International Symposium on Gravity, Geoid and Height Systems 2016

Currently, extensive work is being done in the field of geodesy on producing better gravitational models using purely space-based techniques. With the large datasets spanning a long timeframe, thanks to the GOCE and GRACE missions, it is now possible to compute high quality global gravitational models and publish them in a convenient form: spherical harmonics. For regional geoid modeling, this is advantageous as these models provide a useful reference which can be improved with terrestrial observations. In order for these global models to be usable below the topographical surface, certain considerations are required; topographical masses cause the function that describes the gravity potential to be non-harmonic in the space between the topographical surface and the geoid. This violates the mathematical assumptions behind solid spherical harmonics.

This paper aims to look at the error caused by evaluating solid spherical harmonics when topography is present. It thus provides a more rigorous methodology than the commonly used approach of computing the quasigeoid and then applying an approximate correction term for the geoid-quasigeoid separation. It is therefore well-suited for the Stokes-Helmert approach to high-precision regional geoid computation. Comparisons between the more rigorous methodology and the generally used algorithm are made in order to study the error that is committed. With a range of 23.6 cm and a standard deviation of 0.8 cm, this is a non-trivial error if the ultimate goal is to compute a regional geoid with an accuracy of better than 1 cm.

This study investigates the applicability of the recursive least-squares (RLS) adaptive filter for gravity field modelling applications. Simulated satellite gravity gradients are used to assess the performance of the algorithm. The synthetic data follow the behavior of the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) mission observations. An analysis is carried out, where the convergence speed, computational efficiency and optimal impulse response of the adaptive filter are examined. The behavior of the filtered gravity gradients in the time and spectral domain is also studied. The algorithm is capable of converging to a mean-square error (MSE) of 0.013 Eötvös, which is very close to the level of Gaussian noise (0.011 Eötvös) added to the synthetic observations. Although the RLS algorithm shows a fast convergence speed, a strong disadvantage that should be considered before its implementation is its reduced time efficiency.

Regional geoid models are based on the combination of satellite-only gravity field information and terrestrial data. Satellite information is conveniently provided in terms of spherical harmonic global potential models. Terrestrial information is mostly provided in terms of point or block mean values of gravity in the region of interest. Combination of the two sources of information in the overlapping spectral band is either based on deterministic or on stochastic considerations. We have tested different schemas for weighting satellite and terrestrial information and compared the results to GNSS-levelling data in Norway. The results provide implications for the quality of terrestrial data in the study area and for regional geoid modeling based on GOCE satellite models in general.

In order to minimize the computational burden, we avoid field transformation (from gravity anomalies to geoid heights) by employing an already existing regional geoid model to represent the terrestrial information. Combination is then performed by filtering geoid grids in the spatial domain.

Noises are an inevitable part of gravity observations and they can affect the accuracy of the height datum if they are not treated properly in geoid determination. To provide data for geodetic boundary value problems, surface gravity observations must be transferred harmonically down to the geoid, which is called Downward Continuation (DC). Fredholm integral of the first kind is one of the physically meaningful ways of DC, where the Poisson kernel is used to evaluate the data on the geoid. DC behaves inherently as a high pass filter so it magnifies existing noise in Helmert gravity anomalies on geoid (free air anomalies after applying the Helmert’s second condensation method); although the results on the geoid will be later smoothed by evaluating the Stokes’s integral so the noise is less pronounced in the final geoid heights. The effect of noise in Stokes-Helmert geoid determination approach is numerically investigated in this study. The territory of Iran, limited to 44–62° longitude and 24–40° latitude, is considered as the area of interest in this study. The global gravity model EGM2008, up to degree/order 2160, is used to synthesize the free air gravity anomalies on a regular grid on topography and are then transferred to Helmert space using available Digital Elevation Models (DEMs). Different levels of noise are added to the data and the effects of noise are investigated using the SHGeo software package, developed at the University of New Brunswick (UNB). Results show that if the downward continuation of 5*5 arc-min surface points is required, the standard deviation of differences between “noisy” and “clean” data on the geoid will increase by 15% with respect to the corresponding standard deviation on topography. These differences will increase for denser grid resolutions. For example, the noise of ∆g on geoid will increase up to 100% if 1*1 arc-min points are used. The results of evaluating the Stokes integral show smoother results in terms of noise in the data. For example, 2 mGal noise in the gravity anomalies on a 5*5 arc-min grid can cause 1.5 cm of error in the geoid heights. This value is smaller when denser grids are used. Despite increasing noise in downward continuation steps, the results show smaller error in geoid heights if gravity anomalies are located on a denser grid.

Based on the solution for the Bjerhammar Boundary Value Problem (BVP) in physical geodesy, an approximation method of local quasi-geoid using point masses was proposed in the paper, and a multi-layer point mass model of the local quasi-geoid was constructed for some area within China. In the development of the method, the relation between ground gravity anomalies and disturbing potential was derived, which results in the point mass model of the disturbing potential, and then the formula for the derivation of height anomaly was obtained. Through analysis of the requirements on ground gravity anomaly, a multi-layer point mass model for the calculation of height anomaly was constructed. In the numerical test of the method, the Remove-Compute-Restore (RCR) method was also employed for comparisons of approximation results. Analyses of the results show that the proposed method can also be applied in the estimation of local quasi-geoid.

The precise regional geoid modelling requires combination of terrestrial gravity data with satellite-only Earth Gravitational Models (EGMs). In determining the geoid using the Stokes-Helmert approach, the relative contribution of terrestrial and satellite data to the computed geoid can be specified by the Stokes integration cap size defined by the spherical distance ψ ₀ and the maximum degree l ₀ of the EGM-based reference spheroid. Larger values of l ₀ decrease the role of terrestrial gravity data and increase the contribution of satellite data and vice versa for larger values of ψ ₀. The determination of the optimal combination of the parameters l ₀ and ψ ₀ is numerically investigated in this paper. A numerical procedure is proposed to find the best geoid solution by comparing derived gravimetric geoidal heights with those at GNSS/levelling points. The proposed method is tested over the Auvergne geoid computation area. The results show that despite the availability of recent satellite-only EGMs with the maximum degree/order 300, the combination of l ₀ = 160 and ψ ₀ =  45 arc-min yields the best fitting geoid in terms of the standard deviation and the range of the differences between the estimated gravimetric and GNSS/levelling geoidal heights. Depending on the accuracy of available ground gravity data and reference geoidal heights at GNSS/levelling points, the optimal combination of these two parameters may be different in other regions.

In the last decades several alternative methods of modifying Stokes’ formula were developed. Here, a combination of two existing modifications from Meissl and Sjöberg is developed and presented. The latter applies a least squares method to minimize the truncation error (as well as the total error of the geoid determination), while the former forces the truncation coefficients to converge to zero more rapidly by using a continuous function. The question is whether the combined Least Squares-Meissl modification reduces the truncation and/or the total geoid determination error. To determine the modification parameters, a new system of equations satisfying simultaneously the faster convergence and minimizing the total error, are presented by using (a) Green’s second identity, which is a conventional method, and (b) a set of smoothing averaging filters. The method (b) provides further flexibility when different smoothing filters can be utilized. The new modification reduces the contribution of the inner zone error by ~1 mm of the estimated RMS error. The total error does not necessarily decrease, by using the new modification for cap sizes smaller than 3^o versus the least squares modification of Sjöberg (Manusr Geod 16: 367–375, 1991).

The globally observed melting of mountain glaciers is an indicator of local and regional effects of climate change. From the observational point of view, two research questions need to be answered for individual glaciers, namely how much mass is lost or gained from year to year and how much mass is there in total, i.e., how thick is the glacier. There exist various geophysical/glaciological methods for estimation of mass balance and thickness of mountain glaciers. Most of these methods are geometric in nature and not directly sensitive to mass. In contrast, gravimetry provides a direct measure for mass distribution and mass transport. Satellite gravimetry has proven to provide valuable information on regional to global scales. However, the limited spatial resolution does not allow to infer mass balance or ice thickness of individual mountain glaciers. Therefore, the Bavarian Academy of Sciences and Humanities has set up an observational program at Vernagtferner in the Austrian Alps, to test terrestrial gravimetry for small scale glaciological applications. The work reported in the present paper is conducted in collaboration with the Technical University Munich and the German Federal Agency for Cartography and Geodesy. The results are based on 5 years of repeated relative gravimetry and a first absolute gravity campaign conducted with an A10 instrument. We show, that gravimetric observations can be used to constrain glacier thickness as well as temporal mass variations along various profiles over the glacier. Thereby, reaching the target accuracy of 5–10 μGal   seems to be feasible, at least what the internal accuracy of individual relative gravimetry sessions is concerned. The results also underline the importance of carefully checking instrumental parameters in order to reach such a demanding accuracy in absolute sense and to guarantee stability of long-term time series.

In this study, airborne gravity data from the Gravity for the Redefinition of the American Vertical Datum (GRAV-D) project are compared with terrestrial gravity data in three survey blocks that cross the Canada-US border. One block (AN04) overlaps an area containing Alaska (USA) and the Yukon Territory (Canada) over a rough terrain while the other two blocks (EN05 and EN08) are within the Great Lakes-St-Lawrence River region with flat and moderate terrains. GRAV-D has an average flight altitude of about 6 km in the three blocks, in which each survey/cross line spans 240–700 km. The high flight altitude of GRAV-D puts forth a challenge for the comparisons. We have developed procedures to interpolate and continue the airborne and terrestrial gravity data to a mean flight height for each block. The remove-compute-restore Poisson method is used in the upward continuation of the terrestrial gravity data by removing and restoring the satellite-only geopotential model GOCO05S. The comparison between the datasets is done using Helmert gravity disturbances in order to satisfy the harmonic condition of the upward continuation. The comparisons show that differences between GRAV-D and terrestrial gravity data are 3.6 mGal for AN04, 1.8 mGal for EN05 and 2.3 mGal for EN08 in terms of Root Mean Square (RMS) at the mean flight height. The results can be improved for two blocks when applying a cross-over adjustment. The differences become 1.0 and 1.4 for EN05 and EN08, respectively.

This paper deals with creating a fine digital terrain model (DTM) for Africa and the surrounding region covering the window 42^∘S ≤ ϕ ≤ 44^∘N, 22^∘W ≤ λ ≤ 62^∘E using the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) Global Digital Elevation Model (GDEM) at a 3″ × 3″ resolution (which corresponds to roughly 90 m resolution on the earth’s surface). The ASTER-GDEM model, which is available only on land, has been smoothed from its original 1″ × 1″ resolution to the used 3″ × 3″ resolution using the block average operator technique employing special characteristics at the coastal boarders. The 30″ × 30″ SRTM30+ has been used, after being interpolated to 3″ × 3″ grid size, to fill-in the missing sea regions of the ASTER-GDEM model. The created 3″ × 3″ DTM has been compared with the available point data both on land and on sea areas for a set of more than one million points. Residuals follow perfectly the Gaussian normal distribution.

The AFRGDB_V1.0 gravity database has been generated in 2015 from a set of land, shipborne and altimetry-derived gravity anomalies. This gravity data set had significantly large gaps especially on land. Recently, a new gravity data set on land became available. Most of the points of the new data set are located on the large gaps of the data set used to establish the AFRGDB_V1.0 gravity database. This enables an external check of the AFRGDB_V1.0 gravity database at those new data points. An internal validation of the AFRGDB_V1.0 gravity database has been also carried out. The results show that the AFRGDB_V1.0 has an internal precision of about 9 mgal and external accuracy of about 16 mgal.

To enhance and extend the absolute gravity (AG) measurements in New Zealand, we conducted new measurements using a FG5 (#210 of Kyoto University) in January and March 2016. The measurements in the North Island were made at two existing points (the Warkworth Radio Astronomical Observatory and Wellington A) and at one newly established point at the Wairakei Research Centre, Taupo. The gravity measurements in the South Island were made at five existing AG points; Godley Head, Mt John, the University of Otago, Helipad and Bealey Hotel. At each point more than 4,000 drops were made and AG values were determined with measurement uncertainties better than 3 μGal (mostly better than 2 μGal) at 130 cm instrument height. The values are compared with those of the 2015 campaigns. Although the differences of about 10 μGal were observed at Wellington A and Godley Head, those at the other points were within 5 μGal. At points in the Southern Alps we combined AG with relative gravity measurements and achieved good agreement with the 2015 results. Definite values for long-term gravity trends at the points in Southern Alps and Christchurch could not be obtained from the survey, but the results are consistent with those of the previous studies. Further measurements are planned to accurately determine these gravity changes.

For the past two decades, airborne gravimetry using a Strapdown Inertial Measurement Unit (SIMU) has been producing gravity estimates comparable to the traditional stable-platform single-axis gravimeters. The challenge has been to control the long term drift of the IMU sensors, propagating into the long-wavelengths of the gravity estimates. This has made the stable-platform approach the preferred method for geodetic applications. In the summer of 2016, during a large airborne survey in Malaysia, a SIMU system was flown alongside a traditional LaCoste&Romberg (LCR) gravimeter. The SIMU observations were combined with GNSS observations using the commercial software product “Inertial Explorer” from NovAtel’s Waypoint software suite, and it is shown how gravity estimates can be derived from these results. A statistical analysis of the crossover differences yields an RMS error of 2.5 mGal, which is comparable to the results obtained from the LCR gravimeter. The properties of the SIMU and LCR systems are compared and a merging of the two is performed. A statistical analysis of the crossover differences of the merged product yields an RMS error of 1.3 mGal. These results indicate that the properties of the two units are complementary and that a combination of the two can result in improved gravity estimates.

On December 16th, 2015, the superconducting gravimeter SG038 started to measure again after it was moved from the previous station in Concepcion, Chile to the Argentine-Germany Geodetic Observatory (AGGO) near the city of La Plata in Argentina.

The temporal gravity variations recorded with superconducting gravimeters (SG) enables research in several geodetic and geophysical studies that involve Earth’s changes in the surface gravity field. In particular, it allows computing local models of earth tide parameters. The superconducting gravimeter SG038 at station AGGO was used to monitor gravity for the first 6 months after its installation.

The gravity time series was preprocessed after removing the principal constituents of the largest influences of the gravity signal that can be modeled sufficiently accurate like atmospheric effects, theoretical tides of the solid Earth, ocean loading effects and pole tides. In the remaining residual signal spikes were fixed, earthquake perturbations were reduced. Finally, the theoretical tides of the solid Earth and ocean loading effects previously removed were restored to obtain the corrected gravity signal.

The transfer function of the SG038 was determined by analyzing the step response of the whole system. Empirical amplitude and phase response functions are presented. The group delay at zero frequency was used in the tidal analysis.

By harmonic analysis of the preprocessed hourly data, amplitude factors and phases for tidal wave groups were estimated.

In 2014 a team of researchers from five European universities reported on a high tilt susceptibility of the Scintrex CG-5 Autograv land gravity meter. In a series of experiments they demonstrated that the instrument provides incorrect readings after being tilted by angles of at least about 6^∘ for a period of at least a few minutes. The readings may be offset by tens of μGal, and it may take hours before the first reliable readings can be taken. They recommend to keep the instrument in upright position within less than the critical angle of about 6^∘ during transits, which may be unrealistic during field operations in hilly terrain, during car transportation or when walking with the instrument in a backpack. The instruments tested in 2014 were purchased between 2003 and 2011. Here, we report about the results of a series of experiments with the latest release of the Scintrex CG-5 purchased in 2015 using the same experimental set-up as in 2014. We show that the instrument is still susceptible to tilting though the initial offset has been reduced by about 50%. However, readings may still be offset by tens of μGal if the tilt exceeds about 6^∘ and lasts for more than 1 min. Moreover, the time it takes the instrument to provide reliable readings in line with the specifications may still take several hours depending on the temporal duration of instrument tilting. From this we conclude that the problem of tilt susceptibility has not been solved yet.

Relative gravimeters are calibrated for calibration factors relating observable units to gravity. The calibration correction factors with respect to the instrument calibration factors are estimated by measurements at gravity calibration baseline (GCB) stations. GCB is a gravity network where known gravity differences are compared to those measured by relative gravimeters. The GCB in the Kingdom of Saudi Arabia has endpoints in Jeddah and Taif. The endpoints were observed by FG5 (#111) and A10 (#029) absolute gravimeters in 2013–2014. Twelve new sites in between the endpoints were installed in the late 2014. There are two stations (center/inside and ex-center/outside) at each GCB sites, hence the GCB includes 28 stations. Absolute gravity (AG) at the GCB stations were observed simultaneously by two A10X (#021, #023) absolute gravimeters. The stations were also tied simultaneously by four CG5 relative gravimeters. Besides gravity gradient at each of the stations was measured by two CG5s. The gravity measurements were completed from December 2014 to January 2015. The total uncertainty of A10X is smaller than 6 μGal. The uncertainties of gravity gradient and tie measurements are smaller than 2 μGal/m and 5.4 μGal, respectively. Comparisons of ties observed by CG5 and A10X result in differences less than 9 μGal. The GCB network is adjusted by weighted constraint least squares. Estimated uncertainty of the gravity differences is 1–2 μGal. The gravity differences between the endpoints of the calibration line at Jeddah and Taif is 430.678 ± 0.002 mGal.

The GRACE (Gravity Recovery and Climate Experiment) mission launched in 2002 brought a unique opportunity for the determination of temporal mass variations within the Earth system. Their knowledge is essentially needed to achieve the best accuracy of a regional/local geoid model. They are also needed to investigate temporal displacements of the physical surface of the Earth. The aim of this contribution is to study temporal variations of geoid heights as well as to discuss the vertical displacements of the Earth surface in the perspective of the realization of the modern vertical reference system. The area of Poland has been chosen as a study area. Temporal geoid height variations have been determined over the area of Poland divided into four subareas. They have been analysed and modelled using the seasonal decomposition method. As an example, temporal vertical displacements induced from temporal water variations at the Borowa Gora Observatory (BGO) have been determined using GRACE mission data. The results obtained in a case study for Poland reveal that the combination of temporal geoid height variations and temporal vertical displacements of the physical surface of the Earth result in significant temporal variations of the vertical reference system for the area investigated.

In this paper we evaluate three different geoid models (a pure and an extended satellite-only model and a local geoid solution) for the mainland of Greece and fourteen of its biggest islands in terms of signal content and applicability for height system unification. By comparing local geoid heights from GPS and spirit levelling with the three geoid models it is possible to make statements about the Earth’s gravity signal that is omitted in these models (omission error). In a further step we try to quantify the contribution of the omission error to the height system unification between the investigated islands. It becomes obvious that a satellite-only gravity field model (GOCO05S) until degree and order 200 is not sufficient for the mountainous islands of Greece due to an omission error of up to 2 m. The same model with high frequency corrections from EGM08 as well as topography is able to reduce the omission error drastically and shows similar results as for the local geoid model. As an outcome, we can see homogenous omission errors for the smaller islands and in general a high correlation between the size of the island and the amplitudes of the omission error.

The incorporation of the newly available satellite data of GOCE and GRACE missions into global geopotential model solutions provides valuable information on the low to medium frequency band of the gravity field spectrum, an important connection to height datum control and unification. The use of this enriched contribution to existing national height systems quality control will reveal the well known inconsistencies in previous vertical network establishment methods, as well as strengthen the connection solution between adjacent national networks.

The quality control of the vertical network in Attica region (Central Greece) is evaluated in the present study. Collocated GPS/levelling and gravity observation points are utilized with emphasis to trigonometric benchmarks and height reference sites. A spectral enhanced combination scheme is used for the network quality investigation based on the frequency content of pure satellite solutions (GOCE and GRACE) and combined satellite and ground global geopotential model solutions of high degree of expansion. Detailed DTM (Digital Terrain Model) information is incorporated in order to estimate Residual Terrain Model (RTM) effects, leading to an expansion degree of 648,000 (1 arcsec). Finally, detailed information about the quality of the height network in Attica is presented in conjunction to proposals towards the establishment of a new height network.

From 2001 to 2008, the National Geographic Institute of Spain (IGN) carried out the REDNAP project to the establishment of a National High Precision Levelling Network in the whole Spanish territory. Within REDNAP, spirit levelling and gravity observations were complemented by GNSS data. The levelling network of the continental area and those of the main islands were referred to different tide gauges thus producing different height systems. In the paper, the GOCO-05S model from the GRACE and GOCE gravity missions is used to unify such systems. More precisely, it is used to estimate the normal heights of the mean sea level at the reference tide gauges, i.e. the height system biases. In the proposed solution such biases are determined through the least squares adjustment of the differences between height anomalies derived from GNSS/levelling and height anomalies derived from a proper combination of global gravity models. An accurate modelling of the observation error covariances is taken into account as well. The estimated accuracies of the resulting biases are in the order of few centimetres apart from that of continental Spain which is an order of magnitude better.

Vertical reference system in the Slovak Republic is realized by the first and second order of the National levelling network with the normal heights according to Molodenski. The reference heights are still calculated by the traditional method using the components of gravity correction. Nowadays we are preparing a new realization of the height system which will be based on geopotential numbers. But there is a problem with the absence of the measured gravity values. Only at approximately 8% of levelling points we have the measured values of gravity. Therefore, we are trying to find the most reliable method for estimation of the gravity values and use them subsequently for determination of the geopotential numbers. The aim of this study is to analyze the different ways to the gravity determination and their application for calculation of the geopotential numbers on the points of the National levelling network. The first method is based on the reconstruction of the gravity on levelling points from the interpolated values of the complete Bouguer anomaly using the proprietary software. The second method is based on the modern global geopotential models improved by the residual terrain model approach. Calculated gravity was compared with directly measured gravity. The set of the points contained all geodetic control points within Slovakia where the gravity has been measured. Then, the calculated value of gravity was used to determine the geopotential numbers and normal heights according to Molodenski in the first order levelling lines of the National levelling network which connect the reference points determined within EVRF2007 adjustment for area of Slovakia.

In this study, the consistency of the Greek Vertical Datum (GVD) is examined, focusing on an area in central Greece and following similar efforts made in previous researches for the establishment of an International Height Reference System (IHRS). High precision GNSS measurements are available at trigonometric benchmarks located along the Gulf of Corinth, with benchmarks residing on both coasts along. First, the zero-level geopotential value (\( {W}_o^{LVD} \)) for the two areas, north and south coast, is determined, based on the classical Helmert theory using GNSS/leveling data and surface geopotential values derived from GOCE-based global geopotential models (GO-DIR-R5, GO-TIM-R5, GOCO05s and GECO) and EGM08. Then, the relative offset between the two areas is estimated while subsets of the computed benchmark values are also examined. Significant inconsistencies are detected that depend on the choice of benchmarks used in the computations. Moreover, a per benchmark analysis showed that the inconsistencies present a random spatial distribution and are attributed mainly to the orthometric height values of the benchmarks. Furthermore, the local \( {W}_o^{LVD} \) estimates are compared with previous results related to the GVD and the VD of the Greek islands and the corresponding value adopted by the IHRS. Finally, some remarks are drawn on the feasibility of the unification of the GVD with a global one.

GNSS positioning using network-based real-time kinematic (NRTK) techniques, such as the virtual reference station (VRS) and the master auxiliary concept (MAC), is widely used in surveying and geomatics applications. The accuracy of the estimated height component by those techniques is known to be at the centimeter level although several factors, like the deployment of reference stations, the correction message transmission delay, the satellite signal availability and the employed software package, could limit the vertical accuracy obtained in practice. The scope of this paper is to present preliminary results from several field tests that were conducted by the Department of Geodesy and Surveying of the Aristotle University of Thessaloniki for the purpose of evaluating the heighting accuracy from different commercial providers of NRTK positioning services in Greece. Our aim is to investigate the actual positional quality of the vertical component from an end-user’s point of view by considering how different factors, such as the number of in-view satellites and their geometry, the duration of station occupancy, the distance to the reference stations and the choice of the applied correction method (VRS or MAC) might affect the final accuracy of the estimated heights. The validation of our results is based on high-quality height information that was independently obtained by precise spirit leveling over all considered test points.

Satellite altimetry has provided during the last 30 years an unprecedented amount of high-resolution and high-accuracy data for the state of the oceans. With the latest altimetric satellites utilizing the SAR and SAR-in modes, reliable sea surface heights close to the coastline can be determined more efficiently. The main purpose of this paper is to estimate Sea Level Anomalies (SLAs) close to the coastline and to areas where data are absent, while Least Squares Collocation (LSC) has been used to carry out the prediction. The selected study area is the entire Mediterranean Sea and the estimation of SLA values was carried out using raw Cryosat-2 observations. For LSC to be applied, empirical and analytical covariance function models are defined and evaluated for estimating SLAs within 10° block windows. In order to investigate the accuracy of the analytical covariance functions that provide the most accurate results, prediction has been carried out at a single point, randomly selected in the Greek region being close to the coastline. From the analysis carried out, three types of analytical covariance functions were deemed as the optimal ones, providing a mean prediction accuracy at the 3.7 cm level. These models were then used for the SLA estimation at the 10° windows, specifying local empirical and analytical covariance function models. The prediction accuracies achieved range between 3.7 cm and 12.5 cm depending on the presence of islands.

Fifteen years (2000–2015) of altimetric data from ERS2, ENVISAT, SARAL and GEOSAT-FOLLOW-ON satellites are optimally combined with in situ marine gravity observations employing the spectral Multiple Input/Multiple Output System Theory (MIMOST) for Dynamic Ocean Topography (DOT) estimation. The spectral behavior of the method is investigated by assimilating low frequency information from GOCE-derived geopotential models in a test area of the Eastern Mediterranean Sea. The frequency content of the reference field used in the reductions of the original observations and its effect to the DOT approximation is studied. The evolution of the annual DOT is validated against oceanographic information of recently available circulation models in the area under study. The effect of the reference field used in data reductions to the geostrophic circulation of the Eastern Mediterranean Sea is analyzed and remarks on the combination of gravity, altimetry and pure oceanographic data are outlined.

Groundwater is a main source of fresh water in many parts of the world. Monitoring the global and regional groundwater resources is challenging nowadays because of the very scare and high cost in situ measurement networks, especially in Africa. Satellite gravimetry can be used in combination with land surface hydrological models (e.g., Global Land Data Assimilation System (GLDAS) and WaterGAP Global Hydrology Model (WGHM)) to infer groundwater storage behavior. Since 2002, the Gravity Recovery and Climate Experiment (GRACE) satellite mission provides estimation of the Earth’s dynamic gravity field with unprecedented accuracy. Differences between monthly GRACE gravity field solutions give an estimation of the Terrestrial Water Storage (TWS) changes. The groundwater storage can be obtained using the available hydrological models by subtracting the surface water, soil moisture, snow, ice and canopy water from the TWS. GRACE data are available in terms of spherical harmonics expansion. However, GLDAS and WGHM hydrological models are available in the space domain as grids of 1° and 0.5°, respectively. For consistency, both GLDAS and WGHM are approximated in terms of spherical harmonic expansions to be comparable with the used GRACE data. In this paper, the groundwater storage in Africa is studied using GRCAE data (2003–2016) as well as GLDAS and WGHM models for the same time period. Inter annual variations is investigated from monthly groundwater time series.