Trend in North Sea Tidal Amplitudes

Trend in North Sea Tidal Amplitudes (for M2, S2 and M4

Improved shallow waters tidal estimates using satellite radar altimetry data and numerical modeling

Satellite observations can help in the retrieval of constituents in shallow waters. Noise contamination, however, makes smaller constituents irretrievable and large sources of error. Throughout shallow areas, the constituent’s relevancy changes. For example, near an amphidromic point where M2 relevance drops, so does the potential of satellite contribution for improving its accuracy. Moreover, shallow waters are generally influenced by many constituents (>100). Accurately retrieving all these constituents with satellite radar altimeter data alone is not possible. Series length requirements imposed by the Rayleigh criteria to separate constituents are still unavailable. Removing unwanted signals from satellite observations improves least-squares-based harmonic estimates, given an inversion matrix with the same condition number. This variance reduction is the core of the remove compute restore approach commonly used. First, residual harmonic sets are computed with the difference between observations and model background estimates through conventional or weighted least-squares. Then, the residual harmonics are added to the background model estimates. Here we implemented a method that extends the typical approach by including model background estimate and error covariance in the least-squares step. This inclusion helps to weigh between constituents well represented in the model and those that must be updated. To test the method, we designed a semi-synthetic experiment. First, we used tide gauge data to generate a satellite equivalent dataset and compared estimations between the two methods listed above and the model estimate. Next, we applied the method to compute tidal estimates along satellite radar altimeter tracks (T/P Jason) in the 2D Dutch Coastal Shelf Model (DCSMv6) domain. Results from the synthetic experiment show that the second method produces consistently better estimates reducing RSS consistently through temporal cross-validation. In addition, it provides an effective way of keeping as many constituents estimates as the model series can resolve, adding the benefits of satellite observations. Finally, results from the North Sea implementation show the new estimates increase the variance reduction of satellite residuals across the whole domain relative to background tidal estimates. The range of improvements varies between 0 and 3cm, which is significant given already very accurate model background estimates. The benefited areas include the English Channel, the Irish Sea, the English North-Sea Coast, the Bay of Biscay, the German Bight, and the North Atlantic region close to the upper boundary of the model domain

Modelling of annual sand transports at the Dutch lower shoreface

Dutch coastal policy aims for a safe, economically strong and attractive coast. This is achieved by maintaining the part of the coast that support these functions; the coastal foundation. The coastal foundation is maintained by means of sand nourishments. Up to now, it has been assumed that net transports across the coastal foundation's offshore boundary at the 20 m depth contour are negligibly small. In the framework of the Coastal Genesis 2.0 program we investigated sand transports across this boundary and across other depth contours at the lower shoreface. This paper presents a computationally efficient approach to compute the annual sand transport rates at the Dutch lower shoreface. It is based on the 3D Dutch Continental Shelf Model with Flexible Mesh (3D DCSM-FM), a wave transformation tool and a 1DV sand transport module. We validate the hydrodynamic input against field measurements and present flow, wave and sand transport computations for the years 2013–2017. Our computations show that the net annual sand transport rates along the Dutch coast are determined by peak tidal velocities (and asymmetry thereof), density driven residual flows, wind driven residual flows and waves. The annual mean alongshore transports vary along the continuous 20 m depth contour. The computed total cross-shore transports are onshore directed over the continuous 20 m, 18 m and 16 m depth contours and increase with decreasing water depth. The effect of density difference and wind on the 3D structure of the flow and on the sand transports cannot be neglected along the Dutch lower shoreface. Our computations show that excluding the effect of density results in a significant decrease of the onshore directed transports. Also switching off wind largely counteracts this effect. The net cross-shore transport is determined by a delicate balance between gross onshore and offshore transports, where wave conditions are important. We show an example for Scheveningen where the net cross-shore transport is onshore directed when including all wave conditions but would be offshore directed when excluding waves higher than 3.5 m. In contrast, at Callantsoog the highest waves contribute more to the offshore directed transports. These results suggest that storm conditions play an important role in the magnitude and direction of the net annual transport rates at the lower shoreface

Improved shallow waters tidal estimates using satellite radar altimetry data and numerical modeling

Satellite observations can help in the retrieval of constituents in shallow waters. Noise contamination, however, makes smaller constituents irretrievable and large sources of error. Throughout shallow areas, the constituent’s relevancy changes. For example, near an amphidromic point where M2 relevance drops, so does the potential of satellite contribution for improving its accuracy. Moreover, shallow waters are generally influenced by many constituents (>100). Accurately retrieving all these constituents with satellite radar altimeter data alone is not possible. Series length requirements imposed by the Rayleigh criteria to separate constituents are still unavailable. Removing unwanted signals from satellite observations improves least-squares-based harmonic estimates, given an inversion matrix with the same condition number. This variance reduction is the core of the remove compute restore approach commonly used. First, residual harmonic sets are computed with the difference between observations and model background estimates through conventional or weighted least-squares. Then, the residual harmonics are added to the background model estimates. Here we implemented a method that extends the typical approach by including model background estimate and error covariance in the least-squares step. This inclusion helps to weigh between constituents well represented in the model and those that must be updated. To test the method, we designed a semi-synthetic experiment. First, we used tide gauge data to generate a satellite equivalent dataset and compared estimations between the two methods listed above and the model estimate. Next, we applied the method to compute tidal estimates along satellite radar altimeter tracks (T/P Jason) in the 2D Dutch Coastal Shelf Model (DCSMv6) domain. Results from the synthetic experiment show that the second method produces consistently better estimates reducing RSS consistently through temporal cross-validation. In addition, it provides an effective way of keeping as many constituents estimates as the model series can resolve, adding the benefits of satellite observations. Finally, results from the North Sea implementation show the new estimates increase the variance reduction of satellite residuals across the whole domain relative to background tidal estimates. The range of improvements varies between 0 and 3cm, which is significant given already very accurate model background estimates. The benefited areas include the English Channel, the Irish Sea, the English North-Sea Coast, the Bay of Biscay, the German Bight, and the North Atlantic region close to the upper boundary of the model domain.Mathematical PhysicsPhysical and Space GeodesyEnvironmental Fluid Mechanic

Modelling of annual sand transports at the Dutch lower shoreface

Dutch coastal policy aims for a safe, economically strong and attractive coast. This is achieved by maintaining the part of the coast that support these functions; the coastal foundation. The coastal foundation is maintained by means of sand nourishments. Up to now, it has been assumed that net transports across the coastal foundation’s offshore boundary at the 20 m depth contour are negligibly small. In the framework of the Coastal Genesis 2.0 program we investigated sand transports across this boundary and across other depth contours at the lower shoreface. This paper presents a computationally efficient approach to compute the annual sand transport rates at the Dutch lower shoreface. It is based on the 3D Dutch Continental Shelf Model with Flexible Mesh (3D DCSM-FM), a wave transformation tool and a 1DV sand transport module. We validate the hydrodynamic input against field measurements and present flow, wave and sand transport computations for the years 2013–2017. Our computations show that the net annual sand transport rates along the Dutch coast are determined by peak tidal velocities (and asymmetry thereof), density driven residual flows, wind driven residual flows and waves. The annual mean alongshore transports vary along the continuous 20 m depth contour. The computed total cross-shore transports are onshore directed over the continuous 20 m, 18 m and 16 m depth contours and increase with decreasing water depth. The effect of density difference and wind on the 3D structure of the flow and on the sand transports cannot be neglected along the Dutch lower shoreface. Our computations show that excluding the effect of density results in a significant decrease of the onshore directed transports. Also switching off wind largely counteracts this effect. The net cross-shore transport is determined by a delicate balance between gross onshore and offshore transports, where wave conditions are important. We show an example for Scheveningen where the net cross-shore transport is onshore directed when including all wave conditions but would be offshore directed when excluding waves higher than 3.5 m. In contrast, at Callantsoog the highest waves contribute more to the offshore directed transports. These results suggest that storm conditions play an important role in the magnitude and direction of the net annual transport rates at the lower shoreface

The Evolution of Plume Fronts in the Rhine Region of Freshwater Influence

The Rhine region of freshwater influence (ROFI) is strongly stratified, rotational, relatively shallow and has large tides, resulting in a dynamic field of fronts that are formed by multiple processes. We use a 3D numerical model to obtain a conceptual picture of the frontal structure and the processes responsible for generating this multiple front structure in the Rhine ROFI. The horizontal salinity gradient and numerical tracers are used to identify three different types of fronts: outer, inner, tidal plume and relic tidal plume fronts. Tidal plume front (TPF) trajectories together with the tracers demonstrate that TPFs exist for longer than one tidal cycle. A Lagrangian frontogenesis analysis shows that the fronts are strengthened mainly as a result of increased convergence, which is observed to occur at times when tidal straining is large. Additionally the alongshore tidal excursion and the dominance of the tidal currents over the intrinsic frontal propagation speed, trap TPFs within 20 km from the river mouth. Trapping and re-strengthening maintain several fronts at a time in the mid-field region, resulting in a multi-frontal system. The observation of a complex river plume system is expected to be important for cross-shore exchange, transport and coastal ecology.Environmental Fluid Mechanic

Altimetry-derived tide model for improved tide and water level forecasting along the European continental shelf

With the continued rise in global mean sea level, operational predictions of tidal height and total water levels have become crucial for accurate estimations and understanding of sea level processes. The Dutch Continental Shelf Model in Delft3D Flexible Mesh (DCSM-FM) is developed at Deltares to operationally estimate the total water levels to help trigger early warning systems to mitigate against these extreme events. In this study, a regional version of the Empirical Ocean Tide model for the Northwest European Continental Sea (EOT-NECS) is developed with the aim to apply better tidal forcing along the boundary of the regional DCSM-FM. EOT-NECS is developed at DGFI-TUM by using 30 years of multi-mission along-track satellite altimetry to derive tidal constituents which are estimated both empirically and semi-empirically. Compared to the global model, EOT20, EOT-NECS showed a reduction in the root-square-sum error for the eight major tidal constituents of 0.68 cm compared to in situ tide gauges. When applying constituents from EOT-NECS at the boundaries of DCSM-FM, an overall improvement of 0.29 cm was seen in the root-mean-square error of tidal height estimations made by DCSM-FM, with some regions exceeding a 1 cm improvement. Furthermore, of the fourteen constituents tested, eleven showed a reduction of RMS when included at the boundary of DCSM-FM from EOT-NECS. The results demonstrate the importance of using the appropriate tide model(s) as boundary forcings, and in this study, the use of EOT-NECS has a positive impact on the total water level estimations made in the northwest European continental seas.Mathematical Physic

Modelling of annual sand transports at the Dutch lower shoreface

Dutch coastal policy aims for a safe, economically strong and attractive coast. This is achieved by maintaining the part of the coast that support these functions; the coastal foundation. The coastal foundation is maintained by means of sand nourishments. Up to now, it has been assumed that net transports across the coastal foundation's offshore boundary at the 20 m depth contour are negligibly small. In the framework of the Coastal Genesis 2.0 program we investigated sand transports across this boundary and across other depth contours at the lower shoreface. This paper presents a computationally efficient approach to compute the annual sand transport rates at the Dutch lower shoreface. It is based on the 3D Dutch Continental Shelf Model with Flexible Mesh (3D DCSM-FM), a wave transformation tool and a 1DV sand transport module. We validate the hydrodynamic input against field measurements and present flow, wave and sand transport computations for the years 2013–2017. Our computations show that the net annual sand transport rates along the Dutch coast are determined by peak tidal velocities (and asymmetry thereof), density driven residual flows, wind driven residual flows and waves. The annual mean alongshore transports vary along the continuous 20 m depth contour. The computed total cross-shore transports are onshore directed over the continuous 20 m, 18 m and 16 m depth contours and increase with decreasing water depth. The effect of density difference and wind on the 3D structure of the flow and on the sand transports cannot be neglected along the Dutch lower shoreface. Our computations show that excluding the effect of density results in a significant decrease of the onshore directed transports. Also switching off wind largely counteracts this effect. The net cross-shore transport is determined by a delicate balance between gross onshore and offshore transports, where wave conditions are important. We show an example for Scheveningen where the net cross-shore transport is onshore directed when including all wave conditions but would be offshore directed when excluding waves higher than 3.5 m. In contrast, at Callantsoog the highest waves contribute more to the offshore directed transports. These results suggest that storm conditions play an important role in the magnitude and direction of the net annual transport rates at the lower shoreface.Coastal Engineerin