scholarly journals Modelling Orthometric Heights from a Combination of Ellipsoidal Heights and Gravimetric Geoid Model in Rivers State, Nigeria

2020 ◽  
Vol 11 (04) ◽  
pp. 184-196
Author(s):  
Kurotamuno P. Jackson ◽  
Elochukwu C. Moka
Keyword(s):  
Gravimetric Geoid ◽  
Geoid Model ◽  
Orthometric Heights ◽  
Rivers State

scholarly journals DEVELOPMENT OF A GRAVIMETRIC GEOID MODEL AND A COMPARATIVE STUDY

2016 ◽  
Vol 42 (3) ◽  
pp. 75-84 ◽  
Author(s):  
Upendra Nath Mishra ◽  
Jayanta Kumar Ghosh
Keyword(s):  
Accurate Determination ◽  
Research Work ◽  
Gravimetric Method ◽  
Geoid Undulation ◽  
Gravimetric Geoid ◽  
Geoid Model ◽  
Orthometric Heights ◽  
Gnss Data ◽  
Better Than

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.

scholarly journals A High-Resolution Gravimetric Geoid Model for Kuwait Using the Least-Squares Collocation

2022 ◽  
Vol 9 ◽  
Author(s):  
Hamad Al-Ajami ◽  
Ahmed Zaki ◽  
Mostafa Rabah ◽  
Mohamed El-Ashquer
Keyword(s):  
High Resolution ◽  
Least Squares ◽  
Geopotential Model ◽  
Gravimetric Geoid ◽  
Least Squares Collocation ◽  
Geoid Model ◽  
Terrestrial Gravity ◽  
Digital Elevation ◽  
Elevation Model ◽  
Gps Leveling

A new gravimetric geoid model, the KW-FLGM2021, is developed for Kuwait in this study. This new geoid model is driven by a combination of the XGM2019e-combined global geopotential model (GGM), terrestrial gravity, and the SRTM 3 global digital elevation model with a spatial resolution of three arc seconds. The KW-FLGM2021 has been computed by using the technique of Least Squares Collocation (LSC) with Remove-Compute-Restore (RCR) procedure. To evaluate the external accuracy of the KW-FLGM2021 gravimetric geoid model, GPS/leveling data were used. As a result of this evaluation, the residual of geoid heights obtained from the KW-FLGM2021 geoid model is 2.2 cm. The KW-FLGM2021 is possible to be recommended as the first accurate geoid model for Kuwait.

scholarly journals Impact of different centroid means on the accuracy of orthometric height modelling by geometric geoid method

2020 ◽  
Vol 6 (4) ◽  
pp. 124 ◽  
Author(s):  
Oluyori P. Dare ◽  
Eteje S. Okiemute
Keyword(s):  
Root Mean Square ◽  
Arithmetic Mean ◽  
Orthometric Height ◽  
Harmonic Mean ◽  
Geometric Method ◽  
Mean Square ◽  
Geoid Model ◽  
Microsoft Excel ◽  
Orthometric Heights ◽  
The Impact

<p class="abstract"><strong>Background:</strong> Orthometric height, as well as geoid modelling using the geometric method, requires centroid computation. And this can be obtained using various models, as well as methods. These methods of centroid mean computation have impacts on the accuracy of the geoid model since the basis of the development of the theory of each centroid mean type is different. This paper presents the impact of different centroid means on the accuracy of orthometric height modelling by geometric geoid method.</p><p class="abstract"><strong>Methods:</strong> DGPS observation was carried out to obtain the coordinates and ellipsoidal heights of selected points. The centroid means were computed with the coordinates using three different centroid means models (arithmetic mean, root mean square and harmonic mean). The computed centroid means were entered accordingly into a Microsoft Excel program developed using the Multiquadratic surface to obtain the model orthometric heights at various centroid means. The root means square error (RMSE) index was applied to obtain the accuracy of the model using the known and the model orthometric heights obtained at various centroid means.  </p><p class="abstract"><strong>Results:</strong> The computed accuracy shows that the arithmetic mean method is the best among the three centroid means types.</p><p class="abstract"><strong>Conclusions:</strong> It is concluded that the arithmetic mean method should be adopted for centroid computation, as well as orthometric height modelling using the geometric method.</p>

scholarly journals On the determination of a locally optimized Ellipsoidal model of the Geoid surface in sea areas

2021 ◽  
Vol 906 (1) ◽  
pp. 012036
Author(s):  
Persephone Galani ◽  
Sotiris Lycourghiotis ◽  
Foteini Kariotou
Keyword(s):  
Data Acquisition ◽  
Sea Level ◽  
Reference Ellipsoid ◽  
Triaxial Ellipsoid ◽  
Geoid Model ◽  
Orthometric Heights ◽  
The One ◽  
Best Fit ◽  
Local Geoid

Abstract Deriving a local geoid model has drawn much research interest in the last decade, in an endeavour to minimize the errors in orthometric heights calculations, inherited by the use of global geoid reference models. In most parts of the earth, the local geoid surface may be tens of meters away from the Global Reference biaxial Ellipsoid (WGS84), which create numerus problems in topographic, environmental and navigational applications. Several methods have been developed for optimizing the precision of the calculation of the geoid heights undulations and the accuracy of the corresponding orthometric heights calculations. The optimization refers either to the method used for data acquisition, or to the geometrical method used for the determination of the best fit local geoid model. In the present work, we focus on the reference ellipsoid used for the geometric and geoid heights determination and develop a method to provide the one that fits best to the local geoid surface. Moreover, we consider relatively small sea regions and near to coast areas, where the usual methods for data acquisition fail more or less, and we pay attention in two directions: To obtain accurate measured data and to have the best possible reference ellipsoid for the area at hand. In this due, we use the “GNSS-on-boat” methodology to obtain direct sea level data, which we induce in a Moore Penrose pseudoinverse procedure to calculate the best fit triaxial ellipsoid. This locally optimized reference ellipsoid minimizes the geometric heights in the region at hand. The method is applied in two closed sea areas in Greece, namely Corinthian and Patra’s gulf and also in four regions in the Ionian Sea, which exhibit significant geoid alterations. Taking into account all factors of uncertainty, the precision of the mean sea level surface, produced by the “GNSS on boat” methodology, had been estimated at 5.43 cm for the gulf of Patras, at 3.76 cm for the Corinthian gulf and at 3.31 for the Ionian and Adriatic Sea areas. The average difference of this surface and the local triaxial reference ellipsoid, calculated in this work, is found to be less than 15 cm, whereas the corresponding difference with respect to WGS84 is of the order of 30m.

scholarly journals THE EVALUATION OF THE NEW ZEALAND'S GEOID MODEL USING THE KTH METHOD / NAUJOSIOS ZELANDIJOS GEOIDO MODELIO VERTINIMAS KTH METODU / ОЦЕНКА МОДЕЛИ ГЕОИДА НОВОЙ ЗЕЛАНДИИ С ПРИМЕНЕНИЕМ МЕТОДА КТН

2011 ◽  
Vol 37 (1) ◽  
pp. 5-14 ◽  
Author(s):  
Ahmed Abdalla ◽  
Robert Tenzer
Keyword(s):  
New Zealand ◽  
Least Squares ◽  
Gravity Data ◽  
Spherical Approximation ◽  
Geopotential Model ◽  
Gravimetric Geoid ◽  
Geoid Model ◽  
Marine Gravity ◽  
Gravity Database ◽  
Stokes Integral

We compile a new geoid model at the computation area of New Zealand and its continental shelf using the method developed at the Royal Institute of Technology (KTH) in Stockholm. This method utilizes the least-squares modification of the Stokes integral for the biased, unbiased, and optimum stochastic solutions. The modified Bruns-Stokes integral combines the regional terrestrial gravity data with a global geopotential model (GGM). Four additive corrections are calculated and applied to the approximate geoid heights in order to obtain the gravimetric geoid. These four additive corrections account for the combined direct and indirect effects of topography and atmosphere, the contribution of the downward continuation reduction, and the formulation of the Stokes problem in the spherical approximation. The gravimetric geoid model is computed using two heterogonous gravity data sets: the altimetry-derived gravity anomalies from the DNSC08 marine gravity database (offshore) and the ground gravity measurements from the GNS Science gravity database (onshore). The GGM coefficients are taken from EIGEN-GRACE02S complete to degree 65 of spherical harmonics. The topographic heights are generated from the 1×1 arc-sec detailed digital terrain model (DTM) of New Zealand and from the 30×30 arc-sec global elevation data of SRTM30_PLUS V5.0. The least-squares analysis is applied to combine the gravity and GPS-levelling data using a 7-parameter model. The fit of the KTH geoid model with GPS-levelling data in New Zealand is 7 cm in terms of the standard deviation (STD) of differences. This STD fit is the same as the STD fit of the NZGeoid2009, which is the currently adopted official quasigeoid model for New Zealand. Santrauka Stokholmo Karališkajame technologijos institute (KTH) sukurtu metodu apskaičiuotas naujas Naujosios Zelandijos ir kontinentinio šelfo geoido modelis. Taikoma Stokso integralo mažiausiųjų kvadratų modifikacija, įvertinant paklaidas ir jų nevertinant bei ieškant optimalių stochastinių sprendinių. Modifikuotas Bruno ir Stokso integralas sieja regioninius žemyninius gravimetrinius duomenis su globaliuoju geopotencialo modeliu (GGM). Gravimetriniam geoidui gauti skaičiuojamos keturios papildomos pataisos: topografinės situacijos ir atmosferos tiesioginės ir netiesioginės įtakos, redukcijos įtakos ir Stokso integralo taikymo sferiniam paviršiui. Gravimetrinis geoido modelis apskaičiuotas pagal du duomenų rinkinius: DNSC08 jūrinių gravimetrinių duomenų bazėje (šelfas) esančias altimetriniu metodu nustatytas sunkio pagreičio anomalijas ir žemyninės dalies gravimetrinių matavimų duomenis iš GNS gravimetrinės duomenų bazės (pakrantė). GGM koeficientai imti iš EIGEN-GRACE02S modelio sferinių iki 65 laipsnio harmonikų. Topografiniai aukščiai sugeneruoti iš Naujosios Zelandijos 1×1 sekundės detaliojo skaitmeninio reljefo modelio ir iš 30×30 sekundžių globaliojo aukščių modelio SRTM30_PLUS V5.0. Gravimetriniams ir GPS niveliacijos duomenims sujungti taikytas mažiausiųjų kvadratų 7 parametrų metodas. KTH metodu sudaryto geoido modelio vidutinė kvadratinė paklaida 7 cm. Tai sutampa su NZGeoid 2009 geoido modelio, taikomo Naujoje Zelandijoje, tikslumu. Резюме Модель геоида континентального шельфа Новой Зеландии построена с применением метода, созданного в Королевском технологическом институте Стокгольма. Данный метод основан на модификации решения интеграла Стокса методом наименьших квадратов с оценкой или без оценки погрешностей и поиском оптимальных статистических решений. Модифицированный интеграл БрунаСтокса объединяет региональные надземные гравиметрические данные с глобальной геопотенциальной моделью (GGM). Для определения гравиметрического геоида вычисляются дополнительные поправки прямого и косвенного влияния топографии и атмосферы, редукции и применения проблемы Стокса для сферической поверхности. Гравиметрическая модель геоида вычисляется на основе двух баз данных: альтиметрическим методом определенных аномалий силы тяжести в базе морских гравиметрических данных DNSC08 (шельф) и надземной части гравиметрических измерений из базы данных GNS. Коэффициенты GGM взяты из сферических гармоник до 65 степени модели EIGENGRACEO2S. Топографические высоты сгенерированы из детальной цифровой модели рельефа Новой Зеландии с сеткой 1×1 секунду и из глобальной модели высот SRTM30_PLUSv5.0 с сеткой 30×30 секунд. Для объединения гравиметрических и GPSнивелирных данных применялся метод наименьших квадратов с 7 параметрами. Среднеквадратическая погрешность модели геоида, созданной по методу КТН, равна 7 см. Точность аналогична точности применяемой в Новой Зеландии модели геоида NZGeoid2009.

scholarly journals GRAVIMETRIC GEOID MODELLING OVER PENINSULAR MALAYSIA USING TWO DIFFERENT GRIDDING APPROACHES FOR COMBINING FREE AIR ANOMALY

2019 ◽  
Vol XLII-4/W16 ◽  
pp. 515-522
Author(s):  
M. F. Pa’suya ◽  
A. H. M. Din ◽  
J. C. McCubbine ◽  
A. H. Omar ◽  
Z. M. Amin ◽  
...  
Keyword(s):  
Gravity Data ◽  
Reference Signal ◽  
Digital Terrain Model ◽  
Peninsular Malaysia ◽  
Airborne Gravity ◽  
Geopotential Model ◽  
Gravimetric Geoid ◽  
Geoid Model ◽  
Free Air ◽  
Free Air Anomaly

Abstract. We investigate the use of the KTH Method to compute gravimetric geoid models of Malaysian Peninsular and the effect of two differing strategies to combine and interpolate terrestrial, marine DTU17 free air gravity anomaly data at regular grid nodes. Gravimetric geoid models were produced for both free air anomaly grids using the GOCE-only geopotential model GGM GO_CONS_GCF_2_SPW_R4 as the long wavelength reference signal and high-resolution TanDEM-X global digital terrain model. The geoid models were analyzed to assess how the different gridding strategies impact the gravimetric geoid over Malaysian Peninsular by comparing themto 172 GNSS-levelling derived geoid undulations. The RMSE of the two sets of gravimetric geoid model / GNSS-levelling residuals differed by approx. 26.2 mm. When a 4-parameter fit is used, the difference between the RMSE of the residuals reduced to 8 mm. The geoid models shown here do not include the latest airborne gravity data used in the computation of the official gravimetric geoid for the Malaysian Peninsular, for this reason they are not as precise.

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