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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 applicatio...
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... gravimetric data (Kiamehr and Sjoberg, 2005). In some areas more accurate DEM (produced by the authors from stereo SPOT images via digital photogremmetry techniques) was used. The Geoid Model could be obtained by GPS/ leveling measurements (geometric method) (Duquesne et al ., 1995; Fotopoulos, 2003), or the gravimetric method (Rapp, 1997; Featherstone et al. , 2001). While the geometric method is not easy to implement due to the poor spatial cover- age of geometric leveling lines (Lee and Mazera, 2000), the gravimetric method utilizes a better distribution of terrestrial gravity observations and a global geopotential model (Bottoni and Barzaghi, 1993; Amos and Featherstone, 2003). Moreover, the geoid is considered to be a reference for the Earth gravity field and/or represents the vertical datum that permits the study of the sea-level. The geometric relation between the geoid, ellipsoid and Earth surface is shown in fig. 1, where the separation between orthometric height ( H ) and ellipsoidal height ( h ) is known as the geoid undulation ( N ) (Heiskanen and Moritz, ...
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... observations and a global geopotential model (Bottoni and Barzaghi, 1993;Amos and Featherstone, 2003). More- over, the geoid is considered to be a reference for the Earth gravity field and/or represents the verti- cal datum that permits the study of the sea-level. The geometric relation between the geoid, ellip- soid and Earth surface is shown in fig. 1, where the separation between orthometric height (H) and ellipsoidal height (h) is known as the geoid undulation (N) (Heiskanen and Moritz, 1967) ...
Citations
... The standard error value, which refers to the difference between the measured and the estimated trend models of the investigated gravity points, determines the accepted limits of the reviewed geoid models. For instance, the accuracy of the terrestrial gravity dataset used in local geoid modelling for Tanzania, Ghana, Argentina, Jordan, Sao Paulo (Brazil), and Malaysia ranged from ± 0.05 to ± 25 mGal (Al-Bayari & Al-Zoubi, 2007;Corchete & Pacino, 2007;Ulotu, 2009;Guimarães et al., 2014;Sulaiman et al., 2014;Klu, 2015;Pinon, 2016). Therefore, a standard error of estimate value (± 7 mGal) indicates that the accuracy of the formulated gravity trend model is within the range of the above accuracy instances used for geoid modelling. ...
Geodetic observations in any country or region require a precise local geoid model. Hence, this study has improved the geoid modelling using simulated terrestrial gravity data. However, the sparse and limited number of terrestrial gravity data is the primary reason for the inability to develop an accurate gravimetric geoid model in Iraq, including within the Sulaymaniyah Province selected as the case study in this research work. The ability to use the global navigation satellite system (GNSS) to determine orthometric height has been restricted due to the lack of precise geoid models within the region. Hence, 3327 gravity points from several international and local datasets were applied, 160 of which were collected via gravity survey, to simulate and model the gravity in the Sulaymaniyah Province. A stepwise multiple linear regression with a correlation coefficient (r) of 0.997 and a determination coefficient of (R²) of 0.993 (both very close to 1) was deployed to extract the geographical coordinates and the orthometric height of the points to formulate a cutting-edge gravity model. Next, 120 local gravimetric models were generated using software from KTH (a university in Sweden) with two conditions: (1) the simulated gravity data were composed of a variety of grid and cap sizes, and (2) both the interpolated gravity data and the terrestrial data were combined with the downloaded World Gravity Map 2012 (WGM2012) data. Next, ITU_GRACE16 and IGGT_R1 global geoid models (GGMs) were used to support the cap size area. As the quadratic model fit the 11 available global positioning system (GPS)-levelling points, the simulated gravity data revealed the lowest root mean square error (RMSE) result of ± 17 cm when using IGGT_R1 GGM, in comparison to the other two datasets. Meanwhile, EGM2008 scored an RMSE of ± 31 cm. In conclusion, this new data entry method improves the accuracy of local geoid models by mathematically simulating the gravity data instead of interpolating them.
... Several studies have suggested that the geoid could be obtained either by a gravimetric or geometric approach (Yilmaz et al., 2017;Al-Bayari and Al-Zoubi, 2007). The presented study considered the latter approach in determining the local geoid due to unavailability of gravimetric data for the study area. ...
Geoid determination for national heighting is one of the major research focuses in geodetic sciences. Many studies in the past and recent years have suggested various mathematical techniques for local geometric geoid modelling. This study considered an empirical evaluation of soft computing techniques such as Backpropagation Artificial Neural Network (BPANN), Multivariate Adaptive Regression Spline (MARS), Generalized Regression Neural Network (GRNN), Adaptive Neuro-Fuzzy Inference System (ANFIS), and conventional methods such as Polynomial Regression Model (PRM), and Multiple Linear Regression (MLR). The motive is to apply and assess for the first time in our study area the working efficiency of the aforementioned techniques. Each model technique was assessed based on performance criteria indices such as mean error (ME), mean square error (MSE), minimum and maximum error value (rmin and rmax), correlation coefficient (R), coefficient of determination (R2) and standard deviation (SD). The statistical analysis of the results revealed that ANFIS, GRNN, MARS, BPANN, MLR and PRM, successfully estimate the geoid heights with a good precision for the study area. However, ANFIS outperforms BPANN, MARS, MLR, PRM, and GRNN in estimating a local geoid height. In terms of ME and SD, ANFIS achieved 0.0445 m and 0.0013m as compared to BPANN, MARS, MLR, PRM, and GRNN which achieved 0.1462 m, 0.0059 m, 0.1423 m, 0.0148 m, 0.3117 m, 0.0102 m, 0.1798 m, 0.0208 m, 0.0878 m and 0.0023 respectively. The main conclusion drawn from this study is that, the method of using soft computing is promising and can be adopted to solve some of the major problems related to height issues in Ghana.
... The accuracy of the conversion may be further improved with adoption of regional or local geoid models. A regional geoid model was developed for Jordan using gravity data and compared with the GPS/levelling measurements yielding an accuracy of about ±40 cm (Omar and Abdulla, 2007). Local geoid models are developed for relatively small areas. ...
In geodesy three surfaces, the physical surface of the earth, the geoid and the reference ellipsoid are encountered giving rise to orthometric height (h), the ellipsoidal height (H) and the geoidal separation (N). The orthometric height and the ellipsoidal height are with reference to the geoid and the reference ellipsoid respectively. The vertical separation between the ellipsoid and the geoid is the geoidal separation. A mathematical relation depicting the surface of the geoid with regard to the reference ellipsoid is the geoid model. It relates the geoidal separation with the horizontal location.
The Global Navigational Satellite System provides precise location of points on the surface of the earth. The vertical location provided is the ellipsoidal height which needs conversion to a more usable format, the orthometric height. This is done by integrating ellipsoidal heights with a geoid model. The accuracy of conversion depends on the accuracy of geoid model. Therefore, development of geoid model has become a current area of research in geodesy.
Objective of this study is to develop a local geoid model by employing various polynomial models and thereafter to analyse the accuracy of these models. The test area is in Papua New Guinea. The geometric method is used for computation of the geoidal separation from ellipsoidal and orthometric heights and thereafter the horizontal coordinates and the geoidal separation are used to develop the geoid surface using second, third and fourth degree polynomials. The study shows that the third degree polynomial provided an accuracy of ±20 cm.
... The geoidal separation (N) is computed using the mathematical relation (1). In gravimetric method, one of the accurate methods for large areas [13,14], the control points should have gravity information in lieu of orthometric heights. The gravity information is 123 used to obtain the geoidal undulation N using Stokes formula [15] given below: ...
The Global Navigational Satellite Systems, particularly the Global Positioning System has emerged as state of the art technology for providing precise horizontal and vertical location of points on surface of the earth. The vertical location is with respect to the Reference spheroid and known as ellipsoidal height. However in most of the application areas the heights considered are the orthometric heights (Mean Sea Level heights) with respect to the Geoid. The GPS-derived ellipsoidal heights are converted to corresponding orthometric heights using either a global or a local geoid model. Geoid model is a mathematical relation between the geoidal separation (N) and the horizontal location of a point. The accuracy of the conversion of ellipsoidal heights to orthometric heights depends on the accuracy of the geoid model. The objective of this study is to develop a local geoid model for a region of about 100 × 100 km2 area in Botswana in order to assess the accuracy of orthometric heights obtained from ellipsoidal heights. The geometric method is used for computation of the geoidal separation of control points from available orthometric heights and thereafter these points are used along with their horizontal coordinates and the geoidal separation to develop a surface model using a second degree polynomial as well as a TIN model. From the study it appears that an accuracy of about 20 cm in orthometric heights can be achieved by employing suitable number of well planned control points and an appropriate mathematical model in development of the geoid model.
... GeoJordan model (Al-Bayari and Al-Zoubi, 2007) is mainly used for research purposes. It is not publicly and widely used in jordan even though it has been created before the Earth geoid model (EGM2008). ...
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.
... Przykłady rozwiązań są podane w tabeli 1 -1. (Faskova et al., 2007) Belgia EGM96, GPM98CR quasigeoida (Barzaghi et al., 2003) Południowa Hiszpania i Gibraltar EIGEN5-C-GL04C geoida (Corchete et al., 2008) Argentyna EIGEN5-C-GL04C geoida (Corchete i Pacino, 2007) (Marzooqi et al., 2005) Francja -quasigeoida (Duquenne, 1999) Kanada EGM96 geoida (Grebenitcharsky et al., 2005) Norwegia GGM01S quasigeoida/geoida (Nahavandchi i Soltanpour, 2006) Jordania OSU91A, EGM96 Geoida (Omar Al-Bayari i Abdallah Al-Zoubi, 2007) Nowa Zelandia Combination of EGM96 and GGM02S ...
Different modification methods and software programs were developed to obtain accurate local geoid models in the past two decades. The quantitative effect of the main factors on the accuracy of local geoid modeling is still ambiguous and has not been clearly diagnosed yet. This study presents efforts to find the most influential factors on the accuracy of the local geoid model, as well as the amount of each factor's effect quantitatively. The methodology covers extracting the quantitative characteristics of 16 articles regarding local geoid models of different countries. The Statistical Package of Social Sciences (SPSS) software formulated a strong multiple regression model of correlation coefficient r = 0.999 with a high significance coefficient of determination R2 = 0.997 and adjusted R2 = 0.98 for the required effective factors. Then, factor analysis is utilized to extract the dominant factors which include: accuracy of gravity data (40%), the density of gravity data (25%) (total gravity factors is 65%), the Digital Elevation Model (DEM) resolution (16%), the accuracy of GPS/leveling points (10%) and the area of the terrain of the country/state under the study (9%). These results of this study will assist in developing more accurate local geoid models. Keywords: Accuracy of local geoid model, Multiple regression model, Influence factors
Different approaches were used in the analysis and computation the geoid model, such as GPS/Leveling, Bouguer and Free air anomalies.
The present analysis was carried on 21 gravity stations and 22 points observed by a GPS and level devices available in the study area. Due to the lack of precision of the satellite data (DTED90, DEM90, and DEM30), so
they cannot be relied in calculating terrain correction or the residual terrain model. Consequently, topographic maps were used to provide an accurate RTM for the study area. Hammer chart was used for the computation of
terrain correction precisely. The attained results of the DTED90 with or
without the addition of the undulation value showed the most precise model achieving the best accuracy within the area.
The accuracy of geoid was also estimated by comparing the GPS/leveling method with the geoid undulation EGM2008 model for the study area. The results revealed accuracy within ± 0.034 m for the geoid undulation.
As well as, this study stated the effect of gravity on the values of geoid undulation data. Bouguer and Free air anomaly values of the study area were compiled from the observed gravity database after processing. The residuals of both Bouguer and Free air anomalies were determined. The Remove – Compute – Restore (RCR) techniques were used to compute the gravimetric geoid undulation. The attained accuracies for both anomalies were around ± 0.019 m and ± 0.024 m, respectively. Thus, better results are achieved using Free air anomaly in calculation of the gravitational geoid as it is closer to the undulation accuracy extracted from the GPS/leveling method ± 0.034 m.
