International Journal of Advancements in Research & Technology, Volume 5, Issue 5, May-2016
ISSN 2278-7763
9
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: sujoy2007@gmail.com
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 reference ellipsoid. The EGM 2008, a global geoid model is widely employed for the purpose yielding sub-metre accuracy. In Papua 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 orthometric 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.
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GPS survey as well as spirit levelling was carried out connecting thirty three control points distributed in the area. The ellipsoidal heights from GPS were transformed to orthometric heights by integrating the EGM 2008 geoid model. The accuracy of orthometric 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
T
HE advent of Global Navigational Satellite System (GNSS)
particularly the Global Positioning System (GPS) has revolutionized 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 orthometric heights are differential levelling which includes Spirit levelling, Trigonometric Levelling, Barometric levelling etc. Spirit
levelling is the workhorse for establishing precise vertical control points usually called Bench Marks (BMs) or Permanent
Survey Marks (PSMs). This method has been expensive, labour-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 faCopyright © 2016 SciResPub.
cilitating conversion of GPS based ellipsoidal heights to corresponding 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 Moresby and Lae) and a number of towns in the country where rapid all round development is taking place. The demand for expansion 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 generating 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
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International Journal of Advancements in Research & Technology, Volume 5, Issue 5, May-2016
ISSN 2278-7763
development is active and thus needs a fairly accurate geodetic network for large scale mapping. There exists an old geodetic 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 surveys in and around Madang have used these points with relatively 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 rectify 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 (tertiary) from a Permanent Survey Mark (PSM), thus providing
corresponding orthometric heights.
10
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 Geodetic Data Base)
UT UTM
Remarks
M
Nort
MSL
Poin LonLatiEasthing
Heig
t
gitude tude
ing
ht
145°
Used as
44'
5° 09'
control
AA
55.301 43.799
3613 94292 391.9
for GPS
053
27"E
52"S
11.1 73.7
0
survey
145°
Used as
48'
5° 13'
control
PSM 25.527 31.595
3677 94222
for level3139 17"E
08"S
98.2
90.9
3.19
ling
145°
Used as
46'
5° 12'
control
GS1
56.193 41.288
3650 94238
for GPS
5495 05"E
23"S
44.7
30.7
4.734
survey
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-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 ellipsoidal 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 Nagada, 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.
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 geodetic 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.
3 MATERIALS USED
3.1 Instruments/Equipments
1 x Micro-Z Ashtech GPS receiver and the
choke ring antenna
Copyright © 2016 SciResPub.
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International Journal of Advancements in Research & Technology, Volume 5, Issue 5, May-2016
ISSN 2278-7763
11
(N). The mathematical relation between H, h and N is:
h = H + N, N is positive when spheroid is above geoid & negative 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.
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 control points along with the coordinates of two base stations
were available for subsequent survey. Subsequent DGPS survey 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 constrained stations.
The processed data from GPS survey provided the UTM easting, UTM northing and ellipsoidal heights of the 33 control
points. The processed data from levelling provided the levelling height of these points. Using the EGM 2008 geoid model,
the geoidal undulation (geoidal separation-N) for the corresponding 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 orthometric 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 conversion 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 provision 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].
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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 improve 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 connected through closed levelling network to provide their orthometric heights. The method followed and the accuracy obtained 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 reference 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
Copyright © 2016 SciResPub.
4.3 Development and Evaluation of a Local
Geoid Model
In this case study the geometric method was employed to develop 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 coordinates 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 generating 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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International Journal of Advancements in Research & Technology, Volume 5, Issue 5, May-2016
ISSN 2278-7763
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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 model 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 accuracy 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.
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Figure II: Local Geoid Surface Model (TIN)
Usually an accuracy of few centimetres is achievable depending 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 levelling heights with 15 points has improved the accuracy of orthometric 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 GNSSRTK system in network is expected to bring the accuracy levels to better then 0.2 m [2] whereas GNSS-RTK system combined 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 developed. 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.
Copyright © 2016 SciResPub.
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International Journal of Advancements in Research & Technology, Volume 5, Issue 5, May-2016
ISSN 2278-7763
13
TABLE 1: ORTHOMETRIC HEIGHTS FROM ELLIPSOIDAL HEIGHT & EGM 2008
SL
No
Station
1
2
ECCE8648
GS15495
3
4
5
6
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 h 1
in m
Difference
in height
(m) (h-h 1 )
365442
365045
9420672.5
9423830.7
83.275
73.013
16.228
5.899
14.500
4.734
1.728
1.165
PSM 14560
364165
9424082.2
PSM 3100
368502
9423727.9
81.784
67.165
14.619
13.315
1.304
72.418
66.943
5.475
5.244
0.231
PSM 3105
367637
PSM 3111
367846.8
9423003.3
73.107
66.972
6.135
5.912
0.223
9422602.9
73.151
66.956
6.195
6.044
0.151
67.047
67.114
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
10
PSM 3139
367798
9422290.9
69.368
66.954
2.414
3.19
11
PSM 3288
365271.5
9421264.8
82.137
67.062
15.075
13.933
12
PSM 3292
366100
9421294.5
73.813
67.022
6.791
5.027
13
PSM 3294
365920
9420920.5
70.574
67.027
3.547
4.454
14
PSM 3297
365593
9421256.8
73.218
67.046
6.172
4.904
15
PSM 3309
16
PSM 3311
17
PSM 3312
18
PSM 5330
19
PSM 8645
20
R100
21
R101
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22
R102
23
24
25
0.687
-
0.776
1.142
1.764
-
0.907
1.268
368180
9423983.9
72.763
66.962
5.801
5.54
0.261
367209
9424119.3
70.817
67.012
3.805
2.555
1.250
367299
9422241.2
73.688
66.977
6.711
5.904
0.807
366311
9424357.7
68.977
67.061
1.916
0.83
1.086
365253
9420298.0
82.895
67.053
15.842
14.45
1.392
365770
9423468.9
70.233
67.071
3.162
1.871
1.291
365725
9422966.9
71.679
67.064
4.615
3.311
1.304
366611
9423728.1
71.794
67.034
4.76
3.328
1.432
R103
R104
R105
365176.5
365021
364825
9421838.8
9421373.8
9421083.6
70.597
71.666
74.333
67.074
67.076
67.082
3.523
4.59
7.251
2.457
3.069
5.791
1.066
1.521
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
30
R109
R112
365427
367844
9420956.1
9423920.1
80.433
70.323
67.051
66.977
13.382
3.346
11.775
2.473
1.607
0.873
31
R113
367364
9423761.1
69.973
66.998
2.975
2.055
0.920
32
33
R114
TUSB
367536
366678
9423481.0
9422069.0
69.469
73.035
66.984
67.004
2.485
6.065
2.052
5.213
0.433
0.852
Maximum error: + 1.7 m,
Copyright © 2016 SciResPub.
Min error = - 0.9 m,
Remarks
RMSE = +/- 1.1 m
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International Journal of Advancements in Research & Technology, Volume 5, Issue 5, May-2016
ISSN 2278-7763
14
TABLE 2: GEOIDAL UNDULATION (N) FROM ELLIPSOIDAL HEIGHT AND ORTHOMETRIC HEIGHT
SL No
Station
1
GS15495
2
UTM Easting
(m)
UTM
(m)
Northing
Height
above
ellipsoid (h) in m
Orthometric (H)
in m
Computed N = h-H
365045
9423830.7
73.013
4.734
68.279
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
15
TUSB
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367844
9423920.1
70.323
2.473
66.977
366678
9422069.0
73.035
5.213
67.822
TABLE 3: ORTHOMETRIC HEIGHTS FROM ELLPSOIDAL HEIGHT AND LOCAL GEOID MODEL (TIN)
SL
No
Station
1
ECCE8648
2
UTM E
UTM N
Height
above
ellipsoid
from
GPS (h)
Computed
Geoidal undulation N
from
local
model (TIN)
Derived
MSL
height
h-N =H
MSL
height
from
Levelling
H1
Error
H-H 1
365442
9420672.5
83.275
67.318
15.957
14.50
-1.457
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
Copyright © 2016 SciResPub.
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International Journal of Advancements in Research & Technology, Volume 5, Issue 5, May-2016
ISSN 2278-7763
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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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May 2007
[3] METIN SOYCAN &.ARZU SOYCAN (2008) ‘Surface modeling for GPSlevelling geoid determination’ Yıldız Technical University, Civil Engineering
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International Journal of Advancements in Research & Technology, Volume 5, Issue 5, May-2016
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