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.

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.

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.

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.

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.

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.

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.

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.

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.