Residual Terrain Model Research Articles

Validation of GOCE gravity field models using GPS-leveling data and EGM08: a case study in Brazil

Validation of geopotential models derived from Gravity field and steady-state Ocean Circulation Explorer (GOCE) observations is a challenging task in regions with less advanced geodetic infrastructure such as Brazil. In order to assess the current performance of these models, 262 GPS-leveling sites, Earth Gravitational Model 2008 (EGM08) and Residual Terrain Model (RTM) are employed. The validation is based on the differences between GPS-leveling and GOCE-derived models. For the former, the spectral content beyond the GOCE-derived models’ maximum degree is removed by using EGM08 and RTM. The results indicate that the GOCE-based models: DGM-1S, SPW (Releases 1 and 2), TIM (Releases 1, 2, 3 and 4), and DIR (Releases 2, 3 and 4), at their maximum degrees have a worse performance than EGM08 while DIR-R1 shows an improvement of 11%. Furthermore, from the steepness of the slopes of the root mean square error (RMSE), it is observed that the optimal combination between DIR-R1 and EGM08 occurs at degree 230 (RMSE of 0.201 m). For the satellite-only models, DIR-R3 reduces the RMSE by ~1.4% compared to TIM-R4 at degree 190. These results are important for Brazil where the accuracy of the current geoid model is approximately 0.28 m.

An evaluation of recent GOCE geopotential models in Brazil

An evaluation of recent GOCE geopotential models in BrazilSeveral global geopotential models based on Gravity field and steady-state Ocean Circulation Explorer (GOCE) data have been published in the last two years. Some of these models use combinations of different satellite missions, while others use only GOCE data. This paper presents the evaluation and analysis of each approach using GOCE data in the Southeast of Brazil. Two assessments have been made. We compared the geoid heights derived from GOCE-based models with the geoidal heights from 176 GPS stations on leveling benchmarks. The findings show an improvement in GOCE-based models TIM_R3 (0.40 m) and DIR_R3 (0.39 m) for degree and order 210 in relation to EGM2008 (0.44 m) in terms of RMS. For the other models the results did not exceed 0.44 m. The second evaluation reports the comparison in terms of gravity disturbances between terrestrial gravity data and the models. The results, in terms of RMS and up to degree and order 210, indicate slightly low GOCO 02S values (10.34 mGal), TIM_R2 (10.37 mGal) and TIM_R3 (10.47 mGal) compared to EGM2008 (10.66 mGal). We also applied the residual terrain model and, as a result, the RMS errors were reduced by ~35% (~6.0 mGal) in the entire area and by ~45% in the mountain region.

Regional gravimetric quasi-geoid model and transformation surface to national height system for Turkey (THG-09)

Turkish regional geoid models have been developed by employing a reference earth gravitational model, surface gravity observations and digital terrain models. The gravimetric geoid models provide a ready transformation from ellipsoidal heights to the orthometric heights through the use of GPS/leveling geoid heights determined through the national geodetic networks. The recent gravimetric models for Turkish territory were computed depending on OSU91 (TG-91) and EGM96 (TG-03) earth gravitational models. The release of the Earth Gravitational Model 2008 (EGM08), the collection of new surface gravity observations, the advanced satellite altimetry-derived gravity over the sea, and the availability of the high resolution digital terrain model have encouraged us to compute a new geoid model for Turkey. We used the Remove-Restore procedure based on EGM08 and applied Residual Terrain Model (RTM) reduction of the surface gravity data. Fast Fourier Transformation (FFT) was then used to obtain the residual quasigeoid from the reduced gravity. We restored the individual contributions of EGM08 and RTM to the whole quasi-geoid height (TQG-09). Since the Helmert orthometric height system is adopted in Turkey, the quasi-geoid model (TQG-09) was then converted to the geoid model (TG-09) by making use of Bouguer gravity anomalies and digital terrain model. After all we combined a gravimetric geoid model with GPS/leveling geoid heights in order to obtain a hybrid geoid model (THG-09) (or a transformation surface) to be used in GPS applications. The RMS of the post-fit residuals after the combination was found to be ± 0.95 cm, which represents the internal precision of the final combination. And finally, we tested the hybrid geoid model with GPS/leveling data, which were not used in the combination, to assess the external accuracy. Results show that the external accuracy of the THG-09 model is ± 8.4 cm, a precision previously not achieved in Turkey until this study.

Evaluation of the first GOCE static gravity field models using terrestrial gravity, vertical deflections and EGM2008 quasigeoid heights

Recently, four global geopotential models (GGMs) were computed and released based on the first 2 months of data collected by the Gravity field and steady-state Ocean Circulation Explorer (GOCE) dedicated satellite gravity field mission. Given that GOCE is a technologically complex mission and different processing strategies were applied to real space-collected GOCE data for the first time, evaluation of the new models is an important aspect. As a first assessment strategy, we use terrestrial gravity data over Switzerland and Australia and astrogeodetic vertical deflections over Europe and Australia as ground-truth data sets for GOCE model evaluation. We apply a spectral enhancement method (SEM) to the truncated GOCE GGMs to make their spectral content more comparable with the terrestrial data. The SEM utilises the high-degree bands of EGM2008 and residual terrain model data as a data source to widely bridge the spectral gap between the satellite and terrestrial data. Analysis of root mean square (RMS) errors is carried out as a function of (i) the GOCE GGM expansion degree and (ii) the four different GOCE GGMs. The RMS curves are also compared against those from EGM2008 and GRACE-based GGMs. As a second assessment strategy, we compare global grids of GOCE GGM and EGM2008 quasigeoid heights. In connection with EGM2008 error estimates, this allows location of regions where GOCE is likely to deliver improved knowledge on the Earth’s gravity field. Our ground truth data sets, together with the EGM2008 quasigeoid comparisons, signal clear improvements in the spectral band ~160–165 to ~180–185 in terms of spherical harmonic degrees for the GOCE-based GGMs, fairly independently of the individual GOCE model used. The results from both assessments together provide strong evidence that the first 2 months of GOCE observations improve the knowledge of the Earth’s static gravity field at spatial scales between ~125 and ~110 km, particularly over parts of Asia, Africa, South America and Antarctica, in comparison with the pre-GOCE-era.

Geopotential numbers from GPS satellite surveying and disturbing potential model: a case study of Parana, Brazil

This article deals with the approach to determining the geopotential numbers from Global Positioning System (GPS) satellite surveying and disturbing potential at a point on the Earth's surface. The disturbing potential was solved by the Brovar-type solution of Molodenskii's boundary value problem but in the context of the fixed problem. The solution is compatible with the techniques for smoothing of external field: removerestore techniques, residual terrain model, and use of high-resolution global geopotential models. This method provides an absolute geopotential numbers related to the so-called world height system. As an example, we calculate the disturbing potential model in Southern Brazil. The general condition of the sparse and absent gravity values is the main point to be solved. The absolute and relative accuracies of the quasigeoid model were tested vs. GPS/leveling data. Based on 99 GPS/leveling points, the mean value of fitting for the quasigeoid model was estimated near 0.032 m in the absolute view and 0.2 ppm in the relative view.

Assessment of EGM2008 in Europe using accurate astrogeodetic vertical deflections and omission error estimates from SRTM/DTM2006.0 residual terrain model data

We assess the new EGM2008 Earth gravitational model using a set of 1056 astrogeodetic vertical deflections over parts of continental Europe. Our astrogeodetic vertical deflection data set originates from zenith camera observations performed during 1983–2008. This set, which is completely independent from EGM2008, covers, e.g., Switzerland, Germany, Portugal and Greece, and samples a variety of topography – level terrain, medium elevated and rugged Alpine areas. We describe how EGM2008 is used to compute vertical deflections according to Helmert's (surface) definition. Particular attention is paid to estimating the EGM2008 signal omission error from residual terrain model (RTM) data. The RTM data is obtained from the Shuttle Radar Topography Mission (SRTM) elevation model and the DTM2006.0 high degree spherical harmonic reference surface. The comparisons between the astrogeodetic and EGM2008 vertical deflections show an agreement of about 3 arc seconds (root mean square, RMS). Adding omission error estimates from RTM to EGM2008 significantly reduces the discrepancies from the complete European set of astrogeodetic deflections to 1 arc second (RMS). Depending on the region, the RMS errors vary between 0.4 and 1.5 arc seconds. These values not only reflect EGM2008 commission errors, but also short‐scale mass‐density anomalies not modelled from the RTM data. Given (1) formally stated EGM2008 commission error estimates of about 0.6–0.8 arc seconds for vertical deflections, and (2) that short‐scale mass‐density anomalies may affect vertical deflections by about 1 arc second, the agreement between EGM2008 and our astrogeodetic deflection data set is very good. Further focus is placed on the investigation of the high‐degree spectral bands of EGM2008. As a general conclusion, EGM2008 – enhanced by RTM data – is capable of predicting Helmert vertical deflections at the 1 arc second accuracy level over Europe.

Combining EGM2008 and SRTM/DTM2006.0 residual terrain model data to improve quasigeoid computations in mountainous areas devoid of gravity data

A global geopotential model, like EGM2008, is not capable of representing the high-frequency components of Earth’s gravity field. This is known as the omission error. In mountainous terrain, omission errors in EGM2008, even when expanded to degree 2,190, may reach amplitudes of 10 cm and more for height anomalies. The present paper proposes the utilisation of high-resolution residual terrain model (RTM) data for computing estimates of the omission error in rugged terrain. RTM elevations may be constructed as the difference between the SRTM (Shuttle Radar Topography Mission) elevation model and the DTM2006.0 spherical harmonic topographic expansion. Numerical tests, carried out in the German Alps with a precise gravimetric quasigeoid model (GCG05) and GPS/levelling data as references, demonstrate that RTM-based omission error estimates improve EGM2008 height anomaly differences by 10 cm in many cases. The comparisons of EGM2008-only height anomalies and the GCG05 model showed 3.7 cm standard deviation after a bias-fit. Applying RTM omission error estimates to EGM2008 reduces the standard deviation to 1.9 cm which equates to a significant improvement rate of 47%. Using GPS/levelling data strongly corroborates these findings with an improvement rate of 49%. The proposed RTM approach may be of practical value to improve quasigeoid determination in mountainous areas without sufficient regional gravity data coverage, e.g., in parts of Asia, South America or Africa. As a further application, RTM omission error estimates will allow refined validation of global gravity field models like EGM2008 from GPS/levelling data.

Prediction of vertical deflections from high-degree spherical harmonic synthesis and residual terrain model data

This study demonstrates that in mountainous areas the use of residual terrain model (RTM) data significantly improves the accuracy of vertical deflections obtained from high-degree spherical harmonic synthesis. The new Earth gravitational model EGM2008 is used to compute vertical deflections up to a spherical harmonic degree of 2,160. RTM data can be constructed as difference between high-resolution Shuttle Radar Topography Mission (SRTM) elevation data and the terrain model DTM2006.0 (a spherical harmonic terrain model that complements EGM2008) providing the long-wavelength reference surface. Because these RTM elevations imply most of the gravity field signal beyond spherical harmonic degree of 2,160, they can be used to augment EGM2008 vertical deflection predictions in the very high spherical harmonic degrees. In two mountainous test areas—the German and the Swiss Alps—the combined use of EGM2008 and RTM data was successfully tested at 223 stations with high-precision astrogeodetic vertical deflections from recent zenith camera observations (accuracy of about 0.1 arc seconds) available. The comparison of EGM2008 vertical deflections with the ground-truth astrogeodetic observations shows root mean square (RMS) values (from differences) of 3.5 arc seconds for ξ and 3.2 arc seconds for η, respectively. Using a combination of EGM2008 and RTM data for the prediction of vertical deflections considerably reduces the RMS values to the level of 0.8 arc seconds for both vertical deflection components, which is a significant improvement of about 75%. Density anomalies of the real topography with respect to the residual model topography are one factor limiting the accuracy of the approach. The proposed technique for vertical deflection predictions is based on three publicly available data sets: (1) EGM2008, (2) DTM2006.0 and (3) SRTM elevation data. This allows replication of the approach for improving the accuracy of EGM2008 vertical deflection predictions in regions with a rough topography or for improved validation of EGM2008 and future high-degree spherical harmonic models by means of independent ground truth data.

An estimation of the height system bias parameter N 0 using least squares collocation from observed gravity and GPS-levelling data

This paper deals with the analysis of gravity anomaly and precise levelling in conjunction with GPS-Levelling data for the computation of a gravimetric geoid and an estimate of the height system bias parameter No for the vertical datum in Pakistan by means of least squares collocation technique. The long term objective is to obtain a regional geoid (or quasi-geoid) modeling using a combination of local data with a high degree and order Earth gravity model (EGM) and to determine a bias (if there is one) with respect to a global mean sea surface. An application of collocation with the optimal covariance parameters has facilitated to achieve gravimetric height anomalies in a global geocentric datum. Residual terrain modeling (RTM) technique has been used in combination with the EGM96 for the reduction and smoothing of the gravity data. A value for the bias parameter No has been estimated with reference to the local GPS-Levelling datum that appears to be 0.705 m with 0.07 m mean square error. The gravimetric height anomalies were compared with height anomalies obtained from GPS-Levelling stations using least square collocation with and without bias adjustment. The bias adjustment minimizes the difference between the gravimetric height anomalies with respect to residual GPS-Levelling data and the standard deviation of the differences drops from 35 cm to 2.6 cm. The results of this study suggest that No adjustment may be a good alternative for the fitting of the final gravimetric geoid as is generally done when using FFT methods.

Sensitivity analysis of the gravity geoid estimation: A case study on the Azores plateau

A numerical investigation into the effects of high-resolution heterogeneous data on the estimation of the geoid is presented for the area of the Azores plateau. Gravity data were complemented with high-resolution digital terrain models, mass density models from geophysical information, and the most recent geopotential model from the CHAMP mission (GGM02) to derive a high-precision gravity model. Gravity data were reduced from the residual terrain model effects and the GGM02C model, and a grid with 1.5′ spatial resolution was generated by least squares collocation. The gravimetric geoid model was computed by the direct evaluation of Stokes’ integral with a spherical cap radius of 0.8°, with gravity data reduced by Helmert's second condensation method. The geoid model was evaluated over sea by comparison with 6 years of Topex/Poseidon altimeter data and an absolute agreement of 14 cm RMS was achieved after removing the bias. Over land, the geoid was compared with a total of 223 GPS/levelling points corresponding to five different vertical datums. Locally adjusted solutions were determined for each island with a four-parameter model, and a maximum RMS of 12 cm (on Pico) and a minimum of 2.1 cm (on Faial) were determined. As a result of persistent volcanic and tectonic activity on most of the Azores islands, this geoid residual standard deviation must not be viewed as purely geoid error but containing, in addition, levelling and GPS position errors and vertical displacement. The effect on geoid accuracy of the digital terrain model resolution, of the spatial density of gravity data, and of the mass density was evaluated and two important conclusions were derived. First, the digital terrain model resolution has a clear effect on the geoid accuracy, with a maximum RMS of 3.4 cm on S. Miguel. Second, the mass density model does not affect the accuracy of the geoid. This second result indicates that the effect of variable density models on geoid determination may apply only to extensive areas of high terrain and not to smaller topographic units such as single volcanoes. The high-precision gravity model and gravimetric geoid for Azores (AZGEOD07) generated in this study will allow the conversion of old orthometric heights to ellipsoidal heights at precisions useful for the monitoring of vertical deformation. The geoid will also have application to investigate ocean circulation modulation and dynamic processes of Earth's mantle.

Short-wavelength Spectral Properties of the Gravity Field from a Range of Regional Data Sets

The GRACE (gravity recovery and climate experiment) and GOCE (gravity field and steady-state ocean circulation explorer) dedicated gravity satellite missions are expected to deliver the long-wavelength scales of the Earth’s gravity field with extreme precision. For many applications in Earth sciences, future research activities will have to focus on a similar precision on shorter scales not recovered by satellite missions. Here, we investigate the signal power of gravity anomalies at such short scales. We derive an average degree variance and power spectral density model for topography-reduced gravity anomalies (residual terrain model anomalies and de-trended refined Bouguer anomalies), which is valid for wavelengths between 0.7 and 100 km. The model is based on the analysis of gravity anomalies from 13 test regions in various geographical areas and geophysical settings, using various power spectrum computation approaches. The power of the derived average topography-reduced model is considerably lower than the Tscherning–Rapp free air anomaly model. The signal power of the individual test regions deviates from the obtained average model by less than a factor of 4 in terms of square-root power spectral amplitudes. Despite the topographic reduction, the highest signal power is found in mountainous areas and the lowest signal power in flat terrain. For the derived average power spectral model, a validation procedure is developed based on least-squares prediction tests. The validation shows that the model leads to a good prediction quality and realistic error measures. Therefore, for least-squares prediction, the model could replace the use of autocovariance functions derived from local or regional data.

Improvement in the Determination of the Marine Geoid by Estimating the Bathymetry from Altimetry and Depth Soundings

The contribution of bathymetry to the estimation of gravity field related quantities is investigated in an extended test area in the Mediterranean Sea. The region is located southwest of the island of Crete, Greece, bounded between 33ˆ ≤ ϕ ≤ 35ˆ and 15ˆ ≤ λ ≤ 25ˆ. Gravity anomalies from the KMS99 gravity field and shipborne depth soundings are used with a priori statistical characteristics of depths in a least-squares collocation procedure to estimate a new bathymetry model. Two different global bathymetry models, namely JGP95E and Sandwell and Smith V8, are used to derive the depth a priori statistical information, while the estimated model is compared against both the global ones and the shipborne depth soundings to assess whether there is an improvement. Various marine geoid models are estimated using ERS1 and GEOSAT Geodetic Mission altimetry and shipborne gravity data. In that process, the effect of the bathymetry is computed using both the estimated and the original depths through a residual terrain modeling reduction. The TOPEX/Poseidon Sea Surface Heights, known for their high accuracy and precision, and the GEOMED solution for the geoid in the Mediterranean are used as control for the validation of the new geoid models and to assess the improvement that the estimated depths offer to geoid modeling. The results show that the newly estimated bathymetry agrees better (by about 30 to 300 m) with the shipborne depth soundings and provides smoother residual geoid heights and gravity anomalies (by about 8–20%) than those from global models. Finally, the achieved accuracy in geoid modeling ranges between 6 and 10 cm (1σ).

The Rudzki inversion gravimetric reduction scheme in geoid determination

Gravimetric reduction schemes play an important role in precise geoid determination, especially in rugged areas. The Rudzki inversion is the only gravimetric reduction scheme that does not change the equipotential surface. The topographical masses above the geoid are inverted into its interior in this scheme. Although the potential of the topography is equal to that of the inverted masses, and thus there is no indirect effect on the geoid using this mass reduction scheme, the attractions of the topography and the inverted topography are not equal. The formulas to compute the attraction due to topographical masses above the geoid and due to inverted masses are studied in planar approximation. One of the most rugged areas in the Canadian Rocky Mountains, which lies between 49°N and 54°N latitude and between 236°E and 246°E longitude, is selected to compute the gravimetric geoid solution using the Rudzki method. It is compared with geoid models based on Helmert’s second method of condensation and the residual terrain model (RTM), which are most commonly used in practice, and also with those based on the topographic–isostatic reduction methods of Airy–Heiskanen and Pratt–Hayford. Results show that the Rudzki geoid solution performs as well as the Helmert and RTM geoid solutions (in terms of standard deviation and range of maximum and minimum values) when compared to GPS-leveling data in this test area.

Simulation of the Indonesian land gravity data using a digital terrain model data

The Indonesian gravity field is neither accurately nor comprehensively determined, especially due to inadequacy of land gravity data. This study deals with determination of Indonesian land gravity and proposes the solution to data unavailability by means of a simulation technique. The simulation was carried out by combining short wavelength topographic effects from GTOPO30 and long wavelength information from EGM96. The simulated result was then compared with the observed gravity data. Over Java, Sumatra and Sulawesi islands, using three methods commonly used on the computation of topographic effect; topography, isostatic and RTM (Residual Terrain Model), it was estimated that error propagation by the GTOPO30 into the simulated gravity is about 4.5 to 11.7 mgal, with the RTM method was affected less than others. It was also shown that the simulated gravity from the RTM method gave the best agreement with STD (Standard Deviation) differences of 17 to 42 mgal compared to the observed data. This result was achieved after applying optimal RTM parameters over the Indonesian area: a reference field of 25′–27.5′ and density of 2–2.2 gr/cm3. Compared to STD differences between EGM96 and observed data, that between the simulated gravity and observed data improved by 2.5–7 mgal, and gave more detailed gravity features, especially over areas of high topography.

How to handle topography in practical geoid determination: three examples

Three different methods of handling topography in geoid determination were investigated. The first two methods employ the residual terrain model (RTM) remove–restore technique, yielding the quasigeoid, whereas the third method uses the classical Helmert condensation method, yielding the geoid. All three methods were used with the geopotential model Earth Gravity Model (1996) (EGM96) as a reference, and the results were compared to precise global positioning system (GPS) levelling networks in Scandinavia. An investigation of the Helmert method, focusing on the different types of indirect effects and their effects on the geoid, was also carried out. The three different methods used produce almost identical results at the 5-cm level, when compared to the GPS levelling networks. However, small systematic differences existed.

Precision geoid determination by spherical FFT in and around the Korean peninsula

This paper deals with the precision geoid determination by a gravimetric solution in and around the Korean peninsula. A number of data files were compiled for this work, containing now more than 69,900 point gravity data on land and ocean areas. The EGM96 global geopotential model to degree 360 was used in order to determine the long wavelength effect of the geoid surface. By applying the remove-restore technique the geoid undulations were determined by combining a geopotential model, mean free-air gravity anomalies and height in a Digital Elevation Model (DEM). Computation involves a spherical approximation to conduct the Stokes’ integration by a two dimensional spherical Fast Fourier Transform (FFT) with 100% zero-padding. A terrain correction was also computed by FFT with a spherical approximation of the Residual Terrain Model (RTM) terrain correction integration. Accuracy estimates are given for absolute geoid undulations using 78 GPS/Leveling stations. The comparative evaluation gives the bias of 0.187 meters and standard deviation of 0.28 meters, respectively. The relative accuracy achieved was of the order of 3.1 ppm for baselines between 10 and 350 kilometers.

Different ways to handle topography in practical geoid determination

In this paper two different methods of how to handle topography in geoid determination is investigated. First method employs the Residual Terrain Model (RTM) remove-restore technique and yields the quasigeoid, whereas the second method is the classical Helmert condensation method, yielding the geoid. Both methods were used with the Earth Gravity Model (1996) (EGM96) geopotential model as reference, and results are compared to precise Global Positioning System (GPS) levelling networks in Scandinavia, especially an accurate GPS data set from the very rugged Sognefjord region, where the topography was represented by either a detailed (100 m) or a coarse (1000 m) digital terrain model. The inclusion of bathymetry in the terrain model was also investigated.Even if two different methods were used, they produced almost identical results at the 5 cm level in the mountains, but small systematic differences exist. Results show the importance of comparing the right types of geoid (classical geoid or quasigeoid), since differences in residuals are significant.

Geoid models around Sognefjord using depth data

Bathymetry data from Sognefjord, Norway, have been included in a terrain model, and their influence on the geoid has been calculated. The test area, located in the western part of Norway, was chosen due to its deep fjords and high mountains. Inclusion of bathymetry data in the terrain model altered the computed gravimetric geoid by as much as a few decimeters. The effect was detectable to a distance of more than 100 km. All calculated geoids, both with and without bathymetry data in the terrain model, fit the geoidal heights determined by available Global Positioning System (GPS) and levelling heights at the sub-decimetre level. Contrary to expectations, the accuracy in geoid prediction was reduced when using bathymetric data. The geoid changes were largest over the fjord where no GPS points were located. Different methods on the same area [isostatic and Residual Terrain Model (RTM)-terrain reductions] showed differences of approximately 1 m. Rigorous distinction between quasigeoid and geoid was found to be essential in this kind of area.

Gravity-field improvement in the Mediterranean Sea by estimating the bottom topography using collocation

The contribution of bathymetry to the prediction of quantities related to the gravity field (e.g., gravity anomalies, geoid heights) is discussed in an extended test area of the central Mediterranean Sea. Sea gravity anomalies and a priori statistical characteristics of depths are used in a least-squares collocation procedure in order to produce new depths, giving a better smoothing of the gravity field when using a remove-restore procedure. The effect of the bottom topography on gravity-field modeling is studied using both the original and the new depths through a residual terrain modeling reduction. The numerical tests show a considerable smoothing of the sea gravity anomalies and the available altimeter heights when the new depth information is taken into account according to the covariance analysis performed. Moreover, geoid heights are computed by combining the sea gravity anomalies either with the original depths or with the new ones, using as a reference surface the OSU91A geopotential model. Comparing the computed geoid heights with adjusted altimeter sea-surface heights (SSHs), better results are obtained when subtracting the attraction of the new depth information. Similar results are obtained when predicting gravity anomalies from altimeter SSHs where the terrain effect on altimetry is based on the new bottom topography.

Precise geoid determination using a density variation model

The contribution of a density variation model in combination with a high resolution height model for the precise determination of the Austrian gravimetric geoid is investigated. Numerical results are given for a test area of 2° × 2° in the central part of Austria. The computation follows the well known remove-restore process. Within this process RTM-method (RTM is the abbreviation for residual terrain model) is used to subtract the short wavelength part of the gravity field. Stokes integral is evaluated by FFT-techniques. Additionally the quality of the new released geopotential model EGM96 for the approximation of the long wavelengths of the Austrian gravity field is tested. The numerical tests show that even small changes in the density values can effect the gravimetric geoid by more than 10 cm.