EOT20 is the latest in a series of empirical ocean tide (EOT) models derived using residual tidal analysis of multi-mission satellite altimetry at
DGFI-TUM. The amplitudes and phases of 17 tidal constituents are provided on a global 0.125

The regular fluctuations of the sea surface caused by ocean tides have intrigued and fascinated scientists for centuries based on their influence on
oceanic processes. Understanding ocean tides is vital for a variety of geophysical fields, with it being of particular importance in studies of the
coastal environment and ocean mixing. Precise knowledge of ocean tides is also important for satellite altimetry and in determining high-resolution
temporal gravity fields from, for example, the GRACE missions

In certain studies of non-tidal signals using satellite altimetry data, such as in sea-level and ocean circulation research, ocean tides need to be
removed from the data signal to properly study these processes. These so-called tidal corrections are usually provided by ocean tide models that have
been specially developed to predict the tidal signals throughout the global ocean. The ever-evolving and improving field of ocean tide modelling has
resulted in significant leaps in the accuracy of estimations of ocean tides

One type of ocean tide model, known as semi-empirical models, is derived from empirical harmonic analysis of satellite altimetry data relative to a
reference model. These semi-empirical tide models rely heavily upon satellite altimetry data. Recently, significant advancements have been made to
coastal altimetry in several fields including key improvements in correction fields, more detailed and coastal-specific data editing, and new schemes
for radar echo analysis (retracking)

EOT11a

In this paper, the latest global version of the EOT model, EOT20, is presented based on recent developments made in the field of tide modelling,
coastal altimetry and the availability of an increased number of altimetry missions. The objective of the EOT20 model is to improve the accuracy of
tidal estimations in the coastal region while remaining consistent in the open ocean. In Sect.

The development of EOT20 focused on improving tidal estimations in the coastal region which has been a historically difficult region to accurately estimate tides. EOT20 follows a similar scheme as the former model, EOT11a, consisting of three major steps: the creation of an SLA product including the correction of a reference ocean tide model; the estimation of the residual tides based on this SLA product; and the combination of the reference model with the residual tides to form a new global ocean tide model. These three steps provide a summary of the creation of EOT20 which is expanded in the following sections.

The satellite altimeter data used in this study obtained from OpenADB at DGFI-TUM

List of corrections and parameters used to compute SLA for tidal residuals estimation.

The tidal analysis is based on the analysis of SLA derived from satellite altimetry missions (Table

The same corrections are used for each satellite altimetry mission to allow for consistency, with the only differences occurring in the sea state bias
correction. The ALES retracker

As shown in Table

Once all these corrections are applied, the SLA can be estimated for all 11 altimetry datasets which are then gridded onto a triangular grid based
on the techniques presented in

Once collected, the data are then weighted using a Gaussian function based on the distance to the grid point. The use of data from multiple satellite
tracks for each node provides a long SLA time series, which is important in reducing the aliasing effect and in decorrelating tidal signals with alias
periods close to each other

From the weighted SLA, residual tidal analysis is performed using weighted least-squares and the variance component estimation (VCE) for each grid
point of the model. The least-squares approach is applied to the harmonic formula to derive the amplitudes and phases of single tidal constituents
from the SLA observations. In EOT20, the 17 tidal constituents considered and computed are 2N2, J1, K1, K2, M2, M4, MF, MM, N2, O1, P1, Q1,
S1, S2, SA, SSA and T2. The weighted least square analysis follows a standard procedure solving the following equation for each grid point

The VCE is implemented to allow for the combination of datasets from multiple satellite missions and allows for the appropriate weighting of different
missions

Maps of the residual amplitudes of the M2 and N2 tidal constituents as estimated by residual tidal analysis.

The variances are iteratively calculated by

The tides observed are the residual elastic tides that consist of both the ocean and the load tides. Therefore, additional analysis has been done to
separate these two components for further analysis. There are several techniques that are described that make this possible

The ocean spherical harmonic admittances of the load tides are described as

Once the ocean and load tide residuals are produced, the full tidal signal is restored by adding the residuals to the FES2014 tidal atlas. The
residuals are interpreted onto a 0.125

Future iterations of the EOT model will tackle the estimation of tides in the higher latitudes. A land–sea mask was added to the model based on the
GMT that uses the GSHHG coastline database

The amplitude (in cm) and the phase (in 60

The amplitude (in cm) and phase (in 60

The global array of tide gauges and ocean bottom pressure sensors that were used in the validation of the EOT20 model from the TICON dataset and from

EOT20 presents global estimations of 17 tidal constituents with these tidal atlases being available from

The EOT20 model follows the framework of the EOT11a model when estimating the tide via residual analysis. However, significant changes and additions
have been done to EOT20 with the objective of improving coastal estimations. These changes are in the reference tide model used in the residual
analysis, the use of more recent developments in coastal altimetry (e.g. the development of the ALES retracker

Since the 1800s, tide gauges have been used to study the ocean tides and the variation in sea level. Over the years, more and more tide gauges have
been installed around the world, resulting in a vast array. This comprehensive record of tide gauges can be used to evaluate the changes in sea level
over time as well as to better understand the ocean tides. Tide gauges, therefore, provide a suitable source of data in the validation of ocean tide
models, particularly in the coastal region. There are limitations particularly in the distribution of tide gauges, with certain regions containing a
vast number of tide gauges (e.g. in northern Europe) and some regions containing little to no data (e.g. the Mozambique Channel). Furthermore, tide
gauges are mostly restricted to the coastal region and, therefore, do not provide sufficient observations of the open ocean region. With that in mind,

The rms, in cm, of the tide gauge analysis of 1226 tide gauges for the EOT20 model as well as several other global ocean tide models. The values marked in bold indicate the model with the smallest rms for each row.

Several major ocean tide models are also compared to the same tide gauges in order to act as reference to the ability of the EOT20 model. The models
used are EOT11a

The comparison between EOT11a and EOT20 shows a significant improvement in the EOT20 model for the full dataset
(Table

EOT20 also shows a reduced RSS when compared to the other global models, particularly compared to the reference model, FES2014. The largest
improvement comes in the M2 tidal constituent while the results for the remaining tidal constituents are quite consistent between FES2014 and
EOT20. In the coastal region, EOT20 shows significant improvements compared to the other models, being approximately 0.2

In the shelf region, the reduction of rms in the M2 tide from EOT20 is still seen compared to FES2014 but reduces to less than 1

The constituents not included in the previous analysis are compared to the FES2014 model and the TICON tide gauge dataset (presented in
Fig.

The S1 tidal constituent is the relatively worst performing tidal constituent from the EOT20 model with an increased rms of 0.2

The results of the tide gauge and ocean bottom pressure analysis suggest rather encouraging results from the EOT20 model. The estimated tidal constituents of EOT20 are notably improved compared to the previous EOT11a model. The performance of the model in the coastal region is noteworthy particularly in the representation of the M2 tidal constituent. Furthermore, the model remains on par with the other global tide models in the open ocean and shelf regions.

In order to further assess the models ability, sea level variance reductions of three satellite altimetry missions were assessed and are presented. As
seen in Fig.

The global scaled SLA variances differences for Jason-2, Jason-3 and SARAL in percentages. The colour bar is chosen for ease of understanding with the variance differences scaled to highlight the differences between the results. The colours are chosen so that when there are regions of red colours EOT20 shows a lower variance, while when regions are blue the other tide model (EOT11a or FES2014) has a lower variance.

A line graph showing the mean SLA variance differences between the tide models as a function of distance to coast (in km) for all three satellite altimetry missions. The red line represents FES2014

Figure

For the Jason-3 mission, a reduction in SLA variance can be seen from the EOT20 model, with the discrepancies between the models again being very
small (Fig.

The SARAL mission presents differing results from those seen in the Jason missions. It should be noted that SARAL has considerably fewer cycles and has
a different orbit compared to the Jason missions. However, the results still provide valuable insights into the performances of the models. When
looking at the scaled variance differences, the results become a bit more variable between the models with EOT20 showing reductions in variance in
regions such as the Indian Ocean and the North Atlantic Ocean but showing increased variance in regions such as the South Atlantic Ocean and the South
Pacific Ocean. Overall, EOT20 shows a mean reduction of variance compared to EOT11a of 0.129

The ocean and load tides from EOT20 are available at

In this study, an updated version of a global ocean tide model, EOT20, is presented. Model developments were aimed at updating the previous model,
EOT11a, with a focus on improving the coastal estimations of ocean tides by utilising recent developments in coastal altimetry, particularly the use
of the ALES retracker and sea state bias correction. In the residual analysis, SLA data are gridded into a triangular grid aimed at increasing the
efficiency of the model and thus better-describing tides in the coastal and higher latitudinal regions. A further update was in the use of a newer
version of the reference model (FES2014) for the residual analysis performed to create the EOT20 model, which showed significant improvements to the
previous reference model used, FES2004

To evaluate the performance of the EOT20 model, validation against in situ observations and through sea level variance analysis was done. First, the
models performance was compared with tide gauges and ocean bottom pressure sensors for the eight major tidal constituents. The results suggested that
EOT20 showed significant improvements compared to EOT11a throughout the global ocean, with major improvements being seen in the coastal
region. Furthermore, when compared to other global ocean tide models, EOT20 had the lowest overall RSS for the major eight tidal constituents, In
particular, improvements are seen in the coastal region, where EOT20 shows a reduced RSS of 0.2

The additional tidal constituents provide valuable data for the creation of the tidal correction used for satellite altimetry. The results of these additions show positive results compared to the FES2014 model, but improvements can still be made in determining some of these tides, particularly the S1 tidal constituent. Further investigations will be done at DGFI-TUM into the estimation of additional minor tidal constituents as well as the optimisation of the current estimations.

The sea level variance analysis continued to show positive results for EOT20. EOT20 reduced the mean variance compared to both FES2014 and EOT11a for all three satellite altimetry missions studied. Again, the largest reason for the improvement was seen in the coastal region with EOT20 showing similar results compared to the other models in the open ocean regions. These results of the new EOT20 model suggest that it will serve as a useful tidal correction for satellite altimetry.

Errors resulting from tide models are considered to be one of the main limiting factors for temporal gravity field determination and the derivation of
mass transport processes

As the fields of coastal altimetry and ocean tides develop, the ideas and methods of improving the EOT model continue to grow. A clear next step for
the EOT model is to assess its ability to estimate tides in higher latitudes by including more satellite missions (e.g. CryoSat-2) and to introduce
further data such as synthetic aperture radar altimetry from Sentinel-3. Furthermore, more recent developments in the estimation of internal tide
models

MGHD wrote the manuscript and performed the validation of the model. MGHD and DD were involved with designing the study and in interpreting the results. MGHD and GP were responsible for the development of the EOT20 model. CS and DD were responsible for the appropriate satellite altimetry data and assisted in the variance reduction validation. MP is the author of the retracking algorithm and of the sea state bias correction used in the model. FS provided the resources making the study possible and coordinates the activities of the research group at DGFI-TUM. All authors read, commented and reviewed the final manuscript.

The authors declare that they have no conflict of interest.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

The authors thank NOVELTIS, LEGOS, CLS Space Oceanography Division, CNES and AVISO for providing the FES2014 model. The authors would like to thank the anonymous reviewers for their input on the manuscript. We would also like to thank colleagues within the community for their comments on the model and results presented, particularly Sergiy Rudenko, Mathilde Cancet and Richard Ray.

This paper was edited by Giuseppe M. R. Manzella and reviewed by two anonymous referees.