This study exploits an earlier-developed analytical noise autocovariance model to evaluate two complementary post-processing strategies for noise reduction in SAR altimetry. Firstly, we develop an Optimal Filtering (OF) scheme to produce improved 20 Hz products from data at higher posting rates—and underline that an arithmetic mean is not suited for this purpose, because it leads to spurious along-track correlations. Secondly, we tailor the existing High-Frequency Adjustment (HFA) to SAR altimetry, which can readily be applied to data at a 20 Hz posting rate. In contrast to earlier works, we derive the HFA slope directly from the noise model.Both post-processing strategies are applied to ten days of unfocused SAR (UF-SAR) data from Sentinel-3 and Sentinel-6 processed at a 140 Hz posting rate. The precision gains are quantified by comparison of the 20-Hz noise levels of Sea Level Anomaly (SLA) and Significant Wave Height (SWH) estimates. The application of the HFA yields average noise reductions of 7–9% for both missions, while the OF achieves 14–17% for Sentinel-3 and 9–11% for Sentinel-6. While the OF achieves to reduce the noise floor over the whole spectral range, the HFA can only reduce the noise beyond a chosen cut-off frequency. We find that the achievable precision gains from increased posting rates are much lower than reported in earlier studies, because they applied the unsuited arithmetic mean for the compression to 20 Hz.All the improvements obtained on the data are well predicted by the noise model, so we suggest the latter as a helpful tool for future mission design and algorithm evolution. Some noteworthy conclusions from the model are (i) that optimal filtering of data at 80 Hz and 140 Hz posting rates can yield similar 20-Hz precision gains and (ii) the current UF-SAR 20-Hz noise levels in Sentinel-3 and Sentinel-6 data are far from the theoretically possible performance. Particularly in high sea states SWH > 7 m, LR-RMC processing in combination with Weighted Least Squares fitting of the waveforms can reduce the absolute 20-Hz noise levels of both SSH and SWH by more than 50% with respect to UF-SAR for both Sentinel-3 and Sentinel-6. Our results confirm that a significant fraction of the 20-Hz noise level in UFSAR is instead small scale signal variability, as it is not explained by speckle.

Abstract Coastal regions are increasingly exposed to sea-level rise and intensifying storm surges, underscoring the urgent need for accurate long-term predictions of extreme water levels to support robust adaptation planning. Physics-based hydrodynamic storm surge models remain the gold standard for such projections, but are computationally demanding, limiting their feasibility for producing the large scenario ensembles needed under deep uncertainty. Artificial intelligence surrogate models have emerged as a promising alternative. Yet, current approaches often underrepresent rare extremes and lack validation under future climate conditions, constraining their application for long-term planning. Here, we develop a deep learning surrogate model trained on hydrodynamic simulations from the Global Tide and Surge Model (GTSM), with both historical reanalysis and high-resolution climate projections (CMIP6 HighResMIP). Using New York City, a highly vulnerable urban coastline with extensive surge records, as a testbed, we demonstrate the model's ability to represent extreme storm surges under both historical and mid-21st-century scenarios. To enhance performance on extremes, we propose a novel asymmetric loss function, combining quantile and expectile losses, which substantially improves predictions of rare storm surge events, while maintaining high overall performance. Fine-tuning with climate model outputs further aligns the surrogate's estimates with those of the hydrodynamic model across spatial and temporal scales. Under future climate forcing, projections obtained with the surrogate model closely reproduce the response of GTSM, capturing projected trends in extreme events. This open-data-based framework provides a computationally efficient and globally transferable approach for storm surge projection, enabling the large-scale scenario analyses required for climate-resilient coastal planning.

State space models are well-suited for time series in which the evolution of variables cannot be well represented by deterministic basis functions. A key challenge in using state space models is the selection of the noise variance parameters. To better understand their impact on the model's filtering behavior, we derive the frequency response of several commonly used state space models by utilizing the connection between the Kalman smoother and regularized least squares problems. We show that the frequency response reveals distinguishing spectral features between competing state space models and explains the flattening of the log-likelihood function when the ratio of observation to disturbance variance becomes large. Using Dutch tide gauge data, we illustrate how the frequency response can be used to make informed decisions about the variance parameters, which could in turn support more reliable interpretations of time series data.

A Wave Data Assimilation System based on the Ensemble Kalman Filter (EnKF) is implemented for the North Sea showing improved performance and physical consistency. We first show the EnKF implementation and illustrate the wave data assimilation system using identical twin experiments to assimilate synthetic observations from buoys. A sensitivity analysis shows that the ensemble size, assimilation frequency and observation uncertainty are relatively important settings. Lastly, the potential for assimilating satellite measurements was assessed by assimilating synthetic altimeter measurements with real pass-over tracks. In these experiments, the state contains the full wave spectrum, unlike in most existing schemes. The results show that wave spectra and integral variables beyond significant wave height show physically consistent updates for the buoy and satellite experiments, by assimilating only significant wave height. This is a key advantage of this implementation compared to the more widely used implementations in wave data assimilation. Although the satellite experiment performs slightly worse than the buoy experiment due to decreased temporal availability of measurements, the results underline the potential for assimilation of satellite altimeter measurements. Such a system provides a promising framework for future observation impact study using satellite altimeter measurements.

Accurate storm surge modeling is essential for predicting coastal flooding and mitigating impacts on vulnerable regions. This study evaluates the influence of different sea surface drag parameterizations on surge predictions using the Global Tide and Surge Model (GTSM) over a 10-year period (2006–2015) and two storm events. Four model experiments were tested, ranging from a fully dynamic formulation, including variable air density, atmospheric stability, and sea-state-dependent drag, to a simplified constant-drag approach. Results show that advanced drag formulations reduced the underestimation of annual maximum surge values from 18% to 12% globally, with the variable Charnock parameter contributing the most. Conversely, using a constant Charnock value and thereby neglecting wave-dependent roughness increases prediction errors, especially in regions with highly variable sea states. Case studies of Storm Xaver (2013) and Hurricane Fiona (2022) show that advanced parameterizations better capture wind stress variations, reducing root mean square error from 0.21 m to 0.16 m for Xaver and improving surge predictions by up to 0.30 m for Fiona. Consistent with earlier studies, a persistent underestimation of extreme surge events remains across all experiments. While wave-dependent roughness improves performance, no single parameter fully explains this bias. However, wave-dependent roughness particularly enhances model performance in high-latitude and storm-prone areas, where sea state and atmospheric conditions vary widely. Our results show that variations in air density and atmospheric stability have minimal impact on surge height. As such, prioritizing the implementation of dynamic, sea-state-dependent drag formulations, particularly variable Charnock, is key to further improving the accuracy of storm surge forecasting systems and future projections.

Measurements of tides are relatively sparse in the Arctic. This paper studies GNSS buoy tracks to complement existing data. Existing methods to perform tidal harmonic analysis of the buoy data are inadequate in the Arctic region because these methods for tidal analysis combine data from multiple buoy tracks, which is often infeasible in the Arctic. Moreover, we find that there are significant spatial and temporal variations in amplitudes and phases in baroclinic zones. To address these complexities, we introduce a new approach–Model-derived Fitting Method–to estimate the tidal current constituents (TCC) from a single buoy trajectory. Our study assesses the proposed method by analyzing GNSS buoy data from three Arctic regions characterized by barotropic or baroclinic tidal currents. Through detailed case studies in the Barents Sea, Chukchi Sea, and Baffin Bay, our approach demonstrates accuracy, robustness, and operational capabilities. In the Barents Sea, TCC estimates from two buoys were compared at a common location within their trajectories and compared against model estimates. In the Chukchi Sea's barotropic dominant zone, our method's estimates were evaluated against nearby ADCP mooring data. In Baffin Bay, known for baroclinic currents, a synthetic evaluation confirmed the method's effectiveness. Our study also highlights that phase variations along buoy trajectories can lead to frequency shifts in the spectrum, similar to the Doppler shift effect, particularly notable in regions with baroclinic tides.

The Rhine-Meuse Delta is a low-lying delta in the Netherlands that is subject to both salt intrusion events and storm surges. Typically, storm surges only temporarily cause increased salt intrusion and do not cause severe problems for freshwater availability. However, during the storm surge of December 2013, salt reached the closed southern branch of the delta and higher salinities were observed for weeks after the storm surge. The purpose of this study is to examine the mechanisms controlling salt intrusion in the Rhine-Meuse Delta during and after a severe storm surge event. A three-dimensional hydrodynamic model (Delft3D-FM) of the Rhine-Meuse Delta was developed that successfully reproduces salt intrusion for both normal and storm surge conditions. During the storm, high water levels in the northern branch caused a salt flux toward the southern branch. The southern branch of the Rhine-Meuse Delta is closed off by an estuarine dam, consequently salt was retained landward of the dam. Local stratification in the southern branch caused salt to remain in the deeper parts, limiting the effectiveness of flushing after the storm surge. In the post-storm period, salt was gradually released from the southern branch, raising salinity levels in an adjacent channel. The river discharge was only just below the yearly average, showing prolonged salt intrusion can also occur outside of dry periods.

Tidal models that incorporate satellite altimeter data have historically shown discrepancies in accuracy between shallow and deep marine environments. A recent study suggests that these differences may partly stem from neglecting the nonlinear tide-surge interactions in tidal analyses. In this study, we introduce a novel method for estimating tidal constituents from satellite altimeter data in shallow waters, leveraging a 2D hydrodynamic model that accounts for these nonlinear interactions. This approach substantially reduces the variance of unaccounted water level variability, thereby benefiting the estimation. A distinctive feature of our method is the treatment of prior model tidal constituents as stochastic, which helps manage the low temporal resolution of altimeter data by ensuring that unresolved tidal constituents are not updated. We tested our method in the data-rich northwest European continental shelf region, using the high-resolution 2D Dutch Continental Shelf Model version 7 (DCSM). Results show a substantial reduction in the standard deviations of residual water level time series in the shallow waters around Great Britain and in the German Bight, from 11 cm to 5 cm. In deep waters (>200 m), the median standard deviation decreased from 6.8 cm to 6.2 cm. When compared to state-of-the-art ocean tide and surge corrections from publicly available models, our method outperformed them in shallow waters (median standard deviation of 6.0 cm versus 7.5 cm), though the alternative products performed better in deep waters (median standard deviation of 5.5 cm versus 6.2 cm). An estimate of the accuracy at satellite crossovers resulted in an estimated total tidal error of about 1.5 cm (RSS VD). We acknowledge that comparisons in shallow waters are complicated, as alternative products do not account for nonlinear tide-surge interactions. Overall, the demonstration along-track tidal product developed in this study shows potential for improving the tidal representation in the DCSM model. In data-poor regions, the number of tidal constituents that can be reliably estimated using the method may be limited, and alternative strategies might be needed to evaluate the model’s uncertainty in representing tides.

Deltas are home to billions of people and are often highly developed and engineered systems. Extreme weather events such as droughts are a threat to deltas worldwide. During droughts salt can intrude far inland and threaten the drinking, agricultural and industrial water supply of many people. Under climate change the frequency of extreme events is expected to increase and the threat of salt intrusion may intensify. Here we use data and models to explore salt intrusion in the Rhine-Meuse Delta (RMD) during the severe European drought in the summer of 2022. The RMD is one of the most highly managed deltas in the world, with numerous interconnected waterways and an open connection to the sea at the mouth of the Rotterdam Waterway. The outflow of the Rhine River through the Rotterdam Waterway generates the strongly stratified Rhine River plume. Under normal conditions a salt wedge intrudes about 16-18 km inland on every tide. In contrast, under drought conditions in summer 2022, observations show salt intruding over 42 km inland and the Rhine River plume diminished in size. We explore the changes in estuarine dynamics during the drought using velocity, salinity and temperature data from various field campaigns near the mouth of the Rotterdam Waterway and within the delta, together with numerical models. We also compare drought condition observations with data from prior field campaigns during normal discharge conditions. Shifts in the relative strength of the dominant mechanisms of landward salt flux throughout the drought are explored and linked to the changes in estuarine response.

Traditionally, nadir-looking satellite radar altimeters provide water levels of rivers only at intersections with the satellite's ground track, called virtual stations. These observations have limited spatial coverage because such cross-overs are sparse, depending on the altimeter's orbit. In this work, we introduce the novel concept of Polygon-Informed Cross-Track Altimetry (PICTA), enabling accurate estimation of water levels at cross-track distances — for as long as the target's signal is recorded in the altimeter's range window. Using fully-focused SAR data from the Sentinel-6 altimetry mission, we demonstrate how the new approach can provide detailed river water level profiles over a ground swath of about 14 km cross-track width and with an along-track resolution as fine as 10 m. On the one hand, this marks a drastic improvement in the number of available measurements when compared to the virtual station approach, on the other hand, for the first time, water surface slopes and level variations along the river, caused by rapids, dams, and sluices, can be directly observed using a nadir radar altimeter. The validation over two river segments in France reveals biases as low as ±4 cm and random errors on the order of 3–8 cm at 30 m along-track resolution. The new PICTA concept can potentially be generalized to other targets, such as lakes or even coastlines.

Multi-mission satellite altimetry data have been used to study the spatial and temporal variability in global storm surge water levels. This was done by means of a time-dependent extreme value analysis applied to the monthly maximum detided water levels. To account for the limited temporal resolution of the satellite data, the data were first stacked on a 5^∘× 5^∘ grid. Moreover, additional scaling was applied to the extreme value analysis for which the scaling factors were determined by means of a resampling method using reanalysis data. In addition to the conventional analysis using data from tide gauges, this study provides an insight in the ocean-wide storm surge properties. Nonetheless, where possible, results were compared to similar information derived from tide gauge data. Except for secular changes, the satellite-derived results are comparable to the information derived from tide gauges (correlation > 0.5), although the tide gauges show more local variability. Where limited correlation was observed for the secular change, it was suggested that the satellites may not be able to fully capture the temporal variability in the short-lived, tropical storms, as opposed to extra-tropical storms.

Traditionally, nadir-looking satellite radar altimeters provide water surface elevations of rivers only at intersections with the satellite’s ground track, called virtual stations. These observations have limited spatial coverage because such cross-overs are sparse, depending on the altimeter's orbit. In this work, we introduce the novel concept of Polygon-Informed Cross-Track Altimetry (PICTA), enabling precise measurement of water surface elevations at cross-track distances---for as long as the target's signal is recorded in the altimeter's range window. Using fully-focused SAR data from the Sentinel-6 altimetry mission, we demonstrate how the new approach can provide detailed river elevation profiles over a ground swath of about 14 km cross-track width and with an along-track resolution as fine as 10 m. On the one hand, this marks a drastic improvement in the number of available measurements when compared to the virtual station approach, on the other hand, for the first time, water surface slopes and level variations along the river, caused by rapids, dams, and sluices, can be directly observed using a nadir radar altimeter. The validation over two river segments in France reveals biases as low as [[EQUATION]]4 cm and random errors on the order of 3 to 8 cm at 30 m along-track resolution. The new PICTA concept can potentially be generalized to other targets, such as lakes or even coastlines.

Arctic sea ice leads to a significant dissipation of tidal energy, necessitating its inclusion in global tidal models. However, most global tidal models either neglect or only partially incorporate the impact of sea ice on tides. This study proposes a method to model the dissipative forces exerted by sea ice on tides without directly coupling to a sea ice model, yet utilizing sea ice parameters such as thickness and concentration. Our approach involves (re)-categorizing the sea ice cover into regions dominated either by the velocity difference between sea ice and tides (Vertical Shear (VS)) or by the shear from drifting sea ice on tides (Horizontal Shear (HS)), which primarily govern the energy dissipation between tides and sea ice. The subdivision and resulting areas of these HS and VS regions are based on a nondimensional number referred to as the Friction number, which is the ratio of the internal stress of the sea ice field to the ice–water frictional stress, and directly depends on the thickness and concentration of the sea ice. The new parameterization is validated through a performance assessment comparing it to a commonly used approach of assuming all the sea ice to be stationary (landfast). The seasonal modulation of the M₂ tidal component, quantified as the March–September difference, serves as the performance metric, demonstrating that the new parameterization has better agreement with observations from altimeter- and tide gauge-derived seasonal modulation. The results indicate that the physics of ice–tide interaction is better represented with the new parameterization of sea ice-induced dissipation, making it suitable for investigating the effects of declining sea ice thickness on tides.

Sea surface currents are of significant importance in various scientific and maritime applications. There are several measurement techniques available to study surface currents, however, they have limitations in spatial coverage and resolution. This study presents a proof-of-concept for a new measurement principle that relies on the difference between a ship's speed relative to water and land. The approach involves estimating the ship speed vector relative to water from optical satellite imagery of Kelvin wakes. This ship speed vector is subtracted from the ship speed over ground, which is determined from Automatic Identification System (AIS) data, to estimate the surface current. A case study in the Strait of Gibraltar was performed using two months of Sentinel-2 imagery, which yielded 81 visible Kelvin wakes over 25 images. Surface currents were estimated in directions parallel and perpendicular to the ship's sailing line for each Kelvin wake. The estimated currents were validated with respect to surface currents derived from High-Frequency Radars (HFRs) and modelled currents from the Copernicus Marine Environmental Monitoring Service (CMEMS). The uncertainty in the two surface current components was estimated using triple collocation. After removing 12 data points with large ship course variability, standard deviations of 0.14 and 0.16 m s⁻¹ were estimated for the surface currents along and across the sailing line, respectively. Despite limitations in measurement frequency due to satellite revisit times, cloud cover and Kelvin wake visibility, this new method can provide accurate estimates of sea surface currents in regions with high vessel density.

Under the influence of climate change, estuaries around the world are increasingly exposed to more extreme weather conditions. In recent years droughts specifically have been occurring more frequently and for prolonged periods. During a period of drought, salt intrusion is exacerbated, impacting the availability and quality of water resources and the estuarine ecosystem. As the impacts of droughts can be severe, assessment of droughts and their influence on the estuarine system is of great importance.

Using a high-resolution 3D coupled ocean-delta model we investigate the influence of the record-breaking European drought of the summer of 2022 on the Rhine-Meuse Delta and compare this to the estuarine response under average discharge conditions, putting the drought’s influence into perspective. Spatial patterns of stratification, mixing, and straining and their evolution throughout the drought period are studied by a salinity variance analysis. The progression of the salt wedge and retreat of the tidal plume fronts are examined and related to the changing strength of the individual estuarine processes influencing stratification. We show that as the tidal plume fronts retreat during the drought, we see a corresponding change in the structure of the salt wedge, demonstrating the importance of the coupling between the tidal plume fronts and the estuarine dynamics.

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.

Earlier work has empirically demonstrated some advantages of an increased posting rate of Synthetic Aperture Radar (SAR) altimeters beyond the expected ground resolution of about 320 m in Delay-Doppler (unfocused SAR, UFSAR) processing, corresponding to ∼20 Hz sampling. Higher posting rates of 40–80 Hz were shown to prevent spectral aliasing of the signal, enable to measure swell wave related signal distortions and may lead to a reduced root mean square error of 1 Hz estimates of Sea Surface Heights (SSH), radar cross section (sigma0) and Significant Wave Heights (SWH) from current SAR altimeters. These improvements were explained by the narrow noise autocovariance function of the waveform signal's power speckle noise in along-track direction on one hand, and frequency doubling by power detection (squaring of the signal) on the other. It has not been explained, however, why the power speckle noise decorrelates faster than anticipated by the predicted Doppler resolution, and whether this decorrelation depends on the altimeter and processing configuration. Also, it has not been shown explicitly that the estimates of SSH, SWH and sigma0 decorrelate in the same way. Describing the noise autocovariance function – or equivalently the noise power spectral density via the Wiener-Kintchin theorem – is necessary on two counts: Knowing the noise autocovariance allows to apply optimal filtering strategies that maximize precision on one hand, while the noise power spectral density predicts the frequencies contained in the noise (and signals), which in turn determines the required sampling frequency according to the Nyquist theorem. Using a newly derived analytic noise autocovariance model for UFSAR-processed altimeter data, we show that the swift signal decorrelation is mainly due to the observation geometry. Furthermore, our results demonstrate that the noise autocovariance functions of power speckle, SSH, SWH and sigma0 estimates in along-track direction are different and depend on the sea state. On top of that, the noise autocovariance functions are strongly dependent on the number of Doppler beams used for multilooking, the used retracker, and the processing choices such as antenna gain pattern compensation and windowing within the UFSAR processing (Level-1b). We validated our noise autocovariance model with segments of 42 Sentinel-3B overpasses. Our findings are in accordance to all earlier work, but indicate that the reported precision improvements with respect to 20 Hz may have been too optimistic and that the SSH, SWH and sigma0 generally decorrelate slower than the power speckle noise. We found that the required posting rate is always higher or equal to 40 Hz. Our results will potentially enable improved spectral analysis and optimal filtering of any UFSAR altimetry data. More importantly, our results can be used to trade off different aspects for determining an optimal posting rate in UFSAR altimeter processing in different sea states and with changing processing parameters, which is necessary in view of strict precision requirements of existing and future SAR altimetry missions.

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.

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.

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.