The determination of physical heights is of key importance for a wide spectrum of geoscientific applications and, in particular, for engineering projects. The main scope of the present work is focused on the determination of a high-accuracy and high-resolution gravimetric and hybrid geoid model, to determine orthometric heights without the need of conventional leveling. Both historical and newly acquired gravity data have been collected during dedicated gravity campaigns, around the location of a dedicated GNSS network as well as areas where the existing land gravity database presented voids. Geoid determination was based on the classical remove–compute–restore (RCR) technique and spectral and stochastic approaches. The low frequencies have been modeled based on the XGM2019e global geopotential model (GGM) and the topographic effects have been evaluated with the residual terrain model (RTM) reduction. The evaluation of the final geoid model was performed over 462 GNSS/leveling benchmarks (BMs), where the newly determined gravimetric geoid has shown an improvement of 3.1 cm, in the std of the differences to the GNSS/leveling BMs, compared to the latest national geoid model. A deterministic and stochastic fit to the GNSS/leveling data has been performed, investigating various choices for the parametric models and analytical covariance functions. The scope was to determine a hybrid geoid model, tailored to the area and GNSS/leveling data, which will be the one used for the direct estimation of high-accuracy orthometric heights from GNSS observations. After the deterministic fit, a std to the GNSS/leveling data of 10.1 cm has been achieved, with 54.8% and 83.1% of the absolute height differences being below the 1 cm and 2 cm per square root km of baseline length. The final hybrid geoid model, i.e., after the stochastic treatment of the adjusted residuals, gave a std of the difference to the GNSS/leveling data of 1.1 cm, with 99.8% and 99.9% of the height difference being smaller than the 1 cm and 2 cm standard errors, thus achieving a 1 cm accuracy regional geoid.

One of the main applications of the gravity field and steady-state Ocean Circulation Explorer (GOCE) satellite data is their combination with local gravity anomalies for geoid and gravity field modeling purposes. The aim of the present paper was the determination of an improved geoid model for the wider Hellenic area, using original GOCE SGG data filtered to retain only useful signals inside the measurement bandwidth (MBW) of the satellite. The filtered SGGs, originally at the satellite altitude, were projected to a mean orbit (MO) and then downward continued to the Earth’s surface (ES) in order to be combined with local gravity anomalies. For the projection to an MO, grids of disturbing gravity gradients from a global geopotential model (GGM) were used, computed per 1 km from the maximum satellite altitude to that of the MO. The downward continuation process was then undertaken using an iterative Monte Carlo (MC) simulated annealing method with GGM gravity anomalies on the ES used as ground truth data. The final geoid model over the wider Hellenic area was estimated, employing the remove–compute–restore method and both Fast Fourier Transform (FFT) and Least Squares Collocation (LSC). Gravity-only, GOCE-only and combined models using local gravity and GOCE data were determined and evaluation of the results was carried out against available GNSS/levelling data in the study area. From the results achieved, it was concluded that even when FFT is used, so that a combined grid of local gravity and GOCE data is used, improvements to the differences regarding GNSS/levelling data by 14.53% to 27.78% can be achieved. The geoid determination with LSC was focused on three different areas over Greece, with different characteristics in the topography and gravity variability. From these results, improvements from 14.73%, for the well-surveyed local data of Thessaly, to 32.88%, over the mountainous area of Pindos, and 57.10% for the island of Crete for 57.10% were found.

In the present study, we first examine the contribution of different, satellite-only or combined, global geopotential models in geoid computation employing the remove–compute–restore approach. For this reason, two test areas of about 100 km² each, one in northern and one in central Greece, were selected, and gravity measurements were conducted. These new gravity measurements were used along with the selected geopotential models to produce the reduced gravity field for the study areas. The classical and spectral residual terrain modeling effect is also removed to derive the residual gravity field. The latter is used for geoid computation using the 1D fast Fourier transform. The validation of the geoid models is carried out with gravity/GNSS/leveling measurements, which were conducted in two traverses located in the study areas. Special attention is given to the tidal approach, the geoid separation term as well as the coordinate reference system. Next, the northern study area is extended by incorporating gravity measurements obtained during the last five decades, and geoid models are recomputed. Lastly, using the geoid models computed, reference geopotential values are computed for both areas. From the results achieved for both study areas, the combined model XGM2019 provides the best overall statistical results with differences of 0.065 m and 0.036 m in terms of root mean square error. The incorporation of not recent data into the solutions leads to a degradation in accuracy by about 1.2 cm in terms of standard deviation. Lastly, the computed reference geopotential values present discrepancies between the two study areas, revealing network inconsistencies as well as the dependency on the geopotential model used for the geoid computations.

Gravity field and steady-state Ocean Circulation Explorer (GOCE) data are strongly affected by noise and long-wavelength errors outside the satellite measurement bandwidth (MBW). One of the main goals in utilizing GOCE data for gravity field modeling is the application of filtering techniques that can remove gross errors and reduce low-frequency errors and high-frequency noise while preserving the original signal. This paper aims to present and analyze three filtering strategies used to de-noise the GOCE Level 2 data from long-wavelength correlated errors and noise. These strategies are Finite Impulse Response (FIR), Infinite Impulse Response (IIR), and Wavelet Multi-resolution Analysis (WL), which have been applied to GOCE residual second order derivatives of the gravity potential. Several experiments were performed for each filtering scheme in order to identify the ideal filtering parameters. The outcomes indicate that all the suggested filtering strategies proved to be effective in removing low-frequency errors while preserving the signals in the GOCE MBW, with FIR filtering providing the overall best results.

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.

The determination of a high-accuracy and high-resolution geoid is of indispensable importance as it forms one of the cornerstones of a modern geodetic reference system. With that in mind, the State Authority for Geospatial Information (ASIG) of the Republic of Albania has launched an effort to modernize the gravity infrastructure of the country and as a consequence to make available a new gravimetric geoid model of enhanced resolution and accuracy for the country. In that respect, the necessary procedures to establish the primary and secondary leveling network have been detailed, collocated with gravity measurements, as well as the determination of a preliminary gravimetric geoid based on existing and new gravity data. In this work, we first focus on the gravity campaigns, data processing, reductions, and adjustments carried out as part of establishing the reference benchmarks of the second-order gravity network. Then the methodological steps followed for the determination of the geoid on a 1′ × 1′ grid over Albania, in an area bounded between 38.5° ≤ φ ≤ 43.5° and 18.0° ≤ λ ≤ 22.0°, are outlined. For the geoid determination, the remove-compute-restore (RCR) concept is employed using two global geopotential models (GGMs), namely EIGEN6c4 and XGM2019e, and two approaches for the topographic effects through a residual terrain model (RTM) correction with the spectral and classical computation. Then, the estimation of the geoid is carried out using least squares collocation (LSC) and fast Fourier transform (FFT) methods, and the validation is performed against both GNSS/leveling data over Albania and a high-accuracy leveling traverse connecting Durrës and Tirana. From the results achieved, the FFT-based geoid presented a mean value of the differences at the 3 cm level and an std of 14.1 cm. When compared to the new leveling traverse, the new geoid has shown differences at the ∼16 cm level which indicates the bias between the new gravimetric geoid from FFT and the Albanian vertical datum. The relative differences over the measured leveling BMs are at the 1–7 mm level. A first-guess hybrid geoid was also determined, after the parametric fit with the third-order polynomial model, reaching the 12.7 cm agreement with the old vertical datum, which is very satisfactory considering the fact that the acquired land gravity data manage to cover only a small portion of the gravity variability due to the long distances between them.