Vassilios Grigoriadis

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.

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.

Joint price dynamics of quality differentiated commodities: copula evidence from coffee varieties

The objective of this article is to investigate the intensity and the mode of price linkages for quality differentiated coffee beans. This is pursued using monthly spot prices from 1990 to 2015 and nonparametric copulas. The empirical findings suggest that: (i) The price interrelationships are stronger among the Arabica beans than between the individual Arabica and the Robusta beans; also, price co-movement is higher (lower) where the quality difference is smaller (larger). (ii) There is symmetric price co-movement under positive and negative price shocks; that means, shocks of the same absolute magnitude but of different sign are transmitted from one coffee market to another with the same intensity. The transmission of shocks, however, of the same sign but of different magnitude is asymmetric; in particular, larger (in absolute value) price shocks are transmitted with higher intensity compared with smaller ones.

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.

Combination of multi-satellite altimetry data with CHAMP and GRACE EGMs for geoid and sea surface topography determination

Since the launch of the first altimetric missions a wealth of data for the sea surface has become available and utilized for geoid and sea surface topography modeling. The data from the gravity field dedicated satellite missions of CHAMP and GRACE provide a unique opportunity for combination studies with satellite altimetric observations. This study focuses on the combination of data from GEOSAT, ERS1/2, Topex/Poseidon, JASON-1 and ENVISAT with Earth Gravity Models (EGMs) generated from CHAMP and GRACE data to study the mean sea surface (MSS)/marine geoid in the Mediterranean Sea. Various combination methods, i.e., weighted least squares and least squares collocation are investigated and conclusions on the most appropriate combination strategy are drawn. Then, a remove-compute-restore scheme is followed to estimate the MSS model. Comparisons with other MSS models referenced to EGM96 and CHAMP/GRACE EGMs are performed in terms of the geoid height values at various control points. Finally, a sea surface topography model for the eastern part of the Mediterranean Sea is determined by a combination of the altimetric geoid and the CHAMP/GRACE EGM. The latteris validated against a sea surface topography model derived from altimetric data, in-situ oceanographic observations and an ocean general circulation model.

Combination Schemes for Local Orthometric Height Determination from GPS Measurements and Gravity Data

One of the most interesting and challenging tasks in the field of geodetic surveying is the accurate determination of orthometric heights from GPS measurements taking into account leveling data and additional gravity field information. This paper focuses on the presentation of the currently available various solution strategies which are then properly applied. The first method is based on the integrated geodetic model, where gravity field parameters are treated as signals. A second solution is based on a combination scheme employing least squares collocation as the optimal heterogeneous combination method for gravity and height data. Another method is the spectral domain equivalent of least squares collocation, namely the Multiple Input Multiple Output System Theory, where gravity and height data are treated as stochastic signals with full variance covariance information. The last method consists in a polynomial interpolation model of various orders expressing different geoid representations.

Gravity data inversion for Moho depth modeling in the Hellenic area

The main objective of this study is the determination of the Moho discontinuity in the Hellenic area based on gravity data inversion. High-resolution (2 arcmin) and accuracy (±2 to ±3 mGal) gravity data were used in the computations following the Parker–Oldenburg iterative method, and a low-pass filter was applied to gravity information towards the convergence of the final solution. To determine the cut-off wavenumber of the filter, we tested different mean depths and density contrasts of the crust and the mantle (Mohorovičić discontinuity). The selected density contrast and mean depth of the Mohorovičić discontinuity are those which agree with the Moho depth interpreted from deep seismic imaging data. By comparing the Moho depth estimated, covering both land and marine areas and including the Ionian and Aegean Sea, with those interpreted from previous studies, it is shown that our solution is consistent with the available seismic data interpretation. Moreover, the resolution of the gravity data and the appropriate filtering used in this study contributed to the representation of local features of the Moho discontinuity. Finally, area-dependent discrepancies detected between the Moho depths of the current solution and those derived from previous studies are extensively discussed.

GOCE Variance and Covariance Contribution to Height System Unification

The definition and realization of vertical datum is a key concept in support of not only geodetic works but also for surveying and hydraulic studies to name a few. In the GOCE era, this is customarily done by estimating height and/or geopotential offsets with respect to a conventional reference geopotential value or to available GNSS/Leveling observations on trigonometric BMs and a GOCE-based geoid. This work investigates the influence of GOCE errors in the determination of the Hellenic Local Vertical Datum. This is facilitated through a least-squares adjustment of collocated GNSS/Leveling and GOCE geoid heights over a network of 1,542 BMs. TIM-R5, GOCO05s and GOCO05c Global Geopotential Models (GGMs) are used for representing the contribution of GOCE and GRACE to the Earth’s gravity field. First, a weighted adjustment is carried out employing the GGMs commission error as indicative of the geoid height variance for all stations. Then, full variance-covariance matrices of the GGMs are employed for utilizing realistic GOCE error information and investigating their influence on the adjustment results. Using the available GNSS/Leveling formal errors, a Variance Component Estimation (VCE) is performed to evaluate height (h, H, N) error matrices and assess the stochastic model for the corresponding observational noise. VCE is used to address the impact of a simplified uniform variance assumption for all geoid height data on the final prediction variances in contrast to using the full covariance matrices. Finally, zero-level geopotential values are estimated for the Greek mainland following weighting schemes as the ones described above.

Monitoring water quality parameters in the marine area of Danube Delta using satellite remote sensing: preliminary results

The aim of this work was to produce water quality parameter maps for the marine area of the Danube Delta using remotely sensed data and to validate the results with in-situ measurements. For this reason, satellite images from ENVISAT/MERIS and Aqua/MODIS were used along with collocated in-situ measurements. The latter were in-sync with the satellite images acquisition so that rigorous and validation could be performed. Chlorophyll-a concentration and total suspended matter were estimated using the CASE-II algorithm and MERIS satellite images, while sea surface temperature was estimated from MODIS Ocean Team products. The results show that the satellite images covered the study area completely, with some data gaps due to cloud coverage. Comparisons show a good correspondence with in-situ measurements. Thus, the time series of satellite images that was produced suggests that it is possible to monitor the biological changes on an operational basis. The produced maps described a detailed spatial pattern of chlorophyll-a and total suspended matter that could not have been identified from the sparse in-situ measurements.