robert rosa, sujoy kumar jana, rabindra kumar das and ...€¦ · thometric heights with minimum...

International Journal of Advancements in Research & Technology, Volume 5, Issue 5, May-2016 9 ISSN 2278-7763

Copyright © 2016 SciResPub. IJOART

EVALUATION OF ORTHOMETRIC HEIGHTS FROM GPS SURVEY USING A GEOID MODEL– A CASE STUDY FOR MADANG, PAPUA NEW GUINEA

Robert Rosa, Sujoy Kumar Jana, Rabindra Kumar Das and Dilip Kumar Pal Department of Surveying and Land Studies, Papua New Guinea University of Technology Contact email: [email protected] ABSTRACT Levelling, the workhorse of precise determination of orthometric heights, is expensive, time consuming and tedious. The Global Positioning System (GPS) has emerged as a successful technology in providing precise position of points on the surface of the earth over the reference ellipsoid with sub-metre level of accuracy. The heights from this are ellipsoidal heights necessitating its transformation into orthometric heights by integrating a geoid model, which provides separation (N) of the geoid with the ref-erence ellipsoid. The EGM 2008, a global geoid model is widely employed for the purpose yielding sub-metre accuracy. In Pa-pua New Guinea (PNG) the demand of large scale maps with one or two metre contour interval is ever increasing particularly for urban infrastructure development. Therefore it has become imperative to optimize the use of GPS in derivation of the or-thometric heights with minimum leveling and the present study has been contrived in tune with this where Madang town of PNG, a fast developing town in the country, has been taken up as the study area.

GPS survey as well as spirit levelling was carried out connecting thirty three control points distributed in the area. The ellipsoi-dal heights from GPS were transformed to orthometric heights by integrating the EGM 2008 geoid model. The accuracy of or-thometric heights was found to be about a meter. Also a local geoid model was developed using 15 points from the cited 33 points. The heights of remaining 18 points were used for checking the efficacy of the local model where notable improvement in accuracy level to 0.6 m has been achieved. Keywords : Ellipsoidal height, Orthometric height, Geoidal separation, Geoid model, EGM 2008

1 INTRODUCTION

HE advent of Global Navigational Satellite System (GNSS) particularly the Global Positioning System (GPS) has revo-

lutionized geodetic surveying by providing precise horizontal and vertical locations of points of the order of sub-metres on the reference ellipsoid (e.g. the WGS 84). The vertical location is the height above the ellipsoid and known as ellipsoidal height (h) whereas for surveying and mapping applications it is the orthometric height (H), which matters the most. The orthometric heights are with regard to the Geoid represented by the Mean Sea Level (MSL) and popularly known as MSL heights. Conventional methods of determination of orthomet-ric heights are differential levelling which includes Spirit lev-elling, Trigonometric Levelling, Barometric levelling etc. Spirit levelling is the workhorse for establishing precise vertical con-trol points usually called Bench Marks (BMs) or Permanent Survey Marks (PSMs). This method has been expensive, la-bour-intensive and time consuming and therefore efforts are made to find the orthometric heights by transforming the GPS derived ellipsoidal heights via an accurate geoid model. A number of local, regional and global geoid models came up, out of which Earth Gravity Model 2008 (EGM 2008) - a global geoid model developed by NIMA (National Imagery and Mapping Agency, USA) is the most popular global model fa-

cilitating conversion of GPS based ellipsoidal heights to corre-sponding orthometric heights with sub-meter level of accuracy [9,4].

The Papua New Guinea (PNG) is one of the fast developing countries in Oceania region. There are two cities (Port Mores-by and Lae) and a number of towns in the country where rap-id all round development is taking place. The demand for ex-pansion of infrastructure for development is ever increasing. Therefore physical planning of these areas needs large scale mapping with contour interval of 2 - 5 m or better. This calls for establishment of a geodetic network including orthometric heights which in turn enables proper design of infrastructures such as roads, bridges, building etc. A fairly accurate geodetic network exists for most of the cities and towns of the country with limitations in vertical accuracy. Madang, the capital of Madang Province is a fairly low lying coastal town in the North region of PNG with very good tourist attraction sites, and the home province of two mining locations that are gen-erating revenue for the country. This province is also home to the Pacific Marine Industrial Zone Project (PMIZ), the second fish cannery in Madang. It is one of the emerging towns in the country contributing to the national economy where physical

T

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development is active and thus needs a fairly accurate geodet-ic network for large scale mapping. There exists an old geodet-ic network – the Permanent Survey Marks (PSMs) but with unsatisfactory vertical accuracy. PSMs are used for all survey connections as a requirement to have at least a pair of points connected to all new subdivision surveys and connected to other surveys within the vicinity of old surveys. All past sur-veys in and around Madang have used these points with rela-tively lower accuracy in heights. The permanent survey mark sketches in the National Mapping Bureau of PNG indicated different series of heights. The vertical height system of Madang was identified to be inconsistent with the standards of geodetic network and a resurvey with the application of GNSS/GPS may be required to re-evaluate, identify and recti-fy the problem. Under this background, Madang area has been taken up in this study with the objectives:

-To establish a number of geodetic control points (horizontal and vertical) in and around Madang town using the state-of the art GPS technology. The orthometric heights of these points will be deduced from the ellipsoidal heights by using the global geoid model, the EGM 2008.

-These control points will be connected by spirit levelling (ter-tiary) from a Permanent Survey Mark (PSM), thus providing corresponding orthometric heights.

-The orthometric heights of levelling will be compared with the deduced orthometric heights from GPS survey to evaluate the accuracy.

-Some of the heights of levelling will be independently used to define a local geoid model along with the corresponding ellip-soidal heights. The remaining heights will be used to check the accuracy of the local geoid model.

2 STUDY AREA The study area is about 25 sq. km bounded between 5° 09' to 5° 15.5' South latitude and 145° 44' to 145° 51' East longitude (Figure I). The area is mainly on the Geodetic Network of Madang but the tide-gauge location that is connected to the PNG 94 geodetic datum for the vertical component, is at Na-gada, located on 5° 09 °20.8” S latitude and 145° 47 '59.6” E longitude. Extending to the west there is a geodetic station (AA053) at Nobanomb based on PNG94. This station is located on 5° 09' 43.8” S latitude and 145° 44' 55.3” E longitude. The topography of the study area is characterized with gentle slopes and validation stations were carefully selected along slopes of interest to enable analysis of varying elevations.

3 MATERIALS USED 3.1 Instruments/Equipments

1 x Micro-Z Ashtech GPS receiver and the choke ring antenna

1 x Pro Mark 100 Ashtech GNSS receiver 1 x Pro Mark 200 Ashtech GNSS receiver 1x Leica Runner 24 Auto level 2 x E graduated levelling staves 2 x Staff Bubbles

3.2 Software - The GNSS Solutions Software - Alltrans EGM 2008 Software - ARCGIS software - AUSPOS facility

3.3 Data

Coordinates of Base Stations (Source: National Mapping Geo-detic Data Base)

Point

Lon-gitude

Lati-tude

UTM

East-ing

UTM Northing

MSL Heig

ht

Remarks

AA 053

145° 44' 55.30127"E

5° 09' 43.79952"S

361311.1

9429273.7

391.90

Used as control

for GPS survey

PSM 3139

145° 48' 25.52717"E

5° 13' 31.59508"S

367798.2

9422290.9 3.19

Used as control

for level-ling

GS15495

145° 46' 56.19305"E

5° 12' 41.28823"S

365044.7

9423830.7 4.734

Used as control

for GPS survey

4.0 METHODOLOGY 4.1 Field Observations and Processing:

Thirty three (33) Ground Control Points (GCPs) are planned using the old cadastral map and satellite images. These 33 points include one base station (GS 15495) which falls within the study area. Another base station (AA 053) was also used in the survey. This point falls outside the study area. The geodet-ic latitude and longitude of the base stations are available in terms of PNG 94 horizontal datum including corresponding UTM coordinates. Field visit was carried out for locating and marking the 33 points on ground. The selection of the points were done keeping in view of uniform spatial distribution as well as the range of topographic variation. The distribution of the control points is provided in Figure I.

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Figure I: Overview of the study area and distribution of cotrol

point DGPS survey has been adopted in the study. Three available GPS receivers were utilized simultaneously to carry out the survey. In the first phase two of the receiver/antenna was placed over the two coordinated base stations and one receiver was used as rover to establish three more control points. The epoch interval and mask angle set were 10 seconds and 15o respectively. The common observation time between the base stations and other three stations was minimum 30 minutes. After processing of this the coordinates of the three new con-trol points along with the coordinates of two base stations were available for subsequent survey. Subsequent DGPS sur-vey was carried out for establishing coordinates of remaining 29 points. For this at least two stations from the five were used as base stations and at processing level they were used as con-strained stations. GNSS Solutions software was the major software used here for processing the field observations. AUSPOS Points Positioning Processing Facility was availed at the processing level to im-prove the accuracy by connecting to IGS stations. The Alltrans EGM 2008 software was used for obtaining geoidal undulation (N). The levelling of the area was carried out using an auto level. Point No PSM 3139 was used as control point for levelling. All the thirty three points selected for DGPS survey were connect-ed through closed levelling network to provide their ortho-metric heights. The method followed and the accuracy ob-tained was with respect to tertiary levelling standards. The final adjusted heights of all the 33 points are provided in Table 1. 4.2 Orthometric heights from ellipsoidal heights and Geoid Model

The GPS derived heights are ellipsoidal heights (h) on the ref-erence ellipsoid. The orthometric heights (H) are levels with respect to geoid (MSL). The separation of the geoid and the reference ellipsoid is known as geoidal undulation/separation

(N). The mathematical relation between H, h and N is: h = H + N, N is positive when spheroid is above geoid & nega-tive when it is below [8}. A geoid model defines the geoid with respect to the reference spheroid and thus provides the value of N at any location on the surface of the earth. EGM 2008 is the most popular global geoid model available to user community. This model is an improvement over the EGM 96. Over areas covered with high quality gravity data, the discrepancies between EGM 2008 geoid undulations and independent GPS/Levelling values are reported to be order of centimetre level. The reference ellipsoid WGS 84 for PNG is below the EGM 2008 geoid and has separation (N) ranging between 84.5 to 59.5 meters. For the study area, the Madang town, the N value ranges from 66.93 m to 67.17 m.

The processed data from GPS survey provided the UTM east-ing, UTM northing and ellipsoidal heights of the 33 control points. The processed data from levelling provided the level-ling height of these points. Using the EGM 2008 geoid model, the geoidal undulation (geoidal separation-N) for the corre-sponding points were obtained. The orthometric height of these points are computed using the ellipsoid height and the geoidal undulation. These heights are compared with the or-thometric heights obtained from levelling. The difference in these two was used to compute the Root Mean Square Error (RMSE) thus assessing the accuracy of EGM 2008 for conver-sion of ellipsoidal height to orthometric height (Table 1). The RMSE obtained here is about 1 m. Using EGM 2008, normally the accuracy of orthometric heights is expected to be better than 20 cm provided that adequate gravity data was available at the time of development of this model. However in many areas like Papua New Guinea, neither adequate gravity data was available nor was the deficiency supplemented by provi-sion of sufficient levelling data of precise order. Therefore the accuracy of about 1 m is in expected lines and conforms to a number of studies [6]. 4.3 Development and Evaluation of a Local Geoid Model

In this case study the geometric method was employed to de-velop a local geoid model specific to Madang. Out of the 33 control points, 15 were selected to develop the local geoid model and remaining 18 points were kept aside for quality checking. The points selected are uniformly distributed over the complete area. The GPS based ellipsoidal heights and the levelling based orthometric heights of the 15 points are used to compute the geoidal separation N (Table:2) The UTM co-ordinates and the N values are used to develop a surface model similar to Digital Elevation Model (DEM). The ARCGIS based 3 D analysis tool is used to develop this surface model. Two interpolation techniques are used at the time of generat-ing the surface model viz. the TIN and Krigging [3]. The visual display of TIN model is provided in Figure II. It displays the

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representation of N in format of contours with an interval of 0.1 m. These figures show the distribution of the 15 points used for modelling as well as 18 points used for checking. For quality assessment, the geoidal undulation (N) of the left out 18 points was computed from the developed local geoid model. This was used in computing the orthometric heights from the ellipsoid height. The so computed orthometric heights are compared with the corresponding levelling heights thus providing an assessment of the quality of the geoid mod-el developed in this exercise. The details of this are provided in Table 3. From the results it appears that the RMSE of these 18 check points is of the order of +/- 0.62 m and +/- 0.65 m for the TIN and Krigging interpolation techniques respectively. Therefore there is a notable improvement in using the developed local geoid model in comparison with the global geoid model EGM 2008.

5.0 DISCUSSIONS & CONCLUSION The transformation of orthometric heights by using the global geoid model EGM 2008 are found to be about +/- 1 m (RMSE level) when compared with the levelling heights. The use of EGM 2008 provides centimetre level of accuracy where enough gravity data was available at the time of development of this model. However case studies show that with this geoid model at least 1 m accuracy is achievable [9]. This level of ac-curacy of about a metre is acceptable for Papua New Guinea considering the sparse availability of gravity data as well as accurate level data. This accuracy level when translated to possible contour interval can provide contour survey with intervals of about 3 meters. Therefore the GPS based levelling may replace the conventional levelling for contour surveys where this interval is adequate. Usually an accuracy of few centimetres is achievable depend-ing upon the methodology, type of GNSS/GPS receiver used, the geoid model employed etc. [5, 11, 1,10]. From the study it is further demonstrated that the local geoid model developed here using geometric methods, ellipsoidal heights and level-ling heights with 15 points has improved the accuracy of or-thometric heights to notable extent in comparison to EGM 2008. The RMSE of 0.6 m obtained in this case is in consistency with the previously developed PNG 2008 geoid model where the EGM 2008 was modified with some geometric heights for PNG. Use of more sophisticated techniques such as GNSS-RTK system in network is expected to bring the accuracy lev-els to better then 0.2 m [2] whereas GNSS-RTK system com-bined with laser system is expected to further improve the accuracy [7]. However, the achieved accuracy of 0.6 m can be translated to possible contour interval of 2 m. Therefore, DGPS survey may be adopted for populating with more control points including heights once the local geoid model is devel-oped. This will facilitate the requirement of control points particularly heights for urban areas where normally points at 200/100 m spacing for flat conditions are essential.

Figure II: Local Geoid Surface Model (TIN)

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TABLE 1: ORTHOMETRIC HEIGHTS FROM ELLIPSOIDAL HEIGHT & EGM 2008

SL No

Station UTM Easting

UTM Northing

Ellipsoidal height (H) in m

Geoidal separation from EGM 2008 ( N) in m

Computed orthometric height h = H-N in m

Orthometric height from levelling h1 in m

Difference in height (m) (h-h1)

Remarks

1 ECCE8648 365442 9420672.5 83.275 67.047 16.228 14.500 1.728 2 GS15495 365045 9423830.7 73.013 67.114 5.899 4.734 1.165

3 PSM 14560 364165 9424082.2 81.784 67.165 14.619 13.315 1.304

4 PSM 3100 368502 9423727.9 72.418 66.943 5.475 5.244 0.231

5 PSM 3105 367637 9423003.3 73.107 66.972 6.135 5.912 0.223

6 PSM 3111 367846.8 9422602.9 73.151 66.956 6.195 6.044 0.151

7 PSM 3112 367682 9422625.5 73.694 66.964 6.73 5.807 0.923

8 PSM 3134 366243 9422505.2 71.658 67.031 4.627 4.369 0.258 9 PSM 3136 366604.8 9422618.2 72.358 67.016 5.342 4.655 0.687

10 PSM 3139 367798 9422290.9 69.368 66.954 2.414 3.19 - 0.776 11 PSM 3288 365271.5 9421264.8 82.137 67.062 15.075 13.933 1.142

12 PSM 3292 366100 9421294.5 73.813 67.022 6.791 5.027 1.764

13 PSM 3294 365920 9420920.5 70.574 67.027 3.547 4.454 - 0.907

14 PSM 3297 365593 9421256.8 73.218 67.046 6.172 4.904 1.268

15 PSM 3309 368180 9423983.9 72.763 66.962 5.801 5.54 0.261

16 PSM 3311 367209 9424119.3 70.817 67.012 3.805 2.555 1.250

17 PSM 3312 367299 9422241.2 73.688 66.977 6.711 5.904 0.807

18 PSM 5330 366311 9424357.7 68.977 67.061 1.916 0.83 1.086

19 PSM 8645 365253 9420298.0 82.895 67.053 15.842 14.45 1.392

20 R100 365770 9423468.9 70.233 67.071 3.162 1.871 1.291

21 R101 365725 9422966.9 71.679 67.064 4.615 3.311 1.304

22 R102 366611 9423728.1 71.794 67.034 4.76 3.328 1.432

23 R103 365176.5 9421838.8 70.597 67.074 3.523 2.457 1.066 24 R104 365021 9421373.8 71.666 67.076 4.59 3.069 1.521 25 R105 364825 9421083.6 74.333 67.082 7.251 5.791 1.460 26 R106 364809.5 9422565.5 71.338 67.103 4.235 3.177 1.058

27 R107 364770 9420634.9 74.134 67.079 7.055 5.867 1.188

28 R108 364968 9420656.3 79.67 67.07 12.6 11.547 1.053

29 R109 365427 9420956.1 80.433 67.051 13.382 11.775 1.607 30 R112 367844 9423920.1 70.323 66.977 3.346 2.473 0.873 31 R113 367364 9423761.1 69.973 66.998 2.975 2.055 0.920

32 R114 367536 9423481.0 69.469 66.984 2.485 2.052 0.433 33 TUSB 366678 9422069.0 73.035 67.004 6.065 5.213 0.852 Maximum error: + 1.7 m, Min error = - 0.9 m, RMSE = +/- 1.1 m

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TABLE 2: GEOIDAL UNDULATION (N) FROM ELLIPSOIDAL HEIGHT AND ORTHOMETRIC HEIGHT

SL No Station UTM Easting (m)

UTM Northing (m)

Height above ellipsoid (h) in m

Orthometric (H) in m

Computed N = h-H

1 GS15495 365045 9423830.7 73.013 4.734 68.279

2 PSM 14560 364165 9424082.2 81.784 13.315 68.369

3 PSM 3100 368502 9423727.9 72.418 5.244 67.174

4 PSM 3105 367637 9423003.3 73.107 5.912 67.195

5 PSM 3134 366243 9422505.2 71.658 4.369 67.289

6 PSM 3139 367798 9422290.9 69.368 3.19 66.178

7 PSM 3292 366100 9421294.5 73.813 5.027 68.786

8 PSM 3294 365920 9420920.5 70.574 4.454 66.120

9 PSM 5330 366311 9424357.7 68.977 0.83 68.147

10 PSM 8645 365253 9420298.0 82.895 14.45 68.445

11 R100 365770 9423468.9 70.233 1.871 68.372

12 R106 364810 9422565.5 71.338 3.177 68.161

13 R107 364770 9420634.9 74.134 5.857 67.079

14 R112 367844 9423920.1 70.323 2.473 66.977

15 TUSB 366678 9422069.0 73.035 5.213 67.822

TABLE 3: ORTHOMETRIC HEIGHTS FROM ELLPSOIDAL HEIGHT AND LOCAL GEOID MODEL (TIN)

SL No

Station UTM E UTM N Height above ellipsoid from GPS (h)

Computed Geoidal un-dulation N from local model (TIN)

Derived MSL height h-N =H

MSL height from Levelling H1

Error H-H1

1 ECCE8648 365442 9420672.5 83.275 67.318 15.957 14.50 -1.457

2 PSM 3111 367846.8 9422602.9 73.151 66.50 6.651 6.040 0.611

3 PSM 3112 367682 9422625.5 73.694 66.725 6.966 5.807 1.162

4 PSM 3136 366604.8 9422618.2 72.358 67.281 5.070 4.655 0.422

5 PSM 3288 365271.5 9421264.8 82.137 68.438 13.699 13.933 -0.234

6 PSM 3297 365593 9421256.8 73.218 68.574 4.644 4.904 -0.260

7 PSM 3309 368180 9423983.9 72.763 68.127 4.636 5.54 -0.904

8 PSM 3311 367209 9424119.3 70.817 68.555 2.262 2.55 -0.288

9 PSM 3312 367299 9422241.2 73.688 66.962 6.726 5.90 0.826

10 R101 365725 9422966.9 71.679 67.975 3.722 3.31 0.412

11 R102 366611 9423728.1 71.794 67.895 3.899 3.33 0.569

12 R103 365176.5 9421838.8 70.597 68.362 2.235 2.46 -0.225

13 R104 365021 9421373.8 71.666 68.325 3.341 3.07 0.271

14 R105 364825 9421083.6 74.333 68.261 6.072 5.79 0.282

16 R108 364968 9420656.3 79.67 67.963 11.707 11.55 0.157

16 R109 365427 9420956.1 80.433 68.486 11.947 11.78 0.167

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17 R113 367364 9423761.1 69.973 68.155 1.818 2.06 -0.242

18 R114 367536 9423481.0 69.469 67.867 1.602 2.05 -0.448

RMSE = +/- 0.62 m

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[2] Donald C.T.CHOI, James Y.K.WONG, Ben S.B.CHAN (2007)’ Investigation on GPS Heighting Accuracy with the use of Hong Kong Satellite Positioning Reference Station Network (SatRef)’ TS 5A –GNSS 2, Strategic Integration of Surveying Services, FIG Working Week 2007. Hong Kong SAR, China, 13-17 May 2007

[3] METIN SOYCAN &.ARZU SOYCAN (2008) ‘Surface modeling for GPS-levelling geoid determination’ Yıldız Technical University, Civil Engineering Faculty Geodesy and Photogrametry Engineering Division, Beşik-taş/İSTANBUL: retrieved: http://www.isgeoid.polimi.it/Newton/Newton_1/soycan.pdf

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[5] Omar Al-Bayari and Abdallah Al-Zoubi (2007) ‘ Preliminary study of the Gravimetric Local Geoid Model in Jordan: A case study (GeoJordan Model), Annals of Geophysics, VOL. 50, N. 3, June 2007:PhD Thesis, Dept. of Land Surveying and Geoinformatics, Hongkong Polytechnic University

[6] R.V. Komarov, R.A. Kascheev & R.V. Zagretdinov (2007) ‘Geoid Determina-tion by GPS/Levelling Method in the Republic of Tatarstan’ International Journal of Science Georesources, 2(10), 2007, 43-45

[7] Rinaldo Paar, Mladen Zrinjski, Ante Marendić (2011) Quality check of verti-cal component using GPS RTK method and laser system’ Geodetski Vestnik, 55(4), 689-700

[8] Smith James R. (1997) ‘Introduction to Geodesy – the History and Concepts of Modern Geodesy’ John Wiley and Sons Inc.

[9] Uzodinma, V.N., Oguntuase J.O, Onah E., Chike C., and Ehigiator R (2014) ‘Validation of EGM2008-Based Orthometric Heights in a Micro Environment in Nigeria’), FIG Congress 2014, Engaging the Challenges – Enhancing the Relevance, KualaLumpur, Malaysia 16--‐21 June 2014

[10] Yang Zhangi (1999)’ Precise determination of local geoid and its geophysical interpretation’

[11] Yong-Qi Chen and Zhicai Luo (2004) ‘A hybrid method to determine a local geoid model—Case study’ Earth Planets Space, 56, 419-427, 2004.

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