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.
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.
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
where
and
are coefficients depending on the selected class, and
is the depth. In our case,
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 (
and
b ) and 2 (
and
b ), we computed the percentage of differences for each model that are below the TVU threshold. The results are provided in
Table 6.
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.