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Lowest Astronomical Tide in the North Sea Derived from a Vertically Referenced Shallow Water Model, and an Assessment of its Suggested Sense of Safety
Abstract
Water level reduction with global navigation satellite systems in bathymetric surveying requires knowledge of the ellipsoidal heights of lowest astronomical tide (LAT). The traditional approach uses tidal water levels of an ocean tide model, which are subtracted
from mean sea level (MSL). This approach has two major drawbacks: the modeled water levels refer to an equipotential surface, which differs from MSL, and MSL may not be known close to the coast. Here, we propose to model LAT directly relative to an equipotential surface (geoid). This is conceptually consistent with the flow equations and allows the inclusion of temporal MSL variations into the LAT definition. Numerical experiments for the North Sea show that significant differences between the traditional and the pursued approach exist if average monthly variations in MSL are included. A validation of the modeled LAT using tide gauge records reveals systematic errors, which we attribute to both the model and the tidal analysis procedure. We also show that the probability that water levels drop below LAT is high, with maximum frequency of once per week in the eastern North Sea. Therefore, we propose to reconsider the deterministic concept of LAT by a probabilistic chart datum concept, and we quantified the differences between them.
... Obtaining the tidal correction through the ellipsoidal height of the water level provided by the global satellite navigation systems requires that the CD is also referenced to the ellipsoid, simplifying the calculation and improving the accuracy of the tidal correction applied to the depth soundings (Figure 1). There are programs that link the CD to the ellipsoid, such as: VDATUM in the United States (Myers et al. 2005), AUSHYDROID in Australia (Martin and Broadbent 2004), BLAST for the North Sea (Slobbe et al. 2013) and VORF for UK and Irish waters (Iliffe et al. 2007). ...
... Following the recommendations of the IHO for the choice of the CD, curves of equal value with an equidistance of 0.3m were determined. It is important to note that some meteorological conditions can result in water levels below the LAT, especially in shallow waters (Slobbe et al., 2013); therefore in these regions the effects of negative storm surges can be significant. ...
... GNSS RTK provides accurate position and ellipsoidal height of the GNSS antenna with an accuracy of a few centimeters in the WGS84 reference frame. The seafloor depth relative to the chart is then derived using the ellipsoidal height, GNSS antenna and transducer offsets from the vessel's center of gravity (COG) and chart datum shift, obtained from chart datum models, an example of this is given in [36,37]. Thus, the uncertainty induced by the chart datum has been already included in the vertical positioning uncertainty, and hence there is no need to add this as a separate contributor to the total bathymetry uncertainty. ...
Realistic predictions of the contribution of the uncertainty sources affecting the quality of the bathymetric measurements prior to a survey is of importance. To this end, models predicting these contributions have been developed. The objective of the present paper is to assess the performance of the bathymetric uncertainty prediction model for Phase Difference Bathymetric Sonars (PDBS) which is an interferometric sonar. Two data sets were acquired with the Bathyswath-2 system with a frequency of 234 kHz at average water depths of around 26 m and 8 m with pulse lengths equal to 0.0555 ms and 0.1581 ms, respectively. The comparison between the bathymetric uncertainties derived from the measurements and those predicted using the current model indicates a relatively good agreement except for the across-track distances close to the nadir. The performance of the prediction model can be improved by modifying the term addressing the effect of footprint shift, i.e., spatial decorrelation, on the bottom due to fact that at a given time the footprints seen by different receiving arrays are slightly different.
... Their results indicated that a 2D model constrained within the estuary can sufficiently reproduce depth-averaged flow within the stratified estuary. Slobbe et al. (2012) modeled (LAT) relative to the European Gravimetric Geoid 2008 (EGG2008) using the extended and vertically referenced Dutch continental shelf model (DCSM), after obtaining the ellipsoidal heights of LAT by adding geoid heights to the modeled LAT values. They used the geoid instead of MSL because the former can be realized everywhere and does not leave a gap along the coast as satellite radar altimetry does. ...
Alexandria is the second-largest city in Egypt and the country's largest seaport that serves about 70% of the Egyptian imports and exports, especially the western harbor, which is the main commercial port and contains the Egyptian military naval base. Although Alexandria harbor has significant effect on the Egyptian economical income, there is still a shortage in coastal oceanographic discipline, specifically in the sea-level study that plays an important and effective role in many applications especially in chart production and dredging operations. Sea level is one of the oceanographic parameters that always needed in hydrographic surveying for depth reduction and chart datum realization. An imaginary surface, such as the Lowest Astronomical Tide, is recently used as the vertical tidal datum or chart datum that depths are referred to in all nautical charts. Therefore, sea-level measurements and analysis are always crucial for establishing an accurate datum precisely connected to onshore geodetic vertical datum to achieve the basic needs for mariners and hydrographers. Continuous and precise updating of tidal and terrestrial vertical datums connection and relationship, is of importance to provide essential information to many users including those in; commercial shipping industry, marine construction, water boundaries delimitation, marine safety, coastal areas planning, Engineering, chart datum for nautical charts production, in addition to military operations and many others. The geodetic vertical datum network in Egypt has been set as the mean sea level in Alexandria. This datum was first derived based on sea-level observations for eight years from 1898 to 1906. This imaginary surface was (34 cm) referred to the zero of the graduated staff in Alexandria harbor, and it was called the Egyptian Survey Authority datum. In each annual edition of the Admiralty Tide Tables, it was stated that the chart datum in Alexandria, as a secondary port in Egypt, is (-0.34 m) from mean sea level and all the essential known tidal levels were calculated and referred to Gibraltar as the standard port for Alexandria harbor on Mediterranean Sea. However, limited research has been updating this issue since most of the earlier studies of sea level in Alexandria Harbor dealt with sea level based on statistical computations without referring sea level measurements to a specific geodetic vertical datum. For most of the scientific applications especially in sea-level studies, the International Terrestrial Reference Frame (ITRF) is preferred. ITRF-2014 is the most accurate realization of the international terrestrial reference system. Delft-3D hydrodynamic flow model was used to model hourly sea level time series (19 yrs.). Bathymetric data acquired from chart digitization that was produced from hydrographic surveying operations, together with Era-interim meteorological data (1996-2006) compiled with Ras El-Tin automatic weather station data (2006-2016), all were employed as model's initial conditions beside other physical parameters. Boundary conditions were acquired from Achieving, Validation and Interpretation of the Satellite Oceanographic service (AVISO) for a daily sea level data, compiled with tidal constituents (amplitudes and phase angles) obtained from harmonic analysis of offshore observed sea level data from S4 current meter buoy (depth sensor) and the major tidal constituents parameters in the area from Delft-3D Dashboard tidal data. Model results were validated by results obtained from several observed sea-level data analysis. The analyzed hourly observed sea level time series was accurately referred to the tide gauge zero level which was geo-referenced to the latest geodetic terrestrial reference frame, data was recorded inside the harbor during two time periods (09/11/2008-08/22/2010) and (04/30/2012-10/25/2013). Besides, a short-term sea-level data from S4 buoy offshore outside the harbor during the period (10/26/2008-12/31/2008). From harmonic analysis of both modeled and observed sea level datasets inside and outside the harbor in the two different intervals using Delft-3D tide suit. It was concluded that sea level is mainly derived by tidal power with a power percentage between 53% and 81% to the total sea-level power respectively. These percentages are a result of 13 significant tidal constituents, dominated by the principal diurnal and semi-diurnal lunar tidal constituents (M2-S2-K1-O1). Besides, the solar annual (Sa) along with solar semi-annual (Ssa) tidal constituents which were found to contribute significantly with amplitude percentage ranged between (14% to 23%) for Sa and (2% to 13%) for (Ssa) to the total tidal constituents amplitudes, which reflects the seasonality effect that is related to the annual meteorological variations and thus affects sea-level changes in the area. The amplitude root means square error between both molded and observed datasets equal (0.005 m) and (0.012 m) respectively, that will not affect the accuracy of the major tidal datums determined. The cross-correlation analysis between modeled and observed sea level datasets demonstrated a strong correlation between tidal signals and moderate correlation in residuals with correlation coefficients equal (0.72) and (0.62) respectively, that confirmed the capability of Delft-3D flow model to precisely simulate variabilities and trends of observed oceanic conditions reasonably in Alexandria Harbor. From form factor percentage of both modeled and observed datasets it was signified that the tidal type regime in Alexandria Harbor is semidiurnal with a (0.25) ratio. From analyzing long-term modeled sea-level dataset (19 yrs) during the period (01/01/1996 till 11/30/2015), a positive linear trend was resulted by a rate of 3.4 mm/yr that agrees with the global sea level rise rate. From tidal vertical datums calculations of both modeled and observed datasets, the ellipsoidal heights of lowest and highest astronomical tide datums considering ± 10 cm safety margin were updated and suggested to be (14.29 m) and (15.23 m) referred to the international terrestrial reference frame 2014 respectively, with a range equals (94 cm), while the suggested same datums ellipsoidal height values referred to the world geodetic system 1984 are (14.36 m) and (15.20 m) respectively, with a range equals (84 cm). Finally, the ellipsoidal height values of the most essential used vertical datums referred to both geodetic datums ITRF-2014 and the World Geodetic System 1984 (WGS-84) were re-visited and updated from both modeled and observed sea-level datasets for Alexandria Harbor.
... Adding to the complexity, a country typically operates with different physical vertical datums on land and at sea, to define heights and depths, respectively. The exact relationship between them is often unknown, see, e.g., Pineau-Guillou and Dorst (2013), Slobbe et al. (2013), Albers (2016), and the references therein. This renders collecting and interpreting data for science and engineering applications in the coastal transition zone challenging. ...
The coastal mean sea surface (MSS) has applications within oceanography as well as geodesy. Together with a geoid model, it forms an important component for geodetic mapping of ocean surface currents that are in geostrophic balance. Furthermore, it forms a bridge between open ocean MSS and in situ measurements of mean sea level at or close to land, it contributes to the mapping of the geoid and the marine gravity field, and it is essential for connecting tidal nautical chart datums to physical height systems or global geodetic reference frames.
In this study, we determine a coastal MSS with an associated error field for Norway. The MSS is solely based on new-generation altimetry data, i.e., SAR(In) data from Sentinel-3A and CryoSat-2, as well as Ka-band data from SARAL/AltiKa. The data sets partly overlap in time and cover the time period from 2010 to 2017 inclusive. We have chosen these altimeters because they represent evolutions of conventional altimetry, with reduced footprint sizes as a main benefit. This is especially advantageous in the coastal zone, as a smaller footprint reduces the probability of radar pulses being contaminated by energy backscattered from land areas.
The satellite missions were harmonized by applying inter-mission biases determined in a regional crossover analysis. Furthermore, in a zone closer to land than 25 km, we have replaced the global ocean tide model with a regional ocean tide model provided by the Norwegian Mapping Authority (NMA). We use an optimal interpolation technique to determine a coastal MSS grid and discuss it in context of the estimated error field.
We assess our coastal MSS by comparison to state-of-the-art MSS products along three sections perpendicular to the coast, as well as ellipsoidal mean sea level as observed by an array of permanent tide gauges within the study area. In addition, we assess a higher-resolution version of our MSS in the NMA testbed for vertical datums, by comparison with temporary tide gauges. We find that the coastal MSS outperforms the global MSS models directly at the coast, with standard deviations of differences of ~8 cm to the tide gauges, compared to 14–22 cm, obtained with the global MSS models. All MSS models largely agree along three sections perpendicular to the coast, with standard deviations of differences of 2–4 cm. The higher-resolution version of the coastal MSS performs similarly to the coastal MSS in comparison with the temporary tide gauges (standard deviation of differences of ~8 cm), but its formal error field also quantifies large uncertainties at the coast and in the fjords, mainly due to the lack of altimetry observations. A trustworthy error field is decisive for the combination of altimetry with other sea-level observations.
... The feature between 52 • and 53 • is mainly the contribution of tides to the MWL (cf. Prandle 1978;Slobbe et al. 2013b). In the Wadden Sea, the signal should be interpreted with care. ...
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
≤
1
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.
There have been developments of GNSS heighting in hydrography. These are motivated by the need for improving the efficacy of hydrographic operations, through omission of shore-based tidal surveys and post-processed datum reduction of depth soundings. However, this will demand presence of hydrographic separation model (HSM) that defines the vertical relationship of any tidal datum used in hydrography to ellipsoid. In addition to that, a reliable technique for real-time positioning is also required. At the same time, the overall accuracy the use of the entire system (i.e. height datum, vertical positioning) must be identified. This paper discusses the prospect of using models of sea surface for the construction and operation of HSM for the SW Java Sea, Indonesia. The discussion is based on two models of sea surface: the analytically constructed sea surfaces (i.e. HAT, MSL, LAT) according to data from TPXO.7 missions and models of sea surface database published by the Indonesian Agency for Geospatial Information. In order to verify the operability of such models, observation of geodetic heights of instantaneous sea levels across an approximately 13.5 Nm sailing tracks between Pramuka (Seribu Islands) and Ancol (Jakarta) is made. It is evident that the work presented here results in deviation level in the order of several tens of centimetres. This provides reasonably quantified contribution to the error budget against the standard of depth accuracy for data presented on nautical charts as of Zone of Confidence A and hence confirm the prospect of using existing surface models and vertical positioning respectively for the construction and operation of HSM in the domain in question.
This paper assesses the agreement between observed heights of sea level from Global Navigation Satellite System (GNSS) and a global model of Mean Sea Surface (MSS). The assessment of the agreement is carried out according to the direct comparison between the height of MSS model and the geodetic height of actual sea level. Here, MSS is generated according to Gravity Recovery And Climate Experiment (GRACE) Gravity Model (GGM) and Mean Dynamic Ocean Topography (MDOT). The tracking of geodetic heights of actual sea level are done by Wide Area Differential (WA D) and Real Time Precise Point Positioning (RTPPP) Global Navigation Satellite System (GNSS) along an approximately 180 Nm SW-NE transect of away-return ship track in the west of the Java Sea, Indonesia. It is found that the overall agreement between geodetic height of sea level and MSS observed by WA DGNSS is 7.5 cm (away tracking), while those observed by RTPPP GNSS is 39.5 cm (away tracking) and 36.0 cm (return tracking). This work recommends selection of the best-fit tide model and careful examination on the dynamics of antenna offset due to vessel attitude.
The spatial and temporal resolution of satellite altimetry is usually sufficient for monitoring the changes of sea surface topography in the open ocean. However, coastal ocean dynamics are much more complex, being characterized by smaller spatial and temporal scales of variability. The quality and availability of satellite-derived products along the coasts have to be improved, with a strategy optimized for coastal targets. Therefore a coastal multi-satellite altimetry dataset (TOPEX/Poseidon, Jason-1; Envisat; GFO) at a 10 - 20 Hz sampling rate has been derived from routine geophysical data products using a new processing software dedicated to coastal zone applications. Improved along-track sea level variations with fine space scales are available in the North-western Mediterranean Sea from 2001 to 2003, and are compared with high-resolution numerical model elevations from the eddy-resolving model SYMPHONIE. This preparatory work emphasizes the potential of improved multi-satellite altimetry for validating coastal hydro-dynamical models and could contribute in the future to a better tuning of the boundary conditions of the simulations.
The international Hydrographic Organisation recommends that Lowest Astronomical Tide (LAT) be adopted as the international Chart Datum. LAT is defined as the lowest tide level, which can be predicted in average meteorological situation and in any combination of astronomical conditions. Many hydrographic offices, like SHOM in France, have adopted this recommendation up to now. After a quick review of current methods based on tide predictions and observations in use to locate and recover chart datum, we will focus on modern techniques based on space geodesy and numerical modelling. A new approach to fix chart datum and rectify bathymetric surveys depth measurements will be presented. It is based on modern space techniques, including GPS, lowest astronomical tide calculation and mean sea level ellipsoidal heights. This subsequent chart datum can then be considered as heights related to a well-defined and maintained global geodetic reference frame like ITRF.
The creation of vertical reference surfaces at sea, related to a reference ellipsoid, is a necessary step to enable the use of GPS (Global Positioning System) for referencing depth measurements at sea. Several projects exist for specific parts of the oceans, resulting in surfaces that partly overlap. As an example, we will present the French BATHYELLI project in detail, followed by a comparison of results for the North Sea area.
