Ilias N. Tziavos

Remote sensing is nowadays an essential component of the Earth Observation System. New satellite missions provide a value added in environmental monitoring, as the remote part of an integrated with...

The advent of SWOT mission data in combination with the recent altimetry satellites (CryoSat-2, SARAL-AltiKa, Sentinel-3A, Sentinel-3B) provide additional value in regional Dynamic Ocean Topography (DOT) estimation both in the resolution and the accuracy of the final product. The near-real-time records support the phase of the operational altime-try. Two areas in the Western Mediterranean were chosen in order to study the signal and error covariance of each altimetric product from 2017 to 2024. The repeated altimetric tracks were used for the spectral estimation of the signal and error Power Spectral Density (PSD) and covariance. Various covariance models (exponential, Gaussian, ARMA) were tested to fit the data-driven estimation. A similar computation scheme was tested for ma-rine gravity data using simulated repeated fields. The final analytic gravity covariance from the periodogram PSD approach was tested against the fitted empirical one. Finally, gravity and altimetry PSD information is used in the DOT estimation through a tailored Multiple-Input-Multiple-Output-System (MIMOS).

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.

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.

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.

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.

The overall goal of the GeoGravGOCE project, funded by the Hellenic Foundation for Research Innovation, is to employ GOCE data products, mainly the original Satellite Gravity Gradiometry (SGG) data, and model the geoid in the Hellenic area and the surrounding regions. However, to utilize the original GOCE SGG data for geoid modeling, filtering is needed as well as a reduction to a mean orbit (MO) so that downward continuation to the Earth’s surface (ES) can be realized. After investigating various filtering options (Finite Impulse Response - FIR, Infinite Impulse Response - IIR, and wavelet multi-resolution analysis - MRA), both in the frequency and the space domain, it was concluded that an FIR with order 1500 would be the optimal one. This was based on both comparisons with upward continued gradients from the XGM2019 global geopotential model (GGM) and the spectrum cut-off of the various filters tested within the GOCE measuring bandwidth. Then, downward continuation of the filtered data to a mean sphere (MS) was necessary. With a maximum altitude, within the GOCE 3-year mission, close to 295 km and a minimum of about 240km, GOCE data generated at a mean level of 230 km. Regular 5’x5’ grids of the disturbing potential gradients Tij were generated using both XGM2190 and EGM2008 up to their maximum degree and order, while a combined solution using TIM-R6 to degree and order 165 and EGM2008 as fill-in was also used. The GGM information was used to simulate the downward continuation of Tij, so that this can then be applied to the actual GOCE data. The reduction to a MS was performed by estimating GGM gradient grids per 1 km from the MS to the maximum orbital level, and then using a linear interpolation for the reduction from the actual satellite height. It was found that the reduction with height of the gravity gradients varies linearly, while the use of XGM2019 provided the overall best results. After interpolating from the GGM grids, Tij values from XGM were estimated at the initial GOCE points and then used to reduce the GOCE SGGs to the MO. Finally, and in order to estimate residual Tij at the MO, three different options were tested. First, an analytical spherical harmonic synthesis (SHS) of and  at 230km was carried out. Then, the same effects were estimated using a grid of 1’x1’ disturbing potential gradients as well as a 5’x5’ grid. For each of these cases, the rigorous SHS and the two based on interpolation have been determined, showing that even a global 5’x5’ grid of disturbing potential gradients is sufficient and analytical determination of the GGM contribution is not necessary.

Whilst GOCE SGG data have been widely processed and used in geodetic research, one of the key points of their use is to have a one-stop software for their pre-processing and basic manipulations in terms of frame transformations and filtering operations. Within the GeoGravGOCE project, funded by the Hellenic Foundation for Research Innovation, the main goal is the optimal combination of GOCE Satellite Gravity Gradiometry (SGG) data with in-situ observations for geoid determination. During the project development, it became apparent that GOCE SGG data after using the GOCEPARSER, had to be pre- and post-processed via several own-developed routines in order to perform data quality checks, data consistency tests, reference frame transformations, data reductions and filtering. With that in mind, a standalone open-source software has been developed in MATLAB consisting of a Graphical User Interface (GUI) to perform the aforementioned operation. The software is divided in four tabs and is designed to process the original GOCE gravity gradients, which are the second-order derivatives of the gravitational potential. The first tab of the software is designed to allow the pre-processing of the Level 2 Electrostatic Gravity Gradiometer nominal gravity gradients (EGG_NOM) and Satellite to Satellite Tracking Precise Science Orbits (SST_PSO) products. The second tab enables the transformation of gravity gradients from a Global Geopotential Model (GGM) from the Local North Oriented Frame (LNOF) to the Gradiometer Reference Frame (GRF). The third tab provides filtering options for the reduced SGG observations and encompasses three different methods: Finite Impulse Response (FIR), Infinite Impulse Response (IIR), and Wavelet Multi-Resolution Analysis (WL-MRA). Finally, the fourth tab allows the transformation of SGG data from the GRF to the LNOF and vice versa. In this work, we present the basic software development procedure and outline its basic functionality and results.