M2 Tidal Constituent Research Articles

Accuracy assessment of recent global ocean tide models in coastal waters of the European North West Shelf

The accuracy of global ocean tide models is assessed in coastal waters of the European North West Shelf to ascertain where higher resolution local (forecast) models are most needed for geophysical and navigational applications, and which global models are most suitable for providing boundary conditions for regional and local tide models. Five recent global ocean tide models (FES2014b, EOT20, TPXO9-atlas-v5, GOT4.10c, and DTU16) are considered, with the models first compared by interpolating them onto common grids and computing the mean absolute deviation at each grid point. Coastline tide gauge and offshore bottom pressure sensor data were collated from several sources to give a total of 279 observation sites for evaluating model accuracy, including observational values from 137 locations that have not previously been released and have therefore not been assimilated into any of the global models tested. The residual errors between each model’s predicted phasor and the corresponding observed phasor were calculated at each observation location, and quantified using the root mean square (RMS) and median absolute residual (MAR) for the eight tidal constituents M2, S2, N2, O1, K1, K2, P1, and Q1. To avoid RMS values being biased by observation point density, a Voronoi-weighted RMS based on the water area of the Voronoi polygon about each observation location was also developed and used. Four zones were defined based on ocean depth to gauge model performance, and model inaccuracy is again demonstrated in near-shore regions. Seven further zones were defined based on geographical areas, which reveals inhomogeneity among the global models. The smallest overall root sum square (RSS) RMS error across all eight constituents arises with FES2014b, although TPXO9-atlas-v5 has the best performance when using the MAR and Voronoi-weighted RMS metrics. Using only the 137 observation sites that have not been assimilated by any model and therefore provide an independent accuracy assessment, FES2014b exhibits the smallest errors at the coastline, with an RSS RMS of 24.46 cm. All models exhibit larger errors with the 137 independent observation sites than with all 279 observation sites, with an average overall increase in RSS RMS error of 12%, and an increase of 30% for coastline tide gauges, highlighting the need for local model development in these areas.

Modeling of Barotropic Tide off the Southeastern Coast of the Kamchatka Peninsula in View of the Accuracy of Global Tidal Models in the Northwest Pacific Ocean

This study introduces the development and implementation of a regional numerical finite-volume model FESOM–C, specifically designed to accurately compute barotropic tidal dynamics in the Pacific waters adjacent to the southeastern region of the Kamchatka Peninsula. The dynamics of principal harmonics of the semidiurnal M2 and diurnal K1 tidal constituents are replicated, as well as the total tide, which encompasses 12 constituents. The computed results, obtained using a detailed unstructured grid, are interpreted through the Long-wave approach. The FESOM–C regional model revealed the variability of harmonic constants of tide and current characteristics within the shelf and canyon-cut continental slope, due to topographic scattering of tidal waves. The assessment includes the estimation of maximum currents and eddy structures associated with residual tidal circulation on the shelf and continental slope. To investigate the influence of varying open boundary conditions, sensitivity experiments have been conducted using data from two state-of-the-art global tidal models FES2014 and TPXO9. The findings reveal that the regional model’s solution exhibits only minimal dependency on this choice, and it aligns well with the limited available tidal data. Interestingly, the global models themselves demonstrate significant disparities in the tidal currents. Furthermore, we assess the accuracy of global tidal model solutions in a broader region encompassing the Sea of Okhotsk, as well as the Pacific waters along the Kuril Islands and the Kamchatka Peninsula. This assessment utilizes a verified database of tidal harmonic constants derived from the Soviet and British tide tables. While the average errors in tidal heights calculations remain minor and closely approximate officially declared values, certain areas within the region exhibit notable discrepancies in the outputs of the global models. These discrepancies are site-specific and vary depending on the particular model and tidal harmonic under consideration. This underscores the need for caution when applying results from global tidal models at the regional scale. Meanwhile, the importance of advancing regional tidal dynamics modeling remains evident.

Changes in tide-induced asymmetries in a tidal creek by the presence of intertidal flats: The San Pedro Channel (Cadiz Bay)

A two-dimensional, non-linear, finite difference, hydrodynamic model was applied to the San Pedro channel (Cadiz bay) to study the changes on tidal current asymmetries along its course due to the reconnection of its main channel to a wide tidal lagoon that was artificially desiccated in the mid of 20th century. Results of both experimental in-situ data and model simulations show changes from a flood-dominance of current asymmetries when the channel was isolated, to a stronger and ebb-directed asymmetry after the reconnection to the upper lagoon. The influence of the upstream intertidal flats is revealed on the configuration of tidal current asymmetries induced by the mutual phase-lags between the M2 and M4 tidal constituents, as well as in the tide-induced residual currents. These effects were found to be stronger during spring tides. The impacts of current asymmetry reversal on the morphodynamics of coastal tidal environments and on water quality and pollutants transport are discussed.

Assessment of Ocean Circulation Characteristics off the West Coast of Ireland Using HF Radar

Research on coastal ocean circulation patterns over long time periods is significant for various marine endeavors: environmental protection, coastal engineering construction, and marine renewable energy extraction. Based on sea surface current data remotely observed using a shore-based high frequency radar (HFR) system for one year (2016), spatiotemporal characteristics of surface flow fields of sea surface flow fields along the west coast of Ireland are studied using harmonic analysis, rotary spectral analysis and representative flow fields over different seasons and the whole year. Coastal surface currents in the study area are strongly affected by tidal dynamics of the M2 constituent, showing significant characteristics of regular semidiurnal tide, such as M2 and S2. The energy spectrum distribution indicates that the tidal constituents M2 and S2 are the dominant periodic energy constituents in a counterclockwise spectrum, which mainly presents rotating flow; the representative diurnal tidal constituents is the constituent K1, and its energy spectrum distribution is mainly clockwise. A comparison between probable maximum current velocity (PMCV) and measured maximum current velocity (MMCV) is presented. It shows that although tidal current characteristics in the study area are significant, the main driving force of the currents at the time of the maximum currents is wind energy. These results provide new insights into a region of huge societal potential at early stages of sustainable economic exploitation where few data currently exist.

Characterisation of the Hydrogeological Properties of the Ntane Sandstone Aquifer Using Co-Seismic and Post-Seismic Groundwater Level Responses to the Mw 6.5 Moiyabana Earthquake, Central Botswana

The 3 April 2017 Mw 6.5 Moiyabana earthquake (Central Botswana) had a significant impact on groundwater levels; a gradual co-seismic increase and a stepwise decline in groundwater levels were observed in response to the earthquake at boreholes MH2 and Z12836, respectively. In this study, we investigated the response of groundwater levels to Earth tides by computing the amplitude and phase shift of the M2 tidal constituent to estimate the temporal variations of the storativity, transmissivity, and permeability of the Ntane sandstone aquifer (the main aquifer system) prior to and after the earthquake event. The storativity and permeability computed for borehole MH2 showed a decrease in magnitude of 3.17432 × 10−4 and 1.85 × 10−13 m2 respectively, indicating that strong ground shaking at borehole MH2 might have consolidated the aquifer material, thus resulting in decreased aquifer permeability. The aquifer coefficient of storativity decreased by 2.85 × 10−4 while permeability was enhanced by 0.047 × 10−13 m2 at borehole Z12836. Enhanced permeability might have resulted from increased/enhanced fracturing of the aquifer, fracture clearing and dynamic shaking.

Residual M2 and S2 ocean tide signals in complex coastal zones identified by X-Track reprocessed altimetry data

While the reliability of reprocessed altimetry data from X-Track has been examined for sea level studies, it has not previously been used to study ocean tides in tidally complex coastal zones. Using a new dataset of short-term tide gauges, the aim of this study is to demonstrate the improvements in X-Track reprocessed data for studying ocean tides for the first time in tidally complex regions in northwest Australia. We show that X-Track can be used to evaluate and potentially correct ocean tide models in challenging coastal areas. Our study comprises three components: (1) evaluate the tidal constants from X-Track and RADS datasets using nearby (<12 km) short-term tide gauge data, (2) assess three ocean tide models (FES2014, DTU10, TPXO9) using the X-Track altimetry dataset and (3) extract residual M2 and S2 tidal constants from sea level anomalies (SLAs) computed using the optimal model (FES2014) for ocean tide correction and then use these to predict the residual tidal height to use as an additional correction for the recomputation of the SLAs.Our results show that X-Track data provides users with more valid observations close to coastlines (as close as 5 km) so that the derived M2 and S2 tidal constants show better agreement with nearby tide gauges compared to RADS for both Jason-3 (J3) and GFO missions. In Van Diemen Gulf, where the footprints were 7 km or less from the coast, RADS did not have any valid observations, whereas tidal constants of M2 computed from X-Track J3 and GFO data agreed with the tide gauges within ∼6% of the M2 tidal height. In contrast, X-Track J3 and GFO extracted S2 tidal constants agreed with nearby tide gauges within ∼11–24% (GFO extreme of 47%) of the S2 tidal height. The FES2014-detided SLA time series from X-Track were then analysed to detect the remaining signals of M2 and S2 tidal constituents, with co-range maps suggesting the unmodelled amplitudes for M2 reaches 40 cm and S2 up to 30 cm in Collier Bay. In Van Diemen Gulf, M2 contributes more to the residual tidal signal than S2 with an amplitude of 40 cm compared to 10 cm respectively, in contrast to Joseph Bonaparte Gulf with ∼10 cm for both. When the SLAs, are corrected for the residual tide heights of M2 and S2, the standard deviation of the SLA residuals is decreased by as much as ∼70% in Collier Bay indicating that X-Track altimetry can identify M2 and S2 tidal residuals in complex coastal regions.

Estimation of the Manning’s n coefficient in multi-constituent tidal models by assimilating satellite observations with the adjoint data assimilation

The bottom friction is critical for the dissipation of the global tidal energy. The bottom friction coefficient is traditionally determined using the Manning’s n formulation in tidal models. The Manning’s n coefficient in the Manning’s n formulation is vital for the accurate simulation and prediction of the tide in coastal shallow waters, but it cannot be directly measured and contains large amounts of uncertainties. Based on a two-dimensional multi-constituent tidal model with the adjoint data assimilation, the estimation of the Manning’s n coefficient is investigated by assimilating satellite observations in the Bohai, Yellow and East China Seas with the simulation of four principal tidal constituents M2, S2, K1 and O1. In the twin experiments, the Manning’s n coefficient is assumed to be constant, and it is estimated by assimilating the synthetic observations at the spatial locations of the satellite tracks. Regardless the inclusion of artificial random observational errors associated with synthetic observations, the model performance is improved as evaluated by the independent synthetic observations. The prescribed ‘real’ Manning’s n coefficient is reasonably estimated, indicating that the adjoint data assimilation is an effective method to estimate the Manning’s n coefficient in multi-constituent tidal models. In the practical experiments, the errors between the independent observations at the tidal gauge stations and the corresponding simulated results of the four principal tidal constituents are substantially decreased under both scenarios of the constant and spatially-temporally varying Manning’s n coefficient estimated by assimilating the satellite observations with the adjoint data assimilation. In addition, the estimated spatial and temporal variation trend is robust and not affected by the model settings. The spatially-temporally varying Manning’s n coefficient is negatively correlated with the current speed and shows significant spatial variation in the shallow water areas. This study demonstrates that the Manning’s n coefficient can be reasonably estimated by the adjoint data assimilation, which allows significant improvement in accurate simulation of the ocean tide.

Barotropic tides in MPAS-Ocean (E3SM V2): impact of ice shelf cavities

Abstract. Oceanic tides are seldom represented in Earth system models (ESMs) owing to the need for high horizontal resolution to accurately represent the associated barotropic waves close to coasts. This paper presents results of tides implemented in the Model for Prediction Across Scales–Ocean or MPAS-Ocean, which is the ocean component within the U.S. Department of Energy developed Energy Exascale Earth System Model (E3SM). MPAS-Ocean circumvents the limitation of low resolution using unstructured global meshing. We are at this stage simulating the largest semidiurnal (M2, S2, N2) and diurnal (K1, O1) tidal constituents in a single-layer version of MPAS-O. First, we show that the tidal constituents calculated using MPAS-Ocean closely agree with the results of the global tidal prediction model TPXO8 when suitably tuned topographic wave drag and bottom drag coefficients are employed. Thereafter, we present the sensitivity of global tidal evolution due to the presence of Antarctic ice shelf cavities. The effect of ice shelves on the amplitude and phase of tidal constituents are presented. Lower values of complex errors (with respect to TPXO8 results) for the M2 tidal constituents are observed when the ice shelf is added in the simulations, with particularly strong improvement in the Southern Ocean. Our work points towards future research with varying Antarctic ice shelf geometries and sea ice coupling that might lead to better comparison and prediction of tides and thus better prediction of sea-level rise and also the future climate variability.

Improved Estimation of the Open Boundary Conditions in Tidal Models Using Trigonometric Polynomials Fitting Scheme

Tidal open boundary conditions (OBCs) of the M2 tidal constituent in the Bohai and Yellow Seas (BYS) are estimated via the assimilation of multi-satellite altimeter data to optimize regional tidal numerical simulation. A two-dimensional adjoint assimilation model is used for tidal numerical simulation and, as an improvement, trigonometric polynomials fitting (TPF) is applied in the inversion of OBCs. It is assumed that the linearized amplitudes/phases in the open boundary are spatially varying and can be represented by nonlinear functions. Based on the discrete Fourier series, taking the trigonometric function as the basis function, the spatially varying OBCs are constructed by selecting the maximum truncation period. The independent points scheme used in previous studies was also compared in the experiments. Twin experiments show that the errors of simulations with TPF are the smallest in different schemes, and their results show the highest correlation with observations while maintaining the best performance in terms of observation errors. The mean absolute errors (MAEs) in amplitude/phase between the simulated results using estimated OBCs and the satellite altimeter records are 2.82 cm and 2.26°, respectively.

A Method Using the Huber Function for Inversion of Tidal Open Boundary Conditions of the M2 Constituent in the Bohai and Yellow Seas

Abstract The adjoint assimilation method has been widely used in various ocean models, and a series of technical schemes have been developed at the same time. Open boundary conditions (OBCs) in the two-dimensional (2D) tidal model of the M2 tidal constituent in the Bohai and the Yellow Seas (BYS) were inverted successfully using the adjoint assimilation methods in previous studies. However, the cost function in the adjoint assimilation method usually used the L2 norm in the past, which is difficult to maintain the robustness of the method when there are outliers. Meanwhile, using the L1 norm with strong robustness will shield the outliers’ information fully. Therefore, we propose a new scheme that replaces the L2 norm with the Huber function to improve the robustness of the adjoint assimilation method and absorb the data’s useful information to some extent. This scheme was verified in the ideal experiments in which magnitudes of the misfit vector were significantly reduced and the quality control (QC) process was simplified consequently. In the practical experiments, the introduction of the Huber function improved the accuracy of inversion in the inshore area using mixed data containing tide gauges and satellite altimetry. With this scheme, the root-mean-square errors (RMSEs) between the estimation and the observed values at tide gauge stations were reduced from ∼8 cm with the original scheme to ∼6 cm. Testing the new scheme in more complex models and how it might be affected remains a topic for future study. Significance Statement The adjoint assimilation method has been effectively applied in various ocean models. The cost function in the adjoint assimilation is usually in the form of the L2 norm, which presents poor robustness. By using the Huber function instead of the L2 norm as the cost function, we proposed a new scheme that can perfectly handle the potential outliers in data and noticeably improve the robustness of the adjoint assimilation method. The new method was applied to the inversion of tidal open boundary conditions of the M2 constituent in the Bohai and the Yellow Seas. Both the ideal and practical experiments verified the effectiveness of the developed scheme.

Географическое и сезонное распределение поля приливной объемной силы в Охотском море в контексте динамики внутренних волн

Estimates of the barotropic tidal body force for diurnal and semidiurnal tides are obtained for the Sea of Okhotsk for the summer and winter periods. It is shown that in the study area, the tidal body force for diurnal tides is significantly greater than for semidiurnal ones. The maximum values of this quantity can reach about 2-8 m2s-2, and these values are typical for areas with a sharp bathymetric gradient. A comparison of the tidal body force for the two seasons showed noticeable differences. The features of the transformation of a barotropic tidal wave propagating in the zone of large values of the tidal body force for the K1, O1, M2 tidal constituents are demonstrated. Numerical simulations indicate that baroclinic tidal waves are effectively generated in this area, and intense short-period internal waves are likely to occur.

The Temporal Evolution of Coastlines in the Bohai Sea and Its Impact on Hydrodynamics

Over the past 40 years, increasing coastal reclamation and natural sedimentation has changed coastline positions and resulted in variation in the hydrodynamic environment in the Bohai Sea (BHS), China. Based on the Landsat series images, an interpretative identifier for identifying the coastline was proposed to assess the hydrodynamic changes caused by the coastline change and was applied to a typical case of the Bohai Sea (BHS), China. We combined a grid-based coastline position with an adjoint data assimilation method to seamlessly map the distribution of the amplitude, phase lag, and tidal current of the M2 tidal constituent along the BHS’s coast from 1985 to 2018. Our findings reveal that the coastline change at long time scales dominated reclamation, and around 72.9% of the coastline of the BHS mapped in 2018 had seaward movement compared with its position in 1985. From 1985 to 2018, the BHS volume decreased by 0.17%, the sea surface area decreased by 4.54%, and the kinetic energy increased by 2.53%. The change in the coastline increased the amplitude of the M2 tidal constituent in the Bohai Bay by 6–14 cm and increased the residual current in the eastern coast of the Liaodong Bay by up to 0.07 (0.01) m/s.

Wind-driven ambient noise in seasonally ice-covered waters north of the Svalbard Archipelago

This paper presents analysis of a one-year (2018–2019) recording of ambient noise (40–2000 Hz) at a seasonally ice-covered location on the continental slope between the Svalbard archipelago and the Nansen Basin, northeast Atlantic Arctic. Time series of ambient noise show highest correlations with ice concentration and wind speed. A log-wind speed regression model is fitted to spectral noise data for three categories of ice concentration. Wind-speed dependence decreases with increasing ice concentration and increases with frequency, except at high ice concentration. Periodicity in noise during the ice-covered season is related to the M2 and M4 tidal current constituents.

Wind- and tidal driven ambient noise in seasonally ice-covered waters north of the Svalbard archipelago.

This paper presents analysis of a 1-year (2018-2019) recording of ambient noise (40-2000 Hz) at a seasonally ice-covered location on the continental slope between the Svalbard archipelago and the Nansen Basin, northeast Atlantic Arctic. Time series of ambient noise show highest correlations with ice concentration and wind speed. A log-wind speed regression model is fitted to spectral noise data for three categories of ice concentration. Wind-speed dependence decreases with increasing ice concentration and increases with frequency, except at high ice concentration. Periodicity in noise during the ice-covered season is related to the M2 and M4 tidal current constituents.

Test of ocean tide loading models on the basis of strain data measured at the Vyhne Tidal Station, Slovakia

Tidal strain time series recorded at the Vyhne Tidal Station are used to test thirteen different ocean tide loading models. Ten models have been calculated using SPOTL: EOT11a, HAMTIDE11a, OSU.TPXO72atlas, OSU.TPXO72, TPX070, DTU10, CSR4.0, FES2004, FES95.2.1, SCHW1 and three other models were chosen from the Free Ocean Tide Loading Provider (FOTLP) created by Scherneck and Bos: FES2012, FES2014b, GOT00.2. Hourly sampled strain data, corrected for temperature, were subjected to correction for ocean tide loading. The test of models was focused on the diurnal and semi-diurnal tidal harmonic constituents O1, P1, K1 and M2. A negligible difference between the individual global ocean tide loading models was only found mainly due to using different Earth models and Green functions. The amplitude factors for O1, P1, K1 and M2 derived from the measurements are 1.019, 1.226, 0.842 and 1.131, respectively. The average amplitude factors for these tidal components were obtained after ocean load correction using SPOTL routines: 1.121, 1.332, 0.916, 1.283, and in the case of the three models using FOTLP: 1.046, 1.486, 1.067, 1.317. The corrected amplitude factor became closer to the theoretical value only for K1.

Mapping Ocean Tidal for the Coast of East Sea Area, Viet Nam, by Using the Numerical Model in Curvilinear Coordinates

Tides and their effects on coastal and estuarine water levels are among the most well-known phenomena in coastal research. This study aims to map the tidal constituent features in the near-shore East Sea area, for better understanding of the mechanisms that cause the transport of sediments in the area. Furthermore, the study also points to the potential of tidal energy in the area, clean energy that needs to be studied for exploitation. The authors applied the hydraulic model in the curvilinear coordinates to calculate for 4 main tidal constituents in the near-shore, namely K1, O1, M2, and S2 in the East Sea area, Vietnam. The hydraulic model with two-dimensional orthogonal curvilinear grid has the advantage of increasing the accuracy in the results at the domain boundary, with the applying potential in future small-scale studies in the region. According to this method, the simulation results in areas with complex terrain are better because the velocity field is calculated on a curved grid built by shorelines). The calibration and validation of this model are based on water level data at hydrological stations along the Vietnamese coastline. The result of this model is used to map the harmonic constants and tidal ellipse for four tidal constituents; these help to gain information about the tidal deposition in the East Sea, Viet Nam. The coastal area of Vietnam has potential tidal energy; the largest energy is the tidal constituent O1, followed by the tidal constituents K1, M2, and S2. Tidal ellipses of the residual tidal constituent K1 and O1 are large in the Gulf of Tonkin and the Gulf of Thailand. Meanwhile, residual tidal constituent M2 and S2 are large in the southeast of Vietnam coastal. These results are the primary data for future research in the area.

Tidal dynamics in palaeo‐seas in response to changes in physiography, tidal forcing and bed shear stress

AbstractSimulating hydrodynamic conditions in palaeo‐ocean basins is needed to better understand the effects of tidal forcing on the sedimentary record. When combined with sedimentary analyses, hydrodynamic modelling can help inform complex temporal and spatial variability in the sediment distribution of tide‐dominated palaeo‐ocean basins. Herein, palaeotidal modelling of the epicontinental Upper Jurassic (160 Ma, lower Oxfordian) Sundance and Curtis seas of North America reveals possible regional‐scale variations in tidal dynamics in response to changes in ocean tidal forcing, physiographic configuration and bottom drag coefficient. A numerical model forced with an M2 tidal constituent at the open boundary shows that the magnitude and location of tidal amplification, and the variability in current velocity and bed shear stress in the basin, were controlled by palaeophysiography. Numerical results obtained using a depth of 600 m at the ocean boundary of the system enable the prediction of major facies trends observed in the lower Curtis Formation. The simulation results also highlight that certain palaeophysiographic configurations can either permit or prevent tidal resonance, leading to an overall amplification or dampening of tides across the basin. Furthermore, some palaeophysiographic configurations generated additional tidal harmonics in specific parts of the basins. Consequently, similar sedimentary successions can emerge from a variety of relative sea‐level scenarios, and a variety of sedimentary successions may be deposited in different parts of the basin in any given relative sea‐level scenario. These results suggest that the interpretation of sedimentary successions deposited in strongly tide‐influenced basins should consider changes in tidal dynamics in response to changing sea level and basin physiography.

An estimation of water levels associated with a storm along the coast of Bangladesh using a non-central difference method of lines

In this paper, depth-averaged shallow water equations were solved using a non-central difference method of lines together with the classical RK(4,4) method to estimate water levels associated with a cyclone along the coast of Bangladesh. A 4-point backward finite difference method was adopted in discretizing spatial derivatives retaining time derivatives as continuous. Thus, the shallow water equations together with the boundary conditions were transformed into a system of initial value problems, which was solved using the RK(4,4) method. A nesting approach was employed to incorporate the land-sea interface and bottom topography effectively with economic cost. A stable tidal oscillation was generated in the domain applying the M2 tidal constituent along the southern boundary of the parent model and the surge model was then run to get water levels owing to dynamic tide-surge interaction. Numerical experiments were performed to simulate water levels due to tide, surge, and nonlinear tide-surge interactions associated with the cyclonic storm, AILA. The obtained results were in good agreement with those attained in some previous studies and observations and the WLs due to the nonlinear tide-surge interaction were in a reasonable agreement with respect to the root mean square error values and predictive skills.

M2 tidal energy extraction in the Western Waters of Aceh, Indonesia

The influence of the principal lunar semidiurnal tidal constituent M2 is significant in the Malacca Strait, the Andaman Sea, and the Bay of Bengal. However, in the Indian Ocean, due to depth, the influence is not as strong as in those regions. The Western Waters of Aceh are directly adjacent to the Indian Ocean, the Andaman Sea, and the Malacca Strait. This study aims to map the tidal energy potential of M2 along the west coast of Aceh. The energy derived from tides is used as renewable energy to support the government's development targets. This study considered a power formula produced by a tidal turbine. The current velocity and elevation results showed excellent results. The weak tidal currents are evenly distributed in the south of the domain, but the tidal currents are strong in the north of the research domain because of the shallower depths and narrow gaps. Based on the magnitude of the current velocity, the extracted power is significant in the northern domain, reaching 337.08 kWh in one M2 period, or 507.36 kWh in a day. This amount is obtained from the power generated when the current reaches the blade, with a minimum of 3.79 W and a maximum of 6.37 kW. The total power obtained in the conversion of electrical power units was 507.36 kWh in one day. The location with the highest extraction has a depth of 24–43 m at sea level; thus, building a tidal turbine power plant is very possible.

Morphodynamic Equilibria in Double‐Inlet Systems: Existence and Stability

AbstractThe existence of morphodynamic equilibria of double‐inlet systems is investigated using a cross‐sectionally averaged morphodynamic model. The number of possible equilibria and their stability strongly depend on the forcing conditions and geometry considered. This is illustrated by considering a rectangular double‐inlet system forced by M2 tidal constituents only. Depending on the M2 amplitudes and phases at both entrances, no equilibrium, one equilibrium or multiple morphodynamic equilibria may exist. In case no equilibrium is found, the minimum water depth becomes zero somewhere in the system, reducing the double‐inlet system to two single‐inlet systems. In the other cases, the location of the minimum water depth and the direction of the tidally‐averaged sediment transport, as well as their actual values, depend strongly on the M2 tidal characteristics. Such parameter sensitivity is also observed when including the residual and M4 forcing contributions to the water motion, and when allowing for width variations. This suggests that, when considering a specific system, the number and stability of morphodynamic equilibria, as well as the characteristics of these quantities, can only be assessed by investigating that specific system in detail. As an example, the Marsdiep‐Vlie inlet system in the Dutch Wadden Sea is considered. It is found that, by using parameter values and a geometry characteristic for this system, the water motion and bathymetry in morphodynamic equilibrium are qualitatively reproduced. Also the direction and order of magnitude of the tidally‐averaged suspended sediment transport compare well with those obtained from a high‐complexity numerical model.