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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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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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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We present an efficient and flexible alternative method to connect islands and offshore tide gauges with the height system on land. The method uses a regional, high-resolution hydrodynamic model that provides total water levels. From the model, we obtain the differences in mean water level (MWL) between tide gauges at the mainland and at the islands or offshore platforms. Adding them to the MWL relative to the national height system at the mainland’s tide gauges realizes a connection of the island and offshore platforms with the height system on the mainland. Numerical results are presented for the connection of the Dutch Wadden islands with the national height system (Normaal Amsterdams Peil, NAP). Several choices of the period over which the MWLs are computed are tested and validated. The best results were obtained when we computed the MWL only over the summer months of our 19-year simulation period. Based on this strategy, the percentage of connections for which the absolute differences between the observation- and model-derived MWL differences are (Formula presented.) cm is about 34% (46 out of 135 possible leveling connections). In this case, for each Wadden island we can find several connections that allow the transfer of NAP with (sub-)centimeter accuracy.

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In this paper, we present a novel Kalman filter approach to combine a hydrodynamic model-derived lowest astronomical tide (LAT) surface with tide gauge record-derived LAT values. In the approach, tidal water levels are assimilated into the model. As such, the combination is guided by the model physics. When validating the obtained “Kalman-filtered LAT realization” at all tide gauges, we obtained an overall root-mean-square (RMS) difference of 15.1 cm. At the tide gauges not used in the data assimilation, the RMS is 17.9 cm. We found that the assimilation reduces the overall RMS difference by ∼31% and ∼22%, respectively. In the Dutch North Sea and Wadden Sea, the RMS differences are 6.6 and 14.8 cm (all tide gauges), respectively. Furthermore, we address the problem of LAT realization in intertidal waters where LAT is not defined. We propose to replace LAT by pseudo-LAT, which we suggest to realize similarly as LAT except that all water level boundary conditions and assimilated tidal water levels have to be enlarged by a constant value that is removed afterwards. Using this approach, we obtained a smooth reference surface for the Dutch Wadden Sea that fits LAT at the North Sea boundary within a few centimeters.@en