Orthometric Height Determination Research Articles

The effect of topographic density variations on the geoid and orthometric heights in Hong Kong

Utilizing the adopted average topographic density of 2670 kg/m3 in the reduction of gravity anomalies introduces errors attributed to topographic density variations, which consequently affect geoid modeling accuracy. Furthermore, the mean gravity along the plumbline within the topography in the definition of Helmert orthometric heights is computed approximately by applying the Poincaré-Prey gravity reduction where the topographic density variations are disregarded. The Helmert orthometric heights of benchmarks are then affected by errors. These errors could be random or systematic depending on the specific geological setting of the region where the leveling network is physically established and/or the geoid model is determined. An example of systematic errors in orthometric heights can be given for large regions characterized by sediment or volcanic deposits, the density of which is substantially lower than the adopted topographic density used in Helmert's definition of heights. The same applies to geoid modeling errors. In this study, we investigate these errors in the Hong Kong territory, where topographic density is about 20% lower than the density of 2670 kg/m3. We use the digital rock density model to estimate the effect of topographic density variations on the geoid and orthometric heights. Our results show that this effect on the geoid and Helmert orthometric heights reach maxima of about 2.1 and 0.5 cm, respectively. Both results provide clear evidence that rock density models are essential in physical geodesy applications involving gravimetric geoid modeling and orthometric height determination despite some criticism that could be raised regarding the reliability of these density models. However, in regions dominated by sedimentary and igneous rocks, the geological information is essential in these applications because topographic densities are substantially lower than the average density of 2670 kg/m3, thus introducing large systematic errors in geoid and orthometric heights.

The optimization of marine geoid model from altimetry data using Least Squares Stokes modification approach with additive corrections across Malaysia

ABSTRACT Due to the high cost and time constraints, geoid and gravity surveys utilizing airborne and shipborne surveys can only be implemented in marine areas with limited coverage. Satellite altimeter has become an essential tool for global geoid and gravity field recovery. With approximately 60% observation coverage of the Earth’s surface for ocean height, researchers can replace conventional marine geoid models by conducting faster surveys over massive areas at a minimal cost. This study attempts to develop a marine geoid model from multi-mission satellite altimetry along-track data using the Least Squares Modification of Stokes with Additive Corrections. The gravity anomaly has been computed using Gravity Software, and the planar Fast Fourier Transformation method has been applied. The evaluation, selection, blunder detection, combination, and re-gridding of the altimetry-derived gravity anomalies and Global Geopotential Model data are demonstrated. The cross-validation approach has been employed in the cleaning and quality control the data using the Kriging interpolation method. The optimal condition modification parameters of the spherical cap, terrestrial gravity data error, and correlation length have also been applied. Then, the additive corrections based on Downward Continuation, Atmospheric Effects, and Ellipsoidal corrections were combined with the estimated geoid to provide a precise marine geoid over the Malaysian seas. The findings have been evaluated with the MyGeoid17 model from the Department of Survey and Mapping Malaysia. The validation yields satisfactory results with accuracy up to a centimetre level. Hence, the marine geoid model can be utilized for orthometric height determination in marine areas over the Malaysian seas.

Comparison of Two Corrector Surface Models of Orthometric Heights from GPS/Levelling Observations and Global Gravity Model

The advent of space-based measurement systems such as the Global Positioning System (GPS) offers a new alternative in orthometric height determination over conventional spirit levelling. The ellipsoidal height (h) obtained from GPS observations can be transformed into orthometric height if the geoid undulation (N) is known from a national gravimetric geoid model. However, the lack of a national geoid model in Nigeria hinders the use of the method. This study compares two corrector surface models of orthometric heights from GPS/levelling observations and the Global Gravity Model. Model A (7-parameter) and Model B (8-parameter) are based on the general 7-parameter similarity datum shift transformation. A network of twenty-one (21) GPS/levelling benchmarks within the study area were used and their geoidal heights were computed using GeoidEval utility software with reference to Global Gravitational Model (EGM08). Least squares adjustment was used to compute the coefficients of the models. Root mean square error (RMSE) was used to assess the accuracy of the models with model A having RMSE=0.171m and model B having RMSE=0.169m. Model B with the lowest RMSE is hence the better of the two models. The t-test and hypothesis test conducted at a 95% confidence level, however, revealed that the two models did not differ significantly. The study shows that the use of corrective surface to combine the gravity field model EGM08 and GPS/levelling significantly improves the determination of heights as observed from GPS in the study area.

Determination of Orthometric Heights of Points Using Gravimetric/GPS and Geodetic Levelling Approaches

The importance of practical, as well as orthometric heights in engineering cannot be underestimated as it is required for the determination of proposed construction levels and to direct the flow of water. This study presents the determination of orthometric heights of points using gravimetric/GPS and geodetic levelling approaches and compares the resolution of the two approaches to determine which of the methods is better for orthometric height determination in the study area. A total of 59 stations were occupy for gravity observation using Lacoste and Romberg (G-512 series) gravimeter to obtain the absolute gravity values of the points. GNSS observation was carried out in static mode using South GNSS receivers to obtain the positions and ellipsoidal heights of the points. The modified Stokes’ integral was applied to obtain the geoid heights of the points. Similarly, levelling was carried out using the geodetic level to obtain the level heights of the points. The orthometric correction was applied to the geodetic levelling results to obtain precise level heights of the points. The RMSE index was applied to compute the accuracy of the geoid models. The computed result shows that orthometric heights can be obtained in the study area using the two models with an accuracy of 0.3536m. Z-test was carried out to determine if there is any significant difference between the two methods. The test results show that statistically, there is no significant difference between the two methods. Hence, the two methods can be applied for orthometric heights determination in the study area.

Accuracy Assessment of Different Polynomial Geoid Models in Orthometric Height Determination for Akure, Nigeria

Height is an important component in three dimensional coordinates and determination of the position of points for any meaningful development. Ellipsoidal heights from GNSS require geoid model which could be global, regional and local for transformation to orthometric height. The absence of a national geoid model in Nigeria remains a great drawback to develop local geoid for local application in place of global geoid models. The study aims to assess the accuracy of polynomial geoid models in orthometric height determination. Differential Global Positioning System (DGPS) observations were carried out to determine ellipsoidal heights of the point while nine and eleven coefficients were used for the geoid and orthometric height modelling. Model A and Model C used 2-D (x, y) positions with nine and eleven parameters while model B used 3-D (x, y, ∆h) positions with nine parameters. The least-squares method was adopted in computing the parameters of the models. Root Mean Square Error (RMSE) was used to assess the accuracy of the models with the RMSE of model A is 14.3 cm, model B is 15.7 cm and model C is 14.5 cm, respectively. The inclusion of height term (∆h) in model B does not improve the accuracy over model A and model C. Model A with the lowest RMSE is hence the better of the three models. One-way ANOVA test conducted at 95% confidence level, however, revealed that the three models did not differ significantly. Model A having lower RMSE is recommended with GPS determined ellipsoidal heights as an alternative to conventional spirit levelling for orthometric height determination within Akure for engineering and environmental applications.

ETH-GQS: An estimation of geoid-to-quasigeoid separation over Ethiopia

The determination of accurate orthometric or normal heights remains one of the main challenges for the geodetic community in Ethiopia. These heights are required for geodetic and geodynamic scientific research as well as for extensive engineering applications. The main objective of this study is to estimate the geoid-to-quasi geoid separation (GQS) in Ethiopia (ETH-GQS). Such separation would be required for the conversion between geoid and quasigeoid models, which is mandatory for the determination of accurate geodetic heights in mountain regions. The airborne free-air gravity anomalies and the topographic information retrieved from the SRTM3 (Shuttle Radar Topography Mission of a spatial resolution 3 arc-second) digital elevation model were used to compute the ETH-GQS model according to the Sjöberg's strict formula for the geoid-to-quasigeoid separation. The ETH-GQS was then validated using GNSS-levelling data as well as geoid heights determined from different Global Geopotential Models (GGMs), namely the EGM2008, EIGEN-6C4 and GECO. The results reveal that the standard deviation of differences between the geoid heights obtained from the EIGEN-6C4 model and the geometric geoid heights obtained from GNSS-levelling data were improved by ∼75% (i.e. from ∼24 to ∼6 cm) when considering GQS values obtained from the ETH-GQS.

Determination of Orthometric Height using GNSS and EGM Data: a Scenario of the Federal University of Technology Akure

The advent of Global Navigation Satellite System (GNSS) and Earth Gravitational Model (EGM)particularly Global Positioning System (GPS) has modernized geodetic surveying in providing horizontal and vertical positions of points with a sub-meter level of accuracy over the reference ellipsoid. The GPS gives ellipsoidal heights which makes the conversion of the heights to orthometric heights possible by incorporating a geoid model. The conventional method of determining orthometric height is tedious, time-consuming, and labour intensive. This study entails the determination of orthometric height using GNSS and EGM data. A total of forty-nine (49) stations selected within the study area were occupied for GPS observation using South DGPS instrument in static mode for the position and ellipsoidal height determination. The geoidal height values of the GPS derived data were computed using GeoidEval utility software with reference to three different EGMs (EGM2008, EGM96 and EGM84). In order to determine the orthometric heights of the selected stations, the difference between the EGM geoidal height values (NEGM) and the ellipsoidal heights were computed. The results show that the orthometric height obtained with respect to EGM2008 gives better results with a standard deviation of 9.530m and a standard error of 1.361m. The study reveals that the use of GNSS and EGM data for orthometric height determination is less expensive, less tedious, accurate and time-saving compared to the conventional approach of geodetic and spirit levelling.

Implementation of CORS GNSS and local geoid for precise orthometric height determination in land subsidence region (a case study in Semarang City)

Geoid has an important role in converting geodetic heights to physical heights, both in orthometric height system and normal height systems. At present, Semarang City already has gravimetric geoid with centimeter-level precision. This gravimetric was validated by geometric geoid measured by static method. GNSS (Global Navigation Satellite System) measurement using static method needs long observation time and costly because it requires network that connect baselines and points. This study aims to implement CORS (Continous Operating Reference Station) GNSS in measuring geodetic height and to apply gravimetric geoid in orthometric height calculations. In this research, the gravimetric geoid recalculation process was carried out using gravity disturbance data of 2016. The geoid fitting process was carried out iteratively based on gravity data and modification of the integral of Hotine. Geodetic height measurements were carried out at 40 points distributed olong 50 km leveling network. Geodetic height measurements were refered to CORS GNSS of BIG (Geospatial Information Agency) and UNDIP (Diponegoro University) to produce standard deviation ranged from ±0.003 m to ±0.055. Geometric geoid checking with previous gravimetric geoid before fitting produced standard deviation of ±0.037 m and datum offset of -0.690 m. Geometric geoid checking for recent gravimetric geoid after fitting produces standard deviation of ±0.043 m and datum offset of -0.010 m. This study concluded that the refering geodetic coordinates to CORS stations by 1 hour observation of rapid static method and processing baselines in commercial software are sufficient for the determination of orthometric height in centimeter-level precision. This study also concluded that gravimetric geoid fitting based on gravity data shifting can minimize datum offset and shrinkage in geoid map.

DETERMINATION OF LOCAL QUASI-GEOID IN CENTRAL ANATOLIA FOR ENGINEERING AND GIS PURPOSES

Requirement for a high resolution geoid model has increased substantially during the last few decades especially with the advent of Global Positioning System (GPS). Many countries across the world have already developed their own geoidal model which serve as the means of deriving orthometric heights from GNSS observations. On the other hand, the need for transformation of the ellipsoidal heights derived from GNSS observations to the physical orthometric heights has forced geodesists to determine the high precision local geoid heights. Besides, because orthometric heights are used in engineering and GIS applications, local quasi-geoid determination studies have become especially important. As it is well known, Turkey is situated on a tectonically very active region and earthquakes occurring in different times cause deformations in heights of levelling points of Turkish National Vertical Network. On the other hand, National Mapping Agency of Turkey (GDM: General Directorate of Mapping) which is responsible for the establishment and maintenance of national geodetic networks compute geoid models for whole Turkey and release them for public use in different periods. These GDM-computed geoid models are called “hybrid geoid” models. Hybrid geoid models are computed with the combination of gravimetric geoid models and geoid heights on the GPS_levelling points. And it is also known that the absolute accuracies of these geoid models are nearly at the 10 cm level or even worse. But, the requested accuracy is about better than 5 cm. Hence, in order to prove that the required accuracy levels can be achieved, A local gravimertric and quasi-geoid determination project using the resources of Selcuk University was initiated. Project area has been planned to cover a limited part of Central Anatolia including Konya. Necessary basic data (gravity, levelling etc.) for this Project have been obtained in the field by performing observations/measurements. Some other necessary data such as absolute gravity values have been obtained from GDM. And as the next phase, high accuracy (better than 5 cm) local gravimetric and quasi-geoid models will be computed for the limited part of Central Anatolia using the above mentioned data. In order to be able to reach this goal suitable geoid computations softwares must be used. In this project, we will use DFHRS software developed by the Karlsruhe Applied Sciences. The principle of the DFHRS software is based on the parametric model of N(φ, λ, h) as a continuos polynomial height reference surface (HRS). Following the quasi-geoid computation, when we reach the requested accuracy level, namely better than 5 cm, then it will have been shown that the GNSS based determination of orthometric heights (H) is much faster, easier to handle and much more economic, in comparison to classical geodetic levelling. On the other hand, it is possible to obtain a gravimetric geoid better than 10 cm accuracy by using global models and gravity data with 1-2 mGal accuracy. And you can only check such geoid only with GNSS/Levelling heights which provide better accuracies. Thus, according to the results to be obtained from this Project, a more comprehensive project will be launched and the project area will be expanded. Thus, additional gravity, levelling and GNSS measurements will be carried out in the new Project area for the determination of a high accuracy regional gravimetric geoid. Consequently, in this paper, all works carried out within the framework of this project and the reached preliminary results will be presented.

Comparison of Two Polynomial Geoid Models of GNSS/Leveling Geoid Development for Orthometric Heights in FCT, Abuja

Ellipsoidal heights from GNSS require geoid model for conversion to orthometric height. The geoid model could be global, regional or local. The lack of national geoid model in Nigeria makes development of local geoid very critical to local applications in place of integrated global geoid models. This study compares two polynomial geoid models for terrain representation in the FCT, Abuja. Nine coefficients were used to model the FCT surface for geoid interpolation and orthometric height modeling. Model A involved the use of the 2-D (x, y) positions while model B used 3-D (x, y, ) where = ( – ) the difference in average ellipsoidal height ( ) and each point’s ellipsoidal height ( ). The term is based on the assumption that the geoid varies with topography and may hence possibly lead to some improvements in accuracy of orthometric height determination. DGPS observations were carried out to determine ellipsoid heights. Least squares adjustment was performed to compute the coefficients of the models. Model A achieved standard deviation of σ = 11 cm while Model B achieved σ = 13cm. Though, Model B has a term that included highly accurate ellipsoidal height differences ( ), it has not resulted into any accuracy improvement over the model A. Model A based on 2-D positions is hence the better of the two models. The t-test and hypothesis test at 95% confidence limit, however, showed that the two models did not differ significantly. Model A having lower standard deviation is recommended with GNSS determined ellipsoidal heights to determine orthometric heights within the FCT. This becomes an easy alternative to conventional spirit leveling technique for production of topographical maps, cadastral surveys, and engineering/environmental applications.

A Gravimetric Approach for the Determination of Orthometric Heights in Akure Environs, Ondo State, Nigeria

An important component in position determination of any point is its height. Orthometric height determination has a significant role in geodesy, and it has wide-ranging application in numerous fields and activities. Orthometric height is the height above or below the geoid along the gravity plumb line. Orthometric height system is preferred to ellipsoidal height by many because of its relationship with the mean sea level (MSL). Determination of orthometric height for Akure environs was carried out using gravimetric approach by determining geoidal undulation via Stokes integral and ellipsoidal heights via GPS observations. A total of 59 stations within the study area were occupied for gravity observation using Lacoste and Romberg (G-512 series) and its complete accessories. South GNSS instrument was used for position and ellipsoidal height determination in static mode. In order to determine orthometric heights of the study area, the difference between the tailored geoid height (N Taylor ) and the ellipsoidal heights (h GPS ) were computed. The result shows that the determined orthometric height had an accuracy of 10.6121m standard deviation with a standard error of 1.38159m. The contour map and the 3D surface map of the computed orthometric heights were produced for the study area using kriging gridding method embedded in Surfer 11 software. The study recommends the use of gravimetric method in orthometric height determination when the tailored geoid height is computed. Keywords: Orthometric height, ellipsoidal height, Gravimetric approach, Gravity values, and geoidal height

Analysis of the Effect of Tropospheric Delay on Orthometric Height Determination at High Mountain

The purpose of this study is to precisely determine the orthometric height considering tropospheric delay at the top of the mountain where the height difference with reference ground surface is large. So, GNSS surveying was carried out at Cheonwangbong on Mount Jiri to determine the orthometric height, and GNSS data were processed by both DGNSS and PPP methods to determine ellipsoidal height using Bernese version 5.0 software. In this process, KNGeoid14 Korean geoid model was used and the effects of troposphere delay on the coordinates and orthometric height were analyzed. The study results showed that the tropospheric delay was reduced by 3.04 cm with every 100 m increase of the ellipsoidal height. The orthometric height and RMSE determined by the DGNSS method were found to be 1915.4596 m and 0.0520 m, respectively, and the orthometric height and RMSE determined by the PPP method were found to be 1915.4059 m and 0.0527 m, respectively. So, the difference between the DGNSS method and the PPP method when tropospheric corrections were applied showed a difference of 5.37 cm in orthometric height. And, the results also showed that the difference in whether or not the tropospheric delay model was applied in the calculation of the orthometric height was 1.53 cm in the same DGNSS method.

Comparison of Two Polynomial Geoid Models of GNSS/Leveling Geoid Development for Orthometric Heights in FCT, Abuja

Ellipsoidal heights from GNSS require geoid model for conversion to orthometric height. The geoid model could be global, regional or local. The lack of national geoid model in Nigeria makes the development of local geoid very critical to local applications in place of integrated global geoid models. This study compares two polynomial geoid models for terrain representation in the FCT, Abuja. Nine coefficients were used to model the FCT surface for geoid interpolation and orthometric height modeling. Model A involved the use of the 2-D (x, y) positions while model B used 3-D (x, y, ∆h) where ∆h= (h ave – hi) the difference in average ellipsoidal height (h ave ) and each point’s ellipsoidal height (hi). The ∆h term is based on the assumption that the geoid varies with topography and may hence possibly lead to some improvements in the accuracy of orthometric height determination. DGPS observations were carried out to determine ellipsoid heights. Least squares adjustment was performed to compute the coefficients of the models. Model A achieved standard deviation of σ = 11 cm while Model B achieved σ = 13cm. Though Model B has a term that included highly accurate ellipsoidal height differences (∆h), it has not resulted into any accuracy improvement over the model A. Model A based on 2-D positions is hence the better of the two models. The t-test and hypothesis test at 95% confidence limit, however, showed that the two models did not differ significantly. Model A having lower standard deviation is recommended with GNSS determined ellipsoidal heights to determine orthometric heights within the FCT. This becomes an easy alternative to conventional spirit leveling technique for production of topographical maps, cadastral surveys, and engineering/environmental applications.

Study of the Potential of a Local Geoid Model for Extracting the Orthometric Heights from GPS Measurements in Topographic Works

Due to the rapid development and expansion of geodetic applications, the determination of orthometric heights in an accurate manner is considered as one of the most required conditions to carry out such projects. Obtaining orthometric heights using traditional methods of levelling is time and cost consuming. Hence, investigating other techniques that provide the same accuracy, as leveling methods, but requiring less time and cost is very gainful. Recently, satellite positioning techniques and their applications are being used increasingly in geodetic projects. So, it is interesting to study the efficiency of such techniques for obtaining orthometric heights. GPS methods provide highly accurate measurement of ellipsoidal heights. However, the conversion of ellipsoid heights to orthometric heights may be achieved using geoid models. The objective of this research is to study the efficiency of using a local geoid model as an alternative method to obtain orthometric heights from GPS measurements. This paper proposes a methodology to generate such local geoid models. Then, the results of using the generated local geoid model for Jeddah city in Saudi Arabia are presented. These results indicate that the difference among estimated undulations values from the local geoid model and undulations values calculated from leveling techniques ranges from 1.8 cm to -1.1 cm. with a maximum standard deviation of 56 mm. These results confirm that the creation of a local geoid model is an effective method that gives the required accuracy for topographic works. Keywords: GPS/Levelling method, Local geoid model, Krigging method.

DEVELOPMENT OF A GRAVIMETRIC GEOID MODEL AND A COMPARATIVE STUDY

Site specific geoid model is prerequisite for accurate determination of orthometric heights. No geoid model has been developed so far for India or any of its part. So, development of a geoid model for India or its part is of utmost need to make use of GNSS data towards determination of orthometric heights. In this research work, an attempt has been made to develop geoid undulation models by gravimetric method using Molodensky’s concept. Component parameters in line with the Remove – Compute – Restore (RCR) technique have been used recursively. Models have been developed for two study areas: one of these lies in and around Dehradun (30° 19′ N, 75° 04′E) in Uttarakhand state, India in lower Himalayan region having highly undulating topography and the other near Hyderabad (17° 30′N, 78°30′E) in Telengana state of India having gentle topography. The model has been tested for 7 stations in the first study area and accuracy has been found to be 17.5 cm; whereas, for the second area accuracy has been found to be 7.0 cm for 24 test stations. Further, the performances of the developed models have been evaluated with those from three global geoid models namely EIGEN6C4, EIGEN6C3stat and EGM2008; and have been found to be similar or better in case of first study and for second study area far more superior. Thus, local/regional geoid undulation model requiring accuracy better than 20 cm for any study area may be developed adopting the method. However, the optimality in the number and density of gravity stations may be considered as a future scope of work.

관측조건에 따른 GPS 타원체고 결정의 정확도 분석

GNSS/Leveling technology makes it possible to get geoidal height geometrically using GNSS and Leveling technology. GNSS/Geoid technology refers to a technology for obtaining orthometric height by subtracting geoidal height achieved by Geoid technology from ellipsoidal height achieved by GNSS technology. The purpose of this study is to verify the accuracy of the ellipsoidal height determination in order to verify the accuracy of the orthometric height determination by the GNSS/Geoid technology. For the study, a test bed was selected in Kyungnam province and GNSS Static surveying was accomplished in the test bed and then the GNSS data was processed in accordance with various analysis conditions. So, it was verified the accuracy of the ellipsoidal heights determination in accordance with the surveying conditions under the GNSS Static surveying. According to the research results, to ensure the 3cm goal accuracy of the ellipsoidal height determination, it should be surveyed by four fixed points on the survey area periphery and more than two hours of the GNSS occupation time, And also, it was found that should be limited to a baseline distance of 20km under the GNSS Static surveying.

High-resolution gravity and geoid models in Tahiti obtained from new airborne and land gravity observations: data fusion by spectral combination

Abstract For the first time, we carry out an airborne gravity survey and we collect new land gravity data over the islands of Tahiti and Moorea in French Polynesia located in the South Pacific Ocean. The new land gravity data are registered with GPS-derived coordinates, network-adjusted and outlier-edited, resulting in a mean standard error of 17 μGal. A crossover analysis of the airborne gravity data indicates a mean gravity accuracy of 1.7 mGal. New marine gravity around the two islands is derived from Geosat/GM, ERS-1/GM, Jason-1/GM, and Cryosat-2 altimeter data. A new 1-s digital topography model is constructed and is used to compute the topographic gravitational effects. To use EGM08 over Tahiti and Moorea, the optimal degree of spherical harmonic expansion is 1500. The fusion of the gravity datasets is made by the band-limited least-squares collocation, which best integrates datasets of different accuracies and spatial resolutions. The new high-resolution gravity and geoid grids are constructed on a 9-s grid. Assessments of the grids by measurements of ground gravity and geometric geoidal height result in RMS differences of 0.9 mGal and 0.4 cm, respectively. The geoid model allows 1-cm orthometric height determination by GPS and Lidar and yields a consistent height datum for Tahiti and Moorea. The new Bouguer anomalies show gravity highs and lows in the centers and land-sea zones of the two islands, allowing further studies of the density structure and volcanism in the region.

The mount Cameroon height determined from ground gravity data, global navigation satellite system observations and global geopotential models

Abstract This paper deals with the accurate determination of mount Cameroon orthometric height, by combining ground gravity data, global navigation satellite system (GNSS) observations and global geopotential models. The elevation of the highest point (Fako) is computed above the WGS84 reference ellipsoid. The geoid undulation and the height of Fako above mean sea level were also determined. Ground data consist of a sparse gravity net recorded around 1950, densified with recent data collected on and around the mountain. GNSS data consist of ellipsoidal elevations and precise horizontal point coordinates computed from GPS satellites observations, and those of other systems orbiting around the Earth. Global geopotential models involved are a hybrid model EGM-GGM and the recent Earth Gravity Model EGM2008. The method used appears more flexible than spirit leveling, which is too expensive, time consuming, difficult and of very low accuracy in mountainous areas, where the topography is very rough. Mount Cameroon, which is the highest summit in central and western Africa, is now known to culminate at 4037.7 ± 0.7 m above sea level. This height is nearly 60 m less than the approximate value of 4095 m published by the National Institute of Cartography.

Polynomials, radial basis functions and multilayer perceptron neural network methods in local geoid determination with GPS/levelling

The means for determining reference surfaces when using satellite-based positioning techniques differs from the way they are determined using classical terrestrial positioning techniques. The height of any point on earth, as determined by a global positioning system (GPS), is based on the World Geodetic System of 1984 datum, but when using classical terrestrial measurements this height is based on the geoid. However, GPS-derived ellipsoidal heights must initially be transformed into orthometric heights for practical applications. We use geoid models developed with geoid heights for the height transformation, because orthometric height determination methods using classical techniques require time and manpower. In this study, the performances of polynomials, radial basis functions (RBFs) and multilayer perceptron (MLP) neural network algorithms used in local geoid surface modelling were evaluated in the study area. Upon analysis of statistical results, the artificial neural network method was observed to give better results than the other two methods.

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.