1. 4. RESULTS AND DISCUSSION CONCLUSION AND RECOMMENDATIONS
Approaches for Determination of an Optimum Saudi Arabian Geoid (A Preliminary Report)
K. F. Aleem
Department of Geomatics Engineering Technology, Yanbu Industrial College, Yanbu Industrial City, Saudi Arabia
Mobile No:
Surveying and Geoinformatics Programme, Abubakar Tafawa Balewa University, Bauchi Nigeria
Abstract
Astro-gravimetric:- Differentiating Stokes’s formula equation (4) with respect to φ and λ, we will obtain the corresponding Vening Meinesz expressions given by (Heiskanen and Morizt, 1967):
Geoid Determination This can be achieved with the use of geoid modelling approaches, such as the use of stokes’s formula, astro-geodetic, GPS/Levelling geoid, North Sea Region Model, Zanletnyik Hungarian Polynomial model, 4-Parameter Similarity Datum shift, 5-Parameter Similarity Datum Shift, 7-Parameter Similarity Datum Shift, Geopotential Earth Model 2008, and Satlevel collocation models. Depending on area of coverage, geoid may be determined for the entire earth surface as global geoid, regional or local. Regional geoid models are the best because they are of high resolution, local gravity and terrain data are often added to the global geopotential model for accurate determination of the geoid to suite the study area. The regional geoid is not available in the whole of Saudi Arabia which may hamper the use and applications of such.
In this work, various methods of geoid determination will be examined; available data will be compiled from different sources, which are to be complemented with more observations. The extent of Kingdom will require application of orthometric correction, so as to be get accurate orthometric height. The data will be tested on the existing models. Statistical analysis will be carried using different existing model, so as to be able to select the appropriate method for the regional determination of Saudi Arabian geoid. An attempt will be made to adopt a realistic geoid model for the Kingdom.
The Geoid from the New Earth Gravitational Model (EGM2008): The global
North Sea Region Model
The 4-parameter similarity datum shift
The 5-parameter similarity datum shift
The 7-parameter similarity datum shift
Zanletnyik Hungarian Polynomial Model:
1. INTRODUCTION
The geoid can also be defined as the “surface which coincides with that surface to which the oceans would conform over the entire earth, if free to adjust to the combined effect of the earth's mass attraction (gravitational force) and the centrifugal force of the earth's rotation”
Local Optimum geoid is geoid determined using available methods and data to attain best possible accuracy for a locality. There are several methods of geoid determination
 Kingdom of Saudi Arabia is a very large country occupies over 2 millions square kilometres having mountainous formation along its western part, bounded by Red sea in the west and the Arabian Gulf in the east. The presence of most of these features has contributed to the problems of determination of an acceptable geoid for the kingdom. However, several efforts were made, there is no precise and unified geoid model published for national use in Saudi Arabia. (Alothman, 2011)
Ellipsoidal ‘Satlevel’ Model:
Spherical ‘Satlevel’ Model:
Mean Corrected Observation on the Sphere ‘Satlevel’ Model:
Rectangular ‘Satlevel’ Model:
4. RESULTS AND DISCUSSION
Each of the methods above were used to compute the Geoidal value for points in the Kingdom. Gravimetric methods was not used because, the data was not available in required quantity and spatial distribution can not satisfied the accuracy required. 7 parameters similarity datum shift also produced result with large residuals compared to other. However, further analysis are still required to come up with Optimum geoid for the Kingdom.
CONCLUSION AND RECOMMENDATIONS
Figure 1.0 shows the map of Saudi Arabia with the Exisitng Control Points
The preliminary investigation are data gathering exxercises are still going on in order to determined the Optimum geoid for the Kingdom
There have been some efforts to model the geoid for the kingdom of Saudi Arabia, as discussed by several authors such as (Algarni, 1997, Alrajhi et al., 2008, Alrajhi et al., 2009 and Alothman, 2011). Alrajhi et al, (2009) implemented Two models for this separation between the geoid and ellipsoid using GNSS/Benchmark data:
REFERENCES
Aleem, K. F. (2013). Adaptation of a Global Orthometric to a Local Height Datum Using “Satlevel” Collocation Model”. A PhD Thesis, University of Lagos. Nigeria.
Algarni, D.A., Geoid Modelling in Saudi Arabia, ITC Journal, Netherlands, Vol. 2, p , 1997.
 Alrajhi, M., Hawarey, M., and Alomar, A., Geodetic vertical control network in the KSA, Geophysical Research Abstracts, Vol. 10, SRef-ID: /gra/EGU2008-A-05016, European Geosciences Union. Presented at EGU General Assembly 2008, Vienna, Austria, April 2008.
Alrajhi, M., Yanar, R., Hawarey, M., and Alomar, A., Refinement of Geoid in Saudi Arabia using GNSS/Benchmark data with EGM1996 and EGM2008, Geophysical Research Abstracts, Vol. 11, EGU , European Geosciences Union. Presented at EGU 2009, Vienna, Austria, April 2009.
  Flanigan, V.J., Akhras, M.N., Preliminary report on the gravity net: Kingdom of Saudi Arabia. USGS, Rept. No. 138.
Haagmans R, de Min E, and van Gelderen M Fast evaluation of convolution integrals on the sphere using 1D FFT, and a comparison with existing methods for Stokes' integral. Manuscripta Geodaetica.18(5):
Olaleye, J. B., K. F. Aleem, J. O. Olusina and O. E. Abiodun Establishment of an empirical geoid model for a small geographic area: A case study of Port Harcourt, Surveying and Land Information Science 39-48(10) / /art00006
Zaletnyika, P., L. Völgyesi, and B. Palánczb, Approach of the Hungarian geoid surface with sequence of neural networks. Research supported by the Hungarian National Research Fund (OTKA), Contract No. T
Other efforts may include the determination of GPS/BM geoid based on the vertical reference network of Saudi Arabia, which were established in early 1970’s as first order vertical control network by spirit levelling based on tidal gauges along the Arabian Gulf and Red Sea (Alrajhi et al, 2009 and Alothman, 2011). Also Saudi-SARAMCO a multinational petroleum company based in Saudi Arabia established more than 5000 GPS/BM observations, with an accuracy of 1 to 10 ppm, Alothman, (2011) used these data to compute the point geoid heights using the remove and restore techniques.
In this work different functional geoid models will be examined with a view to adopt a high resolution and optimum local geoid model for Saudi Arabia with suitable accuracy for rapid and efficient surveying methods related to Geodesy
METHODOLOGY
Data Acquisition: Avaialable data will were collected from various sources;
Existing Methods of Geoid determination: some of the existing methods adopted in other countries will be be used. Such methods an models includes:
Stokes’ Formula:-