Both empirical and assimilative global ocean tidal models are significantly more accurate in the deep ocean than in shelf and coastal waters. In this study, we answered whether this is due to the quality of the models used to reduce tide and surge or the general approach to treat tide and surge as two separate components of the water level obtained from stand-alone models, which ignores the nonlinear tide–surge interaction. In doing so, we used tide gauge observations as partially synthetic altimeter time series, tide–surge water-level time series obtained with the 2D Dutch Continental Shelf Model–Flexible Mesh (DCSM), and tide and surge water-level time series obtained using the DCSM, FES2014 (FES) and the Dynamic Atmospheric Correction (DAC) product. Expressed in the root-sum-square (RSS) of the eight main tidal constituents, we obtained a reduction (Formula presented.) % when removing the DCSM tide–surge water levels compared to when we removed the sum of the DCSM tide and DCSM surge water levels. The RSS obtained in the latter case was only 3.3% lower than with FES and DAC. We conclude that the lower tidal estimates accuracy in shelf-coastal waters derives from the missing nonlinear tide–surge interactions.

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Seagrass meadows provide valuable ecosystem services of coastal protection and chemical habitat formation that could help mitigate the impact of sea level rise and ocean acidification. However, the intensification of hydrodynamic forces caused by sea level rise, in addition to habitat degradation threaten the provision of these ecosystem services. With quantitative field measurements of the coastal protection and chemical habitat formation services of seagrass meadows, we statistically model the relationships between hydrodynamic forces, vegetation density and the provision of these ecosystem services. Utilising a high-resolution hydrodynamic model that simulates end of the century hydrodynamic conditions and three scenarios of coral reef degradation (i.e., keep up, remain or loss) we quantify how the environmental conditions within a tropical bay will change given changes to the provision of ecosystem services. Our study shows that increasing hydrodynamic forces lead to a seafloor made up of a larger grain size that is increasingly unstable and more vulnerable to erosion. The loss of a fringing reef leads to larger hydrodynamic forces entering the bay, however, the 0.87 m increase in depth due to sea-level rise reduces the bed shear stress in shallower areas, which limits the change in the ecosystem services provided by the current benthic seagrass meadow. Loss of seagrass constitutes the greatest change in a bay ecosystem, resulting in the sediment surface where seagrass existed becoming unstable and the median sediment grain size increasing by 5-7 %. The loss of seagrass also leads to the disappearance of the unique fluctuating chemical habitat, which leaves the surrounding community vulnerable to ocean acidification. A reduction or complete loss of these ecosystem services would impact the entire community assemblage while also leaving the surrounding coastline vulnerable to erosion, thus exacerbating negative effects brought about by climate change.

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The main objective of this study is to develop and analyze an empirical noise model for model-derived coastal summer mean water levels (SMWLs) and use that to obtain a more realistic quality impact of combining hydrodynamic leveling and Unified European Leveling Network (UELN) data in realizing the European Vertical Reference System (EVRS). We considered three state-of-the-art hydrodynamic models for the Northeast Atlantic Ocean, including the North Sea and Wadden Sea; AMM7, DCSMv6-ZUNOv4, and 3D DCSM-FM. Moreover, we assess the spatiotemporal performance of these three models in representing coastal SMWLs. The empirical noise models are determined from the differences between observation- and model-derived SMWLs at coastal tide gauges. All three noise models show that the model noise is indeed correlated over sea distances up to hundreds of kilometers. At the same time, they all show a relatively large discontinuity at the origin (i.e., nugget effect); between 12.1 cm² (3D DCSM-FM) and 16.3 cm² (DCSMv6-ZUNOv4). The variance (i.e., covariance at zero sea distance) for these two models is 15.3 cm² and 21.7 cm², respectively. Averaging the water levels over three summers, lowered the variance and nugget effect for 3D DCSM-FM to 12.7 cm² and 10.0 cm², respectively. Our analysis also showed that between 30 and 50% of the variance has to be attributed to errors in the vertical referencing of the tide gauges. We lacked the information to assess what proportion of the observed noise covariances should be attributed to these errors. The performance assessments revealed significant variations over both space and time as well as among the three hydrodynamic models. The results suggest that there is still room for model improvement. In the final experiments, we used the noise model of the best overall performing model (i.e., 3D DCSM-FM) to reassess the quality impact of combining hydrodynamic leveling and UELN data in realizing the EVRS. The results suggest that not including the noise covariances leads to an overestimation of the total quality impact by 7 % and 8 % , when we average the water levels over one and three summer periods, respectively.

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Tidal river plumes dominate many shelf seas, transporting freshwater, sediment, nutrients, pollutants and larvae downstream. The Rhine River Plume is one of the largest in Europe, under typical discharge conditions it is dominated by tidal plume fronts in the near to mid-field plume and by tidal straining in the mid- to far field plume. Moreover, in agreement with other tidal river plumes discharging onto the shelf, internal waves generated ahead of tidal plume fronts are an important source of mixing in the river plume. We compare field data collected downstream of the mouth of the Rhine River in 2013 and 2014 under typical discharge conditions, with data collected in the near field plume during 2022 during a major drought. Together with numerical models we explore how extreme variations in freshwater discharge impact both tidal straining and the formation and strength of tidal plume fronts. Furthermore we explore how in turn, this influences the structure and mixing of the near to far-field Rhine River Plume. We use a 3D hydrostatic model of the Rhine River Plume and a potential energy anomaly analysis to explore changes in the mixing. We explore how the river plume adjusts to extremely low discharge conditions and discuss the possible impact on the transport of freshwater, tracers, larvae and fine sediment.@en

All realizations of the European Vertical Reference System (EVRS) computed so far are solely based on geopotential differences obtained by spirit leveling/gravimetry. As such, there are no direct connections between height benchmarks separated by large water bodies. In this study, such connections are added by means of model-based hydrodynamic leveling resulting in a new, yet unofficial realization of the EVRS. The model-derived mean water levels used in computing the hydrodynamic leveling connections were obtained from the Nemo-Nordic (Baltic Sea) and 3D DCSM-FM (northwest European continental shelf) hydrodynamic models. The impact of model-based hydrodynamic leveling on the European Vertical Reference Frame is significant, especially for France and Great Britain. Compared to a solution which only uses spirit leveling/gravimetry, the differences in these countries reach tens to hundreds of kgalmm . We also observed an improved agreement with normal heights obtained by differencing GNSS and the European gravimetric quasi-geoid 2015 (EGG2015) heights. In Great Britain, the south-north slope of 48 mm deg ^{- 1} present in the solution which uses only spirit leveling/gravimetry data reduced to 2.2 mm deg ^{- 1} . In France, the improvement is confined to the southwest. The choice of the period over which water levels are averaged has an impact on the results as it determines, among others, the set of tide gauges available to establish the hydrodynamic leveling connections. When using an averaging period that can be considered as the least preferred choice based on three established criteria, the positive impact for France has gone. For Great Britain, the estimated south-north slope became 12.6 mm deg ^{- 1} . This is larger than the slope obtained using the most preferred averaging period but still substantially lower compared to the slope associated with a solution that uses only spirit leveling/gravimetry.

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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. @en

The sound speed provides insight in ocean properties, as it depends on depth, temperature and salinity. Here, we propose a method to invert sound speed profiles (SSPs) from multibeam echosounder (MBES) measurements, providing a SSP for every ping. Using erroneous SSPs results in a mismatch in the estimated bathymetry between overlapping swaths. The SSP is estimated by minimizing this mismatch using Differential Evolution. In this work, SSPs are described using empirical orthogonal functions (EOFs), which are obtained from historical SSPs. As a proof-of-concept, we apply the inversion on a simulated MBES survey, where the synthetically generated SSPs are fully described by 3 EOFs. The inverted SSPs deviate 1 m/s from the correct profiles. In the case of actual SSPs, more EOFs are possibly required. The number of required EOFs to get an accurate estimate of the SSP is assessed by using SSPs acquired in the North Sea. Results show that including only 2 EOFs is sufficient to accurately estimate the SSP, although larger deviations up to 3 m/s were found. In this paper, we demonstrated the potential of the proposed method to invert SSPs from MBES measurements, which can provide information about the vertical structure of the water column. @en

The first objective of this paper is to assess by means of geodetic network analyses the impact of adding model-based hydrodynamic leveling data to the Unified European Leveling Network (UELN) data on the precision and reliability of the European Vertical Reference Frame (EVRF). In doing so, we used variance information from the latest UELN adjustment. The model-based hydrodynamic leveling data are assumed to be obtained from not-yet existing hydrodynamic models covering either all European seas surrounding the European mainland or parts of it that provide the required mean water level with uniform precision. A heuristic search algorithm was implemented to identify the set of hydrodynamic leveling connections that provide the lowest median of the propagated height standard deviations. In the scenario in which we only allow for connections between tide gauges located in the same sea basin, all having a precision of 3 cm, the median of the propagated height standard deviations improved by 38 % compared to the spirit leveling-only solution. Except for the countries around the Black Sea, coastal countries benefit the most with a maximum improvement of 60 % for Great Britain. We also found decreased redundancy numbers for the observations in the coastal areas and over the entire Great Britain. Allowing for connections between tide gauges among all European seas increased the impact to 42%. Lowering the precision of the hydrodynamic leveling data lowers the impact. The results show, however, that even in case the assumed precision is 5 cm, the overall improvement is still 29%. The second objective is to identify which tide gauges are most profitable in terms of impact. Our results show that these are the ones located in Sweden in which most height markers are located. The impact, however, hardly depends on the geographic location of the tide gauges within a country.

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Shallow tropical bays in the Caribbean, like Orient Bay and Galion Bay in Saint Martin, are often sheltered by coral reefs. In the relatively calm environment behind the reefs, seagrass meadows grow. Together, these ecosystems provide valuable ecosystem services like coastal protection, biodiversity hotspots, nursery grounds for animals and enhancing tourism and fisheries. However, sea-level rise imperils these ecosystems and the services they provide because of changing hydrodynamic conditions, with potential effects on the interdependencies between these ecosystems. By means of a hydrodynamic model that accounts for the interaction with vegetation (Delft3D Flexible Mesh), the impact of sea-level rise (0.87 m in 2100) is investigated for three scenarios of future reef development (i.e. keep-up, give-up and catch-up). If coral reefs cannot keep up with sea-level rise, the wave height and flow velocity increase significantly within associated bays, with the wave height doubling locally in case of eroding reefs in our model simulations. Since the presence of seagrass strongly depends on the hydrodynamic conditions, the response of seagrass to the future hydrodynamic conditions is projected using a habitat suitability model that is based on a logistic regression. The spatial character of the bays determines the response of seagrass. In Orient Bay, which is deeper and partly exposed to higher waves, the seagrass will likely migrate from the deeper parts to shallow areas that become suitable for seagrass because of the surf zone moving landward. In contrast, the conditions for seagrass worsen in Galion Bay for the catch-up and give-up scenario; due to the shallowness of this bay, the seagrass cannot escape to more suitable areas, resulting in significant seagrass loss. It is shown that healthy coastal ecosystems are able to limit the change in hydrodynamic conditions due to sea-level rise. Therefore, preserving these ecosystems is key for ensuring the resilience of shallow tropical bays to sea-level rise and maintaining their ecosystem services.

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