Earth Gravitational Model 2008

TABLE OF CONTENTS.

CONTENTS PAGES

INTRODUCTION 1-9

RESULTS

FKKSA

I. GDM2000 RSO (NEW)

II. GDM2000 MRT48

III. MRT48 RSO OLD

HELIPAD

I. GDM2000 RSO (NEW)

II. GDM2000 MRT48

III. MRT48 RSO (OLD)

ELLIPSOIDAL HEIGHT,GEIOD HEIGHT AND ORTHOMETRIC HEIGHT (FKKSA)

ELLIPSOIDAL HEIGHT,GEIOD HEIGHT AND ORTHOMETRIC HEIGHT (HELIPAD)

10-11

12-13

14-15

16-17

18-19

20-21

22-23

24-25

26-27

28-29

PLOTING 2D IMAGE AND CONTOUR

I. FKKSA

II. HELIPAD

30-32

33-35

CONCLUSION 36

COORDINATES AND HEIGHT | 0

EARTH GRAVITATIONAL MODEL 2008 (EGM2008)

EGM2008 is a spherical harmonic model of the Earth's gravitational potential, developed

by a least squares combination of the ITG-GRACE03S gravitational model and its associated

error covariance matrix, with the gravitational information obtained from a global set of area-

mean free-air gravity anomalies defined on a 5 arc-minute equiangular grid. This grid was

formed by merging terrestrial, altimetry-derived, and airborne gravity data. Over areas where

only lower resolution gravity data were available, their spectral content was supplemented with

gravitational information implied by the topography. EGM2008 is complete to degree and order

2159, and contains additional coefficients up to degree 2190 and order 2159. Over areas covered

with high quality gravity data, the discrepancies between EGM2008 geoid undulations and

independent GPS/Leveling values are on the order of ±5 to ±10 cm. EGM2008 vertical

deflections over USA and Australia are within ±1.1 to ±1.3 arc-seconds of independent

astrogeodetic values. These results indicate that EGM2008 performs comparably with

contemporary detailed regional geoid models. EGM2008 performs equally well with other

GRACE-based gravitational models in orbit computations. Over EGM96, EGM2008 represents

improvement by a factor of six in resolution, and by factors of three to six in accuracy,

depending on gravitational quantity and geographic area. EGM2008 represents a milestone and a

new paradigm in global gravity field modeling, by demonstrating for the first time ever, that

given accurate and detailed gravimetric data, a single global model may satisfy the requirements

of a very wide range of applications.


EARTH GRAVITATIONAL MODEL 1996(EGM96)

EGM96 (Earth Gravitational Model 1996) is a geopotential model of the Earth consisting of

spherical harmonic coefficients complete to degree and order 360. It is a composite solution,

consisting of a combination solution to degree and order 70, a block diagonal solution from

degree 71 to 359 and the quadrature solution at degree 360.This model is the result of

collaboration between the National Imagery and Mapping Agency (NIMA), the NASA Goddard

Space Flight Center (GSFC), and Ohio State University. The joint project took advantage of new

surface gravity data from many different regions of the globe, including data newly released

from the NIMA archives. Major terrestrial gravity acquisitions by NIMA since 1990 include

airborne gravity surveys over Greenland and parts of the Arctic and the Antarctic, surveyed by

the Naval Research Lab (NRL) and cooperative gravity collection projects, several which were

undertaken with the University of Leeds. These collection efforts have improved the data

holdings over many of the world's land areas, including Africa, Canada, parts of South America

and Africa, Southeast Asia, Eastern Europe, and the former Soviet Union. In addition, there have

been major efforts to improve NIMA's existing 30' mean anomaly database through contributions

over various countries in Asia.


MYGEOID

GPS infrastructures that have been established in Malaysia are mainly served as a ground

control stations for cadastral and mapping purposes. Another element that has not been utilized is

the height component due to its low accuracy. Conventional leveling is still the preferred method

by the land surveyors to determine the stations orthometric height (H) with a proven accuracy.

Therefore, Department of Survey and Mapping Malaysia (DSMM) has embarked the Airborne

Gravity Survey, with one of the objectives is to compute the local precise geoid for Malaysia

within centimeter level of accuracy. With the availability of the precise geoid, the “missing”

element of GPS system is solved.

The Malaysian geoid project (MyGEOID) is unique where the whole country is covered

by with dense airborne gravity, with the aim to make the best possible national geoid model. The

basic underlying survey and computation work of the Malaysian geoid project was done by

Geodynamics Dept. of the Danish National Survey and Cadastral (KMS; since Jan 1 part of the

Danish National Space Center) in cooperation with JUPEM. With the new data the geoid models

are expected to be much improved over earlier models (Kadir et al. 1998).


The main objective of the Malaysian geoid model (MyGEOID) is to be able to compute

orthometric heights H that refer to the national geodetic vertical datum (NGVD).

Mathematically, there is a simple relation between the two reference systems (neglecting the

deflection of the vertical and the curvature of the plumb line);

where, hGPS is the GPS height above the ellipsoid and N the geoid separation. In the above

equation it is important to realize that H refers to a local vertical datum, hGPS refers to a

geocentric system (ITRF/ WGS84), to which the computed (gravimetric) geoid also usually

refers.In practice, the expression shows the possibility of using GPS leveling technique, knowing

the geoidal height N, the orthometric height H can be calculated from ellipsoidal height h.

Deriving orthometric height using this technique with certain level of accuracy, could replace

conventional spirit leveling and therefore make the leveling procedures cheaper and faster. The

existence of datum bias (differences between geoid and local mean sea level) will not give

satisfactory results if based on the above formula. In order to overcome this problem, fitting the

gravimetric geoid onto the local mean sea level (NGVD) will minimize the effect of datum

biases.

The Malaysian gravimetric geoid is apparent accurate to few cm r.m.s, with larger errors

closer to the international borders (Forsberg, 2005). The geoid is fitted to GPS leveling

information, and any errors in H Leveling and hGps, will directly affect the high quality of the

gravimetric geoid; in other cases it will help control longer wavelength errors. The balance

between fit of GPS, and errors in geoid and GPS, is delicate, and undoubtedly there will be many

regions in the present geoid where GPS users can expect problems due to fitting of GPS-leveling

data with errors. Based on the statistical analyses, it can be concluded that the accuracy of fitted

geoid models of WMGeoid04 and EMGeoid05 is 0.033 and 0.042 meter respectively, and can be

used for height determination. To achieved certain level of accuracy in determination of

orthometric height (H), accuracy of observed GPS network has to be better than 1 ppm

(relatively) and the vertical errors (95% Conf. Region) have to be less than 3 cm


Real Time Kinematic (RTK) survey and MyRTKnet service provided by DSMM with 3

cm level of accuracy can make use of the models for engineering survey, rapid height monitoring

and establishing leveling route.

Fitted geoid model WMGeoid04 and EMGeoid05 is the product of GPS on Benchmark

observation. In order to improve the results and to achieve 1cm geoid, the recommendations

listed below need further considerations:-

i. New GPS observation on Standard Benchmark (SBM) to dandify current GPS leveling

Network, with the distribution between ˜ 10 km nations wide.

ii. The existing Precise leveling Network based on spirit leveling carried out from 1985 to

1995. The leveling networks need to be carefully analyzed, and possibility of carry out a

new adjustment including analysis of subsidence and land uplift.

iii. Resurvey by leveling and GPS of selected, suspected erroneous points with large

geoid outliers. iv. If long GPS observation is needed, GPS processing software must be

capable of producing the solution with the statistic and to model the troposphere with the

adequate parameters.

v. Make a new GPS-fitted version of the gravimetric geoid as new batches of GPS-

leveling data become available, and as GPS users report problem regions for heights.

vi. GPS leveling technique need the antenna height measure correctly. The use of stable

Bipod with fixed antenna height will minimize the error especially with the shorter

baselines.

vii. Leveling route is always following the federal and states road, hence, the BMs are

established along the roadside, which the clearance of 15° is difficult to get. To overcome

this situation, the use of stable Bipod with more than 2 meter will certainly solve the

problems and also minimize the disturbance of vehicle passing by.


DATUM AND COORDINATES TRANSFORMATION


MRT 48

WGS 84GDM 2000

RSO (OLD) CASSINI (0LD)

RSO (NEW)

CASSINI (NEW)

In geometry, a coordinate system is a system which uses one or more numbers, or

coordinates, to uniquely determine the position of a point or other geometric element on a

manifold such as Euclidean space. The order of the coordinates is significant and they are

sometimes identified by their position in an ordered tuple and sometimes by a letter, as in 'the x-

coordinate'. In elementary mathematics the coordinates are taken to be real numbers, but may be

complex numbers or elements of a more abstract system such as a commutative ring. The use of

a coordinate system allows problems in geometry to be translated into problems about numbers

and vice versa; this is the basis of analytic geometry. An example in everyday use is the system

of assigning longitude and latitude to geographical locations. In physics, a coordinate system

used to describe points in space is called a frame of reference.

Cartesian coordinate system

The prototypical example of a coordinate system is the Cartesian coordinate system. In the plane,

two perpendicular lines are chosen and the coordinates of a point are taken to be the signed

distances to the lines.

In three dimensions, three perpendicular planes are chosen and the three coordinates of a point

are the signed distances to each of the planes. This can be generalized to create n coordinates for

any point in n-dimensional Euclidean space.


http://en.wikipedia.org/wiki/Euclidean_space

http://en.wikipedia.org/wiki/Perpendicular

http://en.wikipedia.org/wiki/Plane_(geometry)

http://en.wikipedia.org/wiki/File:Rectangular_coordinates.svg

Transformations between coordinate systems

Because there are often many different possible coordinate systems for describing geometrical

figures, it is important to understand how they are related. Such relations are described by

coordinate transformations which give formulas for the coordinates in one system in terms of the

coordinates in another system. For example, in the plane, if Cartesian coordinates (x, y) and

polar coordinates (r, θ) have the same origin, and the polar axis is the positive x axis, then the

coordinate transformation from polar to Cartesian coordinates is given by x = r cosθ and y = r

sinθ.

Coordinate curves and surfaces

In two dimensions if all but one coordinates in a point coordinate system is held constant

and the remaining coordinate is allowed to vary, then the resulting curve is called a coordinate

curve (some authors use the phrase "coordinate line"). This procedure does not always make

sense, for example there are no coordinate curves in a homogeneous coordinate system. In the

Cartesian coordinate system the coordinate curves are, in fact, lines. Specifically, they are the

lines parallel to one of the coordinate axes. For other coordinate systems the coordinates curves

may be general curves. For example the coordinate curves in polar coordinates obtained by

holding r constant are the circles with center at the origin. Coordinates systems for Euclidean

space other than the Cartesian coordinate system is called curvilinear coordinate systems.

In three dimensional spaces, if one coordinate is held constant and the remaining

coordinates are allowed to vary, then the resulting surface is called a coordinate surface. For

example the coordinate surfaces obtained by holding ρ constant in the spherical coordinate

system are the spheres with center at the origin. In three dimensional space the intersection of

two coordinate surfaces is a coordinate curve. Coordinate hyper surfaces are defined similarly in

higher dimensions.



RESULTS

GDM 2000 FKKSA

Latitude Longitude Height1 1.563089 103.6401 42.658792 1.563123 103.6400 43.340633 1.563145 103.6400 43.617774 1.563150 103.6400 43.618365 1.563174 103.6400 44.182626 1.563123 103.6401 43.667197 1.563147 103.6401 44.562708 1.563141 103.6401 44.279699 1.563157 103.6401 44.7027310 1.563177 103.6400 45.2226611 1.563201 103.6400 45.1080112 1.563190 103.6400 45.4900413 1.563217 103.6400 45.4220714 1.563199 103.6400 45.4986315 1.563212 103.6400 45.4804716 1.563243 103.6400 45.6818417 1.563262 103.6400 45.7361318 1.563264 103.6400 45.6871119 1.563291 103.6400 46.3640620 1.563281 103.6399 45.8800821 1.563259 103.6399 45.7460922 1.563243 103.6399 45.7959023 1.563226 103.6399 45.7664124 1.563208 103.6399 45.7449225 1.563211 103.6399 45.7470726 1.563221 103.6399 45.8359427 1.563243 103.6399 45.8084028 1.563259 103.6399 45.7484429 1.563281 103.6399 45.8279330 1.563232 103.6399 45.8839831 1.563246 103.6399 45.9138732 1.563272 103.6399 45.8328133 1.563274 103.6399 45.7703134 1.563281 103.6399 45.8410235 1.563312 103.6400 46.0611336 1.563302 103.6399 46.0404337 1.563299 103.6399 45.9105538 1.563294 103.6399 45.7843839 1.563284 103.6399 46.00859


40 1.563280 103.6399 45.9902341 1.563268 103.6399 45.9091842 1.563260 103.6399 45.8806643 1.563260 103.6399 45.8919944 1.563253 103.6399 45.8148445 1.563290 103.6399 46.6648446 1.563297 103.6399 47.0744147 1.563300 103.6399 47.1648448 1.563305 103.6399 47.2005949 1.563298 103.6399 46.5187550 1.563310 103.6399 47.0587951 1.563313 103.6399 47.1369152 1.563307 103.6399 46.5302753 1.563316 103.6399 46.9230554 1.563311 103.6399 46.4648455 1.563319 103.6399 47.0054756 1.563317 103.6399 46.5082057 1.563322 103.6399 46.9125058 1.563324 103.6400 46.6070359 1.563358 103.6399 48.9007860 1.563358 103.6399 48.8972761 1.563377 103.6399 49.0949262 1.563364 103.6399 49.0236363 1.563364 103.6399 49.0181664 1.563345 103.6399 48.9123065 1.563354 103.6399 49.0638766 1.563338 103.6399 48.9636767 1.563338 103.6399 48.9226668 1.563348 103.6399 49.0033269 1.563341 103.6399 49.0212970 1.563329 103.6399 48.8503971 1.563321 103.6399 48.8248072 1.563334 103.6399 48.9695373 1.563340 103.6399 49.0173874 1.563256 103.6400 46.3189575 1.563256 103.6400 46.3175876 1.563178 103.6401 45.7464877 1.563161 103.6401 45.64219


GDM2000 RSO (New)

Northing Easting1 172859.8 627058.72 172863.5 627056.03 172866.0 627054.94 172866.6 627052.85 172869.2 627053.86 172863.6 627061.77 172866.3 627063.08 172865.6 627060.49 172867.3 627058.710 172869.5 627056.111 172872.3 627056.512 172871.0 627054.313 172874.0 627054.014 172872.0 627050.615 172873.5 627051.316 172876.8 627048.917 172879.0 627050.318 172879.2 627052.019 172882.1 627053.820 172881.0 627046.521 172878.6 627045.822 172876.9 627044.323 172875.0 627044.624 172873.0 627042.625 172873.4 627041.526 172874.4 627042.127 172876.9 627044.328 172878.6 627045.829 172881.0 627046.530 172875.7 627038.531 172877.2 627041.532 172880.o 627042.233 172880.3 627043.634 172881.0 627046.535 172884.5 627048.136 172883.4 627045.937 172883.0 627044.838 172882.5 627042.839 172881.4 627040.940 172881.0 627039.9


41 172879.6 627040.542 172878.8 627038.943 172878.8 627038.944 172878.0 627036.845 172882.0 627038.146 172882.9 627038.047 172883.2 627039.248 172883.8 627040.249 172882.9 627040.650 172884.2 627041.551 172884.7 627042.652 172884.0 627042.953 172884.9 627043.954 172884.4 627044.155 172885.3 627045.356 172885.0 627046.857 172885.6 627046.658 172885.9 627048.959 172889.6 627046.660 172889.6 627046.661 172891.7 627045.962 172890.2 627044.063 172890.3 627044.064 172888.2 627044.965 172889.1 627042.066 172887.3 627042.767 172887.3 627042.868 172888.5 627040.569 172887.7 627038.870 172886.4 627040.171 172885.5 627037.672 172886.9 627037.273 172887.6 627038.774 172878.3 627056.775 172878.3 627056.776 172869.7 627061.877 172867.8 627064.2

GDM2000 MRT48

Latitude Longitude Height1 1.563157 103.6417 34.4032 1.56319 103.6417 35.0853 1.563213 103.6417 35.363


4 1.563218 103.6417 35.3635 1.563241 103.6417 35.9286 1.563191 103.6418 35.4127 1.563215 103.6418 36.3078 1.563209 103.6418 36.0249 1.563225 103.6417 36.44810 1.563245 103.6417 36.96811 1.563269 103.6417 36.85312 1.563258 103.6417 37.23513 1.563285 103.6417 37.16714 1.563267 103.6417 37.24415 1.56328 103.6417 37.22616 1.563311 103.6417 37.42717 1.56333 103.6417 37.48118 1.563332 103.6417 37.43219 1.563359 103.6417 38.10920 1.563349 103.6416 37.62521 1.563327 103.6416 37.49122 1.563311 103.6416 37.54123 1.563294 103.6416 37.51224 1.563276 103.6416 37.4925 1.563279 103.6416 37.49226 1.563289 103.6416 37.58127 1.563311 103.6416 37.55428 1.563327 103.6416 37.49429 1.563349 103.6416 37.57330 1.5633 103.6416 37.62931 1.563314 103.6416 37.65932 1.56334 103.6416 37.57833 1.563342 103.6416 37.51634 1.563349 103.6416 37.58635 1.56338 103.6417 37.80736 1.56337 103.6416 37.78637 1.563367 103.6416 37.65638 1.563362 103.6416 37.5339 1.563352 103.6416 37.75440 1.563348 103.6416 37.73641 1.563336 103.6416 37.65542 1.563328 103.6416 37.62643 1.563328 103.6416 37.63844 1.563321 103.6416 37.5645 1.563358 103.6416 38.4146 1.563365 103.6416 38.82


47 1.563368 103.6416 38.9148 1.563373 103.6416 38.94649 1.563366 103.6416 38.26450 1.563378 103.6416 38.80451 1.563381 103.6416 38.88252 1.563375 103.6416 38.27653 1.563384 103.6416 38.66954 1.563379 103.6416 38.2155 1.563387 103.6416 38.75156 1.563385 103.6416 38.25457 1.56339 103.6416 38.65858 1.563392 103.6417 38.35259 1.563426 103.6416 40.64660 1.563426 103.6416 40.64361 1.563445 103.6416 40.8462 1.563432 103.6416 40.76963 1.563432 103.6416 40.76464 1.563413 103.6416 40.65865 1.563422 103.6416 40.80966 1.563406 103.6416 40.70967 1.563405 103.6416 40.66868 1.563416 103.6416 40.74969 1.563409 103.6416 40.76770 1.563397 103.6416 40.59671 1.563389 103.6416 40.5772 1.563402 103.6416 40.71573 1.563408 103.6416 40.76374 1.563324 103.6417 38.06475 1.563324 103.6417 38.06376 1.563246 103.6418 37.49177 1.563229 103.6418 37.387

MRT48 RSO (old)

Northing Easting1 172854.3 627251.82 172858.1 627249.13 172860.5 627248.04 172861.1 627245.95 172863.7 627246.96 172858.1 627254.87 172860.8 627256.18 172860.1 627253.59 172861.9 627251.8


10 172864.0 627249.211 172866.8 627249.612 172865.6 627247.313 172868.5 627247.114 172866.5 627243.715 172868.0 627244.416 172871.4 627242.017 172873.5 627243.418 172873.7 627245.019 172876.6 627246.920 172875.5 627239.621 172873.1 627238.922 172871.4 627237.423 172869.5 627237.724 172867.6 627235.725 172867.9 627234.626 172869.0 627235.227 172871.4 627237.428 172873.1 627238.929 172875.6 627239.630 172870.2 627231.631 172871.7 627234.632 172874.6 627235.333 172874.9 627236.734 172875.5 627239.635 172879.0 627241.236 172877.9 627239.037 172877.6 627237.938 172877.0 627235.939 172875.9 627234.040 172875.5 627233.041 172874.1 627233.642 172873.3 627232.043 172873.3 627232.044 172872.5 627229.945 172876.5 627231.246 172877.4 627231.147 172877.7 627232.348 172878.3 627233.349 172877.5 627233.750 172878.8 627234.651 172879.2 627235.752 172878.5 627236.0


53 172879.4 627237.054 172878.9 627237.255 172879.8 627238.456 172879.5 627239.957 172880.2 627239.758 172880.4 627242.059 172884.1 627239.760 172884.1 627239.761 172886.2 627239.062 172884.7 627237.163 172884.8 627237.164 172882.7 627238.065 172883.6 627235.166 172881.8 627235.867 172881.8 627235.968 172883.0 627233.669 172882.2 627231.970 172880.9 627233.271 172880.0 627230.772 172881.5 627230.373 172882.1 627231.874 172872.9 627249.875 172872.9 627249.876 172864.2 627254.977 172862.3 627257.3

GDM2000 (Helipad).

Latitude Longitude Height1 1.558525 103.6364 36.159962 1.558525 103.6364 36.185553 1.558452 103.6364 34.804304 1.558310 103.6368 40.876375 1.558230 103.6368 39.936526 1.558190 103.6368 39.352547 1.558150 103.6368 38.583798 1.558110 103.6367 37.802739 1.558070 103.6367 36.9023410 1.558051 103.6367 37.2023411 1.558088 103.6368 38.2037112 1.558126 103.6368 38.9865213 1.558164 103.6368 39.7425814 1.558202 103.6368 40.3918015 1.558277 103.6369 41.19688


16 1.558235 103.6370 41.5744117 1.558160 103.6369 40.7527318 1.558122 103.6369 40.1318419 1.558085 103.6369 39.3681620 1.558048 103.6368 38.5109421 1.558011 103.6368 37.6164122 1.557974 103.6368 36.6146523 1.557921 103.6369 37.0402324 1.557960 103.6369 38.0535225 1.558000 103.6369 38.9087926 1.558040 103.6370 39.6709027 1.558080 103.6370 40.4150428 1.558120 103.6370 40.9986329 1.558198 103.6370 41.7466830 1.558172 103.6371 41.7310531 1.558131 103.6371 41.3906332 1.558090 103.6371 40.8894533 1.558050 103.6371 40.3857434 1.558010 103.6371 39.7007835 1.557969 103.6370 38.9914136 1.557929 103.6370 38.3177737 1.557889 103.6370 37.4791038 1.557849 103.6370 36.5349639 1.558122 103.6373 40.7535240 1.558097 103.6373 40.5462941 1.558109 103.6373 40.4824242 1.558094 103.6373 40.4281343 1.558063 103.6373 40.1072344 1.558102 103.6374 40.0960945 1.558085 103.6374 39.8902346 1.558064 103.6373 39.7341847 1.558064 103.6373 39.7525448 1.558119 103.6374 40.1574249 1.558439 103.6372 41.9580150 1.558377 103.6363 34.0412151 1.558339 103.6363 33.5869152 1.558302 103.6363 33.0699253 1.558265 103.6363 32.4875054 1.558228 103.6362 31.87520


GDM2000 RSO (New)

Northing Easting1 172355.5 626656.42 172355.4 626656.53 172347.3 626650.94 172331.7 626699.55 172322.8 626695.06 172318.4 626692.87 172313.9 626690.68 172309.5 626688.49 172305.2 626686.110 172303 626690.211 172307.1 626692.812 172311.3 626695.513 172315.5 626698.114 172319.7 626700.715 172328.0 626705.816 172323.4 626714.117 172315.0 626708.718 172310.9 626705.919 172306.8 626703.320 172302.7 626700.6


21 172298.6 626697.922 172294.5 626695.223 172288.6 626708.024 172293.0 626710.225 172297.3 626712.426 172301.7 626714.627 172306.2 626716.928 172310.6 626719.129 172319.3 626723.430 172316.4 626734.331 172311.8 626732.232 172307.4 626730.033 172302.9 626727.934 172298.4 626725.735 172294.0 626723.536 172289.5 626721.437 172285.1 626719.238 172280.6 626717.139 172310.8 626750.040 172308.1 626748.741 172309.5 626751.642 172307.7 626750.643 172304.3 626748.744 172308.6 626758.145 172306.8 626757.346 172304.4 626755.747 172304.4 626755.748 172310.5 626759.049 172345.8 626745.050 172339.1 626645.251 172334.9 626642.452 172330.8 626639.653 172326.7 626636.854 172322.7 626634.0


GDM2000 MRT48

Latitide Longitude Height1 1.558593 103.6381 27.9082 1.558593 103.6381 27.9343 1.558519 103.6381 26.5534 1.558378 103.6385 32.6235 1.558298 103.6385 31.6836 1.558257 103.6385 31.0997 1.558217 103.6384 30.3318 1.558178 103.6384 29.5499 1.558138 103.6384 28.64910 1.558118 103.6384 28.94911 1.558156 103.6385 29.95012 1.558193 103.6385 30.73313 1.558231 103.6385 31.48914 1.558270 103.6385 32.13815 1.558345 103.6386 32.94316 1.558303 103.6387 33.32117 1.558227 103.6386 32.49918 1.558190 103.6386 31.87819 1.558152 103.6386 31.11420 1.558115 103.6385 30.25721 1.558078 103.6385 29.36322 1.558041 103.6385 28.36123 1.557988 103.6386 28.786


24 1.558028 103.6386 29.79925 1.558067 103.6386 30.65526 1.558107 103.6387 31.41727 1.558147 103.6387 32.16128 1.558187 103.6387 32.74429 1.558266 103.6387 33.49330 1.558240 103.6388 33.47731 1.558199 103.6388 33.13632 1.558158 103.6388 32.63533 1.558117 103.6388 32.13134 1.558077 103.6388 31.44635 1.558037 103.6387 30.73736 1.557996 103.6387 30.06337 1.557956 103.6387 29.22538 1.557916 103.6387 28.28039 1.558189 103.639 32.49840 1.558165 103.639 32.29141 1.558177 103.639 32.22742 1.558161 103.639 32.17343 1.558131 103.639 31.85244 1.558169 103.6391 31.84145 1.558153 103.639 31.63546 1.558132 103.639 31.47947 1.558132 103.639 31.49748 1.558187 103.6391 31.90249 1.558506 103.6389 33.70450 1.558445 103.638 25.7951 1.558407 103.638 25.33552 1.55837 103.638 24.81853 1.558333 103.638 24.23654 1.558296 103.6379 23.624


MRT48 RSO (Old)

Northing Easting1 172350 626849.52 172350 626849.63 172341.9 626843.94 172326.2 626892.65 172317.3 626888.16 172312.9 626885.97 172308.4 626883.78 172304.1 626881.59 172299.7 626879.210 172297.5 626883.311 172301.7 626885.912 172305.8 626888.513 172310.0 626891.214 172314.2 626893.815 172322.5 626898.916 172317.9 626907.217 172309.6 626901.818 172305.4 626899.019 172301.3 626896.420 172297.2 626893.721 172293.1 626891.022 172289.0 626888.323 172283.1 626901.124 172287.5 626903.325 172291.9 626905.526 172296.3 626907.7


27 172300.7 626910.028 172305.1 626912.229 172313.8 626916.530 172310.9 626927.431 172306.4 626925.332 172301.9 626923.133 172297.4 626921.034 172292.9 626918.835 172288.5 626916.636 172284.0 626914.537 172279.6 626912.338 172275.2 626910.239 172305.3 626943.140 172302.6 626941.841 172304.0 626944.742 172302.2 626943.743 172298.9 626941.844 172303.1 626951.245 172301.3 626950.446 172299.0 626948.847 172298.9 626948.848 172305.1 626952.149 172340.4 626938.150 172333.6 626838.351 172329.5 626835.552 172325.3 626832.753 172321.3 626829.854 172317.2 626827.0


Ellipsoidal Height, Geoid Height and Orthometric Height (FKKSA).

h N H42.65878906 7.079 35.5797890643.34062500 7.079 36.2616250043.61777344 7.079 36.5387734443.61835938 7.079 36.5393593844.18261719 7.079 37.1036171943.66718750 7.079 36.5881875044.56269531 7.079 37.4836953144.27968750 7.079 37.2006875044.70273438 7.079 37.6237343845.22265625 7.079 38.1436562545.10800781 7.079 38.0290078145.49003906 7.079 38.4110390645.42207031 7.079 38.3430703145.49863281 7.079 38.4196328145.48046875 7.079 38.4014687545.68183594 7.079 38.6028359445.73613281 7.079 38.6571328145.68710938 7.079 38.6081093846.36406250 7.079 39.2850625045.88007813 7.079 38.8010781345.74609375 7.079 38.6670937545.79589844 7.079 38.7168984445.76640625 7.079 38.6874062545.74492188 7.079 38.6659218845.74707031 7.079 38.6680703145.83593750 7.079 38.7569375045.80839844 7.079 38.7293984445.74843750 7.079 38.6694375045.82792969 7.079 38.7489296945.88398438 7.078 38.80598438


45.91386719 7.079 38.8348671945.83281250 7.079 38.7538125045.77031250 7.079 38.6913125045.84101563 7.079 38.7620156346.06113281 7.079 38.9821328146.04042969 7.079 38.9614296945.91054688 7.079 38.8315468845.78437500 7.079 38.7053750046.00859375 7.078 38.9305937545.99023438 7.078 38.9122343845.90917969 7.078 38.8311796945.88066406 7.078 38.8026640645.89199219 7.078 38.8139921945.81484375 7.078 38.7368437546.66484375 7.078 39.5868437547.07441406 7.078 39.9964140647.16484375 7.078 40.0868437547.20058594 7.078 40.1225859446.51875000 7.078 39.4407500047.05878906 7.078 39.9807890647.13691406 7.079 40.0579140646.53027344 7.079 39.4512734446.92304688 7.079 39.8440468846.46484375 7.079 39.3858437547.00546875 7.079 39.9264687546.50820313 7.079 39.4292031346.91250000 7.079 39.8335000046.60703125 7.079 39.5280312548.90078125 7.079 41.8217812548.89726563 7.079 41.8182656349.09492188 7.079 42.0159218849.02363281 7.079 41.9446328149.01816406 7.079 41.9391640648.91230469 7.079 41.8333046949.06386719 7.078 41.9858671948.96367188 7.079 41.8846718848.92265625 7.079 41.8436562549.00332031 7.078 41.9253203149.02128906 7.078 41.9432890648.85039063 7.078 41.7723906348.82480469 7.078 41.7468046948.96953125 7.078 41.8915312549.01738281 7.078 41.93938281


46.31894531 7.079 39.2399453146.31757813 7.079 39.2385781345.74648438 7.079 38.6674843845.64218750 7.079 38.56318750

Ellipsoidal height, Geoid Height and Orthometric Height (Helipad).

h N H36.15996094 7.0680 29.0919609436.18554688 7.0680 29.1175468834.80429688 7.0680 27.7362968840.87636719 7.0700 33.8063671939.93652344 7.0700 32.8665234439.35253906 7.0700 32.2825390638.58378906 7.0690 31.5147890637.80273438 7.0690 30.7337343836.90234375 7.0690 29.8333437537.20234375 7.0700 30.1323437538.20371094 7.0700 31.1337109438.98652344 7.0700 31.9165234439.74257813 7.0700 32.6725781340.39179688 7.0700 33.3217968841.19687500 7.0700 34.1268750041.57441406 7.0700 34.5044140640.75273438 7.0700 33.6827343840.13183594 7.0700 33.0618359439.36816406 7.0700 32.2981640638.51093750 7.0700 31.4409375037.61640625 7.0700 30.5464062536.61464844 7.0700 29.5446484437.04023438 7.0700 29.9702343838.05351563 7.0700 30.9835156338.90878906 7.0700 31.8387890639.67089844 7.0700 32.6008984440.41503906 7.0700 33.3450390640.99863281 7.0710 33.9276328141.74667969 7.0710 34.6756796941.73105469 7.0710 34.6600546941.39062500 7.0710 34.3196250040.88945313 7.0710 33.8184531340.38574219 7.0710 33.3147421939.70078125 7.0710 32.6297812538.99140625 7.0710 31.9204062538.31777344 7.0710 31.24677344


37.47910156 7.0710 30.4081015636.53496094 7.0710 29.4639609440.75351563 7.0720 33.6815156340.54628906 7.0720 33.4742890640.48242188 7.0720 33.4104218840.42812500 7.0720 33.3561250040.10722656 7.0720 33.0352265640.09609375 7.0720 33.0240937539.89023438 7.0720 32.8182343839.73417969 7.0720 32.6621796939.75253906 7.0720 32.6805390640.15742188 7.0720 33.0854218841.95800781 7.0710 34.8870078134.04121094 7.0680 26.9732109433.58691406 7.0680 26.5189140633.06992188 7.0680 26.0019218832.48750000 7.0670 25.4205000031.87519531 7.0670 24.80819531


PLOTING 2D IMADE AND CONTOUR.

FKKSA

ELLIPSOIDAL HEIGHT, h


GEIOD HEIGHT, N


ORTHOMETRIC HEIGHT, H


HELLIPAD

ELLIPSOIDAL HEIGHT, h


GEIOD HEIGHT, N


ORTHOMETRIC HEIGHT, H


CONCLUSION

In the case of a 3D transformation it is recommended that the procedure in two steps

should be preferred, since the least squares solution becomes more stable and, due to the small

values of the rotation and scale parameters, no iterations appear to be necessary. Another also

acceptable approach is to solve for the translation parameters in three dimensions, and then for

the full two dimensional model. Obviously, the 2D approach for estimating the transformation

parameters is the appropriate choice in the case of small networks. However, when deformation

processes take place in an area, the long term behavior is, often, investigated with geodetic

methods, by comparing older and recently acquired data, such as GPS observations. During the

analysis, pairs of two dimensional coordinate sets are, usually, compared in the projection plane

and the displacements for the time interval between the two epochs are derived. Such coordinate

sets refer, probably, to different reference frames; the older ones to a geodetic datum. Therefore,

an estimation of local transformation parameters should take place before the deformation

analysis.

Since, usually, the two sets of coordinates refer to different epochs, the size of the residuals in

the least squares solution for the transformation parameters, whether the 2D or the 3D approach

is preferred, depends largely on the time interval elapsed and the size of the displacement field

expected. Consequently, the question of choosing the appropriate procedure in the case of

deformation analyses is not easily answered.


Documents

Earth Gravitational Model 2008