FESOM under coordinated ocean-ice reference experiment forcing

Characteristics of the ocean state simulated with the Finite-Element Sea-Ice Ocean Model (FESOM) under the normalized year forcing of Coordinated Ocean-ice Reference Experiments (COREs; Griffies et al., Ocean Model 26:1–46, 2009) are compared with those of other models participating in COREs. In contrast to these models, FESOM is run on an unstructured mesh (with resolution varying between 20 and 150 km). It is shown that the ocean state simulated by FESOM is in most cases within the spread of other models, demonstrating that the unstructured mesh technology has reached the stage when it becomes a reliable tool for studying the large-scale ocean general circulation.     

Storm surge computations for the west coast of Britain using a finite element model (TELEMAC)

An unstructured mesh finite element model of the sea region off the west coast of Britain is used to examine the storm surge event of November 1977. This period is chosen because accurate meteorological data to drive the model and coastal observations for validation purposes are available. In addition, previous published results from a coarse-grid (resolution 7 km) finite difference model of the region and high-resolution (1 km) limited area (namely eastern Irish Sea) model are available for comparison purposes. To enable a “like with like” comparison to be made, the finite element model covers the same domain and has the same meteorological forcing as these earlier finite difference models. In addition, the mesh is based on an identical set of water depths. Calculations show that the finite element model can reproduce both the “external” and “internal” components of the surge in the region. This shows that the “far field” (external) component of the surge can accurately propagate through the irregular mesh, and the model responds accurately, without over- or under-damping, to local wind forcing. Calculations show significant temporal and spatial variability in the surge in close agreement with that found in earlier finite difference calculations. In addition, root mean square errors between computed and observed surge are comparable to those found in previous finite different calculations. The ability to vary the mesh in nearshore regions reveals appreciable small-scale variability that was not found in the previous finite difference solutions. However, the requirement to perform a “like with like” comparison using the same water depths means that the full potential of the unstructured grid model to improve resolution in the nearshore region is inhibited. This is clearly evident in the Mersey estuary region where a higher resolution unstructured mesh model, forced with uniform winds, had shown high topographic variability due to small-scale variations in topography that are not resolved here. Despite the lack of high resolution in the nearshore region, the model showed results that were consistent with the previous storm surge models of the region. Calculations suggest that to improve on these earlier results, a finer nearshore mesh is required based upon accurate nearshore topography.     

On the sensitivity of computed higher tidal harmonics to mesh size in a finite element model

A finite element model of the Irish and Celtic Sea regions with a range of grid resolutions is used to examine the influence of resolution upon the higher harmonics of the tide in the region. Comparisons are also made with published results from finite difference models of the area, and observations. Calculations using fine near-shore elements with non-zero water depths in coastal regions were found to be more accurate and less time consuming than those using a zero coastal water depth. A detailed examination of the spatial variability of the higher harmonics in near-shore regions of the eastern Irish Sea particularly the Solway and Morecambe Bay showed significant small-scale variability. This together with the variation in higher harmonics in the eastern Irish Sea and adjacent estuaries, clearly shows the need for an unstructured grid model of the region that can include the estuaries. To match the high resolution of the model in near-shore regions accurate high-resolution topography is required.     

海洋运动的尺度分析

本文利用尺度分析理论详尽地论述了旋转海洋中各类运动的特性及其相应的控制方程组,指出现实海洋中可能存在五种大尺度运动,并讨论了存在于这种运动中流场和质量场的适应过程,针对不同类型的运动分别分析了升降流的性质以及层化和摩擦对升降流的影响,估计了地球旋转对海水可压缩性的影响以及非静力平衡在各类海洋运动中的作用。     

Seasonal circulation and influence factors of the Bohai Sea: a numerical study based on Lagrangian particle tracking method

Seasonal circulation of the Bohai Sea (BS) in 1992 was investigated using Lagrangian particle tracking method. The hydrography of the BS was simulated based on an unstructured grid, finite-volume, three-dimensional primitive equation ocean model. With the use of the unstructured triangular grid, the model can easily fit the irregular coastal boundary of the BS. The simulated tides, tidal current, and thermohaline field agreed well with the observations. The transport of particles has three-dimensional structure in the BS. Compared with central Bohai and Bohai Strait, the differences of particles’ transportation between surface and bottom layer in three bays are small. The circulation in the summer is stronger than that in the winter, with the average residual velocity in the surface layer being about 3.7 cm/s during the summer while only 1.8 cm/s during the winter. Using the same model, several well-designed numerical experiments were performed to investigate the effect of oceanic tide, river discharge, wind stress, and thermal stratification on the circulation. It is shown that winds play an important role in the circulation of the BS during both the winter and the summer. Density circulation is important during the summer; however, it is negligible during the winter. River runoff only affects the area around the river mouth. Compared with wind and thermohaline effect, the contribution of tides is small during the summer, and the circulation under only M₂ tidal constituent could not reflect the actual circulation of the BS.     

On utility of triangular C-grid type discretization for numerical modeling of large-scale ocean flows

Ocean circulation models based on triangular C-grid discretization are frequently employed to simulate coastal ocean dynamics on unstructured meshes. It is shown that on time and space scales dominated by slow geostrophic dynamics, this discretization tends to exhibit checkerboard noise in the field of horizontal velocity divergence and vertical velocity, respectively. The noise is linked to the geometry of triangular C-grid and is amplified in regimes that are close to geostrophic balance through the particular structure of the Coriolis operator. It can be partly suppressed in some cases but remains a problem in a general case and makes the triangular C-grid a suboptimal choice for large-scale ocean modeling.     

Interactions between wind and tidally induced currents in coastal and shelf basins

This paper addresses the impact of atmospheric variability on ocean circulation in tidal and non-tidal basins. The data are generated by an unstructured-grid numerical model resolving the dynamics in the coastal area, as well as in the straits connecting the North Sea and Baltic Sea. The model response to atmospheric forcing in different frequency intervals is quantified. The results demonstrate that the effects of the two mechanical drivers, tides and wind, are not additive, yet non-linear interactions play an important role. There is a tendency for tidally and wind-driven circulations to be coupled, in particular in the coastal areas and straits. High-frequency atmospheric variability tends to amplify the mean circulation and modify the exchange between the North and the Baltic Sea. The ocean response to different frequency ranges in the wind forcing is area-selective depending on specific local dynamics. The work done by wind on the oceanic circulation depends strongly upon whether the regional circulation is tidally or predominantly wind-driven. It has been demonstrated that the atmospheric variability affects the spring-neap variability very strongly.     

Sensitivities of an adjoint, unstructured mesh, tidal model on the European Continental Shelf

Unstructured mesh models can resolve the model domain with a variable and very fine mesh resolution. Nevertheless, tuning the model setup is still required (for example because of parametrized sub-grid processes). Adjoint models are commonly used to calculate sensitivities of ocean models and optimize their parameters so that better agreement is achieved between model simulations and observations. One major obstacle in developing an adjoint model is the need to update the reverse code after each modification of the forward code, which is not always straightforward. Automatic differentiation is a tool to generate the adjoint model code without user input. So far this method has mainly been used for structured mesh ocean models. We present here an unstructured mesh, adjoint, tidal model using this technique, and discuss the sensitivities of the misfit between simulated and observed elevations with respect to open boundary values, the bottom friction coefficient and the bottom topography. The forward model simulates tides on the European Continental Shelf and we show that the tidal model dynamics in the adjoint simulations can be used to define regions, where parameters or mesh has to be optimized. We analyze the dependence of the sensitivities on the wave type and mesh resolution to specify whether the model misfit originates from physical or numerical model deficiencies. In the sensitivity patterns, it is possible to identify islands not resolved in the mesh. We propose to refine the mesh prior to the parameter optimization.     

On the developments of spectral wave models: numerics and parameterizations for the coastal ocean

The development of numerical wave models for coastal applications, including coupling with ocean circulation models, has spurred an ongoing effort on theoretical foundations, numerical techniques, and physical parameterizations. Some important aspects of this effort are reviewed here, and results are shown in the case of the French Atlantic and Channel coast using version 4.18 of the WAVEWATCH III ^R model. Compared to previous results, the model errors have been strongly reduced thanks to, among other things, the introduction of currents, coastal reflection, and bottom sediment types. This last item is described here for the first time, allowing unprecedented accuracy at some sites along the French Atlantic Coast. The adequate resolution, necessary to represent strong gradients in tidal currents, was made possible by the efficiency brought by unstructured grids. A further increase in resolution, necessary to resolve surf zones and still cover vast regions,will require further developments in numerical methods.     

Effect of coastal boundary resolution and mixing upon internal wave generation and propagation in coastal regions

A non-linear two-dimensional vertically stratified cross-sectional model of a constant depth basin without rotation is used to investigate the influence of vertical and horizontal diffusion upon the wind-driven circulation in the basin and the associated temperature field. The influence of horizontal grid resolution, in particular the application of an irregular grid with high resolution in the coastal boundary layer is examined. The calculations show that the initial response to a wind impulse is downwelling at the downwind end of the basin with upwelling and convective mixing at the opposite end. Results from a two-layer analytical model show that the initial response is the excitation of an infinite number of internal seiche modes in order to represent the initial response which is confined to a narrow near coastal region. As time progresses, at the downwind end of the basin a density front propagates away from the boundary, with the intensity of its horizontal gradient and associated vertical velocity determined by both horizontal and vertical viscosity values. Calculations demonstrate the importance of high horizontal grid resolution in resolving this density gradient together with an accurate density advection scheme. The application of an irregular grid in the horizontal with high grid resolution in the nearshore region enables the initial response to be accurately reproduced although physically unrealistic short waves appear as the frontal region propagates onto the coarser grid. Parameterization of horizontal viscosity using a Smagorinsky-type formulation acts as a selective grid size-dependent filter, and removes the short-wave problem although enhanced smoothing can occur if the scaling coefficient in the formulation is too large. Calculations clearly show the advantages of using an irregular grid but also the importance of using a grid size-dependent filter to avoid numerical problems.     

Application of a finite element model (TELEMAC) to computing the wind induced response of the Irish Sea

Initially a brief overview of the problem of computing the wind-induced circulation on the west coast of Britain is reviewed together with storm surge modelling. To date this work has primarily been performed with finite difference models. However, here new work is presented using a finite element model with a range of mesh refinements in shallow water regions to examine the influence of mesh resolution upon the wind-induced circulation off the west coast of Britain. Steady state current fields are computed for uniform westerly and southerly winds and compared with a uniform grid (of order 7 km) finite difference model solution. Calculations show that in deep water regions away from the coastal influence, the large-scale circulation features in the finite element solution are in good agreement with those found in the finite difference model. This suggests that they can be adequately resolved on a 7 km mesh. In the nearshore region and within estuaries a significantly finer mesh is required, with the variable mesh finite element model showing significant small scale variability in the nearshore area. Refining the mesh in the Mersey and using an accurate topographic data set, shows that although the larger scale features in the estuary can be resolved in the coarser mesh model, accurate topography is required to model their exact location. In addition smaller scale features are found that were not resolved in the coarser mesh models. Due to the effects of “wetting and drying” and the importance of non-linear processes in shallow regions difficulties occurred in de-tiding the full solution in order to determine the wind forced residual. Determining the wind forced solution in shallow water from a calculation in which wind and tidal forcing are included poses problems as to how to “de-tide” the solution in such a highly non-linear region. An approach based upon the harmonic analysis of the total solution, rather than subtracting a “tide only” solution is shown to be most effective and has implications for storm surge prediction.General and specific conclusions on the importance of highly accurate bathymetry, good mesh resolution and de-tiding method upon the accuracy of the wind forced solution in nearshore regions are summarized in the final part of the paper. The implications for storm surge prediction together with suggestions for future research to enhance the accuracy of storm surge prediction, namely “the way forward” are given at the end of the paper.     

An integrated East China Sea–Changjiang Estuary model system with aim at resolving multi-scale regional–shelf–estuarine dynamics

A high-resolution numerical model system is essential to resolve multi-scale coastal ocean dynamics. So a multi-scale unstructured grid-based finite-volume coastal ocean model (FVCOM) system has been established for the East China Sea and Changjiang Estuary (ECS–CE) with the aim at resolving coastal ocean dynamics and understanding different physical processes. The modeling system consists of a three-domain-nested weather research and forecasting model, FVCOM model with the inclusion of FVCOM surface wave model in order to understand the wave–current interactions. The ECS–CE system contains three different scale models: a shelf-scale model for the East China Sea, an estuarine-scale model for the Changjiang Estuary and adjacent region, and a fine-scale model for the deep waterway regions. These three FVCOM-based models guarantee the conservation of mass and momentum transferring from outer domain to inner domain using the one-way common-grid nesting procedure. The model system has been validated using data from various observation data, including surface wind, tides, currents, salinity, and wave to accurately reveal the multi-scale dynamics of the East China Sea and Changjiang Estuary. This modeling system has been demonstrated via application to the seasonal variations of Changjiang diluted water and the bottom saltwater intrusion in the North Passage, and it shows strong potential for estuarine and coastal ocean dynamics and operational forecasting.     

A model study of tidal distributions in the Celtic and Irish Sea regions determined with finite volume and finite element models

An unstructured mesh tidal model of the west coast of Britain, covering the Celtic Sea and Irish Sea is used to compare tidal distributions computed with finite element (FE) and finite volume (FV) models. Both models cover an identical region, use the same mesh, and have topography and tidal boundary forcing from a finite difference model that can reproduce the tides in the region. By this means, solutions from both models can be compared without any bias towards one model or another. Two-dimensional calculations show that for a given friction coefficient, there is more damping in the FV model than the FE model. As bottom friction coefficient is reduced, the two models show comparable changes in tidal distributions. In terms of mesh resolution, calculations show that for the M₂ tide, the mesh is sufficiently fine to yield an accurate solution over the whole domain. However, in terms of higher harmonics of the tide, in particular the M₆ component, its small-scale variability in near-shore regions which is comparable to the mesh of the model, suggests that the mesh resolution is insufficient in the near-coastal regions. Even with a finer mesh in these areas, without detailed bottom topography and a spatial varying friction depending on bed types and bed forms, which is not available, model skill would probably not be improved. In addition in the near-shore region, as shown in the literature, the solution is sensitive to the form of the wetting/drying algorithm used in the model. Calculations with a 3D version of the FV model show that for a given value of k, damping is reduced compared to the 2D version due to the differences in bed stress formulation, with the 3D model yielding an accurate tidal distribution over the region.     

Mesh type tradeoffs in 2D hydrodynamic modeling of flooding with a Godunov-based flow solver

The effect of mesh type on the accuracy and computational demands of a two-dimensional Godunov-type flood inundation model is critically examined. Cartesian grids, constrained and unconstrained triangular grids, constrained quadrilateral grids, and mixed meshes are considered, with and without local time stepping (LTS), to determine the approach that maximizes computational efficiency defined as accuracy relative to computational effort. A mixed-mesh numerical scheme is introduced so all grids are processed by the same solver. Analysis focuses on a wide range of dam-break type test cases, where Godunov-type flood models have proven very successful. Results show that different mesh types excel under different circumstances. Cartesian grids are 2–3 times more efficient with relatively simple terrain features such as rectilinear channels that call for a uniform grid resolution, while unstructured grids are about twice as efficient in complex domains with irregular terrain features that call for localized refinements. The superior efficiency of locally refined, unstructured grids in complex terrain is attributable to LTS; the locally refined unstructured grid becomes less efficient using global time stepping. These results point to mesh-type tradeoffs that should be considered in flood modeling applications. A mixed mesh model formulation with LTS is recommended as a general purpose solver because the mesh type can be adapted to maximize computational efficiency.     

A three-dimensional finite-element model of wind effects upon higher harmonics of the internal tide

A non-linear three-dimensional unstructured grid model of the M₂ tide in the shelf edge area off the west coast of Scotland is used to examine the spatial distribution of the M₂ internal tide and its higher harmonics in the region. In addition, the spatial variability of the tidally induced turbulent kinetic energy and associated mixing in the area are considered. Initial calculations involve only tidal forcing, although subsequent calculations are performed with up-welling and down-welling favourable winds to examine how these influence the tidal distribution (particularly the higher harmonics) and mixing in the region. Both short- and long-duration winds are used in these calculations. Tidal calculations show that there is significant small-scale spatial variability particularly in the higher harmonics of the internal tide in the region. In addition, turbulence energy and mixing exhibit appreciable spatial variability in regions of rapidly changing topography, with increased mixing occurring above seamounts. Wind effects significantly change the distribution of the M₂ internal tide and its higher harmonics, with appreciable differences found between up- and down-welling winds and long- and short-duration winds because of differences in mixing and the presence of wind-induced flows. The implications for model validation, particularly in terms of energy transfer to higher harmonics, and mixing are briefly discussed.     

Long Nonlinear Surface and Internal Gravity Waves in a Rotating Ocean

Nonlinear dynamics of surface and internal waves in a stratified ocean under the influence of the Earth's rotation is discussed. Attention is focussed upon guided waves long compared to the ocean depth. The effect of rotation on linear processes is reviewed in detail as well as the existing nonlinear models describing weakly and strongly nonlinear dynamics of long waves. The influence of rotation on small-scale waves and two-dimensional effects are also briefly considered. Some estimates of the influence of the Earth's rotation on the parameters of real oceanic waves are presented and related to observational and numerical data.     

地震海洋学方法在海洋混合参数提取中的研究与应用——以南海内波和地中海涡旋为例

混合是海洋中普遍存在的一种海水运动形式,对多个海洋学分支的研究具有重要的影响.随着物理海洋学的研究重心从大尺度向中小尺度现象过渡,近年来混合问题的研究重心也逐渐转向了中小尺度现象.内波与中尺度涡都是非常重要的中小尺度物理海洋学现象,对海洋能量在不同尺度中的级联发挥着重要的作用.本文基于地震海洋学研究了海洋混合参数的提取方法,并以南海内波和地中海涡旋为例进行了计算和分析.结果显示,南海内波在200~600m深度范围内所引起的混合可达10-2.79 m2·s-1左右,比大洋的统计结果10-5 m2·s-1高出两个数量级以上.而地中海涡旋所引起的湍流混合率可达10-3.44 m2·s-1左右,与大洋统计结果相比高出1.5个数量级左右,并且地中海涡旋下边界的混合要强于上边界,这一特征与前人的研究一致,另外涡旋上边界之上以及侧边界的外侧也具有非常高的混合率.     

Variability of the meridional overturning circulation of the North Atlantic: sensitivity to overflows of dense water masses

A numerical model of the Atlantic Ocean was used to study the low-frequency variability of meridional transports in the North Atlantic. The model shows a behaviour similar to those used in previous studies, and the temporal variability of certain variables compares favourably to observed time series. By changing the depth and width of the sills between the subpolar North Atlantic and the Nordic Seas, the mean horizontal and overturning circulation as well as some water mass properties are modified significantly. The reaction of meridional oceanic transports to atmospheric forcing fluctuations remains, however, unchanged. The critical role of the surface heat flux retroaction term for the meridional heat transport in stand-alone ocean models is discussed. The experiments underline the role of atmospheric variability for fluctuations of the large-scale ocean circulation on time scales from years to decades, and they support the hypothesis that the mean overturning strength is controlled by the model representation of the density of the overflow water masses.Responsible Editor: Dirk Olbers     

Application of a finite element model to the computation of tides in the Mersey Estuary and Eastern Irish Sea

A variable mesh finite element model of the Irish and Celtic Sea regions with/without the inclusion of the Mersey estuary is used to examine the influence of grid resolution and the Mersey upon the higher harmonics of the tide in the region. Comparisons are made with observations and published results from finite difference models of the area. Although including a high resolution representation of the Mersey had little effect upon computed tides in the western Irish Sea it had a significant effect upon tidal currents in the eastern Irish Sea. In addition the higher harmonics of the M₂ tide in near-shore regions of the eastern Irish Sea particularly the Solway and Mersey estuary together with Morecambe Bay showed significant small scale variability. The Mersey was used to test the sensitivity to including estuaries because high resolution accurate topography was available. The results presented here suggest that comparable detailed topographic data sets are required in all estuaries and near-shore regions. In addition comparisons clearly show the need for an unstructured grid model of the region that can include all the estuaries. Such an unstructured grid solution was developed here within a finite element approach, although other methods in particular the finite volume, or coordinate transformations/curvilinear grids and nesting could be applied.     

Circulation and thermal structure in Lake Huron and Georgian Bay: Application of a nested-grid hydrodynamic model

A nested-grid hydrodynamic modelling system is used to study circulation and temperature distributions in Lake Huron (LH) and adjacent areas. This nested system is based on the three-dimensional, primitive-equation z-level ocean model. The nested system consists of two sub-components: a coarse-resolution outer model covering LH and Georgian Bay (GB) with a horizontal resolution of roughly 2.5 km, and the fine-resolution inner model covering eastern LH and northwestern GB with a horizontal resolution of roughly 900 m. Both the outer and inner models have 30 z-levels in the vertical. To assess the model performance, we simulate the three-dimensional circulation and temperature distributions of LH and GB in 1974–1975 and compare the model results with observations made in the lake. We demonstrate that outer model of the nested system simulates reasonably well the large-scale circulation and seasonal evolution of thermal stratifications in LH and GB, and the inner model produces reasonably well the three-dimensional flow and thermal structure over the coastal boundary layer close to the eastern shore of the lake.