Non-hydrostatic pressure in σ-coordinate ocean models

Numerical ocean modelling is computationally very demanding. Traditionally, the hydrostatic approximation has been applied to reduce the computational burden. This approximation is valid in large scale studies with coarse grid resolution. With faster computers and gradually smaller grid sizes, we may expect that more studies will be performed with non-hydrostatic ocean models. In recent papers several methods for including non-hydrostatic pressure in σ-coordinate models have been suggested. In this paper the sensitivity of the non-hydrostatic pressure field, the velocity fields, and the density fields to changes in the method for computing non-hydrostatic pressure in σ-coordinate ocean models is addressed.The first test case used involves the propagation and breaking of an internal wave at an incline in a tank. The other test case concerns tidally driven flow over a sill in a stratified fjord. The results from our numerical exercises suggest that the velocity and density fields are very robust to the model choices investigated here. The differences between the model results are of the same order as the uncertainty due to the internal pressure gradient error, and they are smaller than an estimate of the uncertainty due to subgrid scale closure.     

海洋资料同化对气候季节-年际预测技巧及初始场的影响试验

集合卡尔曼滤波(Ensemble Kalman filter, EnKF)是一种国内外广泛使用的海洋资料同化方案, 用集合成员的状态集合表征模式的背景误差协方差, 结合观测误差协方差, 计算卡尔曼增益矩阵, 有效地将观测信息添加到模式初始场中。由于季节、年际预测很大程度上受到初始场的影响, 因此资料同化可以提高模式的预测性能。本文在NUIST-CFS1.0预测系统逐日SST nudging的初始化方案上, 利用EnKF在每个月末将全场(full field)海表温度(sea surface temperature, SST)、温盐廓线(in-situ temperature and salinity profiles, T-S profiles)以及卫星观测海平面高度异常(sea level anomalies, SLA)观测资料同化到模式初始场中, 对比分析了无海洋资料同化以及加入同化后初始场的区别、加入海洋资料同化后模式提前1~24个月预测性能的差异以及对于厄尔尼诺-南方涛动(El Niño-southern oscillation, ENSO)预测技巧的影响。结果表明, 加入海洋资料同化能有效地改进初始场, 并且呈现随深度增加初始场改进越显著的特征。加入同化后, 对全球SST、次表层海水温度的平均预测技巧均有一定的提高, 也表现出随深度增加预测技巧改进越明显的特征。但加入海洋资料同化后, 模式对ENSO的预测技巧有所下降, 可能是由于模式误差的存在, 使得同化后的预测初始场从接近观测的状态又逐渐恢复到与模式动力相匹配的状态, 加剧了赤道太平洋冷舌偏西、中东部偏暖的气候平均态漂移。     

Comparison of EnOI and EnKF regional ocean reanalysis systems

This study compares two regional eddy resolving ocean reanalysis systems, based on the ensemble Kalman filter (EnKF) and ensemble optimal interpolation (EnOI), focusing on data assimilation aspects. Both systems are configured for the Tasman Sea using the same ocean model with 0.1° resolution and commonly available observations of satellite altimetry, sea surface temperature and subsurface temperature and salinity. The primary goals are to quantify the difference in performance of the EnKF and EnOI and investigate how important this difference might be from an oceanographic perspective. We find that both systems generally constrain mesoscale circulation in the region, with some exceptions for the East Australian Current separation region, the most energetic and chaotic part of the domain. Overall, the EnKF is found to consistently outperform the EnOI, producing on average 9–21% smaller innovations. The EnKF also has better forecast skill relative to the persisted analysis than the EnOI. For SST the EnKF forecast outperforms persisted analysis by about 17%, which indicates that the surface circulation is mainly constrained. The EnKF and EnOI are shown to produce qualitatively different increments of unobserved or sparsely observed variables; however, we find only moderate improvements of the EnKF over EnOI in subsurface temperature fields when compared against withheld XBT observations. We attribute this lack of a major improvement in subsurface reconstruction to the inability of the EnKF to linearly constrain the system due to initialisation shock, model error caused by open boundaries, and possibly insufficient observations.     

Evaluation of ocean model ventilation with CFC-11: comparison of 13 global ocean models

We compared the 13 models participating in the Ocean Carbon Model Intercomparison Project (OCMIP) with regards to their skill in matching observed distributions of CFC-11. This analysis characterizes the abilities of these models to ventilate the ocean on timescales relevant for anthropogenic CO₂ uptake. We found a large range in the modeled global inventory (±30%), mainly due to differences in ventilation from the high latitudes. In the Southern Ocean, models differ particularly in the longitudinal distribution of the CFC uptake in the intermediate water, whereas the latitudinal distribution is mainly controlled by the subgrid-scale parameterization. Models with isopycnal diffusion and eddy-induced velocity parameterization produce more realistic intermediate water ventilation. Deep and bottom water ventilation also varies substantially between the models. Models coupled to a sea-ice model systematically provide more realistic AABW formation source region; however these same models also largely overestimate AABW ventilation if no specific parameterization of brine rejection during sea-ice formation is included. In the North Pacific Ocean, all models exhibit a systematic large underestimation of the CFC uptake in the thermocline of the subtropical gyre, while no systematic difference toward the observations is found in the subpolar gyre. In the North Atlantic Ocean, the CFC uptake is globally underestimated in subsurface. In the deep ocean, all but the adjoint model, failed to produce the two recently ventilated branches observed in the North Atlantic Deep Water (NADW). Furthermore, simulated transport in the Deep Western Boundary Current (DWBC) is too sluggish in all but the isopycnal model, where it is too rapid.     

An ocean model for climate variability studies

Models of the time dependent ocean circulation can be simplified considerably by filtering out all short term, small scale motions which are unimportant for climatic processes. For time scales large compared with a day and space scales large compared with the internal Rossby radius of deformation (～50 km), the currents in most of the interior ocean can be determined diagnostically as quasi-equilibrium fields, so that only the salinity and temperature fields need be treated prognostically.Regions of closed f/h contours, however, represent exceptions. Here trapped vorticity gyres exist as free flow solutions without external forcing, and in the presence of forcing the barotropic velocity field must therefore be determined prognostically through a potential vorticity equation for the gyres.Lateral boundary layers and the equatorial regions also require separate treatment. These were not considered specifically, but it is suggested that integrated (parametrical) models analogous in structure to mixed-layer models or the integrated boundary layer models of aerodynamics may be the most appropriate technique for coupling these regions to the interior ocean in a comprehensive ocean model suitable for climate studies.A coupled multi-region model of the global ocean circulation based on these scale considerations could be sufficiently cost-effective to permit systematic investigation of the role of the oceanic heat storage and transport in climate variability studies over a wide spectrum of space and time scales.The analysis of the seasonal variations of the interior ocean circulation represents a simple example in which the filtered model yields considerably simpler and more readily interpretable results than a fully three-dimensional, unfiltered model.     

热液系统输向大洋的热通量估算

从四个方面对现代海底热液活动输向大洋的热通量进行了初步估算.热液系统通过集中、高温的热液烟囱和低温、大面积漫溢热水的形式向海洋输送的热通量为357GW;由底热异常边界层计算出的热通量为32GW;根据Baker提出的扩张洋脊的扩张速率和扩张洋脊热液柱覆盖率之间的线性关系,推算的热液通量为1086GW;根据扩张洋脊岩墙冷却和扩张推算的热通量为592GW.不同的方法给出的结果有较大的差异.一方面这些结果反映了热液系统向大洋的供热水平,另一方面反映了目前对现代海底热液活动的认识水平.虽然热液系统向大洋的热输出比太阳的热辐射小,但由于其特殊的供热方式,这部分热能仍有可能对全球气候带来影响,应在今后的研究中给予重视.     

上层海洋对热带气旋的响应与反馈研究进展

对60年来有关上层海洋与热带气旋(Tropical Cyclone,TC)的响应与反馈的研究进行了回顾,通过观测手段的完善和改进模式的应用,人们的认识不断提高:TC直接激发的近惯性流最大可达1 m/s,其导致的强烈的剪切造成混合层对下层冷水的夹卷是引起混合层降温的主要原因,并往往伴随着混合层深度的增加,这一影响在TC右侧更为最著,并可延续几天到几十天不等。TC导致的混合层降温会使得海洋输出的热通量减少,反过来削弱TC的强度,形成一个负反馈,而海洋特殊的热力和环流结构(如暖涡、洋流等)则对TC有正反馈。所以了解TC经过前的海洋初始场对研究TC与海洋之间的相互作用、对预测,TC的强度、路径变化等尤其重要;通过准确的初始场结合越来越完善的模式可以对TC进行更真实的模拟和预测,使得对TC准确的预报和预警成为可能。     

全球海洋模式中CFC-11吸收对次网格尺度混合参数化的敏感性

以描述中尺度涡旋对示踪物的输送作用为目的的湍流混合方案GM90经证明对海洋模式的模拟能力较以前的湍流混合方案有较大的提高.该方案涉及到两个主要参数:等密度面扩散系数(A_I)和等密度面厚度扩散系数(A_ith).该文的目的就是利用中国科学院大气物理研究所(IAP)全球海洋环流模式L30T63研究以上两个系数取值大小对主动示踪物(温盐)以及被动示踪物(CFC-11)海洋分布的影响.实验结果表明这两个系数的取值可明显改变大洋温盐垂直分布以及海洋对CFC-11的吸收,且两个系数在其中起到的作用有很大的差异.从几个剖面的分析结果可知,总的来说,AI的增加使得CFC-11主要储存区的模拟结果更接近观测资料,而A_ith的增大使得模拟结果变差.     

Towards the general circulation of the North Atlantic ocean

After reviewing the inverse method, we apply it to deducing the general circulation of the North Atlantic ocean. We argue that the method is purely classical in nature, being nothing more than a mathematical statement of the principles upon which nearly all previous circulation schemes have been based. The ‘smoothed’ solution is shown to represent the components of the flow field that are determinable independently of the initial reference level. We then produce two circulation schemes based upon two different initial reference levels — 2000 decibars and the bottom — called North Atlantic-1A and North Atlantic-1B respectively. The models share many features in common and are strikingly similar to several previous schemes, most notably those of Jacobsen and Defant in the region west of Bermuda. No simple level-of-no-motion emerges in the flow fields; rather the velocity sections exhibit a complex cellular structure. Zonally integrated meridional cells of models and of the uniquely determined components are very similar, showing a poleward movement of warm saline water compensated at depth by a return flow of cold, fresher water. The magnitudes of the implied polar sea overflows and the heat fluxes are in good agreement with previous estimates. Finally, it is argued that neither these model circulations nor any other circulation pattern based upon the existing data can be regarded as actually representing the true time average ocean circulation because the data are aliased in time; the frequency/wavenumber spectrum of the ocean is inadequately known to determine the resulting errors.     

Assimilating satellite SST/SSH and in-situ T/S profiles with the Localized Weighted Ensemble Kalman Filter

The Localized Weighted Ensemble Kalman Filter(LWEnKF) is a new nonlinear/non-Gaussian data assimilation(DA) method that can effectively alleviate the filter degradation problem faced by particle filtering, and it has great prospects for applications in geophysical models. In terms of operational applications, along-track sea surface height(AT-SSH), swath sea surface temperature(S-SST) and in-situ temperature and salinity(T/S) profiles are assimilated using the LWEnKF in the northern South China ...     

基于地球系统模式的局地化粒子滤波器与集合卡尔曼滤波器同化实验

粒子滤波器(PF)是一种非常具有应用前景的非线性资料同化方法。但由于其算法本身存在的粒子退化问题,目前尚未被广泛地应用于大型地球物理模式。目前主流的集合同化系统仍然倾向于使用集合卡尔曼滤波器(EnKF)及其衍生方法。一种新近被提出的局地化粒子滤波器(LPF)在经典的粒子滤波器算法中引入局地化技术,可以使用较小的计算成本有效地避免退化问题,具有非常大的业务应用潜力。本文在全耦合的通用地球系统模式中开展了LPF和EnKF的同化实验,同化资料为模拟的卫星海表温度资料。着重考察了不同局地化参数对两种方法的不同影响,对比了局地化粒子滤波器与集合卡尔曼滤波器的同化效果差异。比较的结果表明,LPF的同化效果对于局地化参数的选择非常敏感,在使用最优局地化参数的条件下,LPF能达到与EnKF相当甚至优于后者的同化效果,并具有较大的改进空间。     

A note on modeling double diffusive mixing in the global ocean

Though ubiquitous in the global oceans, double diffusive mixing has been largely ignored or poorly represented in the models of turbulent mixing in the ocean and in 3-D ocean models, until recently. Salt fingers occur in the interior of many marginal seas and ocean basins, the Tyrrhenian Sea and the subtropical Atlantic being two examples. Diffusive convection type of double diffusion occurs in the upper layers of many sub-polar seas and polar oceans due to cold melt water from sea ice. Consequently, it is important to be able to properly parameterize double diffusive mixing in basin scale and global ocean models, so that the water mass structure in the interior of the ocean can be properly simulated. This note describes a model for double diffusive mixing in the presence of background shear, based on Mellor–Yamada type second moment closure, more specifically Kantha, 2003, Kantha and Clayson, 2004 second moment closure models of resulting turbulence, following Canuto et al. (2008a) but employing a different strategy for modeling the pertinent terms in the second moment equations. The resulting model is suitable for inclusion in ocean general circulation models.     

Parametric vertical coordinate formulation for multiscale, Boussinesq, and non-Boussinesq ocean modeling

Two physical parameters are introduced into the basic ocean equations to generalize numerical ocean models for various vertical coordinate systems and their hybrid features. The two parameters are formulated by combining three techniques: the arbitrary vertical coordinate system of Kasahara [Kasahara, A., 1974. Various vertical coordinate systems used for numerical weather prediction. Mon. Weather Rev. 102, 509–522], the Jacobian pressure gradient formulation of Song [Song, Y.T., 1998. A general pressure gradient formation for ocean models. Part I: Scheme design and diagnostic analysis. Mon. Weather Rev. 126 (12), 3213–3230], and a newly introduced parametric function that permits both Boussinesq (volume-conserving) and non-Boussinesq (mass-conserving) conditions. Based on this new formulation, a generalized modeling approach is proposed. Several representative oceanographic problems with different scales and characteristics––coastal canyon, seamount topography, non-Boussinesq Pacific Ocean with nested eastern Tropics, and a global ocean model––have been used to demonstrate the model’s capabilities for multiscale applications. The inclusion of non-Boussinesq physics in the topography-following ocean model does not incur computational expense, but more faithfully represents satellite-observed ocean-bottom-pressure data. Such a generalized modeling approach is expected to benefit oceanographers in solving multiscale ocean-related problems by using various coordinate systems on the same numerical platform.     

一个两时间层分裂显格式海洋环流模式(MASNUM)及其检验

A two-time-level, three-dimensional numerical ocean circulation model（named MASNUM） was established with a two-level, single-step Eulerian forward-backward time-differencing scheme. A mathematical model of large-scale oceanic motions was based on the terrain-following coordinated, Boussinesq, Reynolds-averaged primitive equations of ocean dynamics. A simple but very practical Eulerian forward-backward method was adopted to replace the most preferred leapfrog scheme as the time-differencing method for both barotropic and baroclinic modes. The forward-backward method is of second-order of accuracy, computationally efficient by requiring only one function evaluation per time step, and free of the computational mode inherent in the three-level schemes. This method is superior to the leapfrog scheme in that the maximum time step of stability is twice as large as that of the leapfrog scheme in staggered meshes thus the computational efficiency could be doubled. A spatial smoothing method was introduced to control the nonlinear instability in the numerical integration. An ideal numerical experiment simulating the propagation of the equatorial Rossby soliton was performed to test the amplitude and phase error of this new model. The performance of this circulation model was further verified with a regional（northwest Pacific） and a quasi-global（global ocean simulation with the Arctic Ocean excluded） simulation experiments. These two numerical experiments show fairly good agreement with the observations. The maximum time step of stability in these two experiments were also investigated and compared between this model and that model which adopts the leapfrog scheme.     

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.     

The effect of the wave-induced mixing on the upper ocean temperature in a climate model

The significant underestimation of sea surface temperature （SST） and the temperature in the upper ocean is one of common problems in present climate models. The influence of the wave-induced mixing on SST and the temperature in the upper ocean was examined based on a global climate model. The results from the model coupled with wave-induced mixing showed a significant improvement in the simulation of SST and the temperature in the upper ocean compared with those of the original model without wave effects. Although there has still a cold bias, the new simulation is much closer to the climatology, especially in the northern ocean and tropical ocean. This study indicates that some important physical processes in the accurate simulation of the ocean may be ignored in present climate models, and the wave-induced mixing is one of those factors. Thus, the wave-induced mixing （ or the effect of surface waves） should be incorporated properly into climate models in order to simulate or forecast the ocean, then climate system, more accurately.     

一种快速非局部平均合成孔径雷达海洋图像斑点噪声抑制方法

合成孔径雷达在海洋环境监测和海洋研究中扮演着越来越重要的角色。受其成像机制的影响,合成孔径雷达图像总是受到斑点噪声的污染。斑点噪声的存在会增大目标识别、跟踪和分类的难度,也会降低雷达信号的信噪比。合成孔径雷达海洋图像具有一些特殊的性质：海洋现象在雷达图像中主要呈现为条带状或斑块状的结构。这些条带状或斑块状的结构呈现出高度的自相似性或信息冗余。非局部平均方法能够衡量图像中不同图像块之间纹理结构的相似性,并利用图像的自相似性对图像进行去噪。但非局部平均去燥方法存在计算量巨大、计算耗时长的缺点,这几乎限制了其实际应用。本文采用一种自适应方法将雷达图像中的像素点区分为纹理区像素点和平坦区像素点。对纹理区像素点,采用较大的相似窗和搜索窗,对平坦区像素点,采用较小的相似窗和搜索窗,从而提高计算速度。进一步,本文基于计算统一设备并行架构（CUDA）技术,利用计算机图形处理器（GPU）对前述算法进行并行加速。与经典非局部平均算法相比,加速后算法的计算效率提高了200倍。     

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.     

Coupling winds to ocean surface currents over the global ocean

A Wind stress–Current Coupled System (WCCS) consisting of the HYbrid Coordinate Ocean Model (HYCOM) and an improved wind stress algorithm based on Donelan et al. [Donelan, W.M., Drennan, Katsaros, K.B., 1997. The air–sea momentum flux in mixed wind sea and swell conditions. J. Phys. Oceanogr. 27, 2087–2099] is developed by using the Earth System Modeling Framework (ESMF). The WCCS is applied to the global ocean to study the interactions between the wind stress and the ocean surface currents. In this study, the ocean surface current velocity is taken into consideration in the wind stress calculation and air–sea heat flux calculation. The wind stress that contains the effect of ocean surface current velocity will be used to force the HYCOM. The results indicate that the ocean surface velocity exerts an important influence on the wind stress, which, in turn, significantly affects the global ocean surface currents, air–sea heat fluxes, and the thickness of ocean surface boundary layer. Comparison with the TOGA TAO buoy data, the sea surface temperature from the wind–current coupled simulation showed noticeable improvement over the stand-alone HYCOM simulation.     

Developments in terrain-following ocean models: intercomparisons of numerical aspects

During the course of developing new numerical algorithms for a terrain-following ocean modeling system (TOMS), different numerical aspects have been evaluated through a comparison between two widely used community ocean models, the Princeton ocean model (POM) and the regional ocean modeling system (ROMS). While both models aim at modeling coastal to basin-scale problems using similar grids, their numerical algorithms, code structure, and parameterization options are very different. Sensitivity studies with an idealized channel flow and a steep seamount configuration demonstrate how different algorithms in the two models may affect numerical errors, the stability of the code and the computational efficiency. For example, new pressure gradient schemes using polynomial fits and new time stepping algorithms may reduce numerical errors and allow using longer time steps than standard schemes do. However, the new schemes may require more careful choices of time steps and the use of higher order advection schemes to maintain numerical stability.