利用伴随法优化非线性潮汐模型的开边界条件Ⅰ．伴随方程的建立及“孪生"数值试验

本研究采用基于最优控制理论的伴随法,把观测资料同化到陆架海域潮汐数值模型中去,优化开边界条件,提高数值预报的精度．潮汐模型的控制方程为考虑平流项、非线性底摩擦和侧向涡动粘性项的非线性浅水方程组;采用Lagrange乘子法建立了伴随模型．研究分两部分：第一部分即本文,建立非线性浅水方程模型的伴随方程、给出目标函数的梯度,并实现“孪生”数值试验;第二部分另文给出．     

用伴随法优化非线性潮汐模型的开边界条件Ⅰ.伴随方程的建立及“孪生”数值试验

本研究采用基于最优控制理论的伴随法,把观测资料同化到陆架海域潮汐 数值模型中去,优化开边界条件,提高数值预报的精度．潮汐模型的控制方程为考虑 平流项、非线性底摩擦和侧向涡动粘性项的非线性浅水方程组;采用Ｌａｇｒａｎｇｅ乘子 法建立了伴随模型．研究分两部分：第一部分即本文,建立非线性浅水方程模型的伴 随方程、给出目标函数的梯度,并实现“孪生”数值试验;第二部分另文给出．     

渤海开边界潮汐的伴随法反演

潮汐潮流数值模拟中的一个主要难点在于开边界条件的确定。本文采用伴随法 ,由渤海沿岸 1 9个验潮站的潮汐调和常数来反演渤海海域的开边界条件 ,以实现渤海潮波的数值模拟。计算所得调和常数与实测值之差的绝对平均值 :m1 潮波振幅差为 1 4cm ,迟角差为5 0°;M2 潮波振幅差为 2 4cm ,迟角差为 5 0°。数值模拟结果正确地反映了渤海m1 和M2 潮波的基本特征     

利用伴随法优化非线性潮汐模型的开边界条件Ⅱ.黄海、东海潮汐资料的同化试验

本研究基于最优控制理论,采用变分数据同化法,通过建立伴随模型,把观测资料同化到陆架海域潮汐数值模型中去,优化开边界条件,以便提高数值预报的精度.潮汐模型的控制方程为考虑平流项、非线性底摩擦和侧向涡动粘性项的非线性浅水方程组.在第Ⅰ部分建立伴随模型和进行“孪生”数值试验的基础上,给出利用验潮站的水位资料以及TOPEX/Poseidon卫星测高数据在黄海、东海进行变分数据同化试验的数值结果.试验表明利用上述资料对模型进行变分同化校正是可行的.     

北部湾潮汐的伴随同化数值模拟

影响潮汐和潮流模拟精度的两个主要因素是对开边界条件和底摩擦系数的选取。如果能给出优化的开边界条件和底系数摩系数,则必将提高潮汐和潮流模拟的精度。     

基于潮汐逆模型技术对渤黄海正压M_2分潮开边界条件的优化研究:Ⅱ.潮汐特征、潮汐动力学及潮余流

基于该系列文章前文建立的高分辨率数据同化模型系统,研究渤、黄海的M_2分潮的潮汐特征、潮混合、潮余流、潮能及其扩散、潮动量平衡。对同潮图结果的分析表明,渤、黄海内共存在4个无潮点,研究区域内M_2分潮振幅的最大值出现在朝鲜半岛西侧。潮流椭圆的分析结果表明,在35°N附近区域潮流椭圆的旋转方向有着比较突然的改变。朝鲜半岛西侧区域潮流的振幅较大,并且由于该区域地形复杂多变导致朝鲜半岛西侧海域存在着比较强烈的潮混合与潮耗散。对M_2分潮动量分析的结果表明,地形等因素在近海潮汐动力学过程中发挥着比较重要的作用。在渤、黄海内大部分区域,主要的动量平衡基本上介于压强梯度力、局地变化项以及科氏力之间,底应力和对流项都可以忽略不计。但是,线性模型对近海尤其是上述强耗散区内潮波活动的模拟还是存在着缺陷和不足。     

基于潮汐逆模型技术对渤黄海正压M_2分潮开边界条件的优化研究:I.模式的建立与验证

建立了一个高分辨率的数据同化模型系统,针对渤黄海潮汐模型开边界进行优化研究。潮汐调和常数提取自沿岸的潮位计或者近海的水位计观测。数据同化系统包含向前积分的正模型和潮汐逆模型,正模型是三维的、有限积分的、非线性的区域海洋模型ROMS,逆模型是三维的、线性的、有限元模型TRUXTON。数据同化系统通过反演正压潮汐边界条件优化结果,最大可能的减少各同化数据源的差异所带来的误差。研究证明,同化结果能有效的减少潮汐开边界水位强迫的误差,模型/观测误差在调整后减小超过50%。基于posterior潮汐开边界重构的M2分潮图同前人的结果一致。     

基于全和谐型浅水方程的有限体积海啸数值模型开发与应用

数值模拟作为海啸预报的主要研究方法在海啸预警中起着关键作用。本文采用Godunov格式的有限体积方法,使用MUSCL-Hancock格式,并利用HLLC Riemann近似求解器计算单元界面上的流体通量,建立了球坐标系下二阶精度的海啸数值模型。模型所基于的全和谐型浅水方程保证了数值的稳定性,而地形重构方法实现了干湿边界的精准模拟。本文模拟了2015年9月16日智利M_w8.3级地震海啸,通过与智利近岸14个测站和环太平洋20个DART浮标实测数据比较,验证了模型对实际越洋海啸模拟预报的能力。     

Estimation of boundary values in a North Atlantic circulation model using an adjoint method

A 1° × 1° resolution version of the MIT-GCM in the North Atlantic is used to test whether open-boundary conditions can be constrained by observations inside the domain using an adjoint method. In this preliminary feasibility study, the model is run during 1993 with a simplified vertical mixing physics. It is constrained by monthly SST fields, monthly climatological θ, S fields and TOPEX/POSEIDON altimetry. The adjoint model is built using automatic differentiation software. The method aims at bringing the model’s trajectory to consistency with data, by adjusting the initial θ, S fields, the time-varying atmospheric forcing fields and the time-varying open-boundary values. An originality of the work is the ‘nested approach’, which uses optimized fields from a global, coarser resolution model for the open-boundary conditions and for the prior estimates of the surface conditions adjustments. A solution is obtained after 75 iterations. This study shows that significant changes can be obtained on the open-boundary values, and that a general improvement in the circulation is achieved in the constrained solution, mainly in the Gulf Stream and equatorial regions. Changes at the open boundaries are characterized by a large temporal variability and small spatial scales. Large local adjustments are found close to the bottom and are likely unrealistic. There, the method tends to compensate for some model’s deficiencies by computing large corrections on the open-boundary values. The analysis of the cost function gradients with respect to the controls allows us to explore the local consistency between the constraints from the different data sets. This study suggests that no fundamental difficulty emerges when constraining open-boundary values. Its extension to a longer run with complete mixing physics can be envisaged.     

Optimal control of salinity boundary condition in a tidal model using a variational inverse method

A variational inverse data assimilation scheme is developed to estimate the salinity boundary conditions in a three-dimensional tidal hydrodynamic and salinity transport model. In this paper, the maximum incoming salinity value and the recovery time from the outflow salinity to the maximum incoming salinity at model open boundaries are treated as poorly known model control variables, and estimated using a variational inverse data assimilation scheme. The variational inverse model is tested in an idealized estuary using identical twin experiments, in which observed data are generated from the same model. Model tests with different initial guesses of the model control variables are conducted to evaluate the capability of the inverse model. A penalty technique is used to eliminate oscillations in the solution during the minimization process. The effects of preconditioning and penalty terms on the convergence rate are investigated. Model results demonstrate that the variational inverse model can be used to efficiently determine the optimal salinity open boundary conditions and improve the model state when there are no observed data available to specify the proper salinity open boundary conditions in a tidal model.     

Open boundary conditions for regional tidal simulations

The performance of regional tide model simulations is examined in relation to the choice of open boundary conditions. Three barotropic open boundary conditions, clamped elevation, clamped normal velocity, and Flather, give similar results when the prescribed values are exact; however, Flather is much less sensitive to errors in the prescribed values. Of particular concern, it was found that with a phase error between the two boundaries, both the clamped conditions resulted in magnitude errors in the unclamped variable (although the simulation remained stable).A modified flow relaxation scheme for the depth-varying prognostic variables is presented. This implementation allows the transmission of a range of vertical modes while retaining realistic topography at the boundary. It was found to be an excellent internal tide boundary condition in tests comparing simulations of different domain length encompassing a ridge and sloping bottom, and in a comparison to an analytical solution. Mass is conserved without any artificial volume constraint.     

东海M2分潮模拟中开边界条件的探讨

基于POM模式,采用第一类水位、流速和Flather（1976）3种开边界条件,模拟了东海的M2分潮．结果表明,在这3种开边界条件下,均能成功地模拟M2分潮的传播特征,以及在该海区内的三个半无潮点．计算结果与实测的较吻合,并且在Flather开边界条件下,模拟的振幅和迟角与实测资料的偏差分别为5．62cm和7．90°,效果最好．这也说明Flather开边界条件是潮汐模拟当中较可取的一种开边界条件．     

A static drilling riser model using free boundary conditions

A static three-dimensional analytical method for drilling risers experiencing large displacements and slip at the top joint is presented. The riser is described in cylindrical coordinates as a three-dimensional tensioned string, without bending or torsional stiffness. The vertical vessel displacement is not taken into account. The equilibrium configuration is obtained from the stationary condition of the total potential energy functional. Kinematic boundary conditions are introduced for the radial displacement only. The riser orientation at the top directly follows from the natural boundary conditions based on the variational treatment of the energy functional.     

Numerical study of tidal dynamics in the South China Sea with adjoint method

We adopt a parameterized internal tide dissipation term to the two-dimensional (2-D) shallow water equations, and develop the corresponding adjoint model to investigate tidal dynamics in the South China Sea (SCS). The harmonic constants derived from 63 tidal gauge stations and 24 TOPEX/Poseidon (T/P) satellite altimeter crossover points are assimilated into the adjoint model to minimize the deviations of the simulated results and observations by optimizing the bottom friction coefficient and the internal tide dissipation coefficient. Tidal constituents M₂, S₂, K₁ and O₁ are simulated simultaneously. The numerical results (assimilating only tidal gauge data) agree well with T/P data showing that the model results are reliable. The co-tidal charts of M₂, S₂, K₁ and O₁ are obtained, which reflect the characteristics of tides in the SCS. The tidal energy flux is analyzed based on numerical results. The strongest tidal energy flux appears in the Luzon Strait (LS) for both semi-diurnal and diurnal tidal constituents. The analysis of tidal energy dissipation indicates that the bottom friction dissipation occurs mainly in shallow water area, meanwhile the internal tide dissipation is mainly concentrated in the LS and the deep basin of the SCS. The tidal energetics in the LS is examined showing that the tidal energy input closely balances the tidal energy dissipation.     

Open boundary conditions for nonlinear channel flow

Open boundary conditions are derived for the one-dimensional nonrotating two-layer shallow-water equations. The conditions are based on characteristics of the external and internal modes. It is possible to find exact nonlinear characteristic conditions for the external mode, as well as approximate nonlinear conditions for the internal mode. These conditions can also be linearised by Taylor expansion; the approximate linear conditions are similar to those used in several previous studies. Both of the nonlinear and linearised conditions perform well, indicating that either the nonlinear or linearised conditions may potentially be extended to the more general case of multi-layer flows.     

Modified mild slope equation and open boundary conditions

A numerical model to compute wave field is developed. It is based on the Berkhoff diffraction-refraction equation, in which an energy dissipation term is added, to take into account the breaking and the bottom friction phenomena. The energy dissipation function, by breaking and by bottom friction, is introduced in the Berkhoff equation to obtain a new equation of propagation.The resolution is done with the hybrid finite element method, where lagrangians elements are used.