Satlevel Collocation Model for Adapting GEM 2008 to Regional Geoid: A case Study of Yanbu Industrial City in Saudi Arabia Kamorudeen Aleem Department of Geomatics Engineering Technology, Yanbu Industrial College, Yanbu Industrial City, Saudi Arabia Mobile No: +966531259497 e-mail: akfaleem@yahoo.com Surveying and Geoinformatics Programme, Abubakar Tafawa Balewa University, Bauchi, Nigeria 3.5 EGM 2008 Undulations: EGM 2008 undulations were calculated for the study areas using Alltrans EGM 2008 calculator Table 4.1. The result was used as the Long wavelength part of the Adapted Geoidal Undulation. 3.6 Differences Between the GEM 2008 Undulations and the Observed geoidal Undulations were computed which were used to compute the Adapted GEM 2008 Coefficients using ‘satlevel’ collocation Model in a Least Squares Adjustment Observation Equation method Table 4.2. The Adapted GEM 2008 Coefficients was used to compute the short wavelength parts of the Adapted Geoidal undulation. The short wavelength part was then added to the GEM2008 calculated in Section 3.5 above to get the adapted Local geoid of the study area 1. ABSTRACT ‘Satlevel’ Collocation is a new method of geoid. Determination of the geoid has been one of major challenges of geodesists. Gravity data have been used in the past with stokes integration and other approaches. These methods are time consuming, expensive and laborious. Geoid determination using integration of data from geodetic levelling and Global Navigation Satellite System (GNSS) are taking over from the empirical geoid determination. In this work, satlevel collocation model was developed from the combination of orthometric heights, from geodetic levelling, with ellipsoidal heights from Differential Global Positioning System DGPS to obtain both orthometric and ellipsoidal height respectively in Yanbu Industrial city. AltransEGM calculator was used to get the undulations for the Yanbu Industrial city. The mean corrected observation were used get as the residuals between GEM 2008 and geoid in the study area. Statistical test and analyses such as the goodness of fit of the data were carried out. The model was also validated and tested with some of the existing models. The results of the models compared favourably with some of the existing methods. This method of adapting GEM 2008 to Yanbu Industrial city as a regional geoid determination can be extended to other parts of Saudi Arabia. 4. RESULTS AND DISCUSSION .Table 1: Observed Geoidal Undulation and Computed GEM2008 Geoidal Undulations Table 3: the Observed Undulation, Adapted Geoid and the Residuals 2. INTRODUCTION ‘Satlevel’ Collocation is a method of geoid determination in which the ellipsoidal height from any satellite based system is combined with orthometric height from geodetic levelling to model the geoid. Due to the fact that data used for global geoid are always generalized within the area, while the data for local geoid are specific, there may be slight difference between the two results. The development of the ‘Satlevel’ method has been facilitated by the improvement in technology. The Global Navigation Satellite System (GNSS) measurements are serving as important input in geodesy and providing new insights into geoid modelling Point Number Latitude Longitude Ellipsoidal Heights Orthometric Height (H) N Observed GEM 2008   24.0139679 38.23162 20.47 12.271 8.199 7.813 23.9986702 38.25177 21.035 12.879 8.156 7.747 23.0379797 38.20401 16.071 7.819 8.252 5.596 23.9889997 38.29309 19.642 11.521 8.121 7.732 23.9786575 38.30171 15.432 7.328 8.104 7.704 23.9647993 38.32007 9.732 1.651 8.081 7.672 23.9449633 38.36121 8.552 0.501 8.051 7.648 23.9183359 38.36588 8.312 0.291 8.021 7.574 24.0200199 38.26015 25.378 17.197 8.181 7.82 24.0543015 38.17838 13.55 5.253 8.297 7.929 24.0486267 38.23259 25.506 17.261 8.245 7.925 Point Numbers   Latitude Longitude N Observed Adapted Geoid Residuals 24.0139679 38.23162 8.199 8.098292 0.100708 23.9986702 38.25177 8.156 8.032773 0.123227 23.0379797 38.20401 8.252 5.936483 2.315517 23.9889997 38.29309 8.121 8.01754 0.10346 23.9786575 38.30171 8.104 7.98996 0.11404 23.9647993 38.32007 8.081 7.958394 0.122606 23.9449633 38.36121 8.051 7.934737 0.116263 23.9183359 38.36588 8.021 7.862147 0.158853 24.0200199 38.26015 8.181 8.104415 0.076585 24.0543015 38.17838 8.297 8.213025 0.083975 24.0486267 38.23259 8.245 8.208324 0.036676 Table 2: GEM2008 Adapted Coefficients The Study Area : The study was carried out in Yanbu Industrial city located on: Latitude 230 59' 57.840"N and longitude 38013' 39.000"E. Figure 1 shows the map of Saudi Arabia and Yanbu Industrial City. GEM2008 ADAPTED COEFFICIENTS NL 0.93461397 A1 0.53053014 A2 -0.4271126 A3 -1.2146793 H h N Geoid Ellipsoid Topographic Surface h=Ellipsoidal height H= Orthometric height N= geoid height GEM2008 Geoid The values of GEM2008 geoidal Undulation differed from the observed Undulations by an average of 0.274m within the sample size. After adaptation the average of the residual was almost zero because of compensation of both negative and positive values. However, if individual points were considered, the adaptation will satisfy centimetric accuracy, which is good enough for most applications 5. CONCLUSION AND RECOMMENDATION GEM2008 was adapted for the study area Yanbu Industrial City using “Satlevel” Collocation Model. Since GEM2008 geoid is available on the internet, adapting to local equivalent with the use of “Satlevel” Collocation Model will make the usage easier than obtaining geoidal values from the existing methods. It therefore recommended for use in other part of the Kingdom and elsewhere. Figure 1: The Study Area ( Source: Aleem and Aina, 2013 Determination of Geoid is one of the major challenges of Geodesists. Previous Researchers attempted solving the problem using various techniques such as 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. However None of these researches has adapted the use of Global geoid to its local equivalent in Yanbu Industrial City. This is the major focus of this work. 3. METHODOLOGY 3.1 Materials and Data The equipment needed for the exercise are: GNSS receiver and its accessories Level and its accessories to acquire data for orthometric height Any software or program for Least Square Adjustment. “Orthometric Height on Fly” which was used to validate the results. Alltrans Calculator was also downloaded from the INTERNET which was used to compute the undulation for the points in the study areas, 3.2 Data Acquisition: Levelling operation was carried out to obtain data for orthometric height while more data were collected from the survey section of Urban department of Royal Commission. Data for a total of six hundred and thirty (630) points were covered. GNSS observation was carried out to acquire data for geodetic coordinates Other relevant data such constant for the referenced ellipsoid were collected from various literatures and INTERNET websites for data analysis and processing. 3.3 Data Processing: Levelling reduction was done; the reduced levels were assumed to be the orthometric height of each of the points. GNSS observation was processed to get the three dimensional coordinates. These are the geodetic latitude (ϕ), geodetic longitude (λ) and ellipsoidal height (h), which were used in “Satevel” collocation model.   3.4 “Satlevel” Collocation Model: “Satlevel” Collocation model was developed by Aleem, (2013), who gave the detailed explanation of the derivation. The model is of the form: Source: (Aleem, 2013) Where: NL is the long wavelength part of the geoid undulation in the area. A1, A2 and A3 are the geoidal coefficients. ϕ and λ are the WGS ‘84 geodetic coordinates (Latitudes and Longitudes) ri is residue at an observation point. REFERENCES Figure 3.1: Levelling Procedure for acquiring Orthometric Height Data Differential Levelling. H Direction of gravity Mean Sea Level Sea Line of Sight level Level Staff Aleem, K. F. (2013). Adaptation of a Global Orthometric to a Local Height Datum Using “Aleem, K. F. (2013). Adaptation of a Global Orthometric to a Local Height Datum Using “Satlevel” Collocation Model”. A Ph.D Thesis, University of Lagos. Nigeria. Aleem, K. F. and Y. A. Aina (2013) The use of SRTM in Assessing the Vulnerability to Predicted Sea Level Rise in Yanbu Industrial City, Saudi Arabia. Accepted for publication as Proceeding of FIG Working Week 2013. Environment for Sustainability Abuja, Nigeria, 6 – 10 May 2013. http://www.fig.net/pub/fig2013/papers/ts07c/TS07C_aleem_aina_6484.pdf http://www.softpedia.com/progDownload/AllTrans-EGM2008-Calculator-Download-124480.html Olaleye, J. B., K. F. Aleem, J. O. Olusina and O. E. Abiodun 2010. Establishment of an empirical geoid model for a small geographic area: A case study of Port Harcourt, Nigeria. Surveying and Land Information Science. 70(1): 39-48(10) http://www.ingentaconnect.com/content/nsps/salis/2010/ 00000070/00000001/art00006 Aleem, K. F. (2013) Satlevel Collocation Model for Production of Contour Map of Yanbu Industrial City, Saudi Arabia. Journal of Emerging Trends in Engineering and Applied Science. (JETEAS) 4(2): 156-161 April 2013. http://jeteas.scholarlinkresearch.org/articles/Satlevel%20Collocation%20Model%20for%20Production.pdf Olaleye J. B., J. O. Olusina O. T. Badejo, and K. F. Aleem (2013) Geoidal Map and Three Dimension Surface Model of Part of Port Harcourt Metropolis from Satlevel Collocation Model. International Journal of Computational Engineering Research.3(4) 52-58. http://www.ijceronline.com/papers/Vol3_issue4/part.3/G0343052058.pdf