Validation of Recent DSM/DEM/DBMs in Test Areas in Greece Using Spirit Leveling, GNSS, Gravity and Echo Sounding Measurements

Abstract

Recent Digital Surface, Elevation, and Bathymetric Models (DSM/DEM/DBM) aim to provide high-resolution and accurate height and depth information needed for a variety of surveying, geodetic, geophysical, and other applications. In this study, first we aim to validate in two test areas some of the most used models, i.e., ASTER GDEM; AW3D30 DSM; Copernicus DEM; EU-DEM; GEBCO 2020; NASADEM HGT; SRTM15+ and SRTM Global, using GNSS; spirit leveling; and gravity measurements. The validation is performed along two traverses of 14.5 and 12.0 km each in Northern and Central Greece, respectively. Since these models are based on geoid heights obtained from global geopotential models, we also investigate their influence on the validation results. Next, we carry out comparisons between GEBCO 2020, SRTM15+, and the Greek Seas DTM, with depths derived from in situ coastal measurements in six different areas in Northern Greece. From the analysis, we conclude that the heights obtained from the Copernicus DEM provide the best overall results in terms of mean value and standard deviation while also showing consistent results in the two test areas. Similarly, the Greek Seas DTM shows better consistency with the measured depths in the coastal test areas.

1. Introduction

Digital Elevation Models (DEMs), i.e., models of heights defined with respect to a given reference surface, are used in various applications, such as construction works, scientific applications, etc. Depending on the surface defined by the heights, these models may be divided into elevation models representing the top of everything: Digital Terrain Models (DTMs), bare-earth raster grids without natural and building features, and Digital Surface Models (DSMs). It should be noted that there are also other definitions for DEMs and DTMs, but the above is used in the context of the present study.

DEMs were initially created from measurements made with land surveying instruments. These models provided height information, wherever measurements were possible, at a local, national, or regional level. With the satellite era, global models emerged, and, thus, studies could be conducted at a global level. As satellite instruments, processing methodologies and models improved over time, higher accuracy data were made available, while existing datasets were reprocessed or combined with new ones. The latter is the reason why height data acquired more than a decade ago are still used in practice (e.g., [1,2,3]).

On the other hand, Digital Bathymetric Models (DBMs), i.e., models representing depths to the seafloor, were initially difficult to produce because in situ measurements were very sparse. However, they have improved substantially over time as new echo sounding measurements are made available. In addition, some DBMs (e.g., [4]) include depths derived from satellite altimetry measurements (see, e.g., some depth derivation methods in [5,6]) although these cannot fully replace in situ depth measurements in terms of accuracy [7].

Validation of DEM/DSM/DBMs is an important procedure for evaluating the accuracy of the models and, consequently, influences the decision of choosing a model for a specific application and area. Numerous studies have been conducted worldwide for assessing the accuracy of the models either by the research teams that developed the models or by independent ones. Different types of measurements have been used in the validation procedure, including GNSS (e.g., [8,9,10,11,12,13,14,15,16]), altimetry (e.g., [17,18]), laser scanning/LIght Detection And Ranging (LIDAR) data (e.g., [14,18,19,20,21]), or even triangulation pillars with known orthometric height [12,21].

In Greece, a limited number of validation studies have been carried out. For example, [10] compared EU-DEM, Advanced Spaceborne Thermal Emission and Reflection Radiometer Global Digital Elevation Model (ASTER GDEM), Shuttle Radar Topography Mission (SRTM) DEM v4 with kinematic, and static GNSS data in Central Macedonia, Northern Greece. SRTM 3 arcsec DEM (versions 1, 2, 3, 4) were also validated by kinematic GPS measurements in Thessaloniki (Northern Greece) [11]. Ref. [12] used the triangulation pillars of the national network as ground control points for validating the ASTER GDEM all over Greece, as well as GNSS data for validation of Crete Island, Southern Greece. Almost 20 years ago, SRTM Digital Terrain Elevation Data (DTED) level 1 was compared with elevations from topographic maps in Crete Island (Southern Greece) [22]. Ref. [23] compared the ALOS Global Digital Surface Model (AW3D30) with topographic maps along with ALOS optical data. It should be noted that a geoid model was used for deriving heights from GNSS measurements to perform all or part of the assessment in many studies (e.g., [10,11,12]). On the other hand, the validation of DBMs in Greece is much more limited in terms of the number of studies and the areas examined (e.g., [24]).

In this study, we aim to validate, independently of existing geoid and global geopotential models, some of the, nowadays, most commonly used models using spirit leveling, i.e., the most accurate and direct way of obtaining height differences in surveying engineering, GNSS, and gravity measurements for heights and echo sounding measurements for depths. The validated models are: (A) ASTER GDEM [25], (B) AW3D30 DSM [26], (C) Copernicus DEM [27], (D) EU-DEM [28], (E) NASADEM HGT [29], (F) General Bathymetric Chart of the Oceans 2020 (GEBCO 2020) [30], (G) SRTM 1 arcsec Global [31], (H) SRTM15+ v2.1 [4], and (I) the Digital Terrain Model (DTM) of the Greek Seas [32]. Since the DEM/DSMs use geoid models but not the validation data, it is possible to investigate the effect of these geoid models on the validation results. Moreover, the more than 10 km length of the spirit leveling traverses corroborates the examination of the geoid model effect. As for the use of coastal echo sounding measurements, they facilitate the validation of the DBM in the land–sea transition zone.

2. Materials

2.1. Study Areas

For heights validation, two different test areas were selected. The first is located in Central Macedonia, Northern Greece (Figure 1a), a rural area with low vegetation. The second is located in Attica, Central Greece (Figure 1b), a suburban area also with low vegetation. The selection of the areas was based, first, on the presence of a national road network suitable for the safe execution of spirit leveling measurements and unobstructed GNSS measurements. The national road network also allows for better control and access to the area. Second, the availability of benchmarks (Repères) belonging to the national vertical network on both sides of the area was also a requirement. The last criterion was the mean area height to be representative for Greece. Thus, the first area was selected because it is a semi-mountainous area (heights of about 490–650 m), while the second one because it is a coastal area (heights of about 3–155 m).

Six areas in Northern Greece (Figure 2) were selected for depth validation. The criterion for choosing these coastal areas was the availability of in situ depth measurements, with the precondition that they are well documented.

2.2. Data Used in the Evaluation

2.2.1. DEM, DSM and DBM

Table 1. Available DEM/DSM/DBM with their resolution, reference system, and the quantity to be evaluated (H: height, D: depth).

Model	Resolution (Arcsec)	Reference System/Ellipsoid	Evaluation
ASTER GDEM v3	1	WGS84	H
AW3D30 DSM v3.2	1	ITRS97/GRS80	H
Copernicus DEM	1	WGS84	H
DTM of the Greek Seas	15	WGS84	D
EU-DEM	25 m	ETRS89-LAEA/GRS80	H
GEBCO 2020	15	WGS84	H/D
NASADEM HGT	1	WGS84	H
SRTM 1arcsec Global	1	WGS84	H
SRTM15+ v2.1	15	WGS84	H/D

lists the selected DEM/DSM/DBMs that were evaluated in this work. The same Table also includes information regarding the models’ resolution, reference system, as well as the quantity to be evaluated, as they provide values for either heights, depths, or both.

SRTM 1 arcsec Global (version 3) is a model obtained from the processing of SRTM data, but its voids were filled with the use of ASTER GDEM and other models. ASTER GDEM version 3 was released in 2019. This model is based on remote sensing imagery, while, for filling voids, after an extensive error detection procedure, it used, among other models, data from the SRTM Global model and AW3D30 DSM. The AW3D30 DSM version 3.2 is based on scenes obtained by the PRISM panchromatic optical sensor. Void filling was carried out using data from SRTM Global model, ASTER GDEM v3, and others. EU-DEM is a hybrid model that is based on a combination of SRTM data, ASTER GDEM, and Russian topographic maps. EU-DEM is not a global model. It provides heights only for the European Economic Area members states as well as for the respective cooperating countries. Its resolution in Table 1 is given in meters because it uses projected coordinates in the Lambert Azimuthal Equal Area projection. Copernicus DEM is a model derived from WorldDEM, which in turn was created from data obtained by the TanDEM-X Mission. Void filling sources include the ASTER GDEM, SRTM data, SRTM Global model, and AW3D30. NASADEM HGT is a model derived from an improved reprocessing of SRTM data and is, therefore, expected to provide more accurate values than SRTM 1arcsec Global. In NASADEM, void areas were filled using data from ASTER GDEM and AW3D30. From the above brief presentation of the models, it can be seen that no model is independent of the others as they are necessary for filling voids. Another remark that should be made is that for deriving the orthometric heights, ASTER GDEM, AW3D30 DSM, NASADEM HGT, and SRTM Global, use geoid heights derived from the Earth Gravitational Model 1996 (EGM96) [33], EU-DEM uses the European Gravimetric Geoid model 08 (EGG08) [34], and Copernicus DEM uses geoid heights computed from the Earth Gravitational Model 2008 (EGM2008) [35].

GEBCO 2020 and SRTM15+ provide depth values in addition to height values. On land, SRTM15+ height values are based mostly on SRTM CGIAR-CSI V4.1. CGIAR-CSI was computed from SRTM data and compiled by the Consortium for Spatial Information of the Consultative Group for International Agricultural Research (CSI-CGIAR) [36]. For marine areas, depths originate from various sources including single and multi-beam depth soundings and satellite altimetry derived depths. GEBCO2020 is based on SRTM15+ and inherits its values for land and marine areas, although SRTM15+ uses a prior release of GEBCO for coastal areas. However, in marine areas, the depth values have been replaced with values obtained from other sources, including the International Hydrographic Organization (IHO) Data Center for Digital Bathymetry and other organizations. SRTM15+ and GEBCO 2020 use EGM96 to derive orthometric heights, while depths are assumed to refer to the mean sea level. The latter assumption is rather abstract, but it is made because most of the time there are no metadata for the available echo sounding measurements, and this makes the compilation of the model a non-trivial task. As a result, different biases may be expected to exist at different areas with local reference systems or even mean sea level models.

The last available model is the DTM of the Greek Seas, which provides depths only for Greece and the surrounding seas. The original model refers to the Hellenic Terrestrial Reference System 1987 and its coordinates were transformed into WGS84, as it is deduced from its metadata. No other information, however, is available for this model.

2.2.2. GNSS/Leveling and Gravity Data

To validate the heights of the models, one traverse was measured in the Northern and one in the Central Greek mainland (Figure 1), referred to from now on as the Northern traverse and Central traverse. The first traverse consists of 175 points and has a length of 14.5 km, while the second includes 138 points and extends over 12.0 km, respectively. The measurement points were marked with nails on the ground.

The position of each point was obtained with the use of two dual frequency GNSS receivers, the Topcon Hiper V in the Northern area and the Javad Triumph-1 in the Central area, employing the Network Real-Time Kinematic (NRTK) method and the Virtual Reference Station (VRS) principle. The VRS differential corrections were taken from the URANUS Continuously Operating Reference Stations (CORS) network, which consists of 114 permanent reference stations throughout Greece [37]. Both GPS and GLONASS observations were obtained for at least 30 s, after carrier phase ambiguities were fixed and Position Dilution of Precision (PDOP) remained less than 4 for at least ¾ of the total observation time. The cut-off measurement angle was set equal to 10°. The accuracy of the derived geometric heights was estimated to be 2–4 cm. The obtained measurements refer to the Hellenic Terrestrial System (HTRS) 2007 [38] that uses the European Terrestrial Reference Frame (ETRF) 2005 at epoch 2007.5. These values were transformed to the International Terrestrial Reference Frame (ITRF) 2014 [39]—epoch 2007.5 following [40].

The gravity value for each point of the traverses was derived from relative gravity measurements. The fundamental point for gravity was a station located in the Laboratory of Gravity Field Research and Applications (GravLab) at the Aristotle University of Thessaloniki in Northern Greece. This station was measured using a Microg-Lacoste A10-#27 absolute gravimeter in the frame of work for the validation of Greek Gravity Reference System [41]. All measurements were carried out relative to this station with the aid of two Scintrex CG5 relative gravimeters at the same points as the GNSS observations along the two aforementioned traverses. The total measurement time varied depending on the site conditions (ambient noise) with a minimum of 3 min. Measurements were processed as in [41], i.e., the tidal effects were recomputed and removed, the instrument’s drift was considered linear with time, and all measurements were referred to the ground (from the measuring center of the instrument) using the normal gravity gradient value of 0.3086 mGal·m⁻¹. The final corrected gravity values are in the zero-tide approach [42] and have an internal accuracy of about 0.03 mGal. The zero-tide values were converted to mean-tide, to be consistent with the tidal approach of the Greek Vertical Reference System. The conversion was made according to Equation (9) of [43].

Spirit leveling was used to measure height differences between the traverses’ points. The measurements started and ended at four benchmarks, i.e., points with known height, of the national vertical network of Greece for the Northern area (Repères with code: 81871100Γ4, 81871100A3, 8187110316 and 8187110022) and two for the Central area (Repères with code: 18020027 and 5018020104). Consequently, orthometric heights for each point were derived. It should be mentioned that the Greek vertical datum is a tidal-based datum and is tied to the tide-gauge station at Piraeus Port in Attica, Central Greece. Thus, all the derived heights refer to the national tidal-based datum.

Two digital levels were used for the measurements, namely the Leica Sprinter 150 M for the Northern area (height accuracy ±1.5 mm/km) and the GEOMAX ZDL-700 for the Central area (height accuracy ±0.7 mm/km). Each traverse was measured as a closed loop (forward and backward runs). The loop closure error was evaluated with significance testing using the instrument’s accuracy ${\sigma }_o$. More specifically, we first define the loop closure error as

$$w=\Delta H_{fr}-\Delta H_{br},$$

(1)

where $\Delta H_{fr}$ and $\Delta H_{br}$ are the sum of height differences in the forward and backward runs, respectively. The standard deviation of the loop closure error ${\sigma }_w$ would be given by

$${\sigma }_w=2{\sigma }_o\sqrt{L},$$

(2)

where $L$ is the mean length of both runs given in km. The null hypothesis is H_ο: $w=0$ and the alternative hypothesis H_a: $w\ne 0$. The hypotheses are evaluated according to

$$\left|z\right|=\left|\frac{w}{{\sigma }_w} \right|\le z^{a/2},$$

(3)

where $z^{a/2}$ is obtained from the standard normal $z$-table for significance level $a$. For significance level equal to 0.05 the maximum value of the loop closure error is

$$w_{max}=3.91{\sigma }_o\sqrt{L}.$$

(4)

${\sigma }_o$ was set equal to 1.5 mm/km for both areas. Hence, the Northern traverse had a loop closure error equal to 14 mm/$\sqrt{\mathrm{km}}$ with a maximum value of 22 mm/$\sqrt{\mathrm{km}}$, while the Central traverse 13 mm/$\sqrt{\mathrm{km}}$ with a maximum of 21 mm/$\sqrt{\mathrm{km}}$, respectively. All heights obtained by spirit leveling were corrected using the orthometric correction $OC$ (see Equations (4)–(46) in [44]), i.e., the orthometric correction from point $A$ to point $B$ is given by:

$$O{C}_{AB}=\frac{g-{\gamma }_0}{{\gamma }_0}\Delta H+\frac{{\overline{g}}_A-{\gamma }_0}{{\gamma }_0}{H}_A-\frac{{\overline{g}}_{{\rm B}}-{\gamma }_0}{{\gamma }_0}{H}_{{\rm B}}$$

(5)

where $g$ is the measured gravity, ${\gamma }_0$ is the normal gravity at 45° N latitude (computed by Equations (2)–(146) in [44]), $H$ the orthometric height, and $\overline{g}$ is the mean gravity given by (Equations (4)–(31) in [44]):

$$\overline{g}=g+0.0424H$$

(6)

for mass density equal to 2.67 g/cm³. The computed orthometric corrections are at the sub mm level or less.

2.2.3. Echo Sounding Measurements

For the validation of the DBMs, in situ depth measurements were used for six different areas as depicted in Figure 2. These depth values originate from the GravLab database, which contains well documented data obtained in the frame of various research projects and undergraduate and postgraduate theses.

All measurements were carried out using the Bruttour CeeStar single beam echo sounding device together with GNSS receivers. Wave, tidal, and other correction were applied to the data as described in [24], while outlier and blunder detection procedures were carried out to remove erroneous data. All depth values refer to the Greek Vertical Reference System and their accuracy is estimated at 5 cm.

Table 2. Statistical results of the depth values obtained from in situ measurements for the six test areas (m).

Area	Min	Max	Mean	Std
A/L/A Estuaries	−28.87	−0.41	−14.44	9.45
Katerini	−5.33	−0.38	−2.34	0.90
N. Iraklitsa	−8.03	−0.82	−4.18	1.45
N. Marmaras	−92.29	−0.45	−31.34	20.80
N. Moudania	−10.18	−0.45	−3.69	1.78
Thessaloniki	−24.01	−5.73	−14.96	2.91
All areas	−92.29	−0.38	−17.55	16.92

provides the statistics of the depth values for each test area. Apart from N. Marmaras, all areas have depths less than 30 m, where Katerini, N. Iraklitsa, N. Moudania, and Thessaloniki present smoother variations of the sea bottom topography (the standard deviation of the values is less than 3 m). It should also be noted that the depth values of N. Moudania, N. Iraklitsa, and Thessaloniki are located in port areas.

3. Validation Procedure

The validation procedure includes the comparison of the heights derived from spirit leveling along the two traverses with values obtained from each DEM, while for the coastal areas the comparison of in situ depth measurements with those from the DBMs. These comparisons will lead to conclusions for the absolute accuracy [45] of the DEMs and DBMs, with the leveling heights and in situ depths considered as true values.

For land areas, the DEM validation usually includes a classification of land coverage (see, for example, [46]). In our case, all the traverse points were located along the national road network and GNSS measurements were carried out at each one of them. The latter was possible because the points were selected to have a clear view of the sky. Therefore, no classification was required. For the validation on land, the bilinear interpolation scheme was used to compute heights at each point with a known orthometric height from leveling. All models were kept in their original form to avoid aliasing, i.e., no coordinate transformations were made. Models that have WGS84 as their coordinate reference system are compatible with the ITRF2014 coordinate system within a few centimeters. Therefore, the interpolation for these models was straightforward. For models though that have a different coordinate system, we took a different approach in carrying out the bilinear interpolation. The two models whose coordinates refer to a different coordinate system other than WGS84 are AW3D30 (uses ITRF97) and EU-DEM (uses ETRS89 along with the LAEA projection). Hence, the coordinates of the points along the two traverses were first transformed from ITRF2014 to ITRF97 and ETS89/LAEA for the two models, respectively. Then, the heights were obtained by interpolation from the two models and the interpolated height values were matched with the original coordinates, i.e., those referring to ITRF2014. The differences computed by subtracting the heights of the models from the orthometric heights derived from leveling produced the statistical results presented in the next sections.

The same procedure was used in the validation of the DBM models. Since the coordinate reference system for all models providing depth values is WGS84, no transformation was required. Again, the bilinear interpolation scheme was used to obtain depth values from the models, while their difference from the depths derived from echo sounding measurements led to the results presented in the next sections. In the marine areas, it was not possible to interpolate depth values from the Greek Seas DTM for all the available in situ measurement points. Thus, the comparison was limited only to points whose depth value could be obtained from all examined models (Greek Seas DTM, GEBCO 2020, and SRTM15+). This limitation is due to the lower resolution of the DBMs as well as the fact that the Greek Seas DTM does not contain height values.

4. Results

4.1. Validation of Models in Central Greece

Table 3. Statistics of height differences between models and leveling at Central traverse (m).

Model	Min	Max	Mean	Std
ASTER GDEM v3	−8.12	12.02	1.82	3.32
AW3D30 DSM v3.2	−9.37	−1.21	−4.73	1.48
Copernicus DEM	−4.69	3.45	1.25	1.04
EU-DEM	−13.51	−0.13	−4.34	2.64
GEBCO 2020	−20.13	1.58	−8.82	4.83
NASADEM HGT	−15.15	1.79	−4.51	2.26
SRTM 1arcsec Global	−14.43	4.38	−2.95	2.24
SRTM15+ v2.1	−20.13	1.58	−8.89	4.78

shows the statistics of the differences between DEM/DSM and leveling in points of the Central traverse, while Figure 3, Figure 4 and Figure 5 depict the points’ absolute heights from leveling and the models. The results may be divided into three categories. The first category includes the models GEBCO 2020 (Figure 3a); SRTM15+ (Figure 3b), that present the largest differences in all statistical results; and ASTER GDEM (Figure 3c), which also has the largest differences except for a very low mean value of 1.82 m. The second category includes EU-DEM (Figure 4a), NASADEM HGT (Figure 4b), and SRTM Global (Figure 4c) that all have a lower standard deviation of about 2–2.5 m and a narrower range than those in the first category. The third category includes the models AW3D30 DSM (Figure 5a) and Copernicus DEM (Figure 5b), which have the lowest standard deviation (between 1 and 1.5 m). Their range is also lower than the other models, but AW3D30 DSM has a significant mean difference of −4.73 m.

4.2. Validation of Models in Northern Greece

Table 4. Statistics of height differences between models and leveling at Northern traverse (m).

Model	Min	Max	Mean	Std
ASTER GDEM v3	−22.44	17.47	2.84	5.65
AW3D30 DSM v3.2	−2.85	3.59	0.14	1.26
Copernicus DEM	−5.23	2.03	−0.68	1.38
EU-DEM	−16.82	14.89	−1.36	3.67
GEBCO 2020	−20.83	19.72	1.02	8.27
NASADEM HGT	−9.29	3.7	−0.87	2.26
SRTM 1arcsec Global	−10.63	3.55	−1.55	2.32
SRTM15+ v2.1	−20.13	19.72	1.02	8.27

contains the statistics of height differences between DEM/DSM and leveling at the points of the Northern traverse. Figure 6, Figure 7 and Figure 8 show the points’ absolute heights from the leveling and the models. As can be seen, there are some models with different behavior and better or worse results when compared with the statistical results of Table 3. More specifically, GEBCO 2020 (Figure 6a), SRTM15+ (Figure 6b), and ASTER GDEM (Figure 6c), again, show the worst results in terms of standard deviation, but this time with higher values. They also have a wider range of differences compared to the Central traverse. An improvement can only be observed in the mean value of the differences between GEBCO 2020 and SRTM15+. On the other hand, EU-DEM (Figure 7a) shows worse results compared to the Central traverses, especially in the range of differences that exceeds 31 m, while NASADEM HGT (Figure 7b) and SRMT Global (Figure 7c) present better statistical results. The AW3D30 DSM (Figure 8a) and Copernicus DEM (Figure 8b) still provide the best results, with AW3D30 DSM showing better statistics compared to the Central traverse.

4.3. Bathymetric Models

Table 5. Statistics of differences between in situ depths measurements and bathymetry models. (m.)

Model	Min	Max	Mean	Std
GEBCO2020	−28.68	36.75	−3.79	8.84
SRTM+15 v2.1	−30.08	41.35	−2.52	10.14
DTM of the Greek Seas	−22.69	29.02	−3.51	6.60

presents the statistical results of the comparisons between the models that provide depth values and all the available in situ depth measurements (72,970 values).

The DTM of the Greek Seas that is based solely on in situ measurements provides the best statistical results. GEBCO 2020 has a higher standard deviation of about 2 m than the DTM of the Greek Seas, while SRTM15+ has a much higher standard deviation and range. It should be noticed that all the models examined have a resolution of 15 arcsec, which corresponds to about 450 m. Therefore, it is expected to have significant differences from the in situ measurements. However, this does not invalidate the comparisons, as all models have the same resolution.

The statistical results provided in Table 5 refer to all the areas studied. Thus, it would be more useful to also examine the statistics per area. Figure 9 shows a comparison between the range, mean, and standard deviation of the differences per area and per model. The DTM of the Greek Seas shows again better statistical results, but the situation is different for the other two models. SRTM15+ shows better results than GEBCO in four out of six areas in terms of standard deviation, but the range is almost always worse. As mentioned before, it is not clear for all models which is the reference system for the depths. Consequently, examining the mean value of the differences is rather indicative. However, in at least two areas (N. Moudania and N. Iraklitsa), SRTM15+ shows a mean value of more than 10 m (10.74 m in N. Moudania and −15.36 m in N. Iraklitsa), which cannot be attributed to problems in the vertical reference system. Regarding the mean value, another remark can be made pertaining to the mean value differences per area. As can be seen from Figure 9a, the DTM of the Greek Seas has a more consistent mean value difference for each area than the other models.

5. Discussion and Conclusions

The height comparisons along the two traverses lead to the conclusion that Copernicus DEM and AW3D30 DSM show the smallest differences from the leveling data, with Copernicus performing best along the Northern traverse and AW3D30 along the Central one. Despite the differences, these two models are at the same accuracy level when compared to other models. Ref. [13] provide similar results for the Taklamakan Desert in China when comparing the above models with ICESat-2 measurements, while [17] also finds that Copernicus DEM is the best model, and AW3D30 DSM is second. In [23], the same accuracy for AW3D30 is also reported for a low-relief island in Greece.

NASADEM shows similar results to SRTM Global, with the first model providing slightly better results along the Northern traverse and the opposite for the Central traverse. Therefore, no significant improvement is seen in the two test areas for NASADEM, which is expected to be an improved version. This result was also reported by [18] for different test areas, although [21] found that there was an improvement for flat areas in Mexico. On the other hand, EU-DEM shows similar accuracy to NASADEM and SRTM Global along the Central traverse, but the Northern semi-mountainous area results become worse, and, most importantly, the range of values is significantly larger. Therefore, the finding by [10] that the lower resolution version of SRTM (3 arcmin) gives poorer results compared to EU-DEM no longer appears to be the case for the 1 arcsec resolution of SRTM Global.

For the last three models, GEBCO 2020 and SRTM15+ were expected to provide the least accurate results due to their low resolution (15 arcsec), as well as similar statistics, since both share the same land dataset. Other than that, ASTER GDEM provides the worst results even though it has a 1 arcsec resolution, similar to the rest of the models. Figure 3a and Figure 6a show that the data obtained with this model are noisy and have spikes and sudden fluctuations. This also confirms the results of previous studies that determined that ASTER GDEM gives poor results [10,17,21], although the standard deviation of the differences for the two traverses (5.65 and 3.32 m) is lower than the 7.6 m reported by [10] for Central Macedonia in Northern Greece.

Since Copernicus DEM and AW3D30 DSM have very similar statistics and use a different global geopotential model to derive orthometric heights (EGM2008 and EGM96, respectively), we examined the role of the geoid heights in the differences. As mentioned earlier, this is possible because no geoid model or heights were used for deriving orthometric heights along the two traverses, but only spirit leveling. Figure 10 depicts height anomalies computed from EGM96 and EGM2008 along the two traverses and their difference. The same Figure also shows the height difference between Copernicus DEM and AW3D30 DSM. Although the same tendency (trend) is observed in both the geoid heights differences and the height differences, especially in the Northern traverse where both have a negative slope, the large variations in height differences make it clear that they are due to the missions’ instruments and the corresponding methodology used for processing the data. When the latter becomes more accurate, e.g., reaching differences of less than 30 cm, then it may be possible to state that the results are influenced by the choice of a geoid model. However, at this level of accuracy, we conclude from our results that the accuracy of the models needs to be improved by an order of magnitude to further investigate the geoid model heights effect on the differences. Finally, we believe that the aforementioned conclusion, concerning the differences between the two models are due to the different mission instrumentation and the corresponding methodology used for processing the data, may also apply for the rest of the model comparisons.

As for the validation with the in situ depth measurements, the results presented show significant differences with the studied models in the coastal areas. The Greek Seas DTM shows better results in the compared differences and is more consistent. Another way to examine the results, taking into account the magnitude of depth, is to use the Total Vertical Uncertainty (TVU) of depth measurements defined in IHO standard S44 [47]. The TVU may be computed by

$$\mathrm{TVU}=\sqrt{a^2+b^2{d}_m}$$

(7)

where $a$ and $b$ are coefficients depending on the selected class, and $d_m$ is the depth. In our case, $d_m$ is the depth obtained from in situ measurements and TVU is considered as the limit for examining the depth differences between the models and the in situ measurements. In the standard, there are various classes defined but here we consider only class 2, where a general description of the sea bottom topography is adequate, and classes 1a/1b, which are stricter than class 2 and may be used for navigation. After calculating the TVU for classes 1a/1b ($a=0.5$ and b $=0.013$) and 2 ($a=1$ and b $=0.023$), we computed the percentage of differences for each model that are below the TVU threshold. The results are provided in

Table 6. Percentage of values for each model based on error percentage [%].

Class	Greek Seas DTM	GEBCO 2020	SRTM15+
2	29.26	8.11	8.89
1a/1b	21.46	4.64	5.17

.

Table 6 shows that about 30% of the Greek Seas DTM differences are within the class 2 limit, while this percentage is less than 9% for GEBCO 2020 and SRTM15+. Regarding classes 1a/1b, which are much stricter and most multibeam echo sounding devices adhere to them, the percentage is significantly lower. Aside from the possibility that models lack data for the test areas or that the data are in error, these high error percentages could also be attributed to their low resolution. Although the resolution is usually selected based on the spatial density of the available data used to make the models, this selection leads to degradation in areas with a high data density. Therefore, we believe that it would be better to oversample the bathymetric models, even for areas with voids, rather than doing the opposite.

In summary, our results show that Copernicus DEM (standard deviation of 1.04–1.38 cm) provided the best results for the test areas compared to the other models examined. It should be emphasized that our comparisons were made along the national road network, where the terrain slope is lower. Therefore, it is suggested to carry out additional measurements in steep areas with higher terrain slopes. For the coastal areas studied, the DTM of the Greek Seas (standard deviation 6.6 cm) showed the best statistical results. These results should be further verified by conducting similar studies for the rest of Greece, as well as for the open sea.