Local Geoid Model Research Articles

Vertical datum and coordinate systems in Jordan

Advancement in satellites and telecommunication technologies has created a great interest in global positioning system (GPS) applications. The lack of a good geoid model for Jordan has limited the use of GPS applications. This has lead to refining the Jordanian geoid model for better GPS measurements in order to obtain reliable results in the triplet coordinates. The objective of this work is to present a practical method for Jordanian datums transformation, we order to be able to use directly a combination of local and global heights information (levelling data, local geoid model and global geoid models) for engineering applications. This method will resolve the height problem in GPS measurements and reduce the usage of levelling measurements. Our work is based on the implementation of all existing data such as level data and local/global geoid model data into software to directly transform GPS ellipsoidal height into normal height including datums transformation.

Ability of the EGM2008 high degree geopotential model to calculate a local geoid model in Valencia, Eastern Spain

A new generation of global geopotential models (GGM) is being developed. These solutions offer a file with fully-normalized spherical harmonic coefficients of the Earth’s gravitational potential up to a degree greater than 2000 with very low commission errors. This paper analyses the recent Earth Gravitational Model EGM2008, developed up to degree and order 2159 with additional coefficients to degree 2190 and order 2159, which means recovering the gravitational field up to approximately 20 km wavelengths. 223 GPS/levelling points of the new Spanish High Precision Levelling Network in the Valencia region (Eastern Spain) are used as external tool for evaluation in that particular region. The same evaluation has been performed to other different global (EGM96 and EIGENCG03C), continental (EGG97), regional (IGG2005 and IBERGEO2006) and local (GCV07) geoid models for comparison purposes only. These comparisons show that EGM2008 is the geoid model that best fits to the GPS/levelling data in that region.

Determination of the deflection of vertical components via GPS and leveling measurement: A case study of a GPS test network in Konya, Turkey

Deflection of the vertical is used in reducing geodetic measurements related to geoid networks (vertical and horizontal directions observations and length measurement, etc.) to ellipsoid plane and in geoid modeling processes. Generally, it is obtained by Astro-Geodetic and gravimetric techniques. These techniques are very complex and time-consuming. Ellipsoidal coordinates of points are easily obtained thanks to the widespread use of Satellite Positioning Techniques (GNNS) such as GPS in geodesy. When the orthometric heights of points are determined via geometric leveling, geoid height differences and deflection of the vertical components can be measured faster and much more easily by using GPS and leveling measurements than the other techniques. This study discusses the calculation of the deflection of vertical components via GPS and leveling measurements. The deflection of the vertical components obtained from GPS and leveling measurements were compared with global (EGM96 and CG03C) and local (TG03) geoid models. Deflection of the vertical components ξ (north-south) and η (east-west) were calculated as ξ = -4.15” ± 0.61”, η = 8.75” ± 0.69” via a GPS and leveling model; as ξ = -5.64”, η = 1.95” via the EGM96 geoid model; as ξ = -4.85”, η = 1.82” via the CG03C geoid model; as ξ = -7.47”, η = -0.51” via the TG03 model; and as ξ = -3.9”, η = 4.6” via Astro-Geodetic deflection of a vertical map of Turkey produced by Ayan (1976). When the values obtained from GPS and leveling measurements were compared with the values produced by the other techniques, the north-south component was found to be approximately consistent, while east-west component differed to same extent. Since very little data on the terrestrial gravity of Turkey was present in the EGM96 and CG03C global geoid models, it was not anticipated that the results obtained via these models would be comparable with other methods. Key words: Deflection of the vertical, deflection of the vertical components, GPS/Leveling, EGM96, CG03C.

Preliminary Study of the Gravimetric Local Geoid Model in Jordan:

Recently, there is an increased interest in studying and defining the Local and Regional Geoid Model worldwide, due to its importance in geodetic and geophysics applications. The use of the Global Positioning System (GPS) is internationally growing, yet the lack of any Geoid Model for Jordan has limited the use of GPS for geodetic applications. Therefore, this work aims to present the preliminary results that we propose for The Gravimetric Jordanian Geoid Model (GeoJordan). The model is created using gravimetric data and the GravSoft program. The validation of this model is done by using GPS measurements and precise leveling at Amman area. However, a comparison between the Global Geopotential Models OSU91A and EGM96 showed great discrepancies through the presented results. Also, presenting the approach used to obtain the orthometric height from GPS ellipsoidal height measurements. Nevertheless, the error margin; obtained in this initial study of the GeoJordan after fitting the data with GPS/leveling measurement; is about (10cm), in tested area whereas the standard error of the created model is about (40cm).

Preliminary study of the Gravimetric Local Geoid Model in Jordan: case study (GeoJordan Model)

Recently, there has been an increased interest in studying and defining the Local and Regional Geoid Model worldwide, due to its importance in geodetic and geophysics applications.The use of the Global Positioning System (GPS) is internationally growing, yet the lack of a Geoid Model for Jordan has limited the use of GPS for the geodetic applications in the country. This work aims to present the preliminary results that we propose for «The Gravimetric Jordanian Geoid Model (GeoJordan)». The model is created using gravimetric data and the GRAVSOFT program. The model is validated using GPS and precise level measurements in the Amman area. Moreover, we present a comparison using the Global Geopotential Model OSU91A and the EGM96 Model and the results showed great discrepancies. We also present the approach used to obtain the orthometric height from GPS ellipsoidal height measurements. We found that the error margin obtained in this work of the GeoJordan after fitting the data with GPS/leveling measurements is about (10 cm) in the tested area whereas the standard error of the created model is about (40 cm).

Precision assessment of the orthometric heights determination in northern part of Algeria by combining the GPS data and the local geoid model

The main purpose of this article is to discuss the use of GPS positioning together with a gravimetrically determined geoid, for deriving orthometric heights in the North of Algeria, for which a limited number of GPS stations with known orthometric heights are available, and to check, by the same opportunity, the possibility of substituting the classical spirit levelling. For this work, 247 GPS stations which are homogeneously distributed and collected from the international TYRGEONET project, as well as the local GPS/Levelling surveys, have been used. The GPS/Levelling geoidal heights are obtained by connecting the points to the levelling network while gravimetric geoidal heights were interpolated from the geoid model computed by the Geodetic Laboratory of the National Centre of Spatial Techniques from gravity data supplied by BGI. However, and in order to minimise the discordances, systematic errors and datum inconsistencies between the available height data sets, we have tested two parametric models of corrector surface: a four parameter transformation and a third polynomial model are used to find the adequate functional representation of the correction that should be applied to the gravimetric geoid. The comparisons based on these GPS campaigns prove that a good fit between the geoid model and GPS/levelling data has been reached when the third order polynomial was used as corrector surface and that the orthometric heights can be deducted from GPS observations with an accuracy acceptable for the low order levelling network densification. In addition, the adopted methodology has been also applied for the altimetric auscultation of a storage reservoir situated at 40 km from the town of Oran. The comparison between the computed orthometric heights and observed ones allowed us to affirm that the alternative of levelling by GPS is attractive for this auscultation.

On the selection of optimal global geopotential model for geoid modeling: A case study in Pakistan

A statistical comparison has been made between gravity field parameters derived from different global geopotential models (GGMs) and observed gravity anomalies, gravimetric geoid and GPS-Leveling data. The motivation behind this study is the selection of best possible global geopotential model that best matches statistically with the local observed data in Pakistan. This will facilitate in decreasing the load on observed data for the development of regional gravimetric geoid in remove-compute-restore technique when used in the Stokes’s integral for computation of the residual part. It is observed that combined geopotential models such as EGM96 and PGM200A, EIGEN-GL04C and EIGEN-CG03C reflect the better match in the total spectral range of gravity and GPS-Leveling data. Results of the precise local geoid model also indicate similar characteristics. A very-high-degree model “EGM2008” (degree/order 2160) exhibits relatively superior statistical fit with observed ground data in Pakistan region. For satellite-only models an increasing trend in the standard deviation can be seen with maximum of about ∼4 m in difference between GPS-Leveling and corresponding GGM’s geoid with increase in the order from 50 to 120 and then it decreases afterwards. However, for the EIGEN-CHAMP03SP, standard deviation saturates to a value of 3.4 m. This is an indication of contamination in the long to medium wavelength part, i.e. 50–100° for the satellite-only models. Moreover, the models DEOS-CHAMP-01C, GGM02C and then ITG-GRACE03 appear to have better fit for medium to long wavelength and can possibly be recommended for use as long wavelength part with the local observed data. While a hybrid geopotential model selection can be achieved through the selection from either of DEOS-CHAMP-01C, GGM02C, GGM02S, EIGEN-GRACE02S or ITG-GRACE03 in the long wavelength (to degree and order 40) and EGM96, PGM200A, EIGEN-GL04C, EIGEN-CG03C or even EGM2008 in medium to short wavelength, i.e. from degree 41 to maximum degree and order.

Geoid and high resolution sea surface topography modelling in the mediterranean from gravimetry, altimetry and GOCE data: evaluation by simulation

The determination of local geoid models has traditionally been carried out on land and at sea using gravity anomaly and satellite altimetry data, while it will be aided by the data expected from satellite missions such as those from the Gravity field and steady-state ocean circulation explorer (GOCE). To assess the performance of heterogeneous data combination to local geoid determination, simulated data for the central Mediterranean Sea are analyzed. These data include marine and land gravity anomalies, altimetric sea surface heights, and GOCE observations processed with the space-wise approach. A spectral analysis of the aforementioned data shows their complementary character. GOCE data cover long wavelengths and account for the lack of such information from gravity anomalies. This is exploited for the estimation of local covariance function models, where it is seen that models computed with GOCE data and gravity anomaly empirical covariance functions perform better than models computed without GOCE data. The geoid is estimated by different data combinations and the results show that GOCE data improve the solutions for areas covered poorly with other data types, while also accounting for any long wavelength errors of the adopted reference model that exist even when the ground gravity data are dense. At sea, the altimetric data provide the dominant geoid information. However, the geoid accuracy is sensitive to orbit calibration errors and unmodeled sea surface topography (SST) effects. If such effects are present, the combination of GOCE and gravity anomaly data can improve the geoid accuracy. The present work also presents results from simulations for the recovery of the stationary SST, which show that the combination of geoid heights obtained from a spherical harmonic geopotential model derived from GOCE with satellite altimetry data can provide SST models with some centimeters of error. However, combining data from GOCE with gravity anomalies in a collocation approach can result in the estimation of a higher resolution geoid, more suitable for high resolution mean dynamic SST modeling. Such simulations can be performed toward the development and evaluation of SST recovery methods.

Impact of the new GRACE Geopotential Model and SRTM data on the geoid modelling in Algeria

Abstract In Algeria and since 2000, two published geoid models have been produced by the Geodetic Laboratory of the National Centre of Space Techniques using different data sets and techniques. Although these results were satisfactory and internally consistent they do not have the required accuracy to be able to transform a GPS ellipsoidal height to an orthometric height. Recently, the quantity and quality of terrestrial gravity data increased slightly and, especially, several new geopotential models from the recent satellite missions (e.g., GRACE) were released. At the same time, the new high-resolution SRTM (Shuttle Radar Topography Mission) global DEM was constructed. The main purpose of this paper is to study the impact of the above new data on geoid heights in Algeria. For this reason, a new gravimetric geoid determination has been carried out including these new data. This solution was based on the land gravity data supplied by the BGI (Bureau Gravimetrique International), Digital Elevation model derived from SRTM for topographic correction and the optimal gravity field model GRACE (EIGEN-GL04C), which were combined using the remove–restore technique in connection with the Fast Fourier transformation technique. This gravimetric geoid and previous geoids existing for this study area are compared to the geoid undulations corresponding to 62 GPS/levelling points located in northern part of Algeria. The study shows that the new gravimetric geoid model agrees considerably better with GPS/levelling than any of the other local geoid models in the tested area. Its standard deviation fit with GPS/levelling data are ±27 and ±25.0 cm before and after fitting using the four-parametric model as corrector surface in minimizing the long-wavelength geoid errors and the datum inconsistencies between our height data and GPS. The new geoid model will be used in low accuracy scientific applications and in low-order levelling network densification with regard to the national levelling network coverage considered as good in the north and becomes poor in the south and west of the country. It is an important contribution to geophysics, because it can provide a constraint for density distribution, thermal state of the lithosphere and viscosity in the mantle.

Towards the redefinition of the Egyptian geoid: Performance analysis of recent global geoid and digital terrain models

Launches of the CHAMP (CHAllenging Minisatellite Payload) and GRACE (Gravity Recovery And Climate Experiment) satellite missions have produced a new generation of global geopotential models (GGMs). The performance of seven recent GGMs has been analyzed using a local geodetic dataset (terrestrial gravity and GPS/levelling points) in Egypt. The results show that the EIGEN‐CG01C model is best at representing the long and medium wavelengths of the gravity field in Egypt. Its average accuracy, in terms of geoid undulations, when compared to known points, is estimated to be 0.36 m. Additionally, four digital terrain models (GTOPO30, SRTM, DTM2002, LDTM) have been investigated, leading to the conclusion that DTM2002 should be utilized in computing the terrain corrections for gravimetric geoid development in Egypt. When combined with local geodetic data, these two global models (EIGEN‐CG01C and DTM2002) will support the production of a precise local geoid model, to be used in conjunction with Global Positioning System‐based surveying and mapping projects in Egypt.

Geophysical signature of geological units inferred from the analysis of geoid maps in Cameroon and its surroundings

The geoid is the equipotential surface of the earth’s gravity field approximated by mean sea level. The use of the geoid in geophysics is illustrated in Cameroon and its surroundings, by the analysis of geoid maps obtained from the local geoid model, CGM05. The medium and short wavelength geoid components, signatures of near-surface geological units, are revealed by removing the long wavelength geoid features. These regional wavelengths are predominant on a geoid contour map. They are due to deep-seated or to near-surface large-extent structures. The regional trends are removed here by filtering, using a hybrid global geopotential model. The geophysical signatures of near-surface small-extent geological structures are therefore revealed. The results help constrain the limiting depths of some geological features of the Cameroon subsurface. These quantities are very useful for the gravity and magnetic subsurface modeling. The analysis also enables the precise mapping of the positions of some structural units and the completion of their geological and geophysical studies. An unknown geologically dense unit, never identified by any previous study, was detected near the Mamfe basin.

Accurate Linking of Lake Erie Water Level with Shoreline Datum Using GPS Buoy and Satellite Altimetry

There is a need to accurately link the water level to the shoreline vertical datum for various applications including coastal management, lake/river/estuary/wetland hydrological or storm surge modeling/forecasting. Coastal topography is historically surveyed and referenced to the predetermined vertical datum in terms of orthometric heights, or the heights above the geoid, which is poorly known in terms of accuracy and lack of adequate spatial resolution for coastal applications such as estuary or storm surge modeling. We demonstrate an accurate linking of the lake surface to a shoreline datum using satellite techniques, including GPS buoy and satellite altimetry, water level gauges, and local geoid and lake circulation models. The possible error sources are analyzed and an error budget is reported in this study. An innovated method to estimate geoid height near the water level gauge using a GPS buoy is proposed. It is found that at a 95% confidence interval, the method is consistent with the National Geodetic Survey GEOID03 geoid model. The lake surface represented using a lake circulation model provided by the Great Lakes Forecasting Systems is also verified with kriging based on the data (1999 - 2001) from the water level gauge, and TOPEX/POSEIDON altimeter. Mean discrepancies of 2.7 and 7.2 cm are found with the data from the gauges around Lake Erie, and from the combination of the gauges and the altimeter, respectively. It reveals that the current dominant limitation of more accurate linking of water surface to shoreline is the insufficient knowledge of geoid in the current models. Further improvement is feasible through more accurate and higher resolution modeling of the lake geoid.

On the non-uniqueness of local quasi-geoids computed from terrestrial gravity anomalies

We consider the problem of local (quasi-)geoid modelling from terrestrial gravity anomalies. Whereas this problem is uniquely solvable (up to spherical harmonic degree one) if gravity anomalies are globally available, the problem is non-unique if gravity anomalies are only available within a local area, which is the typical situation in local/regional gravity field modelling. We derive a mathematical description of the kernel of the gravity anomaly operator. The non-uniqueness can be removed using external height anomaly information, e.g., provided by GPS-levelling. The corresponding problem is formulated as a Cauchy problem for the Laplace equation. The existence and uniqueness of the solution of the Cauchy problem is guaranteed by the Cauchy–Kowalevskaya theorem. We propose several numerical procedures to compute the solution of the Cauchy problem from given differences between gravimetric and geometric height anomalies. We apply the numerical techniques to real data over the Netherlands and Germany. We show that we can compute a unique quasi-geoid from observed gravimetric and geometric height anomalies, which agree with the data within the expected noise level. We conclude that observed differences between gravimetric height anomalies and geometric height anomalies derived from GPS and levelling cannot only be attributed to systematic errors in the data sets, but are also caused by the intrinsic non-uniqueness of the problem of local quasi-geoid modelling from gravity anomalies. Hence, GPS-levelling data are necessary to get a unique solution, which also implies that they should not be used to validate local quasi-geoid solutions computed on the basis of gravity anomalies.

Comparisons of GPS-Derived Orthometric Heights Using Local Geometric Geoid Models

The purpose of the research was to compare measuring orthometric heights using differential leveling, static global positioning observations, and real-time kinematic (RTK) Global Positioning System (GPS) observations in the vicinity of the University of Conn. campus. Height observations were recorded at temporary and permanent monuments using differential leveling, static GPS, and RTK. Heights at permanent monuments with published elevations were observed using each method and served as control and to check the quality of all measurements. Three-dimensional reference ellipsoid coordinates derived from GPS observations and published orthometric heights were used to create local geoid models, which were then used to convert ellipsoid heights observed with the static GPS and RTK to orthometric heights. The resulting values were used to compare between the measuring methods. In general, static GPS performed better than RTK. Several polynomial surface models of different orders were fitted to the geoid heights, from a constant up to a quadratic. No meaningful distinctions could be drawn between the models indicating that, for a small geographical area, shifting the national geoid model, GEOID03, by a constant vertical amount performs as well as the more complicated approaches. Experience showed that multiple, independent RTK observations on the same day are not sufficient to ensure freedom from systematic errors.

Local Geoid Improvement Using GPS and Leveling Data: Case Study

National leveling height networks have recently been set up in Taiwan, and global positioning system (GPS) observations were carried out at the benchmarks of the networks. The purpose of this paper is to develop an improved local geoid model for Taiwan by integrating a local gravimetric geoid model with the GPS and leveling height data. To overcome the problems of datum inconsistencies and possible systematic errors in height data of different types, the least squares collocation technique was applied. The result from fit of the improved geoid model to the control data at 300 benchmarks shows that a mean accuracy of geoidal heights at a 2 cm level is obtainable.

High Precision Geoid Models HKGEOID-2000 for Hong Kong and SZGEOID-2000 for Shenzhen, China

High precision geoid models HKGEOID-2000 for Hong Kong and SZGEOID-2000 for Shenzhen, China, have been developed with a hybrid approach of so-called sequential processing, using high precision GPS/leveling data, land and sea gravity anomalies, and digital terrain models. These two local geoid models have the same 1-km resolution. The estimated accuracy (external accuracy) is better than 1.7 cm for HKGEOID-2000 and 1.4 cm for SZGEOID-2000. Some common areas are covered by HKGEOID-2000 and SZGEOID-2000. So these two geoid models, along with high quality GPS/leveling data collected on the overlapping areas, can be used to detect the systematic bias between HKGEOID-2000 and SZGEOID-2000, as well as the difference between Hong Kong Principal Datum and 1956 yellow sea height datum of China, yielding RMS errors of 1.011 m and 1,003 m, respectively. Moreover, HKGEOID-2000, along with GPS ellipsoidal heights, is employed to determine the errors of the “orthometric heights” from purely trigonometric heighting, yielding an RMS error of 0.102 m. The combination of SZGEOID-2000 and GPS ellipsoidal heights has been used to replace the traditional spirit leveling and mapping, called GPS mapping.

A hybrid method to determine a local geoid model—Case study

This paper studies the methodology to construct an accurate local/regional geoid model. To achieve the objective an integration of all the information/data available must be performed. A hybrid approach of so-called sequential processing is employed in this study. It involves three steps: the construction of a gravimetric geoid using the wellknown remove-restore technique; the least squares fitting of 3-parameter transformation to remove the bias and tilts between the gravimetric geoid and GPS/leveling data; further refinement of the geoid model with GPS/leveling data and other information. The study is focused on the last step of signal extraction. The proposed approach was used in the determination of the Hong Kong geoid model and the Shenzhen geoid model. Their accuracy was evaluated with independent GPS/leveling data. These case studies indicate that the absolute accuracy of a centimeter and relative accuracy of some 1 part per million (ppm) of a local geoid model are achievable if the methodology is carefully designed and all the information/data are fully utilized.