G. S. Vergos

Statistical Models and Latest Results in the Determination of the Absolute Bias for the Radar Altimeters of Jason Satellites using the Gavdos Facility

The dedicated calibration site for satellite radar altimeters in Gavdos, Greece, has been operational as of 2004. The island of Gavdos is located along a repeating ground track of Jason satellites, adjacent to Envisat, where the altimeter and radiometer do not experience significant land intrusion. In this article, the models and techniques for calculating the satellite altimeter bias, as well as the software tool called “TUCalibrit,” are presented. In summary, over cycles 209–259 for Jason-1 and cycles 1–40 for Jason-2, the altimeter biases have been estimated as B(J1) = +103.6 mm ± 4.7 mm and B(J2) = +181.9 mm ± 6.7 mm, respectively.

On the Determination of Marine Geoid Models by Least-Squares Collocation and Spectral Methods Using Heterogeneous Data

In the frame of the EU-sponsored GAVDOS project the need of a new high-resolution and high-accuracy geoid model for the calibration of altimeters onboard satellites like JASON-1, ENVISAT and EURO-GLOSS and for sea level monitoring purposes has become apparent. That was mainly due to the fact that the already available models have been estimated using outdated datasets and fail to meet the wanted, cm-level, accuracy requirements. To determine the new geoid models multi-satellite (ERS1 and GEOSAT) altimetry and land and marine gravity data have been used. The EGM96 global geopotential model has been employed, while the effect of the bathymetry has been taken into account using recently developed local Digital Depth Models (DDMs). Several solutions have been estimated based on the different datasets used and the two main methodologies followed, i.e., the Fast Fourier Transform (FFT) based Input Output System Theory (IOST) and Least Squares Collocation (LSC). The accuracy of the new models was assessed through comparisons with TOPEX/POSEIDON (T/P) data and the GEOMED geoid solution for the area under study. Finally, the consistency between the estimated solutions has been determined by comparing the geoid height value they provide at the Gavdos Tide Gauge (TG) station on the isle of Gavdos. From the results it was found that the precision of the new geoid models is between ±0.9 and ±3.3 cm, their accuracy ranges between ±5 and ±10 cm and their consistency is at the ±0.5 − 6 cm level.

Evaluation of GOCE/GRACE Global Geopotential Models over Greece with Collocated GPS/Levelling Observations and Local Gravity Data

The advent of the GOCE and GRACE missions during the last decade have brought new insights and promising results both in the static and time-variable representation of the Earth’s gravity field. The focus of this work is directed to the evaluation of most available Global Geopotential Models (GGMs) from GOCE and GRACE, both satellite only as well as combined ones. The evaluation is carried out over an extensive network of collocated GPS/Levelling benchmarks (BMs) which covers the entire part of continental Greece and with respect to the reductions the GGMs provide in existing gravity data in order to assess their performance in a scenario that a remove-compute-restore procedure would be followed for geoid determination. From the evaluation with GPS/Levelling BMs, it was concluded that the GOCE/GRACE GGMs provide an absolute accuracy at the 12–15 cm level, up to degree and order (d/o) 250, when considering the geoid omission error. This is comparable and in some cases better than the performance of EGM2008 in Greece. Moreover, the latest (Release 3) versions of the GGMs provide considerably better results compared to the earlier version by 1–5 cm. In terms of relative errors, GOCE/GRACE GGMs reach the 1 cm level for baselines between 50 and 60 km, while for longer ones, 80–90 km, their performance is analogous to the local geoid model and the ultra-high degree combined GGMs. Finally, GOCE/GRACE GGMs manage to provide the same, as EGM2008, level of reduction to the local gravity anomalies, with a std at the 26.7–27.8 mGal level, when evaluated up to d/o 250.

Gravity Data Base Generation and Geoid Model Estimation Using Heterogeneous Data

The computation of high-resolution and high-precision geoid models in the Eastern part of the Mediterranean Sea usually suffers from the few gravity observations available. In the frame of the EU-sponsored GAVDOS project, a systematic attempt has been made to collect all available gravity data for an area located in the Southern part of Greece and determine new and high-resolution geoid models. Thus, all available gravity data have been collected for both land and marine regions and an editing/blunder-removal processing scheme has been followed to generate an optimal gravity dataset for use in geoid determination. The basic analysis and validation of the gravity data-bank was based on a gross-error detection visualization and collocation scheme. The Least Squares Collocation (LSC) method was employed to predict gravity at known stations and then validate the observations and detect blunders. The finally generated gravity database presents a resolution of 1 arcmin in both latitude and longitude while its external and internal accuracies were estimated to about ±5 mGal and ±0.2 – ±0.4 mGal, respectively. Based on the derived gravity database a gravimetric geoid model was developed using the well-known remove-compute-restore method with an application of a 1D Fast Fourier Transform (FFT) to evaluate Stokes’ integral. Altimetric geoid solutions have been also determined from the GEOSAT and ERS1 geodetic mission altimetry data. Finally, combined geoid models have been computed using the FFT-based Input Output System Theory (IOST) and the LSC methods. The consistency of the geoid models estimated was assessed by comparing the geoid height value at the Gavdos Tide Gauge (TG) station on the isle of Gavdos. Their accuracy was determined through comparisons with stacked T/P sea surface heights. From the comparisons performed it was found that the accuracy of the gravimetric, altimetric and combined models was at the ±14.5 cm, ±8.6 cm and ±12.5 cm level, and their consistency at about ±2 cm.

Ascending and Descending Passes for the Determination of the Altimeter Bias of Jason Satellites using the Gavdos Facility

This paper presents the improvements made on the calibration methodology conducted at the Gavdos calibration/validation facility along with the latest altimeter calibration results for Jason-1 and Jason-2 satellite missions. Calibration results are presented, for the first time, for both ascending and descending passes of Jason satellites. The altimeter bias for Jason-2 has been estimated to be +173 ± 4 mm for Pass No. 109 and +171 ± 5 mm for Pass No. 018 over cycles 1–79. In tandem mission, the difference between Jason-1 and Jason-2 has been determined to be 72mm (Pass No. 109) and 68 mm (pass No. 018) and over cycles 2–20.

Evaluation of GOCE/GRACE Derived Global Geopotential Models over Argentina with Collocated GPS/Levelling Observations

This paper presents the results of the evaluation of recent GOCE/GRACE Global Geopotential Models (GGMs) over Argentina. Since the Gravity and steady state Ocean Circulation Explorer (GOCE) dedicated satellite gravity field mission was launched in March 2009, several global geopotential models have been computed and released. GOCE’s mission was designed to provide models of the Earth’s gravity field on a global scale with high-accuracy in the medium wavelength spectral band (maximum degree/order 200–250). Comparisons of geoid heights derived from different GGMs with GPS/Levelling derived geoid heights over Argentina have been carried out in both absolute and relative sense, to assess and validate the accuracy of GGM models over the entire country. The analysis has been carried out with actual GOCE-only, GOCE/GRACE and combined global gravity field models. In all cases, EGM2008 has been used as the baseline model, since it provides the overall best results. From the results, it was concluded that the latest Release 3 GOCE-only, TIM and SPW, GGMs provide improved accuracies by 1–4 cm compared to the Release 1 models. As far as the combined GOCE/GRACE models, GOCO and DIR, are concerned, the overall best results come from the Release 1 of the DIR model, probably due to the a-priori information from EIGEN5C used in its development. The Release 3 version of the GOCO GGMs improves the Release 1 model by 4 cm, while the same level of improvement is found between the Release 3 and Release 2 of the DIR GGMs.

Estimation of the Reference Geopotential Value for the Local Vertical Datum of Continental Greece Using EGM08 and GPS/Leveling Data

Estimation of the zero-height geopotential level represented by W o LVD in a local vertical datum (LVD) is a problem of main importance for a wide range of geodetic applications related to different height frames and plays a fundamental role in the connection of traditional height reference systems into a global height system or even a modern geoid-based vertical datum. This paper aims primarily at the estimation of W o LVD for the continental part of Greece, with the use of surface gravity data and geopotential values computed from EGM08 in conjunction with GPS and orthometric heights over an extensive network which covers sufficiently the test area. The method used focuses on the estimation of W o LVD from a least squares adjustment scheme that is applied on the Helmert model for orthometric heights, using surface geopotential and gravity values (as obtained from EGM08 and the known 3D geocentric coordinates of each benchmark) along with the local Helmert heights over all network stations. Moreover, an attempt is made towards the modeling and removal of any height correlated errors in the available data according to this adjustment procedure. Different weighting schemes are tested, and, finally, some conclusions are drawn considering the accuracy of the obtained results.

Adjustment of Collocated GPS, Geoid and Orthometric Height Observations in Greece. Geoid or Orthometric Height Improvement?

The combined adjustment of GPS/Levelling observations on benchmarks with gravimetric geoid heights has been the focus of extensive research both from the theoretical and practical point of view. Up until today, with few exceptions, the main blame for the inconsistencies/disagreement between these three types of heights has been put to the geoid heights due mainly to their poorer accuracy. With the advent of the new CHAMP- and GRACE-based global geopotential models and the realization of EGM2008 the achievable cumulative geoid accuracy has improved significantly so that its differences to GPS/Levelling heights reach the few cm level. In Greece, GPS observations on BMs are very scarce and cover only small parts, in terms of spatial scale, of the country. Recently, an effort has been carried out to perform new GPS measurements on levelling BMs, so that reliable GPS/Levelling and gravimetric geoid height adjustment studies can be carried out. This resulted in part of North-Western Greece to be covered with reliable observations within an area extending 3° in longitude and 1° in latitude. Therefore, some new potential for the common adjustment of the available geometric, orthometric and geoid heights, using various parametric surfaces to model and interpret their differences, are offered. These are used to come to some conclusions on the accuracy of the various geoid models used (both global geopotential and local gravimetric models), while an extensive outlook is paid to the questionable behaviour of the orthometric heights. The latter is especially important for the Greek territory since the available benchmarks are delaminated in so-called “map-leaflets” and a common adjustment of the entire vertical network has not been carried out so far. It is concluded that even between neighbouring “map-leaflets” large biases in the adjusted GPS/Levelling and gravimetric geoid heights exist, which indicates distortions in the Greek vertical datum as this is realized by the levelling benchmarks. Given that the latter are commonly used for everyday surveying purposes, conclusions and proposals on the determination of adjusted orthometric heights are finally drawn.

Validation of GOCE/GRACE Satellite Only and Combined Global Geopotential Models Over Greece in the Frame of the GOCESeaComb Project

The GOCESeaComb project, funded by ESA in the frame of the PRODEX program, aims to utilize GOCE data within combination schemes in order to achieve high-quality and accuracy predictions related to Earth’s gravity field, sea level and dynamic ocean topography. In this work the results from the detailed validation of the latest GOCE, GOCE/GRACE and combined global geopotential models are presented referring to the fourth release of the models and the various strategies (TIM, DIR, GOCO, EIGEN-S/c) employed for their determination. The validation is performed following two approaches. The first one refers to the evaluation of the GGMs signal and error in the form of the provided degree and error variances. The second refers to an external evaluation of the GGMs against local gravity, GPS/Leveling data and deflections of the vertical. In this validation step we follow a spectral enhancement approach of GOCE GGMs, where EGM08 is used to fill-in the medium and high-frequency content along with RTM effects for the high and ultra high part. From the evaluation with GPS/Levelling benchmarks, it is concluded that the GOCE/GRACE GGMs provide improved accuracies compared to EGM2008 by about 2 cm in the spectral range between d/o 120–230. Finally, GOCE/GRACE GGMs manage to provide the same, as EGM2008, level of reduction to the local gravity anomalies, with a standard deviation at the 6.1–6.2 mGal level and marginally better residuals, at the sub-arcsec level in the reduction of deflections of the vertical.

Optimal Marine Geoid Determination in the Atlantic Coastal Region of Argentina

The determination of an optimal, in terms of resolution and accuracy, marine geoid model for the Atlantic coastal region of Argentina is investigated using satellite altimetry and shipborne gravity data. The altimetric data used are those of the geodetic phase of the ERS 1 mission while marine gravity data have been employed as well to determine a gravimetric geoid solution. Furthermore, the effect of the Quasi-Stationary Sea Surface Topography (QSST) was taken into account in correcting the altimetric Sea Surface Heights (SSHs) to derive geoid undulations. Special emphasis was placed on reducing the effects of the Sea Surface Variability (SSV) on the densely spaced altimetric SSHs with low-pass filtering. The satellite and shipborne data were combined in the spectral domain to improve the accuracy of the altimetric solution close to the coastline and derive a more rigorous solution. The accuracy of the final geoid models is assessed through comparisons with stacked TOPEX/POSEIDON (T/P) SSHs, known for their high precision. From the results achieved it was concluded that an altimetric geoid accurate to about 5–8 cm (1σ) is feasible in some areas, while the gravimetric solution gives poorer results by about 5–6 cm. The combination of satellite and shipborne data with the proposed algorithm improves the accuracy of the gravimetric geoid model by about 2 cm.