Sensitivity to open boundary forcing in a fine-resolution model of the Iberian shelf-slope region

A fine-resolution primitive equation numerical model is constructed for the Iberian continental shelf and slope region, with open boundaries to the north, south and west. The model is forced by climatological wind fields and relaxed at the surface to climatological temperature and salinity fields. A series of numerical experiments is conducted to investigate the influence of the open boundary conditions. The numerical results include coastal upwelling in summer and a poleward current in winter. The effects of advection of Mediterranean Water and eastern North Atlantic Central Water feature in the circulation. Qualitative comparisons are made with observations.     

A simple approach to adjust tidal forcing in fjord models

To model currents in a fjord accurate tidal forcing is of extreme importance. Due to complex topography with narrow and shallow straits, the tides in the innermost parts of a fjord are both shifted in phase and altered in amplitude compared to the tides in the open water outside the fjord. Commonly, coastal tide information extracted from global or regional models is used on the boundary of the fjord model. Since tides vary over short distances in shallower waters close to the coast, the global and regional tidal forcings are usually too coarse to achieve sufficiently accurate tides in fjords. We present a straightforward method to remedy this problem by simply adjusting the tides to fit the observed tides at the entrance of the fjord. To evaluate the method, we present results from the Oslofjord, Norway. A model for the fjord is first run using raw tidal forcing on its open boundary. By comparing modelled and observed time series of water level at a tidal gauge station close to the open boundary of the model, a factor for the amplitude and a shift in phase are computed. The amplitude factor and the phase shift are then applied to produce adjusted tidal forcing at the open boundary. Next, we rerun the fjord model using the adjusted tidal forcing. The results from the two runs are then compared to independent observations inside the fjord in terms of amplitude and phases of the various tidal components, the total tidal water level, and the depth integrated tidal currents. The results show improvements in the modelled tides in both the outer, and more importantly, the inner parts of the fjord.     

M<Subscript>2</Subscript> tidal dynamics in Bohai and Yellow Seas: a hybrid data assimilative modeling study

A high-resolution hybrid data assimilative (DA) modeling system is adapted to study the M₂ barotropic tidal characteristics and dynamics in the Bohai and Yellow Seas. In situ data include tidal harmonics extracted from both coastal sea level and bottom pressure observations. The hybrid DA system consists of both forward and inverse models. The former is three-dimensional, finite-difference, nonlinear Regional Ocean Modeling System (ROMS). The latter is a three-dimensional, linearized, frequency-domain, finite-element model TRUXTON. The DA system assimilates in situ observations via the inversion of the barotropic tidal open boundary conditions (OBCs). Model skill is evaluated by comparing misfits between the observed and modeled tidal harmonics. The assimilation scheme is found effective and efficient in correcting the tidal OBCs, which in turn improves ROMS tidal solutions. Up to 50% reduction of model/data misfits is achieved after data assimilation. M₂ co-tidal maps constructed from the posterior (data assimilative) ROMS solutions agree well with observational analysis of (Fang et al. 2004). Detailed analyses on tidal mixing, residual current, energy flux, dissipation, and momentum term balance dynamics are performed for M₂ constituent, revealing complex M₂ tidal characteristics in the study region and the important role of coastal geometry and topography in affecting regional tidal dynamics.     

A multigrid methodology for assimilation of measurements into regional tidal models

This paper presents a rigorous, yet practical, method of multigrid data assimilation into regional structured-grid tidal models. The new inverse tidal nesting scheme, with nesting across multiple grids, is designed to provide a fit of the tidal dynamics to data in areas with highly complex bathymetry and coastline geometry. In these areas, computational constraints make it impractical to fully resolve local topographic and coastal features around all of the observation sites in a stand-alone computation. The proposed strategy consists of increasing the model resolution in multiple limited area domains around the observation locations where a representativeness error is detected in order to improve the representation of the measurements with respect to the dynamics. Multiple high-resolution nested domains are set up and data assimilation is carried out using these embedded nested computations. Every nested domain is coupled to the outer domain through the open boundary conditions (OBCs). Data inversion is carried out in a control space of the outer domain model. A level of generality is retained throughout the presentation with respect to the choice of the control space; however, a specific example of using the outer domain OBCs as the control space is provided, with other sensible choices discussed. In the forward scheme, the computations in the nested domains do not affect the solution in the outer domain. The subsequent inverse computations utilize the observation-minus-model residuals of the forward computations across these multiple nested domains in order to obtain the optimal values of parameters in the control space of the outer domain model. The inversion is carried out by propagating the uncertainty from the control space to model tidal fields at observation locations in the outer and in the nested domains using efficient low-rank error covariance representations. Subsequently, an analysis increment in the control space of the outer domain model is computed and the multigrid system is steered optimally towards observations while preserving a perfect dynamical balance. The method is illustrated using a real-world application in the context of the Philippines Strait Dynamics experiment.     

Inversion for tides in the Eastern North Pacific Ocean

A regional model of tides in the Eastern North Pacific Ocean is developed through the use of inversion with two-dimensional finite element codes. Since global tide models are least accurate in coastal environments, modeling tides on a regional scale allows tidal propagation and interaction along the coast to be more accurately represented. In this respect, a regional model can act as a liaison between open ocean dynamics and physical processes more pertinent to coastal systems. The region of interest in this study extends from the Aleutian Islands to Southern California and includes deep ocean, continental shelf, and shallow water features. Boundary conditions are determined from nonlinear inversion of harmonic data from both shallow water and deep ocean tide gauges. Spatial patterns of amplitudes and phases from the model are examined for major constituents. Results are also compared to global tide models at selected stations.     

On the sensitivity of computed surges to open-boundary formulation

A coarse-grid (resolution of order 7 km) model of the west coast of Britain is used to examine the sensitivity of computed storm-surge elevations and currents to a range of open-boundary conditions. The storm-surge period 1 to 26 March 1994 is used for this comparison, as it is a time of significant wind activity. Also current measurements in the North Channel of the Irish Sea together with coastal elevation measurements are available for model validation. Elevations and currents previously computed with a coarse-grid shelf-wide model can also be incorporated into the open-boundary condition to examine the influence of far-field effects. Initial model calculations with no far-field input show the importance of including shelf-wide effects from either the external shelf model, or by using observations from coastal gauges interpolated along the open boundary of the west-coast model. Provided the west-coast models open boundary is taken sufficiently far away from the region of interest, in this case the Irish Sea, then either a radiation condition or an elevation-specified condition is appropriate provided far-field effects are taken into account. If these are not included, then neither boundary condition is successful. For the radiation condition it is necessary to include both elevations and currents from a far-field model in order to reproduce the surge. In the case of an elevation-specified boundary condition far-field effects can be incorporated in hindcast calculations by including observed sea-level changes. In a storm-surge prediction calculation the radiation condition with a far-field model is required. Calculations show that computed elevations are spatially more coherent than currents, with flows through the western Irish Sea showing the greatest sensitivity to open-boundary formulation during storm events.Responsible Editor: Phil Dyke     

Evaluation of Global Ocean Data Assimilation Experiment products on South Florida nested simulations with the Hybrid Coordinate Ocean Model

The South Florida Hybrid Coordinate Ocean Model (SoFLA-HYCOM) encompasses a variety of coastal regions (the broad Southwest Florida shelf, the narrow Atlantic Keys shelf, the shallow Florida Bay, and Biscayne Bay) and deep regions (the Straits of Florida), including Marine Protected Areas (the Florida Keys Marine Sanctuary and the Dry Tortugas Ecological Reserve). The presence of the strong Loop Current/Florida Current system and associated eddies connects the local and basin-wide dynamics. A multi-nested approach has been developed to ensure resolution of coastal-scale processes and proper interaction with the large scale flows. The simulations are free running and effects of data assimilation are introduced through boundary conditions derived from Global Ocean Data Assimilation Experiment products. The study evaluates the effects of boundary conditions on the successful hindcasting of circulation patterns by a nested model, applied on a dynamically and topographically complex shelf area. Independent (not assimilated) observations are employed for a quantitative validation of the numerical results. The discussion of the prevailing dynamics that are revealed in both modeled and observed patterns suggests the importance of topography resolution and local forcing on the inner shelf to middle shelf areas, while large scale processes are found to dominate the outer shelf flows. The results indicate that the successful hindcasting of circulation patterns in a coastal area that is characterized by complex topography and proximity to a large scale current system requires a dynamical downscaling approach, with simulations that are nested in a hierarchy of data assimilative outer models.     

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.     

Performance of a nowcast/forecast system for Prince William Sound,Alaska

A coastal ocean extended Prince William Sound nowcast/forecast system (EPWS/NFS) has been running semi-automatically for an extended domain of Prince William Sound (PWS), Alaska for 2 years. To determine the performance of this modeling system, an assessment is conducted. EPWS/NFS and PWS/NFS (viz., its predecessor) nowcasts are compared with observed time series of sea surface temperature (SST) and coastal sea level (CSL) at a few stations, and to velocity profiles from a moored ADCP. With the extension of the model domain to include the continental shelf outside PWS and forced by an operational global ocean model (Global-Navy Coastal Ocean Model (Global-NCOM)) and a 2D tidal model at the open boundary, EPWS/NFS has achieved significant improvement over PWS/NFS, which covered only PWS per se, for most of the predicted variables in this study. In both magnitude and phase, EPWS/NFS accurately predicts the coastal tide fluctuations, as well as M2 tidal currents in Central Sound, although significant errors in coastal tides exist during some spring and neap tide cycles. Other than for the tidal motions, EPWS/NFS generally produces less energetic CSL and velocity variations than those observed. In comparison, although PWS/NFS well predicts the coastal tides, it suffers from the absence of low-frequency CSL variations, as well as misprediction of M2 tidal currents in Central Sound. For 40 h low-passed PWS/NFS and EPWS/NFS velocities, significant phase error occurs during the model–date comparison period, while EPWS/NFS nowcasts generally produce less root-mean-square-error (rmse) and smaller correlations with the observations than PWS/NFS does. Both observations and EPWS/NFS have similar vertical profiles of baroclinic velocity standard deviations, but some substantial discrepancies occur in the velocity direction. Also, in the Central Sound, EPWS/NFS predicts well the SST seasonal cycle and a major cooling event during the summer 2005. However, for periods shorter than 1 week, both PWS/NFS and EPWS/NFS SST underestimated the observed fluctuations by an order of magnitude.     

Patos Lagoon outflow within the Río de la Plata plume using an airborne salinity mapper: Observing an embedded plume

Major river systems discharging into continental shelf waters frequently form buoyant coastal currents that propagate along the continental shelf in the direction of coastal trapped wave propagation (with the coast on the right/left, in the northern/southern hemisphere). The combined flow of the Uruguay and Paraná Rivers, which discharges freshwater into the Río de la Plata estuary (Lat. ∼36°S), often gives rise to a buoyant coastal current (the ‘Plata plume’) that extends northward along the continental shelf off Uruguay and Southern Brazil. Depending upon the prevailing rainfall, wind and tidal conditions, the Patos/Mirim Lagoon complex (Lat. ∼32°S) may also produce a freshwater outflow plume that expands across the inner continental shelf. Under these circumstances the Patos outflow plume can be embedded in temperature, salinity and current fields that are strongly influenced by the larger Plata plume. The purpose of this paper is to present observations of such an embedded plume structure and to determine the dynamical characteristics of the ambient and embedded plumes.     

Tidal influence on the hydrodynamics of the French Guiana continental shelf

This study investigates the circulation on the French Guiana continental shelf under tidal influence. Indeed, hydrodynamics are characterised by a weak salinity tongue located in the middle of the shelf and induced by the Amazon River, a coastal current flowing from the southeast, and a tidal standing wave whose co-range lines are parallel to the coast.     

A model for grain-size sorting over tidal sand ridges

A model was developed and analyzed to quantify the effect of graded sediment on the formation of tidal sand ridges. Field data reveal coarse (fine) sediment at the crests (in the troughs), but often phase shifts between the mean grain-size distribution and the bottom topography occur. Following earlier work, this study is based on a linear stability analysis of a basic state with respect to small bottom perturbations. The basic state describes an alongshore tidal current on a coastal shelf. Sediment is transported as bed load and dynamic hiding effects are accounted for. A one-layer model for the bed evolution is used and two grain size classes (fine and coarse sand) are considered. Results indicate an increase in growth and migration rates of tidal sand ridges for a bimodal mixture, whilst the wavelength of the ridges remains unchanged. A symmetrical externally forced tidal current results in a grain-size distribution which is in phase with the ridges. Incorporation of an additional external M₄ tidal constituent or a steady current results in a phase shift between the grain-size distribution and ridge topography. These results show a general agreement with observations. The physical mechanism responsible for the observed grain-size distribution over the ridges is also discussed.Responsible Editor: Jens Kappenberg     

Sensitivity of the half-life time of water exchange in coastal waters

A three-dimensional model was established to investigate water exchange in coastal waters, and applied to Qinzhou Bay(QZB) in the South China Sea. Given the strong tidal current in QZB, a half-life time was calculated for water exchange by filtering the tidal signal from the concentrations of a conservative substance. In a control run driven by the tide, without external inputs and an open boundary concentration of zero, it was estimated that the average half-life time in QZB was 54.8 d. Numerical experiments showed that wind accounted for an 11.9% reduction in the half-life time to 48.3 d. When rivers were included in the model, the half-life time decreased by 74.6% to 13.9 d. Sensitivity experiments showed that the half-life time for water exchange was greatly affected by the concentration of the conservative substance which was used at the open boundary. In response to 10,20, 30, and 40% increases in the boundary concentration, the half-life time increased to 91.5, 168.3, 186.2, and 229.1 d,respectively. Results also suggested that for coastal bays with large intertidal areas such as QZB, consideration of the wet and dry processes produced more accurate simulations of the hydrodynamics and the half-life times. Simulations, which did not incorporate wet and dry processes, were more than likely to have overestimated or underestimated the half-life times for water exchange.     

Bottom instrumented tripods: History,applications, and impacts

Instrumented bottom tripods have provided important data on sediment transport processes on continental shelves and in estuaries for four decades. Since the initial deployment in a tidal channel in Puget Sound, WA, in 1965 numerous tripods have been constructed to investigate bottom boundary layer and sediment dynamics worldwide. Tripod data have led to new understanding of near-bottom wave and current flows in the coastal ocean, and have been crucial to the development of shelf circulation and sediment transport models. Calculations of bottom stress, bottom roughness, and sediment flux that resulted directly from tripod data have been compared to bottom boundary layer model results. Where these have differed, new or revised model components have been developed to improve the skill of the models. The many discoveries that have been made from tripod experiments include dense, near-bottom fluid mud layers that transport large quantities of suspended sediment offshore into deeper regions of the continental shelf. This process has been linked to the seaward progradation of subaqueous deltas and to the boundaries of mid-shelf mud deposits off rivers with high fine-sediment discharge.     

Tidal currents in the central Great Barrier Reef

Observations at 8 sites in the outer central Great Barrier Reef show M₂, S₂, K₁, and O₁ tidal currents flow directly off-shelf (northeast), when the corresponding tide at Townsville is at zero height and falling, with typical amplitudes of 12, 6, 3, and 2 cm s^?1. On the slope (at 300 m depth), the vertically averaged long-shelf component was small. On the shelf, the eccentricity of the tidal ellipses decreases shoreward and the tidal ellipses rotate anticlockwise. The major axes of the tidal ellipses tilt left of cross-shelf, especially for the diurnal constituents. There is satisfactory agreement between the observed and modelled cross-shelf currents. The long-shelf velocity is sensitive to the long-shelf changes in amplitude and phase of the tide heights and high quality tidal data for open boundary conditions will be required if numerical models are to model these currents satisfactorily.     

Evaluation of DC, FDEM and IP resistivity methods for imaging perched saltwater and a shallow channel within coastal tidal flat sediments

Presently, electrical resistivity methods are applied in a wide variety of geological and environmental site investigations. Geologically, the coastal tidal flat sediments formed shallow channel-like features at the northern part of Germany. Three geoelectrical methods are applied to image the near surface sediments including a shallow conductive zone within the tidal deposits at the North Sea coast. These methods, direct current (DC) resistivity, frequency domain electromagnetic (FDEM) and spectral induced polarization (SIP), are evaluated to show which one can provide the required spatial resolution under study area conditions. This evaluation also includes a synthetic modeling to assess the DC resistivity imaging technique.The results constitute an encouraging example using these geophysical methods in characterizing the coastal aquifers. The inversion results show that the subsurface resistivity distribution of tidal sediments can change rapidly within a short distance. A thin high conductive layer is observed above the peat and clay layers reflecting a perched saltwater. The 2D IP section shows that the perched saltwater is restricted to patched forms above an impermeable layer of clay. According to the IP images the boundaries of the clay layer are recognized with a good resolution due to the high membrane polarization of the clays. The EM and DC profiles show a shallow channel-like feature within tidal deposits. In this paper, the best FDEM field parameters and the role of EM in lithologic studies are emphasized. Two main limitations can be observed from DC synthetic modeling: (a) A smearing in the lower boundary of the perched saltwater; (b) an amplification of the lateral effect of the highly conductive layer. These limitations decrease the resolution of DC imaging for accurate defining our targets. Because the IP response depends on microgeometry, fluid chemistry and saturation, the 2D IP results demonstrate the suitability of this method to characterize the tidal deposits in the coastal area with a good resolution. In this study, the success of SIP method supports further investigations into studying the hydraulic parameters of tidal deposits in this area. The obtained results during this investigation provide an overview of the coastal aquifer and they can serve as a basis for refining the conceptual model of morphological elements and sedimentary sequences of the coastal tidal flat.     

The predictability of near-coastal currents using a baroclinic unstructured grid model

A limited domain, coastal ocean forecast system consisting of an unstructured grid model, a meteorological model, a regional ocean model, and a global tidal database is designed to be globally relocatable. For such a system to be viable, the predictability of coastal currents must be well understood with error sources clearly identified. To this end, the coastal forecast system is applied at the mouth of Chesapeake Bay in response to a Navy exercise. Two-day forecasts are produced for a 10-day period from 4 to 14 June 2010 and compared to real-time observations. Interplay between the temporal frequency of the regional model boundary forcing and the application of external tides to the coastal model impacts the tidal characteristics of the coastal current, even contributing a small phase error. Frequencies of at least 3 h are needed to resolve the tidal signal within the regional model; otherwise, externally applied tides from a database are needed to capture the tidal variability. Spatial resolution of the regional model (3 vs 1 km) does not impact skill of the current prediction. Tidal response of the system indicates excellent representation of the dominant M ₂ tide for water level and currents. Diurnal tides, especially K ₁, are amplified unrealistically with the application of coarse 27-km winds. Higher-resolution winds reduce current forecast error with the exception of wind originating from the SSW, SSE, and E. These winds run shore parallel and are subject to strong interaction with the shoreline that is poorly represented even by the 3-km wind fields. The vertical distribution of currents is also well predicted by the coastal model. Spatial and temporal resolution of the wind forcing including areas close to the shoreline is the most critical component for accurate current forecasts. Additionally, it is demonstrated that wind resolution plays a large role in establishing realistic thermal and density structures in upwelling prone regions.     

Internal waves over the shelf in the western Bay of Bengal: a case study

Generation and propagation of internal waves (IWs) in the coastal waters of the extended shelf of the western Bay of Bengal are investigated for late winter by using the Massachusetts Institute of Technology General Circulation Model (MITgcm). The model is forced with astronomical tides and daily winds. Monthly climatological temperature and salinity fields are used as initial conditions. The simulations are compared with time series observations of temperature and currents from acoustic Doppler current profiler (ADCP) and conductivity-temperature-depth (CTD) moored at three locations south of Gopalpur: two at a local depth of 100 m and another at 400-m depth during 19–21 February 2012. The comparison of the spectral estimates for the time series of temperature from the model and observations are in reasonable agreement for the near-tidal frequency waves. The peak of temperature spectra is always found near the shelf break region which steadily lost its intensity over the continental shelf. The calculation of Richardson number reflected the presence of local mixing due to density overturning in the shelf region. To understand further the generation and propagation of internal tides in the region, energy flux and conversion of barotropic-to-baroclinic M₂ tidal energy are examined. The model simulations suggest that the internal tide is generated all along the shelf slope. The energy flux analysis shows that the internal tides propagate to either side of the generation sites.     

A numerical study of island wake generated by an elliptical tidal flow

An idealized numerical study of the influence of a tidal flow around an island has been undertaken with ROMS. The study focusses on coastal island wakes which are mainly controlled by elliptical tidal current flows on shallow shelves. This model is typical of some isolated continental shelf islands. The model is forced by a semi-diurnal barotropic inertia gravity wave imposed on the four open boundaries of a rectangular domain and its propagation results in an elliptical tidal flow within the domain in which the circular island lies. The influence of the surrounding island bathymetry and of the ellipse shape has been studied both in two and three dimensions. In the island vicinity, the residual circulation patterns over a tidal period show alongshore flow divergence along the major axis and convergence along the minor axis. A thin tidal ellipse (i.e. with a large ratio between major and minor axes) leads to strong eddy activity periods in the lee of the island during the flood and ebb phases, with eddy dissipation phases in between. By contrast, an almost round ellipse (axis ratio nearly 1) leads to vorticity filaments which continuously progress around the island without eddy shedding. The presence of a topographic slope in the vicinity of the island strengthens the eddy activity. This study suggests that the tidal current rotation favors the development of the eddy rotating in the same direction and weakens the development of the second eddy. In three dimensions with a surrounding bathymetry, an intense upwelling occurs in a large area in the lee of the island and the vertical velocities are stronger with thinner ellipses. With a flat bottom the vertical motions are almost fully generated by convergence and divergence of the secondary flow. With a varying bottom topography, the vertical motions come from a combination of this mechanism with convergence and divergence of the depth averaged flow.     

Three‐dimensional hydrodynamic and salinity transport modelling of Danshuei River estuarine system and adjacent coastal sea,Taiwan

A three‐dimensional, time‐dependent hydrodynamic and salinity model was applied to the Danshuei River estuarine system and adjacent coastal sea in Taiwan. The model forcing functions consist of tidal elevations along the open boundary and freshwater flows from the main stem and tributaries in the Danshuei River system. The bottom roughness height was calibrated and verified with model simulation of barotropic flow, and the turbulent diffusivities were calibrated through comparison of time‐series of salinity distributions. The overall model verification was achieved with comparisons of residual current and salinity distribution. The model simulation results are in qualitative agreement with the available field data. The model was then used to investigate the tidal current, residual current, and salinity patterns under the low freshwater flow condition in the modelling domain. The results reveal that the extensive intrusion of saline water imposes a significant baroclinic forcing and induces a strong residual circulation in the estuary. The downriver net velocity in the upper layer increases seaward despite the enlargement of the river cross‐section in that direction. Strong residual circulation can be found near the Kuan‐Du station. This may be the result of the deep bathymetric features there. Copyright © 2007 John Wiley & Sons, Ltd.