper develops a two-dimensional (2-D) adjoint tidal model and studies the spatially varying BFC based on the numerical simulation of M2 tide in the Bohai, Yellow and East China Seas (BYECS). In the twin experiments the prescribed BFC distributions that the spatial structure is very complex are inverted successfully with the combination of spatially varying BFC and the adjoint method. Obviously the inversion would not succeed if the traditional ways about BFC were used. The bottom friction effect is decided by the ocean bottom topography. This study establishes a method of selecting the independent BFC according to the spatial characteristics of ocean topography. The numerical results show that the method can increase the simulation precision even if a small number of independent parameters are employed. The M2 tide in BYECS is simulated by assimilating the TOPEX/Poseidon (T/P) altimeter data. The results also prove that the spatially varying BFC is more powerful than the traditional ways in obtaining reasonable simulation results. The co-tidal charts obtained coincide with the observed M2 tide in BYECS fairly well.By assimilating the T/P data, the 2-D tidal model above is employed to optimize the OBC and BFC for the simulation of M2, S2, K1 and O1 constituents in BYECS, and the average absolute differences of amplitudes and phase-lags between simulation results and observations of 152 tidal gauge stations (independent data) are (5 .7cm ,5.2), (3 .2cm ,6.9), ( 2.6cm ,6.3) and ( 2.1cm ,8.5), respectively. The co-tidal charts obtained show that both the M2 and S2 constituents have three amphidromic points: one in the Bohai Sea and two in the Yellow Sea. Near the Yellow River mouth the amphidromes appear as degenerated systems. There are three amphidromic points for both the K1 and O1 constituents located in the Bohai Strait, in the Southern Yellow Sea and in the Tsushima Strait, respectively.In this study a numerical tidal model based on the discretization of three-dimensional (3-D) primitive equations is established to simulate the barotropic tides and tidal currents in the Bohai Sea and the North Yellow Sea (BNYS). The numerical schemes for solving the equations of motion and continuity use the internal-external mode splitting technique. The ADI method is employed for the external mode computations which give the surface elevations and depth-averaged currents. The time step of external mode is thus not restricted by the CFL condition. A semi-implicit scheme is used for the internal mode computations which give the vertical structure of the currents. The time step of internal mode can be significantly longer than that of the external mode. As a consequence, the overall computational speed can be several times faster than that of the general explicit models. For the bottom friction effect, turbulent boundary layer models of the near-bottom flow indicate that it is physically realistic to use a quadratic dependence of bottom friction on the bottom velocity. In our model the bottom friction is expressed in terms of bottom velocity, which is different from the previous works on 3-D adjoint tidal models. Based on the simulation of M2 tide and tidal current in BNYS, this study carries out twin experiments to invert the prescribed distributions of model parameters. The parameters inverted are the Fourier coefficients of OBC, the BFC and the vertical eddy viscosity profiles. In these twin experiments, the real topography of BNYS is installed. The inversion has obtained satisfying results and the prescribed distributions have been successfully inverted, which demonstrates the strong ability of the adjoint model. In order to research the ill-posedness of parameter estimation inverse problems, the experiments also discuss the influences of parameter distributions, initial guesses, model errors and data number on the inversion. The results indicate the inversion of BFC is more sensitive to data error than that of OBC and vertical eddy viscosity profiles.更多还原