Gravimetric Geoid Model Research Articles

A software package for computing a regional gravimetric geoid model by the KTH method

Nowadays, the geodetic community has aimed to determine 1-cm accuracy gravimetric geoid model, which satisfies the demands of most engineering applications. However, the gravimetric geoid determination is a difficult mission which needs an exclusive attention to obtain reliable results for this purpose. Today, Least-Squares Modification of Stokes (LSMS) formula which is so-called the KTH method (Swedish Royal Institute of Technology) has been performed in the regional geoid studies. Based upon the earlier investigations, the KTH method provides more reasonable results than the Remove Compute Restore technique, especially in roughly terrain with sparse terrestrial gravity data. Nevertheless, a compact and practical software package is now not available for users and researchers in geosciences. Thus, in this paper, a scientific software called “LSMSSOFT” is developed and presented by adding a new algorithm which speeds up the evaluation of Stokes’ integral. Afterwards, the LSMSSOFT is applied to a case study for the construction of a geoid model over the Auvergne test area in France. Consequently, the algorithm treated in the software and its results imply that the LSMSSOFT is an alternative software package for modelling the gravimetric geoid by the KTH method.

Confirming regional 1 cm differential geoid accuracy from airborne gravimetry: the Geoid Slope Validation Survey of 2011

A terrestrial survey, called the Geoid Slope Validation Survey of 2011 (GSVS11), encompassing leveling, GPS, astrogeodetic deflections of the vertical (DOV) and surface gravity was performed in the United States. The general purpose of that survey was to evaluate the current accuracy of gravimetric geoid models, and also to determine the impact of introducing new airborne gravity data from the ‘Gravity for the Redefinition of the American Vertical Datum’ (GRAV-D) project. More specifically, the GSVS11 survey was performed to determine whether or not the GRAV-D airborne gravimetry, flown at 11 km altitude, can reduce differential geoid error to below 1 cm in a low, flat gravimetrically uncomplicated region. GSVS11 comprises a 325 km traverse from Austin to Rockport in Southern Texas, and includes 218 GPS stations ( $$\sigma _{\Delta h }= 0.4$$ cm over any distance from 0.4 to 325 km) co-located with first-order spirit leveled orthometric heights ( $$\sigma _{\Delta H }= 1.3$$ cm end-to-end), including new surface gravimetry, and 216 astronomically determined vertical deflections $$(\sigma _{\mathrm{DOV}}= 0.1^{\prime \prime })$$ . The terrestrial survey data were compared in various ways to specific geoid models, including analysis of RMS residuals between all pairs of points on the line, direct comparison of DOVs to geoid slopes, and a harmonic analysis of the differences between the terrestrial data and various geoid models. These comparisons of the terrestrial survey data with specific geoid models showed conclusively that, in this type of region (low, flat) the geoid models computed using existing terrestrial gravity, combined with digital elevation models (DEMs) and GRACE and GOCE data, differential geoid accuracy of 1 to 3 cm (1 $$\sigma )$$ over distances from 0.4 to 325 km were currently being achieved. However, the addition of a contemporaneous airborne gravity data set, flown at 11 km altitude, brought the estimated differential geoid accuracy down to 1 cm over nearly all distances from 0.4 to 325 km.

Canadian gravimetric geoid model 2010

A new gravimetric geoid model, Canadian Gravimetric Geoid 2010 (CGG2010), has been developed to upgrade the previous geoid model CGG2005. CGG2010 represents the separation between the reference ellipsoid of GRS80 and the Earth’s equipotential surface of $$W_0=62{,}636{,}855.69~\mathrm{m}^2\mathrm{s}^{-2}$$ . The Stokes–Helmert method has been re-formulated for the determination of CGG2010 by a new Stokes kernel modification. It reduces the effect of the systematic error in the Canadian terrestrial gravity data on the geoid to the level below 2 cm from about 20 cm using other existing modification techniques, and renders a smooth spectral combination of the satellite and terrestrial gravity data. The long wavelength components of CGG2010 include the GOCE contribution contained in a combined GRACE and GOCE geopotential model: GOCO01S, which ranges from $$-20.1$$ to 16.7 cm with an RMS of 2.9 cm. Improvement has been also achieved through the refinement of geoid modelling procedure and the use of new data. (1) The downward continuation effect has been accounted accurately ranging from $$-22.1$$ to 16.5 cm with an RMS of 0.9 cm. (2) The geoid residual from the Stokes integral is reduced to 4 cm in RMS by the use of an ultra-high degree spherical harmonic representation of global elevation model for deriving the reference Helmert field in conjunction with a derived global geopotential model. (3) The Canadian gravimetric geoid model is published for the first time with associated error estimates. In addition, CGG2010 includes the new marine gravity data, ArcGP gravity grids, and the new Canadian Digital Elevation Data (CDED) 1:50K. CGG2010 is compared to GPS-levelling data in Canada. The standard deviations are estimated to vary from 2 to 10 cm with the largest error in the mountainous areas of western Canada. We demonstrate its improvement over the previous models CGG2005 and EGM2008.

New solutions for the geoid potential W0 and the Mean Earth Ellipsoid dimensions

Earth Gravitational Models (EGMs) describe the Earth’s gravity field including the geoid, except for its zero-degree harmonic, which is a scaling parameter that needs a known geometric distance for its calibration. Today this scale can be provided by the absolute geoid height as estimated from satellite altimetry at sea. On the contrary, the above technique cannot be used to determine the geometric parameters of the Mean Earth Ellipsoidal (MEE), as this problem needs global data of both satellite altimetry and gravimetric geoid models, and the standard technique used today leads to a bias for the unknown zero-degree harmonic of the gravimetric geoid height model. Here we present a new method that eliminates this problem and simultaneously determines the potential of the geoid (W0) and the MEE axes. As the resulting equations are non-linear, the linearized observation equations are also presented.

Evaluation of W0 in Canada using tide gauges and GOCE gravity field models

AbstractThe existing Canadian Geodetic Vertical Datum of 1928 (CGVD28) does not meet the needs of the modern user in terms of accuracy and accessibility. As a result, Canada plans to implement a geoid-based and global navigation satellite system (GNSS)-accessible vertical datum by 2013. One of the primary concerns in realizing this new vertical datum is to determine a W0 value that will represent the potential of the zero height surface. The objective of this study is to evaluate W0 by averaging the potential of points on the mean sea water surface utilizing tide gauge recordings and gravity field and steady-state ocean circulation explorer (GOCE)-based global geopotential models. In order to assess the performance of the GOCE-based models for the computation of W0, the models are extended with the high resolution gravitational model EGM2008. Regional gravimetric geoid models are also used for the estimation of W0. Additionally, local sea surface topography models are utilized in order to validate the W0 results at the tide gauges. Excluding the Arctic coast, the W0 values obtained from both tide gauges and oceanic sea surface topography models are not statistically different from the International Earth Rotation and Reference Systems Service (IERS) 2010 global conventional value 62636856.00 m2/s2.

Coastal geoid improvement using airborne gravimetric data in the United Arab Emirates

Military survey department (MSD) of The United Arab Emirates (UAE) has undertaken the Airborne Gravity Survey Project for the marine area of the country. The main purpose for the implementation of the airborne gravity survey for the marine area is to improve the existing gravimetric geoid of the UAE. The airborne gravity data was estimated to have accuracy better than 2.0 mGal. The first gravimetric geoid for the country has been established after the completion of nation-wide gravity survey of 5 km grid spacing by the MSD in 2003. The 2003 geoid was hampered by the lack of gravity data along the near coast area (including marine) as well as the eastern part of the country. The geoid has subsequently been computed from all available data: airborne gravity, surface gravity (including older data), satellite altimetry gravity and EGM08 reference field, as well as detailed height data from the shuttle radar topography mission (SRTM). The geoid computations were all done with the GRAVSOFT suite of programs from DTU-Space and University of Copenhagen. The computations involve a rigorous downward continuation from airborne to surface level by least-squares collocation. The result is a gravimetric geoid model “uae2009_gravgeoid2”, that is, a geoid model which refers to a global vertical datum. The change of geoid models computed with or without the new airborne gravity data showed differences of 30 cm or more, largest along the coast of the Northern Emirates and Fujairah. Using available global positioning system (GPS) leveling data from the 2003 report, a new geoid fitted to the UAE height system “uae2009_geoid” has been constructed and made available. The fitted geoid is dependent on the quality of the available GPS-leveling data, which have many apparent errors. Therefore the gravimetric geoid has been transformed by a single constant as well, to yield a shifted gravimetric geoid, “uae2009_gravgeoid”, roughly consistent with the UAE vertical datum and more suitable for any future adaptions of the geoid to local GPS-levelling data. The accuracy of the gravimetric geoid is estimated to be 3 to 5 cm across most of the UAE. Lower geoid accuracy of about 5 cm is expected over mountainous region in the north-eastern part of the country. Key words: Geoid, gravity, airborne gravimetry, global positioning system (GPS), satellite altimetry.

Proposal for Geoid Model Evaluation from GNSS-INS/Leveling Data: Case Study along a Railway Line in Greece

A surveying-engineering procedure is presented for gravimetric geoid model verification along selected railway traverse lines using collocated ellipsoid and orthometric heights. The proposed method relies on (1) a tactical-grade, multisensor [Global Navigation Satellite System (GNSS)/inertial navigation system (INS)] kinematic-surveying system used to measure the ellipsoid heights along the traveled section and (2) the orthometric heights derived from the railway-line construction and/or maintenance works. Compared with the standard static GPS/leveling technique, the proposed approach produces geoid height profiles in a very short acquisition time, with dense point spacing, and in a considerably inexpensive manner. The quality of the final results reflects the accuracy of modern GNSS/INS systems and available rail-track orthometric height information. The method was applied to a long (101-km) railway traverse in central Greece using a custom-built mobile mapping system. Gravimetric geoid model verification was undertaken in an absolute and relative manner for the Earth Gravitational Model 2008 (EGM08) and 1996 (EGM96) geopotential models. Analysis of the results has demonstrated the potential of the method both in terms of efficiency and in terms of the evaluation checks performed. Based on the absolute- and relative-quality tests undertaken, the superiority of EGM08 over EGM96 is clearly evident for the tested line. Also, these results are cross compared and evaluated with the findings obtained from previous studies in Greece.

우리나라 지오이드 모델 구축 및 정밀도 검증

2000년대 초반까지 우리나라 지오이드 모델의 정밀도는 지상 중력 자료 및 GPS/Leveling 자료의 낮은 분포 및 정밀도로 인해 약 14cm 수준에 머물렀다. 그러나 2007년 이후 높은 정밀도와 고른 분포를 나타내는 새로운 지상 및 항공 중력 자료, GPS/Leveling 자료가 획득됨에 따라 지오이드 모델의 정밀도를 향상할 수 있는 기반이 마련되었으며, 2011년 초반에 발표된 중력 지오이드 모델의 정밀도는 약 5.29cm로 기존 모델에 비해 약 27% 향상되었다. 2010년 이후에도 많은 중력 자료가 통합기준점, 수준점 및 삼각점에서 획득되었고, 특히 2010년 통합기준점 구축 사업이 완료됨에 따라 우리나라 전역에서 약 10km의 간격을 나타내는 GPS/Leveling 자료가 구축되어 보다 정밀한 지오이드 모델의 구축 및 검증이 가능하게 되었다. 본 연구에서는 2012년 현재 우리나라에서 가용한 지상, 항공, 위성고도계 중력 자료를 기반으로 하여 중력지오이드 모델을 구축하였다. 그 결과 우리나라 전역에서 중력 지오이드 모델은 18.05m부터 32.70m의 범위의 값을 나타내며, 정밀도는 약 5.76cm로 산출되었다. 또한, 중력 지오이드 모델과 GPS/Leveling 자료를 융합하여 구축한 합성 지오이드 모델의 적합도 및 정밀도는 각각 3.60cm와 4.06cm로 계산되었다. 마지막으로 건설현장 등에서 합성 지오이드 모델을 활용할 수 있는지 검증하기 위하여 15km 기선거리에 대한 상대 정밀도를 계산한 결과 약 3.35cm로 나타났다. 상대 정밀도가 낮게 나타나는 이유는 강원도 및 동해안, 서 남해안 등에서 우리나라 수직기준체계간의 불일치로 인해 지역적인 편이가 존재하며, 일부 내륙에서도 주변 성과와의 일관성 저하문제가 나타나는 점들이 있기 때문으로 향후 통합기준점 성과에 대한 신뢰도 검증이 필요한 것으로 사료된다. The previous geoid model developed in early 2000s shows 14cm level of precision due to the problems on distribution, and quality of the land gravity and GPS/Leveling data. From 2007, the new land and airborne gravity data as well as GPS/Leveling data having high quality and regular distribution has been obtained. In 2011, a new gravimetric geoid model has been constructed with precision of 5.29cm which was improved about 27% comparing to the previous model. However, much more land gravity data has been collected at the control point, bench marks and triangulation points since 2010. Also, GPS/Leveling data having 10km spacing over whole country has been obtained through the project which is for the construction of new control points. In this study, new gravimetric geoid has been calculated based on the all available gravity data up to present. The geoid height shows the range from 18.05m to 32.70m over whole country and its precision is 5.76cm. The degree of fit and precision of hybrid geoid model are 3.60cm and 4.06cm, respectively. At the end, 3.35cm of the relative precision in 15km baseline has been calculated to confirm its practical usage. Especially, it has been founded that regional bias occurred at the Kangwon and coastal area due to problems on the leveling data. Also, some inland points show inconsistent large difference which needs to be verified by analyzing the unified control points results.

Obtaining instantaneous water levels relative to a geoid with a 2D storm surge model

Current and new applications of 2D storm surge models such as the Dutch Continental Shelf Model (DCSM) require that the models provide proper estimates of the instantaneous water levels expressed relative to a particular geoid, rather than only the tide and surge components expressed relative to the ill-defined model's zero height surface. For DCSM, this is realized by adding the depth-averaged horizontal baroclinic pressure gradients to the model equations, which are derived from 4D salinity and temperature fields provided by the Proudman Oceanographic Laboratory hydrodynamic model (POL's hindcast). The vertical datum of the extended model is fixed to that of the European Gravimetric Geoid model 2008 (EGG08). This is done by an adjustment of the model parameters that depend on the choice of the reference surface (e.g., bathymetry) and by referring the water levels along the open boundaries to this reference surface. Using different numerical experiments we investigate the effects on the water levels of several approximations we have made during the implementation. The ability of the model to reproduce both the mean sea level (MSL) and instantaneous water levels is assessed by a comparison with the MSL derived from POL's hindcast as well as with instantaneous water levels acquired by various radar altimeter satellites. From this comparison we conclude that our modeled MSL is in good agreement with the MSL derived from POL's hindcast; the standard deviation of the differences is below 2cm. However, larger differences in MSL are observed when comparing the model output with the MSL derived from radar altimeter data. They are attributed to either geoid errors or errors in the used salinity and temperature fields. The root mean squared (rms) differences between observed and modeled instantaneous water levels over the entire model domain varies from 9cm for data acquired by the TOPEX satellite to 11cm for data acquired by the GFO-1 satellite. These numbers improve to 8–10cm on the North Sea, for data acquired by the TOPEX and ERS-2 satellites, respectively. These numbers are a factor two to three larger than the expected accuracy of water levels derived from radar altimeter data (which is ∼4cm). About 25% of these differences can be explained by a bias between the modeled and observed water levels of a single satellite pass. These biases are attributed to errors in the applied correction for the net steric expansion/contraction of the global oceans as this is not captured by DCSM that makes use of the Boussinesq approximation, as well as other errors in model and data.

Gravimetric geoid of a part of south India and its comparison with global geopotential models and GPS-levelling data

Precise information of geoid undulations is essential for obtaining the orthometric heights from Global Positioning System (GPS) measurements over any region; apart from providing the information of subsurface density distribution. This paper presents computation of geoid undulations over a part of southern Indian region from terrestrial gravity and elevation data using remove–restore technique that involves spherical Fast Fourier Transform (FFT) to compute ‘Stokes’ coefficients. Computed geoid undulations are compared with geoid obtained from global geopotential models such as EGM2008 and EIGEN-GRACE02S and measured GPS-levelling records at 67 locations. Statistical analysis of comparison suggests that the computed gravimetric geoid model has a good match with the geoid determined from GPS-levelling with rms of 0.1 m whereas EGM2008 has 0.46 m. The differences of GPS-levelling with EGM2008 at majority of stations fall in the range of ±0.5 m, which indicates that EGM2008 may be used for orthometric height determination with an accuracy of <0.5 m in the south Indian region and offers a reasonably good transformation platform from ellipsoid to local datum. However, local determination of geoid is necessary for better accuracy of orthometric height from GPS. The gravimetric geoid calculated from the available gravity data shows considerable improvement to the global model and can be used to achieve orthometric height with an accuracy of 0.1 m.

The contribution of local gravimetric geoid models to the calibration of satellite altimetry data and an outlook of the latest GOCE GGM performance in Gavdos

The use of geoid heights has been one of the available methodologies utilized for the independent calibration/validation of altimeters on-board satellites. This methodology has been employed for long in the Gavdos dedicated cal/val facility (Crete, Greece), where calibration results for the Jason satellites have been estimated, both for ascending and descending passes. The present work gives a detailed overview of the methodology followed in order to estimate a high-resolution and accuracy gravimetric geoid model for the wider Gavdos area, in support of the on-going calibration work. To estimate the geoid model, the well-known remove-compute-restore method is used while residual geoid heights are estimated through least-squares collocation so that associated errors are determined as well. It is found that the estimated formal geoid errors from LSC along passes 018 and 109 of Jason satellites, used for the bias estimation, range between ±0.8–1.6cm. The so-derived geoid heights are employed in the determination of the Jason-2 altimeter bias for all available cycles (cycles 1-114, spanning the period from July 2008 to August 2011) together with the RioMed DOT model. From the results acquired the Jason-2 bias has been estimated to be +196.1±3.2mm for pass 109 and +161.9±5.1mm for pass 018. Within the same frame, the GOCE/GRACE-based geopotential model GOCO02s has been used to estimate the mean dynamic ocean topography and the steady-state circulation in the area around Gavdos. The so-derived DOT model was used to estimate the Jason-2 bias in an effort to evaluate the performance of satellite-only geoid models and investigate whether their spatial resolution and accuracy provides some improvement w.r.t. traditional local gravimetric geoids. From the results acquired with geoid heights from GOCO02s, the estimated Jason-2 bias deviates significantly from that of the local gravimetric model, which can be attributed to a possible mean offset and the low resolution of GOCE-based GGMs. On the other hand, when the newly estimated GOCE-based DOT was employed with geoid heights from the local gravimetric geoid model, the Jason-2 bias has been estimated to be +185.1±3.2mm for pass 109 and +130.2±5.1mm for pass 018.

Assessment of the GOCE-Based Global Gravity Models in Canada

The aim of this study is to test the first, second and third generation GOCE geoid solutions, obtained from the first 2, 8 and 18-month observations, respectively. These solutions are assessed over Canada and for two sub-regions (the Great Lakes and Rocky Mountains). The Canadian GPS/leveling-derived geoid heights are used as independent control values in the assessment of the GOCE geoid models. The study is conducted in two steps. First, the geoid models are computed from satellite-only models and truncated to different spherical harmonic degrees. These models are compared with the GPS/leveling geoid heights which are reduced to the same spectral band as the satellite models by EGM2008 predicted frequency components higher than the truncation degrees. The results suggest that the GOCE models show a full power of signal up to about spherical harmonic degree 180. Moreover, the second and third generation GOCE models (with the exception of the direct approach models) provide better agreement with the GPS/leveling-derived geoid undulations than the first generation models due to the longer observation period. The second step involves the combination of the two third generation GOCE models with terrestrial data. These models are tested against to the GPS/leveling-derived geoid undulations in full spectrum. EGM2008 global geopotential model and Canadian gravimetric geoid model CGG2005 are also included in the comparisons to measure improvement provided by the GOCE models. The GOCE-combined models yielded GPS/leveling results that are comparable with those obtained from EGM2008 and CGG2005 models. The best comparative results with the combined models give standard deviations of 4.8 cm, 6.0 cm and 12.2 cm for the Great Lakes, Rocky Mountains and Canada, respectively. These results indicate that the third generation GOCE models conform to the Canadian terrestrial gravity data from degrees 90 to 180. The new generation models show evident improvement over the first and second generation models.

Comparison of the KTH and remove–compute–restore techniques to geoid modelling in a mountainous area

In mountainous regions, a gravimetric geoid determination is a difficult task which needs special attention to obtain reliable results satisfying the demands, e.g. of the engineering infrastructure. The present study compares the KTH (Royal Institute of Technology) method with the remove–compute–restore (RCR) technique to attain a precise geoid model for the Konya Closed Basin (KCB) and thus aims to clarify the theoretical and numerical differences between these techniques. The KCB located in the central part of Turkey is a mountainous area with a very limited amount of the ground gravity data. Various data sources, such as the Turkish Digital Elevation Model with 3″×3″ resolution (TRDEM3), a recently published satellite-only global geopotential model and terrestrial gravity observations are combined in the gravimetric geoid models of the KCB by applying the KTH and RCR techniques, separately. The both gravimetric geoid models (KG-KTH11 and KG-RCR11) are compared with GNSS/levelling data at the control points in the target area, resulting the RMS (Root Mean Square Error) differences of ±6.7cm and ±9.8cm in the absolute sense, respectively. These results show that the KTH method gives more reasonable accuracy than the RCR technique in a mountainous area with scarce terrestrial gravity data.

A high-resolution gravimetric geoid model for Japan from EGM2008 and local gravity data

A high-resolution geoid model covering the four main islands of Japan has been developed on a 1 by 1.5 arc-minute grid from EGM2008 and terrestrial gravity data. The Stokes-Helmert scheme in a modified form is applied for the determination of the geoid using an empirically-determined optimal spherical cap, and Kriging is used for gridding the residual gravity anomalies. In comparison with the previous geoid model for Japan (JGEOID2008), there is a slight improvement in the standard deviation from ±8.44 cm to ±8.29 cm. It is noted that although the determined gravimetric geoid model represents the geoid over Japan fairly well, there is still a need for more gravity data especially in the northern parts of Japan.

A precise gravimetric geoid model in a mountainous area with scarce gravity data: a case study in central Turkey

In mountainous regions with scarce gravity data, gravimetric geoid determination is a difficult task that needs special attention to obtain reliable results satisfying the demands, e.g., of engineering applications. The present study investigates a procedure for combining a suitable global geopotential model and available terrestrial data in order to obtain a precise regional geoid model for Konya Closed Basin (KCB). The KCB is located in the central part of Turkey, where a very limited amount of terrestrial gravity data is available. Various data sources, such as the Turkish digital elevation model with 3 ″ × 3″ resolution, a recently published satellite-only global geopotential model from the Gravity Recovery and Climate Experiment satellite (GRACE) and the ground gravity observations, are combined in the least-squares sense by the modified Stokes’ formula. The new gravimetric geoid model is compared with Global Positioning System (GPS)/levelling at the control points, resulting in the Root Mean Square Error (RMS) differences of ±6.4 cm and 1.7 ppm in the absolute and relative senses, respectively. This regional geoid model appears to be more accurate than the Earth Gravitational Model 2008, which is the best global model over the target area, with the RMS differences of ±8.6 cm and 1.8 ppm in the absolute and relative senses, respectively. These results show that the accuracy of a regional gravimetric model can be augmented by the combination of a global geopotential model and local terrestrial data in mountainous areas even though the quality and resolution of the primary terrestrial data are not satisfactory to the geoid modelling procedure.

Development of regional gravimetric geoid model and comparison with EGM2008 gravity-field model over Korea

We constructed a regional geoid model and compared it with the EGM2008 global gravity-field model to evaluate the performance of EGM2008 for Korea. By using the Remove–Compute–Restore (RCR) technique, we developed an improved gravimetric geoid model JNUGEOID2010 on a 1 × 1′ grid by combining the EIGEN-GL04C global geopotential model (GGM), 8316 land-gravity data, an altimetry-derived marine gravity model DNSC08, and the Shuttle Radar Topography Mission (SRTM) digital elevation model (DEM). The computations were done using a two-dimensional four-band spherical fast Fourier transform (FFT) with 100% zero padding. In addition, we compared the Korean national gravimetric geoid model KGEOID98 to EGM2008. For the comparison, geometric geoid heights derived from 735 GPS-levelling stations were used. The smallest standard deviation of geoid height differences is ± 0.163 m for EGM2008 to degree and order 2190. Thus, we conclude that the new model EGM2008 is superior to the two regional gravimetric geoid models, JNUGEOID2010 and KGEOID98, for Korea. Key words: Regional geoid model, EGM2008, Global geopotential models, GPS-levelling, geoid height, Korea.

Ortalama gravite anomalilerinin enterpolasyonunda basit ve tamamlanmış Bouguer yaklaşımının karşılaştırılması

Comparison between simple and complete Bouguer approaches in interpolation of Mean Gravity Anomalies The determination of the geoid, which is a real shape of the Earth, with an accuracy of 1 cm is one of the most important aim of the today’s geodetic community. The gravimetric geoid modeling is the most preferred technique in order to reach to this target. Nevertheless, the gravity values measured on the physical surface of the Earth can not be directly included to this process. First of all, surface gravity values should be reduced to gravity anomalies and, during this step they should not lose their topographic features of the Earth's surface where the data is collected. On the other hand, in order to generate gravity anomalies on a regular grid, it is expected that dependency of gravity anomalies (to be used as reference data in interpolation) to local topography should be minimum. While free-air anomalies are the basic data source for determining the geoid, Bouguer anomalies describing the smoother Earth’s shape, are convenient to the interpolation of gravity anomalies. Therefore, the dependence of Bouguer gravity anomalies, which is a main data in the interpolation procedure, should be reduced to minimum. Although the simple Bouguer anomalies are preferred in practice, it is known that they contain more or less the negative effects of irregular topography. In this study, the differences between simple and complete Bouguer anomalies are presented in a test area. It is seen that the differences between free-air anomalies derived from both approximations are numerically increased up to 16 mGal, correlated with the topography. This result indicates that complete Bouguer anomalies should be used in interpolation process in regions posing irregular topography, such as Turkey.

Application of the BEM approach for a determination of the regional marine geoid model and the mean dynamic topography in the Southwest Pacific Ocean and Tasman Sea

Application of the BEM approach for a determination of the regional marine geoid model and the mean dynamic topography in the Southwest Pacific Ocean and Tasman SeaWe apply a novel approach for the gravimetric marine geoid modelling which utilise the boundary element method (BEM). The direct BEM formulation for the Laplace equation is applied to obtain a numerical solution to the linearised fixed gravimetric boundary-value problem in points at the Earth's surface. The numerical scheme uses the collocation method with linear basis functions. It involves a discretisation of the Earth's surface which is considered as a fixed boundary. The surface gravity disturbances represent the oblique derivative boundary condition. The BEM approach is applied to determine the marine geoid model over the study area of the Southwest Pacific Ocean and Tasman Sea using DNSC08 marine gravity data. The comparison of the BEM-derived and EGM2008 geoid models reveals that the geoid height differences vary within -25 and 18 cm with the standard deviation of 6 cm. The DNSC08 sea surface topography data and the new marine geoid are then used for modelling of the mean dynamic topography (MDT) over the study area. The local vertical datum (LVD) offsets estimated at 15 tide-gauge stations in New Zealand are finally used for testing the coastal MDT. The average value of differences between the MDT and LVD offsets is 1 cm.

Estimating geoid height change in North America: past, present and future

The forthcoming GRAV-D gravimetric geoid model over the United States is to be updated regularly to account for changes in geoid height. Its baseline precision is to be at the 10–20 mm level over non-mountainous regions. The aim of this study is to provide an estimate of the magnitude, time scale, and spatial footprint of geoid height change over North America, from mass redistribution processes of hydrologic, cryospheric and solid Earth nature. Geoid height changes from continental water storage changes over the past 50 years and predicted over the next century are evaluated and are highly dependent on the used model. Groundwater depletion from anthropogenic pumping in regional scale aquifers may lead to geoid changes of 10 mm magnitude every 50–100 years. The GRACE time varying gravity fields are used to (i) assess the errors in a glacial isostatic adjustment model, which, if used to correct the GRAV-D model, may induce errors at the 10 mm geoid height level after ~20 years, (ii), evaluate geoid height change over ice mass loss regions of North America, which, if they remain unchanged in the future, may lead to geoid height changes at the 10 mm level in under a decade and (iii), compute sea level rise and its effect on the geoid, which is found to be negligible. Coseismic gravitational changes from past North American earthquakes are evaluated, and lead to geoid change at the 10-mm level for only the largest thrust earthquakes. Finally, geoid change from volcanic processes are assessed and found to be significant with respect to the GRAV-D geoid model baseline precision for cataclysmic events, such as that of the 1980 Mt. St. Helens eruption. Recommendations on how to best monitor geoid change in the future are given.

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.