A spectral barotropic model of the wind-driven world ocean

A global spectral barotropic ocean model is introduced to describe the depth-averaged flow. The equations are based on vorticity and divergence (instead of horizontal momentum); continents exert a nearly infinite drag on the fluid. The coding follows that of spectral atmospheric general circulation models using triangular truncation and implicit time integration to provide a first step for seamless coupling to spectral atmospheric global circulation models and an efficient method for filtering of ocean wave dynamics. Five experiments demonstrate the model performance: (i) Bounded by an idealized basin geometry and driven by a zonally uniform wind stress, the ocean circulation shows close similarity with Munk’s analytical solution. (ii) With a real land–sea mask the model is capable of reproducing the spin-up, location and magnitudes of depth-averaged barotropic ocean currents. (iii) The ocean wave-dynamics of equatorial waves, excited by a height perturbation at the equator, shows wave dispersion and reflection at eastern and western coastal boundaries. (iv) The model reproduces propagation times of observed surface gravity waves in the Pacific with real bathymetry. (v) Advection of tracers can be simulated reasonably by the spectral method or a semi-Langrangian transport scheme. This spectral barotropic model may serve as a first step towards an intermediate complexity spectral atmosphere–ocean model for studying atmosphere–ocean interactions in idealized setups and long term climate variability beyond millennia.     

A spectral barotropic model of the wind-driven world ocean

A global spectral barotropic ocean model is introduced to describe the depth-averaged flow. The equations are based on vorticity and divergence (instead of horizontal momentum); continents exert a nearly infinite drag on the fluid. The coding follows that of spectral atmospheric general circulation models using triangular truncation and implicit time integration to provide a first step for seamless coupling to spectral atmospheric global circulation models and an efficient method for filtering of ocean wave dynamics. Five experiments demonstrate the model performance: (i) Bounded by an idealized basin geometry and driven by a zonally uniform wind stress, the ocean circulation shows close similarity with Munk’s analytical solution. (ii) With a real land–sea mask the model is capable of reproducing the spin-up, location and magnitudes of depth-averaged barotropic ocean currents. (iii) The ocean wave-dynamics of equatorial waves, excited by a height perturbation at the equator, shows wave dispersion and reflection at eastern and western coastal boundaries. (iv) The model reproduces propagation times of observed surface gravity waves in the Pacific with real bathymetry. (v) Advection of tracers can be simulated reasonably by the spectral method or a semi-Langrangian transport scheme. This spectral barotropic model may serve as a first step towards an intermediate complexity spectral atmosphere–ocean model for studying atmosphere–ocean interactions in idealized setups and long term climate variability beyond millennia.     

Implementation of variable time stepping in an ocean general circulation model

Ocean general circulation models (OGCMs) which represent the governing equations on a finite difference grid require shorter time steps with increasing resolution. Thus, until now, in the absence of filtering, the time step length has been determined by the smallest grid spacing within the model domain. Here we present a method for reducing the time step length (and increasing the number of time steps taken) at selected points in the grid, so as to minimise the computational cost of integrating the OGCM, whilst achieving numerical stability throughout the model domain without filtering. This variable time stepping method can be used to overcome numerical constraints associated with the convergence of longitude–latitude grids at the poles, and also to allow efficient integration of model domains with variable resolution. Examples of the computational saving are given.     

A coastal ocean model of semi-implicit finite volume unstructured grid

A two-dimensional coastal ocean model based on unstructured C-grid is built, in which the momentum equation is discretized on the faces of each cell, and the continuity equation is discretized on the cell. The model is discretized by semi-implicit finite volume method, in that the free surface is semi-implicit and the bottom friction is implicit, thereby removing stability limitations associated with the surface gravity wave and friction. The remaining terms in the momentum equations are discretized explicitly by integral finite volume method and second-order Adams-Bashforth method. Tidal flow in the polar quadrant with known analytic solution is employed to test the proposed model. Finally, the performance of the present model to simulate tidal flow in a geometrically complex domain is examined by simulation of tidal currents in the Pearl River Estuary.     

An unstructured-grid, finite-volume, nonhydrostatic, parallel coastal ocean simulator

A finite-volume formulation is presented that solves the three-dimensional, nonhydrostatic Navier–Stokes equations with the Boussinesq approximation on an unstructured, staggered, z-level grid, with the goal of simulating nonhydrostatic processes in the coastal ocean with grid resolutions of tens of meters. In particular, the code has been developed to simulate the nonlinear, nonhydrostatic internal wave field in the littoral ocean. The method is based on the formulation developed by Casulli, in that the free-surface and vertical diffusion are semi-implicit, thereby removing stability limitations associated with the surface gravity wave and vertical diffusion terms. The remaining terms in the momentum equations are discretized explicitly with the second-order Adams–Bashforth method, while the pressure-correction method is employed for the nonhydrostatic pressure in order to achieve overall second-order temporal accuracy. Advection of momentum is accomplished with an Eulerian discretization which conserves momentum in cells that do not contain the free surface, and scalar advection is discretized in a way that ensures consistency with continuity, thereby ensuring local and global mass conservation using a velocity field that conserves volume on a local and global basis. The nonhydrostatic pressure field is solved efficiently using a block-Jacobi preconditioner, and while stability is limited by the internal gravity wave speed and vertical advection of momentum, applications requiring relatively small time steps due to accuracy or stability constraints are run efficiently on parallel computers, since the present formulation is written entirely with the message-passing interface (MPI). The ParMETIS libraries are employed in order to achieve a load-balanced parallel partitioning that minimizes interprocessor communication, and the grid is reordered to optimize per-processor performance by limiting cache misses while accessing arrays in memory. Test cases demonstrate the ability of the code to efficiently and accurately compute the nonhydrostatic lock exchange and internal waves in idealized as well as real domains, and we evaluate the parallel efficiency of the code using up to 32 processors.     

A reduced grid for a parallel global ocean general circulation model

A limitation of many global climate models with explicit finite-difference numerics is the timestep restriction caused by the decrease in cell size associated with the convergence of meridians near the poles. To keep the longitudinal width of model cells as uniform as possible, we apply a “reduced” grid to a three-dimensional primitive equation ocean-climate model. With this grid the number of cells in the longitudinal direction is reduced at high latitudes. The grid consists of subgrids which interact at interfaces along their northern and southern boundaries, where the resolution changes by a factor of three. We extend the finite-difference techniques to these interfaces, focusing on the conservation required to perform long time integrations, while preserving the staggered spatial arrangement of variables and the numerics used on subgrids. The common alternative used to reduce the timestep restriction caused by the spherical grid is the filtering of high-frequency modes from the high-latitude solution. The reduced grid allows an increased timestep while eliminating the need for filtering and reduces execution time per model step by roughly 20%. We implement the reduced grid model for parallel computer architectures with two-dimensional domain decomposition and message passing, with speedup results similar to those of the original model. We present results of model runs showing small effects on the solution and sizable improvements to the execution time.     

Efficient identification of ocean thermodynamics in a physical/biogeochemical ocean model with an iterative Importance Sampling method

Efficient identification of parameters in numerical models remains a computationally demanding problem. Here we present an iterative Importance Sampling approach and demonstrate its application to estimating parameters that control the heat uptake efficiency of a physical/biogeochemical ocean model coupled to a simple atmosphere. The algorithm has similarities to a previously-developed ensemble Kalman filtering (EnKF) method applied to similar problems, but is more flexible and powerful in the case of nonlinear models and non-Gaussian uncertainties. The method is somewhat more computationally demanding than the EnKF but may be preferred in cases where the approximations that the EnKF relies upon are unsound. Our results suggest that the three-dimensional structure of ocean tracer fields may act as a useful constraint on ocean mixing and consequently the heat uptake of the climate system under anthropogenic forcing.     

基于观测的南海西沙海域深层近惯性振荡特征分析

近惯性内波运动普遍存在于全球大洋中,影响大洋中的质量、动量和能量输送,是大气强迫与海洋混合之间的重要纽带。由于目前海洋深层观测资料的缺乏,对于深层近惯性内波生消演变特征研究甚少。利用2009-2012年的潜标观测资料,采用带通滤波和谱分析方法研究了南海西沙海域深层近惯性内波生成、传播和消亡等演变特征。通过研究发现,南海西沙海域深层存在较强的近惯性振荡,其生成源为台风过境能量输入,绝大部分时段内,近惯性振荡能量在海洋浅层耗散,不向海洋深层传播;仅在少部分时段内,近惯性振荡能量的80%～85%耗散在500 m以浅区域,有大概15%～20%继续向海洋深层传播。     

The mixing mechanism in the formation of ocean shear waves

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A three-dimensional semi-implicit unstructured grid finite volume ocean model

A new three-dimensional semi-implicit finite-volume ocean model has been developed for simulating the coastal ocean circulation, which is based on the staggered C -unstructured non-orthogonal grid in the horizontal direction and z -level grid in the vertical direction. The three-dimensional model is discretized by the semi-implicit finite-volume method, in that the free-surface and the vertical diffusion are semi-implicit, thereby removing stability limitations associated with the surface gravity wave and vertical diffusion terms. The remaining terms in the momentum equations are discretized explicitly by an integral method. The partial cell method is used for resolving topography, which enables the model to better represent irregular topography. The model has been tested against analytical cases for wind and tidal oscillation circulation, and is applied to simulating the tidal flow in the Bohai Sea. The results are in good agreement both with the analytical solutions and measurement results.     

海洋对热带气旋风应力响应的准平衡解析解

为考察海洋上层各物理量对热带气旋风应力的响应问题,本文利用海洋线性化约化重力方程组开展了解析研究,所得主要结论如下:求解该问题使用跟随热带气旋中心移动的极坐标较为方便,当热带气旋风应力在热带气旋云墙内即热带气旋眼中为静止,在云墙处及之外随该极坐标半径增加而成反比衰减时,可求得该问题在此极坐标系中的定常解析解,该解强度与风应力成正比;解的流场在热带气旋云墙内为静止,在云墙处及之外呈现有向外流出的气旋式涡旋形态,且随极坐标半径增加而衰减。在云墙之外离云墙较近处,解的切向流速大于径向流速,在更远处则反之。解的径向流与热带气旋切向风应力平衡,切向流是梯度流,流动呈水平无辐散状态。在热带气旋眼中以及云墙处,海洋上层的厚度不变,且达到最小值。从云墙向外则厚度值逐渐增加。厚度值的变化反映了密度跃层的变化,在厚度值最小处附近,跃层位置有明显抬升,这会造成跃层附近海水涌升,从而海洋上层的响应涡旋是冷性的。略去海洋上层对热带气旋移动的响应,将此移动极坐标系中的解返回到固定坐标系后,则解的空间分布形态不变,但由定常解转变为非定常解,且随热带气旋一起移动;此解最重要的物理性质是其具有准平衡性,这与非平衡的近惯性振荡与重力惯性内波有本质区别。     

A better,more discriminating test problem for ocean tracer transport

Many test problems have been posed in which the behavior of schemes may be examined within the simplified context of passive tracer transport. Most often these tests involve transport of a tracer containing sharp or discontinuous gradients within a smooth advecting field. Hecht et al. [J. Geophys. Res. 100 (1995) 20763–20778] presented a test problem, using the simple analytical gyre of Stommel [Trans. Am. Geophys. Union 29 (1948) 202–206], in which an initially smooth tracer field is transported through a highly sheared circulation, representing another scenario of relevance to ocean modeling. We present a modification of that test in which the underlying grid is rotated relative to the gyre, such that the western boundary falls at 45° to the principal grid axes. The advection schemes used by most ocean modelers to date are examined within this test problem. We find, in two cases, that methods which performed acceptably under the original formulation of the problem, and which have seen extensive application to geophysical fluid dynamics, fail to perform acceptably within the reformulated problem. The important qualities of this more discriminating test include the skewing of the fast boundary current flow relative to the underlying grid axes and the high shear in that boundary current.     

Application of a vanishing, quasi-sigma, vertical coordinate for simulation of high-speed, deep currents over the Sigsbee Escarpment in the Gulf of Mexico

Recent observations over the Sigsbee Escarpment in the Gulf of Mexico have revealed extremely energetic deep currents (near 1 m s⁻¹), which are trapped along the escarpment. Both scientific interest and engineering needs demand dynamical understanding of these extreme events, and can benefit from a numerical model designed to complement observational and theoretical investigations in this region of complicated topography. The primary objective of this study is to develop a modeling methodology capable of simulating these physical processes and apply the model to the Sigsbee Escarpment region. The very steep slope of the Sigsbee Escarpment (0.05–0.1) limits the application of ocean models with traditional terrain-following (sigma) vertical coordinates, which may represent the very complicated topography in the region adequately, can result in large truncation errors during calculation of the horizontal pressure gradient. A new vertical coordinate system, termed a vanishing quasi-sigma coordinate, is implemented in the Navy Coastal Ocean Model for application to the Sigsbee Escarpment region. Vertical coordinate surfaces for this grid have noticeably gentler slopes than a traditional sigma grid, while still following the terrain near the ocean bottom. The new vertical grid is tested with a suite of numerical experiments and compared to a classical sigma-layer model. The numerical error is substantially reduced in the model with the new vertical grid. A one-year, realistic, numerical simulation is performed to simulate strong, deep currents over the Escarpment using a very-high-resolution nested modeling approach. The model results are analyzed to demonstrate that the deep-ocean currents in the simulation replicate the prominent dynamical features of the observed intense currents in the region.     

热带气旋下海浪对大气向海洋输入的动量和能量的影响

海浪不仅决定着海洋表面的粗糙度,由热带气旋引起的海浪,还通过其发展演化控制着大部分的海气之间的动量和能量传递。本文采用热带气旋观测数据IBTrACS和海浪模式WW III的模拟结果探究了热带气旋下海浪对大气向海洋输入的动量和能量的影响。结果发现,近30 a热带气旋的强度约每10 a增加 1 m/s,但移速没有明显变化。热带气旋的强度越大,从大气输入到海浪和从海浪输入到海流中的动量之差和能量之差也越大。由于热带气旋的风场和海浪场都有较强的不对称性,海气动量差和能量差也表现出非均匀分布:动量差较大的区域在热带气旋移动方向的后方,能量差的最大值则分布在右后象限,且二者均为左前方比较小。逆波龄与动量差和能量差呈高度正相关,相关系数约为0.95,说明波越年轻吸收的动量和能量越多。气旋移速越快逆波龄越大,且热带气旋移动速度与动量差和能量差呈正相关,相关系数在0.8以上。因此,海浪影响着大气向海洋输入的动量和能量的分布和大小,在以后关于海洋边界动力学和热力学的研究中,考虑海浪的演化可能会使结果更加准确。     

适用于并网型海洋能发电装置的防孤岛检测方法研究及系统设计

针对海洋能发电装置的研究现状和未来发展,预计并网型海洋能发电装置会成为重要发展方向,主要是在用户侧并网。发电装置与本地负载会产生孤岛效应,对电网和发电装置的安全性和稳定性产生严重影响。因此,并网前对海洋能发电装置进行防孤岛能力的检测成为必然环节。文中设计了一种适用于并网型海洋能发电装置的防孤岛检测系统,介绍了系统的功能与结构,参考分布式发电装置接入电网的相关标准,探讨了适合并网型海洋能发电装置的防孤岛检测方法,为检测工作的开展打下基础。     

Oceanic tidal angular momentum and Earth's rotation variations

Luni-solar tides affect Earth's rotation in a variety of ways. We give an overview of the physics and focus on the excitation of Earth rotational variations by ocean tides under the conservation of angular momentum. Various models for diurnal and semidiurnal tidal height and tidal current fields have been derived, following a legacy of a number of theoretical tide models, from the Topex/Poseidon (T/P) ocean altimetry data. We review the oceanic tidal angular momenta (OTAM) predicted by these T/P models for the eight major tides (Q₁, O₁, P₁, K₁, N₂, M₂, S₂, K₂), and their excitations on both Earth's rotational speed variation (in terms of length-of-day or UT1) and polar motion (prograde diurnal/semidiurnal components and retrograde semidiurnal components). These small, high-frequency effects have been unambiguously observed in recent years by precise Earth rotation measurements via space geodetic techniques. Here we review the comparison of the very-long-baseline-interferometry (VLBI) data with the T/P OTAM predictions. The agreement is good with discrepancies typically within 1 – 2 microseconds for UT1 and 10 – 30 microarcseconds for polar motion. The eight tides collectively explain the majority of subdaily Earth rotation variance during the intensive VLBI campaign Cont94. This establishes the dominant role of OTAM in exciting the diurnal/semidiurnal polar motion and paves the way for detailed studies of short-period non-OTAM excitations, such as atmospheric and oceanic angular momentum variations, earthquakes, the atmospheric thermal tides, Earth librations, and the response of the mantle lateral inhomogeneities to tidal forcing. These studies await further improvements in tide models and Earth rotation measurements.     

Controlling spatial oscillations in bed level update schemes

A frequent problem with process-based coastal morphological models is the appearance of high wave number spatial oscillations in the simulated bed levels with time. After a sufficiently long time, these oscillations become dominant and mask the large-scale features of the bed level evolution.The equation for conservation of sediment mass is used to show that the spatial oscillations are generated by the dependence of the bed celerity (celerity of the bed level oscillations) with bed levels, which is due to the non-linear relationship between sediment transport and bed levels. This breeds higher spatial harmonics of the bed level oscillations with time. In this situation, using a Finite Difference (FD) scheme that does not damp oscillations with high wave numbers leads to the generated harmonics being kept in the solution. These generate further harmonics until the entire solution is dominated by high wave number oscillations.In this paper, a finite difference scheme, in combination with a filtering procedure, is used to dissipate high wave number oscillations. Analysis of the amplification portraits show that the filtering procedure in combination with a Lax–Wendroff scheme does not affect oscillations with lower wave numbers (larger scale features resolved with seven or more grid points). Some examples are also presented to illustrate these features.     

Energy dissipation in sloshing waves in a rolling rectangular tank—II. Solution method and analysis of numerical technique

In Part I of these series of papers, the complete problem formulation in a linearized form was presented. In order to provide the engineer with an in-depth knowledge about the exact solution of the problem, it is natural and essential to start with a linear solution. This will be the objective of Part II, together with an exposition to the analysis of numerical technique utilized.A truncated infinite Fourier series-type solution is adopted for the linearized boundary value problem. It is shown that such a solution is mathematically consistent and represents the phenomenon properly by satisfying all of the field equations and the imposed boundary conditions. The dependence of the Fourier coefficients on the truncation limit has been investigated. The best lower and upper “cutoff limits” for the truncation of an infinite series are determined. An error analysis of the solution technique is performed.     

抗差Vondrak滤波方法在内孤立波提取中的应用研究

声学多普勒流速剖面仪(ADCP)是对海洋内波监测的有效手段,但受到仪器本身和复杂的海洋环境噪声等影响,走航式ADCP记录的海流数据存在大量噪声,且混有流速异常值。为了进一步提高海洋内孤立波的提取精度与准确性,本文针对走航式ADCP海流数据特点引入IGG3方法的权函数因子,设计了一种抗差Vondrak滤波器,并与快速傅里叶变换、小波分析和滑动平均3种传统滤波方法进行对比,以验证抗差Vondrak滤波方法的有效性与优越性。研究结果表明,抗差Vondrak滤波方法不仅可以有效地滤除流速噪声,还可以自适应剔除海流观测数据中的异常值,由其提取出的内孤立波准确且各层水平流速清晰。因此,与传统滤波方法相比,抗差Vondrak滤波方法在内孤立波提取方面具有一定的优越性。     

Adaptive estimation of wave parameters by Geno-Kalman filtering

Prediction of wave parameters is very important for planning, designing and operation of ocean structures. Accurate estimation of these parameters provides engineers to construct more economical and reliable ocean structures such as harbors, breakwaters, oil production platforms and ocean wave energy converters. For this reason, optimum operation of these plants has become a must. Various methods have been introduced to determine the relation among wind speed previous and current wave parameters. Method proposed in this paper consists of genetic algorithms and Kalman filters which is called as Geno-Kalman filtering. It is based on adaptive calculation to reach the solution. Also a comparison has been made between perceptron Kalman filtering and Geno-Kalman filtering techniques. The application of Geno-Kalman filtering was performed for station 46002 which located in the Coos Bay at Oregon, USA. It is observed that the Geno-Kalman filtering methodology has smaller absolute, mean-square and relative errors than perceptron Kalman filtering. Also coefficient of efficiency value which was used to evaluate results between observed and estimated is higher at Geno-Kalman filtering than perceptron Kalman filtering.