1. 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:
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 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
20.47
12.271
8.199
7.813
21.035
12.879
8.156
7.747
16.071
7.819
8.252
5.596
19.642
11.521
8.121
7.732
15.432
7.328
8.104
7.704
9.732
1.651
8.081
7.672
8.552
0.501
8.051
7.648
8.312
0.291
8.021
7.574
25.378
17.197
8.181
7.82
13.55
5.253
8.297
7.929
25.506
17.261
8.245
7.925
Point Numbers
Latitude
Longitude
N Observed
Adapted Geoid
Residuals
8.199
8.156
8.252
8.121
8.104
8.081
8.051
8.021
8.181
8.297
8.245
Table 2: GEM2008
Adapted Coefficients
The Study Area : The study was carried out in Yanbu Industrial city located on: Latitude ' "N and longitude 38013' "E. Figure 1 shows the map of Saudi Arabia and Yanbu Industrial City.
GEM2008 ADAPTED COEFFICIENTS NL A1 A2 A3 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 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 Environment for Sustainability Abuja, Nigeria, 6 – 10 May
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, Nigeria. Surveying and Land Information Science. 70(1): 39-48(10) / /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): April
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)