A coupled oscillator model of shelf and ocean tides

The resonances of tides in the coupled open ocean and shelf are modeled by a mechanical analogue consisting of a damped driven larger mass and spring (the open-ocean) connected to a damped smaller mass and spring (the shelf). When both masses are near resonance, the addition of even a very small mass can significantly affect the oscillations of the larger mass. The influence of the shelf is largest if the shelf is resonant with weak friction. In particular, an increase of friction on a near-resonant shelf can, perhaps surprisingly, lead to an increase in ocean tides. On the other hand, a shelf with large friction has little effect on ocean tides. Comparison of the model predictions with results from numerical models of tides during the ice ages, when lower sea levels led to a much reduced areal extent of shelves, suggests that the predicted larger tidal dissipation then is related to the ocean basins being close to resonance. New numerical simulations with a forward global tide model are used to test expectations from the mechanical analogue. Setting friction to unrealistically large values in Hudson Strait yields larger North Atlantic _M2$M_2$ amplitudes, very similar to those seen in a simulation with the Hudson Strait blocked off. Thus, as anticipated, a shelf with very large friction is nearly equivalent in its effect on the open ocean to the removal of the shelf altogether. Setting friction in shallow waters throughout the globe to unrealistically large values yields even larger open ocean tidal amplitudes, similar to those found in simulations of ice-age tides. It thus appears that larger modeled tides during the ice ages can be a consequence of enhanced friction in shallower water on the shelf in glacial times as well as a reduced shelf area then. Single oscillator and coupled oscillator models for global tides show that the maximum extractable power for human use is a fraction of the present dissipation rate, which is itself a fraction of global human power consumption.     

Tides, sea-level rise and tidal power extraction on the European shelf

An established numerical tidal model has been used to investigate the impact of various sea-level rise (SLR) scenarios, as well as SLR in combination with large-scale tidal power plants on European shelf tidal dynamics. Even moderate and realistic levels of future SLR are shown to have significant impacts on the tidal dynamics of the area. These changes are further enhanced when SLR and tidal power plants are considered in combination, resulting in changes to tidal amplitudes, currents and associated tidal dissipation and bed shear stresses. Sea-level rise is the dominant influence on any far-field impacts, whereas tidal power plants are shown to have the prevailing influence over any changes close to the point of energy extraction. The spatial extent of the impacts of energy extraction is shown to be affected by the sea level when more than one tidal power plant in the Irish Sea was considered. Different ways to implement SLR in the model are also discussed and shown to be of great significance for the response of the tides.     

Coastal tides in West Greenland derived from tide gauge records

Based on pressure tide-gauge observations, sea-level records are derived for ten sites along the coast of West Greenland. The ocean tidal signal is extracted by a harmonic tidal analysis. The accuracy of the determined tidal constants is discussed in detail. The tides account for 85% of the observed sea-level standard deviation. The tide gauge records reveal significant shallow-water tidal effects, in particular compound and overtide amplitudes reaching 5 cm. The propagation of the tidal waves into the fjords depends strongly on local conditions and is in some cases accompanied by an amplification of the tidal amplitudes. The observed tidal signals are compared to the predictions of the global ocean tide model FES2004. At the outer coast, a good agreement is found. Inside the fjords, however, the model performs worse and tide gauge observations may still be indispensable when accurate tidal signals are required.     

Evolution of bed shear stress distribution over the northwest European shelf seas during the last 12,000 years

Due to changes in relative sea level of order 100 m, the contribution of tides and waves to net bed shear stress in shelf sea regions has varied considerably over the Late Glacial and Holocene. Understanding the spatial and temporal distribution of this ratio leads to a deeper understanding of the erosion and deposition of sediments over the shelf seas throughout this time period. Tidal and wave models are here applied to palaeo time slices of the northwest European shelf seas over the last 12,000 years. The model simulations include a series of sensitivity tests to account for the influence of interannual variability in wind conditions on the resulting bed shear stress. The results show that there has been a significant decrease over the last 12,000 years in shelf-scale mobilisation of coarse sediment. Since there was a lower magnitude of wave orbital velocity penetrating to the sea bed as a result of increasing relative sea level, this reduction in sediment mobilisation was primarily controlled by a shelf-scale decrease in wave-induced bed shear stress over the last 12,000 years. The predictions of mean and residual bed shear stress for the modelled palaeo time slices are a useful tool with which to inform site-selection and subsequent interpretation of sediment cores. In addition, the modelled reconstructions of palaeo tidal range over the shelf seas demonstrates the potential errors associated with assuming a present-day tidal range when correcting palaeo sea-level proxies from their deposited datum (e.g. palaeo mean high water spring tide) to palaeo mean sea level.     

On the generation and propagation of internal solitary waves in the southern Andaman Sea: A numerical study

Numerous internal solitary waves(ISWs) have been observed in the southern Andaman Sea. In this study, the two-dimensional Massachusetts Institute of Technology general circulation model is applied to investigate the dynamics of ISWs and explore the effects of the bottom topography and tidal forcing on the generation and propagation of ISWs in the southern Andaman Sea. The results show that the large-amplitude depression ISWs are mainly generated via the oscillating tidal flow over the sill of the Great Channel, and the generation of ISWs is subject to the lee wave regime. The Dreadnought Bank cannot generate ISWs itself; however, it can enhance the amplitudes of eastward-propagating ISWs generated from sill A, owing to constructive interference of internal tide generation between the sill of the Great Channel and the Dreadnought Bank. The eastward-propagating ISWs generated by the eastern shallow sill near the continental shelf can propagate to the shelf, where they evolve into elevation waves because of the shallow water. Sensitivity runs show that both the semidiurnal and diurnal tides over the sill of the Great Channel can generate ISWs in this area. However, the ISWs generated by diurnal tides are much weaker than those generated by semidiurnal tides. Mixed tidal forcing has no significant effect on the generation of ISWs.     

Tide circulation patterns in a coastal lagoon under sea-level rise

This study evaluates the patterns and effects of relative sea-level rise on the tidal circulation of the basin of the Ria Formosa coastal lagoon using a process-based model that is solved on an unstructured mesh. To predict the changes in the lagoon tidal circulation in the year 2100, the model is forced by tides and a static sea level. The bathymetry and the basin geometry are updated in response to sea-level rise for three morphological response scenarios: no bed updating, barrier island rollover, and basin infilling. Model results indicate that sea-level rise (SLR) will change the baseline current velocity patterns inside the lagoon over the ~100-year study period, due to a strong reduction in the area of the intertidal basin. The basin infilling scenario is associated with the most important adjustments of the tidal circulation (i.e., increases in the flood velocities and delays in the ebb tide), together with an increase in the cumulative discharges of the tidal inlets. Under sea-level rise and in the basin infilling scenario, the salt marshes and tidal flats experience increases in the tidal range and current asymmetry. Basin infilling changes the sediment flushing capacity of the lagoon, leading to the attenuation of the flood dominance in the main inlet and the strengthening of the flood dominance in the two secondary inlets. The predictions resulting from these scenarios provide very useful information on the long-term evolution of similar coastal lagoons that experience varying degrees of SLR. This study highlights the need for research focusing on the quantification of the physical and socio-economic impacts of SLR on lagoon systems, thus enabling the development of effective adaptation strategies.     

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.     

A test of the influence of tidal stream polarity on the structure of turbulent dissipation

Vertical mixing by the tides plays a key role in controlling water column structure over the seasonal cycle in shelf seas. The influence of tidal stirring is generally well represented as a competition between surface buoyancy input and the production of turbulent kinetic energy (TKE) by frictional stresses, a competition which is encapsulated in the Qh/u³ criterion. An alternative control mechanism arises from the limitation of the thickness of the bottom boundary layer due to the effects of rotation and the oscillation of the flow. Model studies indicate that, for conditions typical of the European shelf seas, the energy constraint exerts the dominant control but that for tidal streams with large positive polarisation (i.e. anti-clockwise rotation of velocity vector), some influence of rotation in limiting mixing should be detectable. We report here measurements of flow structure (with ADCPs) and turbulent dissipation (FLY Profiler) made at two similar locations in the Celtic Sea which differ principally in that the tidal currents rotate in opposite senses with approximately equal magnitude (polarity P=±0.6). A clear contrast was observed between the two sites in the vertical structure of the currents, the density profile and the rate of dissipation of TKE. At the positive polarity (PP) site (P≈+0.6), the bottom boundary layer in the tidal flow was limited to ∼20 mab (metre above the bed) and significant dissipation from bottom boundary friction was constrained within this layer. At the negative polarity (NP) site (P≈−0.6), the dominant clockwise rotary current component exhibited a velocity defect (i.e. reduction relative to the free stream) extending into the upper half of the water column while significant dissipation was observed to penetrate much further up the water column with dissipation levels ∼10^−4.5 W m⁻³ reaching to the base of the pycnocline at 70–80 mab. These contrasting features of the vertical distribution of dissipation are well reproduced by a 1-D model when run with windstress and tidal forcing and using the observed density profile. Model runs with reversed polarity at the two sites, support the conclusion that the observed contrast in the structure of tidal velocity, dissipation and stratification is due to the influence of tidal stream polarity. Increased positive polarity reduces the upward penetration of mixing which allows the development of stronger seasonal stratification, which, in turn, further inhibits vertical mixing.     

Application of data assimilation for improving forecast of water levels and residual currents in Singapore regional waters

Hydrodynamic models are commonly used for predicting water levels and currents in the deep ocean, ocean margins and shelf seas. Their accuracy is typically limited by factors, such as the complexity of the coastal geometry and bathymetry, plus the uncertainty in the flow forcing (deep ocean tide, winds and pressure). In Southeast Asian waters with its strongly hydrodynamic characteristics, the lack of detailed marine observations (bathymetry and tides) for model validation is an additional factor limiting flow representation. This paper deals with the application of ensemble Kalman filter (EnKF)-based data assimilation with the purpose of improving the deterministic model forecast. The efficacy of the EnKF is analysed via a twin experiment conducted with the 2D barotropic Singapore regional model. The results show that the applied data assimilation can improve the forecasts significantly in this complex flow regime.     

Thermal tides and studies to tune the mechanistic tidal model using UARS observations

Monthly simulations of the thermal diurnal and semidiurnal tides are compared to High-Resolution Doppler Imager (HRDI) and Wind Imaging Interferometer (WINDII) wind and temperature measurements on the Upper-Atmosphere Research Satellite (UARS). There is encouraging agreement between the observations and the linear global mechanistic tidal model results both for the diurnal and semidiurnal components in the equatorial and mid-latitude regions. This gives us the confidence to outline the first steps of an assimilative analysis/interpretation for tides, dissipation, and mean flow using a combination of model results and the global measurements from HRDI and WINDII. The sensitivity of the proposed technique to the initial guess employed to obtain a best fit to the data by tuning model parameters is discussed for the January and March 1993 cases, when the WINDII day and night measurements of the meridional winds between 90 and 110 km are used along with the daytime HRDI measurements. Several examples for the derivation of the tidal variables and decomposition of the measured winds into tidal and mean flow components using this approach are compared with previous tidal estimates and modeling results for the migrating tides. The seasonal cycle of the derived diurnal tidal amplitudes are discussed and compared with radar observation between 80 and 100 km and 40° S and 40°N.     

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.     

Influence of mantle anelasticity on the phase and amplitude of Earth tides

The effect of the anelasticity of the mantle on the phase and amplitude of Earth tides is calculated for recent models of the internal structure of the Earth and its rheological characteristics. The anelastic properties of the mantle are modelled by the Maxwell and Knopoff-Lomnitz rheological bodies. For numerical calculations two different methods of solution are used. Results indicate that the effect of mantle anelasticity on tidal amplitudes is practically zero. For both types of rheological models the phase shifts of the functions characterizing solid tides are small, none of them exceeding values of some minutes of arc. These phase shifts have a very weak dependence on the variation of attenuation and viscosity within the mantle. The present study is closely related to an important problem: what proportion of the observed tidal friction arises not in the ocean but is due to the anelasticity of the mantle? The results suggest that dissipation by solid friction at present is an insignificant, almost negligible component of tidal energy sink.     

Resonance and sea level variability in Chesapeake Bay

A numerical model is used to determine the resonant period and quality factor Q of Chesapeake Bay and explore physical mechanisms controlling the resonance response in semi-enclosed seas. At the resonant period of 2 days, the mouth-to-head amplitude gain is 1.42 and Q is 0.9, indicating that Chesapeake Bay is a highly dissipative system. The modest amplitude gain results from strong frictional dissipation in shallow water. It is found that the spatial distribution of energy dissipation varies with forcing frequency. While energy at tidal frequencies is dissipated around topographic hotspots distributed throughout the Bay, energy dissipation at subtidal frequencies is mainly concentrated in the shallow-water lower Bay. An analytic calculation shows that the bottom friction parameter is much larger in Chesapeake Bay than in other coastal systems with strong resonance response. The model-predicted amplitude gains and phase changes agree well with the observations at semidiurnal and diurnal tidal frequencies. However, the predicted amplitude gain in the resonant frequency band (34–54 h period) falls below that inferred from band-passed sea level observations. This discrepancy can be attributed to the local wind forcing which amplifies the sea level response in the upper Bay. The model is also used to show that rising sea levels associated with global warming will shift the resonance period of Chesapeake Bay closer to the diurnal tides and thus exacerbate flooding problems by causing an increase in tidal ranges.     

A study of tides and currents in Cook Strait, New Zealand

Greater Cook Strait (GCS) lies between the North and the South Islands of New Zealand. Its location at the convergence of the Pacific and Indo-Australian tectonic plates leads to interesting bathymetry with an adjacent shallow shelf and deep ocean trench as well as numerous crossing faults and complex shoreline geometry. Our purpose in this study is to examine tides and currents in GCS and, in particular, identify the major forcing mechanisms for the residual currents. Toward this end, we use an unstructured-grid numerical model to reproduce the tides and currents, verify these results with observations and then use the model to separate the various forcing mechanisms. The physical forcing includes nonlinear generation from tides and tidal currents, differences in sea level between the Pacific Ocean and Tasman Sea boundaries, density variations, wind stress and river discharge into GCS. Each of these mechanisms is important in different areas.     

Post-glacial sediment dynamics in the Irish Sea and sediment wave morphology: Data–model comparisons

The irregular seafloor of the narrow Irish Sea on the NW European Shelf has been documented over several decades. From recently collected swath bathymetry data, very large trochoidal, nearly symmetrical sediment waves are observed in many parts of the Irish Sea and appear similar to those described from other continental shelf seas in North America that were covered by glacigenic sediments during the Last Glacial Maximum. Swath multibeam and single beam bathymetry data, backscatter intensity, shallow seismic imagery, video footage and sediment cores from the Irish Sea high sediment waves have been integrated to identify their genesis with reference to present and past hydrodynamic variability. From cross-sectional profiles over asymmetrical sediment waves in the Irish Sea the direction of asymmetry is used to map residual bed stress directions and associated bedload transport paths. Irish Sea peak bed stress vectors were generated using a two-dimensional palaeo-tidal model for the NW European shelf seas and compare well with the observations. Tidally induced bed stresses are modelled to have increased between 7–10 ka BP, to be nearly symmetrical in magnitude and to have reversed in dominant direction on a millennial scale. These environmental conditions during the post-glacial marine transgression are suggested here to help comprehend the construction of the very large sediment waves, with local variations due to differences in sediment grain size, sediment supply, water depth and intensified currents due to seafloor slopes. Model parameterisation using an open ocean boundary with time-dependent tidal changes and the implementation of high-resolution bathymetric information will improve future models of small-scale bed shear stress patterns and improve the predictive value of such modelling efforts.     

A numerical study of the barotropic tides and tidal energy distribution in the Indonesian seas with the assimilated finite volume coastal ocean model

The tides and tidal energetics in the Indonesian seas are simulated using a three-dimensional finite volume coastal ocean model. The high-resolution coastline-fitted model is configured to better resolve the hydrodynamic processes around the numerous barrier islands. A large model domain is adopted to minimize the uncertainty adjacent to open boundaries. The model results with elevation assimilation based on a simple nudge scheme faithfully reproduced the general features of the barotropic tides in the Indonesian Seas. The mean root-mean-square errors between the observed and simulated tidal constants are 2.3, 1.1, 2.4, and 1.5 cm for M₂, S₂, K₁, and O₁, respectively. Analysis of the model solutions indicates that the semidiurnal tides in the Indonesian Seas are primarily dominated by the Indian Ocean, whereas the diurnal tides in this region are mainly influenced by the Pacific Ocean, which is consistent with previous studies. Examinations of tidal energy transport reveal that the tidal energy for both of the simulated tidal constituents are transported from the Indian Ocean into the IS mainly through the Lombok Strait and the Timor Sea, whereas only M₂ energy enters the Banda Sea and continues northward. The tidal energy dissipates the most in the passages on both sides of Timor Island, with the maximum M₂ and K₁ tidal energy transport reaching about 750 and 650 kW m^–1, respectively. The total energy losses of the four dominant constituents in the IS are nearly 338 GW, with the M₂ constituent dissipating 240.8 GW. It is also shown that the bottom dissipation rate for the M₂ tide is about 1–2 order of magnitudes larger than that of the other three tidal components in the Indonesian seas.     

The temperature minimum at tidal fronts

This paper presents a mechanism to explain the observed formation of a surface temperature minimum at tidal fronts in shelf seas. Tidal fronts mark the boundary between water which is kept vertically mixed by fast tidal currents and water which stratifies in summer. The fronts are associated with strong horizontal surface gradients of several water properties, including temperature. In the early studies of tidal fronts, a minimum in surface temperature was occasionally observed between the cool surface waters on the mixed side of the front and the warm surface waters on the stratified side. It was suggested that this was caused by upwelling of deep water at the front. In this paper we describe an alternative and simpler explanation based on the local balance of heating and stirring. The net heat flux into the sea in spring and early summer is greater on the mixed side of the front than on the stratified side. This happens because the heat loss mechanism is dependent on sea surface temperature and stratified waters, having a higher surface temperature, lose more heat. The stratified water near the front therefore has lower heat content (and lower depth-mean temperature) than the mixed water. If some of the stratified water becomes mixed, for example with increased tidal stirring at spring tides, a zone of minimum surface temperature will be formed at the front. A numerical model for the study of this mechanism shows that the temperature minimum at tidal fronts can be explained by the process described above. The minimum appears most clearly at spring tides, but can still be present in a weaker form at neap tides. A further prediction of the model is an increase of the horizontal temperature gradient at spring tides, which is in agreement with observations. An unexpected outcome of the modelling is the prediction of the formation of a marked sea surface temperature minimum, not yet observed, occurring in the autumn and located at the summer position of the tidal front.     

The influence of tides, wind and waves on the net sand transport in the North Sea

Large-scale redistribution of sand by hydrodynamical processes in shelf seas is important for basin and coastal evolution on time scales of a thousand to tens of thousands of years. The influence of tides on the large-scale net sand-transport patterns in the North Sea has received much attention, but the influence of wind-driven flow and wind waves has hardly been investigated. Here, to establish the present-day situation and to develop a method that can also be used for palaeo-situations and forecasts for different sea levels, this influence is assessed for the present southern North Sea using a numerical flow model, a parametric wave model and a wave-averaged sand-transport formulation. Various forcing combinations are used to identify the dominant transport mechanisms: tides only, tides and wind, tides and waves, and combined tides, wind and waves. Wind forcing is applied in two ways to find an efficient, but still representative, method of incorporating this stochastic process: a statistical wind climatology and an observed time series. The results show that (i) the wind climatology yields a good approximation of the sand transport computed using the time series; (ii) wind-driven flow and waves only contribute significantly to the net sand transport by tides when acting together where tidal currents are small; and (iii) various combinations of forcings dominate the net sand transport in different regions of the southern North Sea: (a) tides dominate in the southern, middle and northwestern parts of the Southern Bight and in the region of The Wash; (b) tides, wind-driven flow and waves all are important in the northeastern part of the Southern Bight; and (c) wind-driven flow and waves dominate north of the Friesian Islands, in the German Bight and on the Dogger Bank. Qualitative comparison with observations shows good agreement.     

Modeling the morphodynamic response of tidal embayments to sea-level rise

Sea-level rise has a strong influence on tidal systems, and a major focus of climate change effect studies is to predict the future state of these environmental systems. Here, we used a model to simulate the morphological evolution of tidal embayments and to explore their response to a rising sea level. The model was first used to reproduce the formation of channels and intertidal flats under a stable mean water level in an idealised and initially unchannelled tidal basin. A gradual rise in sea level was imposed once a well-developed channel network had formed. Simulations were conducted with different sea-level rise rates and tidal ranges. Sea-level rise forced headward erosion of the tidal channels, driving a landward expansion of the channel network and channel development in the previously non-inundated part of the basin. Simultaneously, an increase in channel drainage width in the lower part of the basin occurred and a decrease in the overall fraction of the basin occupied by channels could be observed. Sea-level rise thus altered important characteristics of the tidal channel network. Some intertidal areas were maintained despite a rising sea level. However, the size, shape, and location of the intertidal areas changed. In addition, sea-level rise affected the exchange of sediment between the different morphological elements. A shift from exporting to importing sediment as well as a reinforcement of the existing sediment export was observed for the simulations performed here. Sediment erosion in the inlet and the offshore transport of sediment was enhanced, resulting in the expansion of the ebb-tidal delta. Our model results further emphasise that tidal embayments can exhibit contrasting responses to sea-level rise.

     

Modeling the morphodynamic response of tidal embayments to sea-level rise

Sea-level rise has a strong influence on tidal systems, and a major focus of climate change effect studies is to predict the future state of these environmental systems. Here, we used a model to simulate the morphological evolution of tidal embayments and to explore their response to a rising sea level. The model was first used to reproduce the formation of channels and intertidal flats under a stable mean water level in an idealised and initially unchannelled tidal basin. A gradual rise in sea level was imposed once a well-developed channel network had formed. Simulations were conducted with different sea-level rise rates and tidal ranges. Sea-level rise forced headward erosion of the tidal channels, driving a landward expansion of the channel network and channel development in the previously non-inundated part of the basin. Simultaneously, an increase in channel drainage width in the lower part of the basin occurred and a decrease in the overall fraction of the basin occupied by channels could be observed. Sea-level rise thus altered important characteristics of the tidal channel network. Some intertidal areas were maintained despite a rising sea level. However, the size, shape, and location of the intertidal areas changed. In addition, sea-level rise affected the exchange of sediment between the different morphological elements. A shift from exporting to importing sediment as well as a reinforcement of the existing sediment export was observed for the simulations performed here. Sediment erosion in the inlet and the offshore transport of sediment was enhanced, resulting in the expansion of the ebb-tidal delta. Our model results further emphasise that tidal embayments can exhibit contrasting responses to sea-level rise.