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．     

POM and Two-Way Nesting POM Study of Kuroshio Damping Phenomenon Caused by a Strong Wind

A Kuroshio damping phenomenon of a few days scale caused by a strong wind was studied using the Princeton Ocean Model (POM) and a two-way nesting model for the POM. We simulated an idealized eastward Kuroshio in a zonal channel in terms of the inflow/outflow condition at the western/eastern boundaries and examined responses of the idealized Kuroshio to a strong easterly wind. This study was motivated by observations of JMA research vessel Shumpu Maru which reported deformation of isopycnals and damping of the Kuroshio before and after the attack of Typhoon 6804. Deformation of isopycnals and damping of the Kuroshio are found to depend on magnitude of wind stress, intensity of stratification, distance of the Kuroshio from coast, and grid resolution. The deformation of isopycnals is related to the vertical circulation pattern caused by the divergence/convergence of the onshore Ekman transport. A simple stratification model composed of Niiler (1969)'s modification of the Ekman transport and the coastal boundary is proposed to explain the damping phenomenon. An idealized cape was added in other experiments in order to study whether the Kuroshio damping mechanism discussed here works in three dimensions. The newly developed two-way nesting model for the POM was applied for this experiment and made it possible to clarify more detailed features of response in the nested area than did the coarse grid model.     

A diagnostic stabilized finite-element ocean circulation model

A stabilized finite-element (FE) algorithm for the solution of oceanic large scale circulation equations and optimization of the solutions is presented. Pseudo-residual-free bubble function (RFBF) stabilization technique is utilized to enforce robustness of the numerics and override limitations imposed by the Babuška–Brezzi condition on the choice of functional spaces. The numerical scheme is formulated on an unstructured tetrahedral 3d grid in velocity–pressure variables defined as piecewise linear continuous functions. The model is equipped with a standard variational data assimilation scheme, capable to perform optimization of the solutions with respect to open lateral boundary conditions and external forcing imposed at the ocean surface. We demonstrate the model performance in applications to idealized and realistic basin-scale flows. Using the adjoint method, the code is tested against a synthetic climatological data set for the South Atlantic ocean which includes hydrology, fluxes at the ocean surface and satellite altimetry. The optimized solution proves to be consistent with all these data sets, fitting them within the error bars.The presented diagnostic tool retains the advantages of existing FE ocean circulation models and in addition (1) improves resolution of the bottom boundary layer due to employment of the 3d tetrahedral elements; (2) enforces numerical robustness through utilization of the RFBF stabilization, and (3) provides an opportunity to optimize the solutions by means of 3d variational data assimilation. Numerical efficiency of the code makes this a desirable tool for dynamically constrained analyses of large datasets.     

On the nudging terms at open boundaries in regional ocean models

For open boundary conditions (OBCs) in regional models, a nudging term added to radiative and/or advective conditions during the wave or flow propagation outward from the model domain of interest is widely used, to prevent the predicted boundary values from evolving to become quite different from the external data, especially for a long-term integration. However, nudging time scales are basically unknown, leading to many empirical selections. In this paper, a method for objectively estimating nudging time scales during outward propagation is proposed, by using internal model dynamics near the boundary. We tested this method and other several commonly used OBCs for cases of both an idealized model domain and a realistic configuration, and model results demonstrated that the proposed method improves the model solutions. Many similarities are found between the nudging and mixing time scales, in magnitude, spatial and temporal variations, since the nudging mainly replaces the effect of the mixing terms in this study. However, the mixing time scale is not an intrinsic property of the nudging term because in other studies the nudging term might replace terms other than the mixing terms and, thus, should reflect other characteristic time scales.     

How does the Red Sea outflow water interact with Gulf of Aden Eddies?

As the Red Sea overflow water (RSOW) enters the Gulf of Aden (GOA), it interacts with a sequence of nearly barotropic, mesoscale eddies originating in the Indian Ocean. To investigate how these eddies impact the dispersal and eastward transport of the RSOW toward the Indian Ocean, a high resolution 3D regional model is employed to explore systematically the interaction between the RSOW and mesoscale eddies. Two types of experiments are conducted. In the first set, we simulate the behavior of RSOW in the presence of an idealized cyclone and an idealized anticyclone. The second type of simulation involves nesting of the regional model (ROMS) within a data-assimilating global model (HYCOM), in which a sequence of mesoscale eddies entering the Gulf of Aden is realistically captured. This simulation is integrated for one year, and includes a simple representation of the seasonality of the RSOW.Bower et al. (2002) suggest that the Red Sea overflow might be a western boundary undercurrent. Consistent with these expectations, the idealized simulations show that the preferred pathway of the RSOW in the absence of eddies is along the coast of Somalia (southern continental shelf) as a western boundary undercurrent. Simultaneously, a cyclonic circulation is generated in the far western GOA due to vortex stretching by the descending outflow. The presence of a cyclone in the western GOA increases the peak RSOW transport, but the cyclone itself rapidly loses its coherence after interacting with the rough topography in the western GOA. The presence of an anticyclone tends to block the preferred boundary pathway and inhibits the eastward transport of the RSOW. The eddies also result in substantially increased mixing of the RSOW in the western GOA.On the basis of the more realistic ROMS experiment, it is found that the modeled RSOW leaves the western part of the Gulf of Aden in short episodic bursts with transports that are an order of magnitude greater than that associated with the quasi-steady RSOW inflow into GOA. Such enhancement in RSOW transport is shown to be induced by cyclonic eddies that cause a rapid discharge of RSOW from the western part of the GOA. We conclude that mesoscale eddies play a key role in the transport and mixing of the RSOW within GOA.     

Wave-adjusted boundary condition for longshore current in finite-volume circulation models

Numerical modeling of coastal circulation encompassing the nearshore requires forcing by tide, surface gravity waves, and possibly other factors. In the nearshore, the wave-induced longshore current and setup are dominant hydrodynamic processes, and lateral boundary conditions representing tide and oceanic forcing typically do not include surface-wave contributions. Without proper boundary conditions, significant gradients in current and water level can occur that contaminate the solution in the internal domain. A standard strategy is to place the boundaries far from the site of interest, but this strategy greatly increases computational demands, and it may not be appropriate for long-term simulations. This paper describes a wave-adjusted boundary condition that accounts for wave-induced water level and current acting in combination with tidal forcing. The wave-adjusted boundary condition is demonstrated for an idealized case of a parallel-contour beach and for an engineering application at Ocean City, MD.     

A pretty good sponge: Dealing with open boundaries in limited-area ocean models

The problem of computing within a limited domain surrounded by open boundaries is discussed within the context of the shallow-water wave equations by comparing three different treatments, all of which surround the domain by absorbing zones intended to prevent reflections of outgoing waves. The first, which has attracted a lot of attention for use in electromagnetic and aeroacoustic applications, is intended to prevent all reflections. However, it has not yet been developed to handle the second important requirement of open boundaries, namely the ability to pass information about external conditions into the domain of interest. The other two treatments, which absorb differences from a specified external solution, allow information to pass through the open boundary in both directions. One, based on the flow relaxation scheme of [Martinsen, E.A., Engedahl, H., 1987. Implementation and testing of a lateral boundary scheme as an open-boundary condition in a barotropic ocean model. Coastal Eng. 11, 603–627] and termed here the “simple sponge,” relaxes all fields toward their external counterparts. The other, a simplification and generalization of the perfectly matched layer, referred to here as the “pretty good sponge,” avoids absorbing the component of momentum parallel to the open boundary. Comparisons for a case that is dominated by outgoing waves shows the pretty good sponge to perform essentially as well as the perfectly matched layer and better than the simple sponge. In comparisons for a geostrophically balanced eddy passing through open boundaries, the pretty good sponge out-performed the simple sponge when the only external information available was about the advecting flow, but when information about the nature of the eddy in the sponge zones was also available, the simple sponge performed better. For the case of an equatorial soliton passing through the boundary and no information provided about its nature outside the open domain, again the pretty good sponge performed better. Proving useful for situations governed by nonlinear equations forced by external conditions and being easy to implement, the pretty good sponge should be considered for use with existing limited-area ocean models.     

Zonally asymmetric response of the Japan Sea to synoptic pressure forcing

We investigated the sea level response of the Japan Sea to changes in atmospheric pressure using barotropic shallow water models driven by idealized synoptic pressure forcing. The regional response lags behind the synoptic pressure forcing because the adjustment is slowly established by water exchange through narrow, shallow straits. The sea level response of the realistic Japan Sea to the idealized forcing varies with geographical location and shows zonally asymmetric variations in amplitude and phase. The simulated response is in good agreement with the observed response of sea level recorded at Japanese coastal tide gauges. The results of a simple one-dimensional model indicate that the zonally asymmetric pattern, with an eastward-propagating pressure system, is essentially caused by bottom friction in shallow straits. This asymmetry arises if the typical wavelength of the synoptic pressure system is slightly larger than the spatial scale of the Japan Sea.     

Influence of the White Sea on tides in adjacent marginal seas of the North European Basin

An investigation into the interaction of surface M ₂ tides in the system of marginal seas of the North European Basin is carried out using the three-dimensional finite-element hydrostatic model QUODDY-4. Three numerical experiments are performed for this purpose. In the first (control), the model equations are solved in the system of the Norwegian, Greenland, Barents, and White seas; thereby the interaction of the tides in these seas is explicitly taken into account. In the second experiment, the White Sea is excluded from consideration and the no-flux condition is posed at the entrance to the sea. The third experiment uses an approach in which the observed tidal elevations that determine the existence of a finite horizontal transport of barotropic energy to the White Sea are specified at the open boundary of the White Sea. It is shown that changes in tidal dynamics represented by changes in the amplitudes and phases of tidal elevations and in the barotropic tidal velocity ellipse parameters are within the model noise in experiments 2 and 3 when compared with the control experiment. On the contrary, changes in energy characteristics (the horizontal wave transport, density, and dissipation rate of barotropic tidal energy) are equal to or greater (in order of magnitude) than the energy characteristics themselves.     

Simulation of Typhoon-Driven Waves in the Yangtze Estuary with Multiple-Nested Wave Models

Typhoon-generated waves are simulated with two numerical wave models, the SWAN model for the coastal and Yangtze Estuary domain, nested within the WAVEWATCHIII （WW3） for the basin-scale East China Sea domain. Typhoon No. 8114 is chosen because it was very strong, and generated high waves in the Estuary. WW3 was implemented for the East China Sea coarse-resolution computational domain, to simulate the waves over a large spatial scale and provide boundary conditions for SWAN model simulations, implemented on a fine-resolution nested domain for the Yangtze Estuary area. The Takahashi wind model is applied to the simulation of the East China Sea scale （3-hourly） and Yangtze Estuary scale （1-hourly） winds. Simulations of significant wave heights in the East China Sea show that the highest waves are on the right side of the storm track, and maxima tend to occur at the eastern deep-water open boundary of the Yangtze Estuary. In the Yangtze Estuary, incoming swell is dominant over locally generated waves before the typhoon approaches the Estuary. As the typhoon approaches the Estuary, wind waves and swell coexist, and the wave direction is mainly influenced by the swell direction and the complex topography.     

一个近岸海流数值计算模式的开边界条件

为了计算的省时性,ＩＡＰ近岸海流数值模式采用了分解算法,即将控制方程分解为３个过程并用不同的时间步长进行积分。文章在此基础上对分解后的控制方程作局地线性化,得到了适合不同过程的开边界条件。对于适应过程,控制方程变换为等价的表示沿不同方向传播波动的特征方程。传出计算区域的波动用特征方程来描述,而传入波动则由无反射边界条件来消除。对于演变过程,求出了解析形式的通解。在流出点上,边界条件可以借助解析解由上一时刻区域内部或边界上的已知值求得;而在流入点上,边值保持定常。对于耗散过程,不需要边界条件。最后对所提出的开边界条件进行了数值检验,结果是令人满意的。     

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.     

WaveWatch的操作系统移植及其与SWAN嵌套接口的改进

为使WaveWatch和SWAN两种海浪预报模式能够有效地嵌套运行,将WaveWatch模式从UNIX移植到Windows系统下运行,同时对SWAN模式与WaveWatch模式的嵌套接口格点座标读取精度进行修改,使其能够应用于不规则边界的曲线网格和小间距规则网格的嵌套;作为检验个例,使用WaveWatchIII与SWAN模式多重嵌套的方法在Windows系统下对长江口海浪场进行数值模拟实验,得到了理想的模拟结果。     

Alternating zonal flows in a two-layer wind-driven ocean

Alternating zonal flows in an idealized wind-driven double-gyre ocean circulation have been investigated using a two-layer shallow-water eddy-permitting numerical model. While the alternating zonal flows are found almost everywhere in the time-mean zonal velocity field, their meridional scales differ from region to region. In the subpolar western boundary region, where the energetic eddy activity induces quasi two-dimensional turbulence, the alternating zonal flows are generated by the inverse energy cascade and its arrest by Rossby waves, and the meridional scale of the flows corresponds well to the Rhines scale. In the eastern part of the basin, where barotropic basin modes are dominant, the zonal structure is formed through the nonlinear effect of the basin modes and is wider than the Rhines scale. Both effects are likely to form zonal structure between the two regions. These results show that Rossby basin modes become an important factor in the formation of alternating zonal flows in a closed basin in addition to the arrest of the inverse energy cascade by Rossby waves. The wind-driven general circulation associated with eddy activities plays an essential role in determining which mechanism of the alternating zonal flows is possible in each region.     

Active open boundary forcing using dual relaxation time-scales in downscaled ocean models

Regional models actively forced with data from larger scale models at their open boundaries often contain motion at different time-scales (e.g. tidal and low frequency). These motions are not always individually well specified in the forcing data, and one may require a more active boundary forcing while the other exert less influence on the model interior. If a single relaxation time-scale is used to relax toward these data in the boundary equation, then this may be difficult. The method of fractional steps is used to introduce dual relaxation time-scales in an open boundary local flux adjustment scheme. This allows tidal and low frequency oscillations to be relaxed independently, resulting in a better overall solution than if a single relaxation parameter is optimized for tidal (short relaxation) or low frequency (long relaxation) boundary forcing. The dual method is compared to the single relaxation method for an idealized test case where a tidal signal is superimposed on a steady state low frequency solution, and a real application where the low frequency boundary forcing component is derived from a global circulation model for a region extending over the whole Great Barrier Reef, and a tidal signal subsequently superimposed.     

Variability of the meridional transport processes in the Southern Ocean and its possible relation to El Niño

The article deals with the influence of wind and atmospheric pressure on the barotropic variability of the Antarctic Circumpolar Current (ACC). This effect is studied using a global barotropic model under idealized and realistic atmospheric forcings. The results of barotropic modeling demonstrate that variations in the wind forcing over the ACC, together with the effects of the topography and coastline, lead to the variability in the meridional water flux in the Southern Ocean. The variability of these fluxes is negatively correlated with the wind strength over the ACC. A possible link between the short-period variability of the water flux in the Pacific sector of the Southern Ocean and El Niño is demonstrated using 3D ocean modeling and correlation analysis. It is shown that the variability of the meridional water flux caused by atmospheric perturbations over the ACC can lead to short-period density anomalies in the Southern Ocean north of 47°S, which later can be transferred to low latitudes by means of the wave mechanism described in [15] and strongly influence the tropical region.     

Tests and Applications of An Approach to Absorbing Reflected Waves Towards Incident Boundary

If the upstream boundary conditions are prescribed based on the incident wave only, the time-dependent numerical models cannot effectively simulate the wave field when the physical or spurious reflected waves become significant. This paper describes carefully an approach to specifying the incident wave boundary conditions combined with a set sponge layer to absorb the reflected waves towards the incident boundary. Incorporated into a time-dependent numerical model, whose governing equations are the Boussinesq-type ones, the effectiveness of the approach is studied in detail. The general boundary conditions, describing the down-wave boundary conditions are also generalized to the case of random waves. The numerical model is in detail examined. The test cases include both the normal one-dimensional incident regular or random waves and the two-dimensional oblique incident regular waves. The calculated results show that the present approach is effective on damping the reflected waves towards the incident wave boundary.     

Application of a two-way nested model to the seamount problem

A two-way nested model has been constructed and applied to the idealized ocean where a uniform mean flow impinges on the isolated Gaussian-shaped seamount and produces two eddies (cold and warm) in the depths. The performance of the nested model has been evaluated subjectively and objectively. Both subjective and objective analyses confirm the traditional view that the nested model can well capture the performance of isolated eddies. Objective analysis, however, reveals some quantitatively important features of a two-way nested model. One is penetration of improved features into the coarse domain and another is the deterioration of mean flow field inside the nested area, neither of which is clear from subjective analysis. With successful application of two-way nested model to the seamount problem, we expect that such a nested model will also be applicable to other oceanic phenomena, particularly to some coastal problems whose time scale is short and where the topographic effects are dominant.