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．     

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“？…

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性项的非线性浅不方程组;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     

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。     

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.     

南海潮汐的伴随同化数值模拟

把利用正交潮响应方法对 2 4 8个周期超过 6年的南中国海的TOPEX/Poseidon卫星高度计资料进行潮波分析提取的沿轨分潮调和常数同化到二维非线性潮汐数值模式中去 ,优化模型中的开边界条件和底摩擦系数 ,模拟了南海m1 和M2 分潮的潮汐。所用的同化方法是伴随同化。根据计算结果给出了m1 和M2 分潮的同潮图。计算结果与 5 9个验潮站资料的比较结果是 :m1 分潮的振幅和迟角的平均绝对误差分别是 4.8cm和 8.7°;M2 分潮的振幅和迟角的平均绝对误差分别是 4.3cm和 1 1 .0°,表明计算结果与验潮站资料符合良好。研究结果表明 ,利用伴随同化方法把TOPEX/Poseidon资料同化到潮汐数值模式中去对模式进行校正是有效的     

波浪与大开孔消浪结构作用非线性数值模拟

基于二维Laplace方程和边界条件,经过Green转换得到以势函数及势函数法向导数为未知量的积分方程。结合0-1混合型边界元和分区边界元方法建立一个适用于求解波浪与大开孔消浪结构相互作用的强非线性波浪变形数值模式,同时给出开孔板上波动压力的计算方法。通过数模与物模结果对比,该数值模式具有较好的精度,可应用于开孔沉箱防波堤消浪效果的计算和研究,其处理原则对其他低反射海工结构物计算也将有适用性。     

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。     

二阶全非线性Boussinesq方程的二维数值模拟研究

在非交错网格下采用有限差分法首次对一组非线性精确至O(μ2)阶的全非线性Boussinesq方程数学模型进行了二维数值模拟分析.首先通过在方程的非线性项中引入缓坡假定,考察了其对模型数值精度的影响;其次,在模型中对二阶非线性项采用不同精度,考察了其对模型数值结果的影响.数值模拟结果表明,所建立的二阶完全非线性Boussinesq方程二维数值模型具有良好的适用性,模型非线性项中引入缓坡假定以及在二阶非线性项选用不同的精度对数值模拟结果影响不明显.     

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。     

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．     

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.     

A novel high resolution model without open boundary conditions applied to the China Seas: first investigation on tides

We developed a Global Ocean Circulation and Tide Model (GOCTM) with coarse grids in the open deep ocean degrading ‘smoothly’ into the highly resolved China Seas (CS) of refined grids to study the tides and circulation there.GOCTM is based on the framework of the Finite Volume approach for better mass conservation through improved transports across the discrete individual control volume.It also takes a full advantage of the geometric flexibility of unstructured mesh using a realistic global topography including the Arctic Ocean.The CS are given a special focus by refining the unstructured grids,but they are embedded into global domain naturally.Furthermore,GOCTM not only successfully avoids the treatment of the open boundaries,but also optimizes the trade-off between computational cost and model accuracy.Meanwhile,GOCTM is driven by the astronomical tide-generating potential and the secondary tide-generating potential directly,together with the wind stress and heat flux.GOCTM succeeds in reproducing the global eight principal tidal harmonic constants.Particularly,the simulated tidal results in the CS are improved compared to some other regional models with the discrepancy of 3.9 cm for M 2 tide.This idea of GOCTM can also be referred for other regional ocean study.     

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.     

Correcting the errors in the initial conditions and wind stress in storm surge simulation using an adjoint optimal technique

An adjoint data assimilation methodology is applied to the Princeton Ocean Model and is evaluated by obtaining “optimal” initial conditions, sea surface forcing conditions, or both for coastal storm surge modelling. By prescribing different error sources and setting the corresponding control variables, we performed several sets of identical twin experiments by assimilating model-generated water levels. The experiment results show that, when the forecasting errors are caused by the initial (or surface boundary) conditions, adjusting initial (or surface boundary) conditions accordingly can significantly improve the storm surge simulation. However, when the forecasting errors are caused by surface boundary (or initial) conditions, data assimilation targeting improving the initial (or surface boundary) conditions is ineffective. When the forecasting errors are caused by both the initial and surface boundary conditions, adjusting both the initial and surface boundary conditions leads to the best results. In practice, we do not know whether the errors are caused by initial conditions or surface boundary conditions, therefore it is better to adjust both initial and surface boundary conditions in adjoint data assimilation.     

胶州湾潮汐潮流动边界数值模拟

基于普林斯顿海洋模式,通过干湿网格判别法引入潮汐潮流的漫滩过程,考虑M₂,S₂,K₁,O₁,M₄和MS₄六个主要分潮,建立了胶州湾潮汐潮流数值模拟和预报模型,研究了该海域潮汐潮流特征,并讨论了漫滩对潮流模拟的影响。与实测资料的对比验证表明,该模式能够对胶州湾的潮汐和潮流做出较为合理的预测。给出了胶州湾潮汐、潮流、余流等分布特征,模拟的潮流场以及余流场涡旋等现象与观测符合良好;计算了潮波能通量,从能量角度探讨了潮波的传播特性;对潮位与潮流场演变规律,以及潮能通量的分析表明,胶州湾内的潮波以驻波为主。通过数值试验发现,漫滩过程的引入对胶州湾潮流速度的模拟至关重要,不考虑漫滩过程的模式会夸大或者低估潮流流速。对于滩涂面积广阔的海域来说,潮流数值模式中考虑漫滩的影响是必要的。