MODELLING LOCAL GPS/LEVELLING GEOID WITH THE ASSESSTMENT OF 
INVERSE DISTANCE WEIGHTING AND GEOSTATISTICAL KRIGIN 
G METHODS 
B. Erol* *, R. N. Celik" 
à ITU, Civil Engineering Faculty, Geodesy Div 
ision, 34469 Maslak Istanbul, Turkey - (bihter, celikn)@itu.edu.tr 
Commission IV, WG IV/1 
KEY WORDS: Geodesy, Modelling 
ABSTRACT: 
According to wide sprea 
attention has started to be paid to precise determination o 
measurements with GPS measurements during geodetic 
surface fitting problem according to GPS and Levelling 
analytical surface to serve practica 
Systems) based studies, engineering applic 
Inverse Distance Weighting (IDW) 
addition to compare these two popular interpolation techniques, 
techniques as a tool for modelling the geoid in 
geodesy. Also, the importance of precise 
1. INTRODUCTION 
To accomplish the transformation between ellipsoidal heights 
and orthometric heights has become more important since the 
satellite based positioning techniques, especially GPS (Global 
Positioning System), were being used in a wide range of 
applications. Using GPS technique, the 
geodetic and surveying 
geocentric WGS84 
positions are determined as related to 
(World Geodetic System 1984) reference ellipsoid of which 
surface is assumed as the datum of points’ heights which are 
derived from GPS measurements. However, in most of the 
geodetic applications, it is necessary to use orthometric heights 
referenced to geoid. 
The geoid height (or geoid undulation) can be defined as the 
separation of the reference ellipsoid with the geoid surface 
measured along the ellipsoidal normal (see Figure 1). The 
classical Gauss-Listing definition of the geoid is given as an 
equipotential surface of the Earth's gravity field that coincides 
with the mean sea level (Fotopoulos, 2003). Today, it is well 
known that this is not a strictly correct definition as mean sca 
level departs from the equipotential surface by up to two meters 
due to various oceanographic phenomena, such as variable 
temperature, salinity, instantaneous sea surface topography etc. 
(Fotopoulos, 2003). 
The fundamental expression of relationship between ellipsoidal 
heights obtained from GPS measurements and heights with 
respect to a vertical geodetic datum established from spirit 
levelling data with gravimetric corrections is as given in the 
equation | (Heiskanen and Moritz, 1967). 
h-H-N-0 (1) 
a a 
* Corresponding author. This is usef 
d use of satellite based positioning techniques, especiall 
f geoid models with an aim to replace the 
and surveying works. 
data and the main focus is model 
| geodetic applications such as large 
ations etc. During implementation of the subject, two differ 
and Kriging methods are evaluated according to cre 
mainly it is going to emp 
a local area precisely using GPS/ 
local geoid models as a part of geodetic infrastructur 
ul to know for communication with the appropriate p 
ng. DEM/DTM, Method, Observations, Accuracy, Spatial Infrastructures, GPS 
y GPS (Global Positioning System), a greater 
geometric levelling 
In this paper, geoid modelling is evaluated as a 
ling the geoid of a local area as an 
scale map production, GIS (Geographical Information 
ent interpolation methods, 
ated program routines. In this paper, in 
hasize the applicability of interpolation 
Levelling data to serve practical applications of 
e is underlined with Turkey example. 
where  h = ellipsoidal height 
H = orthometric height 
N = geoid undulation 
> 
  
  
  
  
  
| 
i 
| 
| Di 
i 
| ms] 
| | Surface | 
| \H jl | 
| \ Hf { 
| s j | 
se es TE. rn jl | 
A h | | eel s Geoid | 
} i — | 
| IN H = Orthometric height i | h | 
i i h = Ellipsoidal height Nj i 
| | N = Geoid undulation | Ellipsoid i 
i i UU UU eem 
| TT Tm 
Figure 1. Relations between ellipsoidal height, orthometric 
height and geoid undulation (geoid height) 
(http://kartoweb.itc.nl/geometrics/, accessed August 2000) 
So, as parallel to the wide range of applications of GPS 
technique, a demanding for a high precision geoid model 
preferably referring to a global geocentric datum appeared. As 
the result of this, configuring a geodetic infrastructure concept 
has become included to structure a precise geoid model as an 
important component of these studies. 
In this chronology, the method of GPS /Levelling for obtaining 
orthometric heights can not be assumed as a new concept. In 
fact, as a result of case studies that have been conducted in 
different regions of Turkey, it is proved that the GPS/Levelling 
can provide a viable alternative to trac 
levelling | measurement techniques, which are 
However, the answer of this 
onerous 
applications as well known. 
erson in cases with more than one author. 
76 
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