P a g e | 403 Available online at http://arjournal.org

ISSN: 2423-4796

Applied Research Journal Vol.2, Issue, 10, pp.403-411, October, 2016

*Corresponding author: Amal Mahdi Ali, Email: amal.mahdi09@yahoo.com Department of Civil Engineering in Baghdad University, Iraq.

APPLIED RESEARCH JOURNAL

RESEARCH ARTICLE

DETERMINATION OF THE GEOID HEIGHT (GEOID UNDULATION) BY USING MODERN SURVEYING TECHNOLOGIES

* Amal Mahdi Ali

Department of Civil Engineering in Baghdad University, Iraq.

ARTICLE INFO ABSTRACT

Article History:

Received: 03, October, 2016 Final Accepted: 11, November, 2016 Published Online: 25, November, 2016

In this work, a large part of Baghdad University campus has been selected. The determination of Geoidal height for the local area requires Ground Control Points which both Ellipsoidal and Orthometric heights are known to compute the difference between them. The first step of the leveling process began by selected the Ground Control Points (GCPs) around the area of the work, and then divided them into two groups of the network traverse stations. They were leveled and adjusted depend on the number of the Bench Marks (B.M.s). Total Station TS (Nikon Nivo 5C) and Global Positioning System (GPS-Garmin 78 map) are used to do this application. The aim of the proposed work was to determine the height of the Geoid surface in the study area. The Geoidal height is calculated from the difference between the two different heights (Orthometric and Ellipsoidal) for the same point and using Geoid Model (EGM) method, then to compare between them. Maximum and the minimum values for the Geoid Undulation are (1.6261 m), and (1.5964 m) respectively with average (1.61 meter) by using (EGM 2008). When it is used the difference method (h-H), maximum and the minimum values for the Geoid Undulation are (5 m), and (2 m) respectively. Finally, the model EGM-2008 represents the best method to determine the Geoid Undulation. dN value between the two different methods is a maximum (3.40) m, a minimum (0.40 m), the average value (1.5 m), and a standard deviation (SD)= ±0.030. At last, image map was produced using Arc GIS 10.1.

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Key words:

Geoidal Height, GCPs, Geoid Model, Orthometric, Ellipsoidal, Total Station.

1. INTRODUCTION

The elevation of a station is a vertical distance above or below an assumed level surface. The approximate surface is the mean sea level (M.S.L.) which fit to the geoid surface. Another surface is the surface of the ellipsoid, see Fig. 1. The difference in elevation between two stations is the value of the vertical distance between the two different level surfaces which this elevation assigned to it [1]. Total Station and Global Positioning System (GPS) is the modern technologies to determine the heights above the Geiod and ellipsoid respectively [1]. Total Station contains three components: the electromagnetic distance measurement (EDM), the angle measuring, and an onboard microprocessor [3]. Total Station now performs the fastest digital data collection methods. One of the best features of the total station is the ability to download data directly into a computer without human errors [4]. Total station data are converted into a graphic file for use in GIS and CAD programs.

1.1. Definition of the Orthometric and Ellipsoid Heights

To determine the geoid height, the height from the point to the different surfaces (datum) is measured. The ellipsoidal height which is measured by using GPS represents the height from the surface of any reference ellipsoid to the point on the ground. In geodesy, the height from the geoid surface to the point on

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the ground surface represents the orthometric height. The separation between the ellipsoid and geoid surface is called the Geoid height (Geoid Undulation) [5]. Fig. 2 shows the ellipsoidal and orthometric height then the vertical difference between them. The determination of the Geoid Undulation at each point can be calculated using a well-known formula:

N = h – H (1)

h is ellipsoidal height, H is orthometric height and N is geoid undulation

Figure 1 Model of the reference surface [2].

Figure 2 The different surfaces and their heights [6].

1.2. Geoid Undulation

Geoid Undulation (N) is the difference between ellipsoidal and orthometric heights. In other meaning, each of geoid and ellipsoid surface intersect at the geoid undulations [1]. 1.3. Earth Gravity Model (EGM 2008)

EGM2008 represents the spherical harmonic model (gravity model) of the earth's gravitational potential. It has been publicly freed by the United States EGM Development Team.EGM2008 is used to compute Geoid height with respect to ellipsoid -WGS 84. An ESRI GRID data is covering a 45 x 45-degree area. Raster file found on theEGM2008-WGS 84 Version web page [7].

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Figure 3 EGM2008 -WGS 84 [7].

1.4. Global Positioning System Measurements

The United States Department of Defense developed the global navigation satellite system to form the Global Positioning System GPS. Now, GPS can be used freely at any time and by anyone. It is used by civilians for the navigation purposes.

The system includes at least twenty-four satellites that orbit the earth at a height of 20,200 km and inclined 55 from the equator. Three satellites are enough to solve for any position [6]. The coordinates of GPS are on a Cartesian system (X-Y-Z) having the same origin as the WGS84 ellipsoid. WGS84 geocentric Cartesian system (X-Y-Z) can easily be converted into WGS84 ellipsoid coordinate's geodetic latitude, geodetic longitude and height of ellipsoid, see Fig. 4.

Figure 4 WGS 84 Ellipsoid and (X-Y-Z) system [6].

1.5. Navigation Positioning Method

A GPS receiver measures its precise position by calculating the transit time of each signal and computes the distance to each known satellite. Trilateration method is used to determine the receiver's location as shown in Fig. 5. GPS measurements relates to the reference ellipsoid, while the height of (MSL) determined with respect to Geoid [8, 9].

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Figure 5 Principles the geometric trilateration of GPS [6].

2. THE METHODS AND MEASUREMENTS

The Baghdad University campus at Al-Jaderiyais the area of this study, see Fig. 6.Orthometric and Ellipsoidal heights for selected Control Points are observed accurately with Nikon Total Station (Nivo 5C) and Garmin GPS (map 78S) respectively. Geoid Undulation or the Geoidal height (N) for the Control Points can be calculated by using two different methods to compare between them, one of these was Geoid Model (EGM) method and the other was the difference between heights.

Figure 6 Satellite Image of The Study Area (Google), 2016.

2.1. Total Station Observations

After establishing the GCPs around the survey area, the leveling of these points was done by traversing. Total Station (type Nivo 5C) with LCD screen was employed to collect the field data. Traversing data were digitally adjusted and stored inside its internal memory with the unique mapping feature codes file for plotting and digital ground modeling. The height of points that measured using Total Station system is called Orthometric height (H).It is measured respect to the Geoid which approximated by MSL. These adjusted observations for the Control Points are shown in Table .1. 2.2. The Global Positioning System (GPS) Measurements

The navigator GPS instrument (type: Garmin GPS MAP 78S) are used to collect the positioning on the same points which are determined with the first system. This instrument has a high accuracy with a small error percentage doesn't exceed 3-5 meter. Table .1 illustrates the GPS observations of the GCPs which referred to geodetic ellipsoid WGS-84.

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2.3. Comparison Method between Total Station and GPS

After observations are acquired and adjusted, the Geoidal height or Geoidal undulation (N) is calculated by using the difference between the heights obtained from the different methods, as equation bellow.

N = h–H

Where: (H) Represents Orthometric height; (h) represents Ellipsoidal height (N) Represents Undulation or Geoid Height or the difference in height, the relationship between Orthometric heights and Ellipsoid heights are shown in Fig. 7.

Figure 7Orthometric and ellipsoid height

2.4. EGM 2008 Computation Method

The Geoid Model EGM2008 is the second method which is adopted to calculate the Geoid Undulation (N) for the same Control Points in this study, see link below:

http://geographiclib.sourceforge.net/cgi-bin/GeoidEval?input=33+45&option=Submit

The results for the first and the second methods are shown in Table .2.

3. THE RESULTS AND DATA ANALYSIS USED

There are some differences in the results between total station and GPS observations because of each of that are acquired depend on the different datum. GPS provide ellipsoid heights, while the total station heights are based on a level surface called the geoid (M.S.L).The results in Table .1 represent a part of GCPs which are observed by using Total Station and GPS. The total number of these points was thirty- eight pointsdistributed in the site.Fig.8shows the whole points distributed along the survey line against heights.

Table1 Total station and GPS observations for the ground control points

GCP ID Total station observations GPS observations

Easting (m) Northing (m) Orthometric height m (H) Easting (m) Northing (m)

Ellipsoidal height m (h)

1 441816.790 3681083.889 36.068 441820 3681087 41 2 441762.064 3681094.040 35.853 441766 3681097 39 3 441697.239 3681107.256 35.750 441701 3681110 41 4 441643.355 3681119.341 36.139 441647 3681122 41 5 441587.952 3681131.629 36.091 441591 3681135 39 6 441529.642 3681150.319 36.004 441533 3681154 40 7 441468.022 3681207.140 37.641 441472 3681210 40 8 441474.141 3681288.327 37.585 441477 3681292 40 9 441482.564 3681370.015 38.953 441486 3681373 41 10 441489.057 3681416.854 38.920 441493 3681420 42

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Figure 8 Comparison between the orthometric and ellipsoid height.

Fig. 9 below shows the Digital Map for the study area and the selected GCPs using ArcGIS 10.

Figure 9 The digital map of the work in ArcGIS 10.1 environment.

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Table .2 illustrates the Geoid height or Geoid undulation (N) for some of points in the work. The Geoid Undulation for these points is computed using the comparison method and by using EGM 2008 geodetic model.

Table 2Geoid undulation (N) computed by using (H-h) method and EGM 2008 model.

GCP ID

height from GPS (h) in meter

height from TS (H) in meter

Undulation (N) from h-H

Undulation (Nʹ ) from

EGM 2008 model. 1 41 36.068 5.0 1.6138 2 39 35.853 3.5 1.6119 3 41 35.750 5.0 1.6097 4 41 36.139 5.0 1.6078 5 39 36.091 2.5 1.6059 6 40 36.004 4.0 1.6037 7 40 37.641 2.5 1.6007 8 40 37.585 2.5 1.5992 9 41 38.953 2.0 1.5978 10 42 38.920 3.0 1.5971

The average value for the Geoid undulation (N av.) by using the two different methods adopted was equal (3m) for (H-h) method and equal (1.61 m) for EGM2008 geodetic model. To calculate Geoid undulation by using EGM2008, Online calculations is used as Fig. 10.

Figure 10 Online geoid calculations by using the Geoid Eval utility.

Fig. 11 and Fig. 12 are statistic figures that declare the relationship between points distributed along the

survey line against the Geoid undulation by using the two different methods respectively. It can be noticed that, the EGM 2008 is the regular geometrical model which used to the local geodetic dataset.

Figure 11 Undulation or geoid height at each point using (h-H method).

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Figure 12 Undulation or geoid height at each point using EGM 2008.

Table 3 illustrates (dN) values between the Geoid undulation (N) and (N ʹ) for some points in the work.

Also, Fig. 13 shows these differences.

Table 3 The comparison between (N) and (N ʹ) and the differences between them.

GCP ID Geoid undulation (N) by using H-h

Geoid undulation (N ʹ ) by using EGM 2008 model dN = N- N ʹ

1 5.0 1.6138 3.4 2 3.5 1.6119 1.9 3 5.0 1.6097 3.4 4 5.0 1.6078 3.4 5 2.5 1.6059 0.9 6 4.0 1.6037 2.4 7 2.5 1.6007 0.9 8 2.5 1.5992 0.9 9 2.0 1.5978 0.4 10 3.0 1.5971 1.4

Figure 13 The differences (dN) between N and N ʹ.

Maximum and the minimum values for the Geoid Undulation are (1.6261 m), and (1.5964 m)

respectively with average (1.61 meter) by using (EGM 2008). When it is used the difference method (h-H), maximum and the minimum values for the Geoid Undulation are (5 m), and (2 m) respectively. Finally, the model EGM-2008 represents the best method to determine the Geoid Undulation. dN value between the two different methods is a maximum (3.40) m, a minimum (0.40 m), the average value (1.5 m), and a standard deviation (SD)= ±0.030. At last, image map was produced using Arc GIS 10.1.

4. CONCLUSIONS AND RECOMMENDATIONS

4.1. Conclusions

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From the results obtained in this work the following conclusions have been made:- 1. The accuracy of determination of the Geoid undulation N depend on several factors, for example: Number of the surveying stations ( GCPs) Distribution the GCPs must be covered a greatly part of the surveying area. The methods which using to determine the geoidal heights or geodial undulation (N) for the

surveying area. 2. The accuracy of height of the GCPs depends on the accuracy of the instruments that uses. 3. Earth Gravity Model 2008 is the most precise gravity model which is depended for the

determination of the geoid undulation in the work.

4.2. Recommendations Depend on the results obtained, the following recommendations are made:

1. Because of the rapid development of science and technology, the Differential Global Positioning System DGPS (Topcon GNSS RTK HiPer Pro systems) with millimeter accuracy can be used.

2. If the Orthometric heights cannot be observed in the field, it may be calculated their values using the mathematical relationship between the GPS ellipsoid height (h) and EGM 2008 Geoid undulation (Nʹ) of the points.

5. REFERENCES

[1] Ahamed, Abd Elrahim Elgizouli Mohamed. 2013. GPS ellipsoid height calibration to determine the approximate mean sea level (orthometric) height. International Journal of Advanced Research in Engineering and Applied Sciences. 2 (8): 10-20.

[2] Fraczek, W. (2003). Mean sea level, GPS, and the geoid. ArcUsers Online. [3] Anderson, J. M., Anderson, J. M., & Mikhail, E. M. 1998. Surveying, theory and practice. McGraw-Hill

Science/Engineering/Math. [4] Gopi, S. 2007. Advanced Surveying: Total Station, GIS and Remote Sensing. Pearson Education India. [5] Heiskanen, W. A., & Moritz, H. 1967. Physical geodesy. Bulletin Géodésique (1946-1975). 86(1): 491-

492. [6] US Army Corps of Engineering. 2003. Navistar global positioning system surveying, Technical Manual

No. EM1110-1-1003, Washington, D.C., USA. [7] http://earthinfo.nima.mil/ gandg/ wgs84/gravitymod/EGM2008. [8] Ali S. H. 2008. Determination of the orthometric height inside Mosul University campus by using GPS

data and EGM96 geoid model, Mosul. J.Edu. & Sci. 21(2). [9] AL- khashab H.A. and AL-Hindni R.D.,Oct. 2009. Application of GIS for development and

maintenance pipeline network with the aid of GPS, 10th Scientific Conference 24-25, AL-Mansour Journal / No.14/ Special Issue / (Part2).