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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XXXIX-B4, 2012 
XXII ISPRS Congress, 25 August — 01 September 2012, Melbourne, Australia 
Especially, unlike conventional GGMs, EGM2008 contains 
gravity data of 15' resolution for Asian regions and also gravity 
data calculated from SRTM terrestrial data. Therefore, it is 
known to be 3-6 more accurate than a previous model, EGM96 
(Pavlis et al., 2008; Pavlis et al., 2012). 
2.2 GPS/levelling data 
GPS/levelling data is a very important factor not only to 
evaluate accuracy of the developed gravimetric geoid models 
but also fit gravimetric geoid models to local vertical datum. 
And accuracy for GGMs is evaluated primarily by cross- 
validation between geoid heights calculated from SHA and 
geometric geoid heights calculated from GPS/levelling data. 
This paper, in order to evaluate the accuracy of EGM2008- 
derived geoid heights and to fit the EGM2008-derived geoid 
heights to local vertical datum, used a total of 1,175 points of 
the GPS/levelling data which is acquired from unified control 
points (UCPs) installed with 10 km spacing in South Korea 
(Figure 1). 
  
  
  
124°E 126°E 128°E 130°E 132°E 
Figure 1. Distribution of a total of 1175 points of the 
GPS/levelling data (blue square) 
3. METHODS 
3.1 Spherical harmonic analysis 
SHA is a process of decomposing a function on a sphere into 
components of various wavelengths using surface spherical 
harmonic as base functions. Newtonian gravitational potential V 
satisfies Poisson's equation and gravitational potential satisfies 
Laplace's equation in free space. Solution of Laplace's equation 
can be expressed by harmonic functions series. And disturbing 
potential is calculated and then it substitutes Bruns's formula 
and finally geoid heights N is calculated. Further details on this 
spherical harmonic analysis are given in Rapp and Pavlis 
(1990), Heiskanen and Moritz (1996), and Kenyon and Pavlis 
(1996). 
3.2 Least-squares collocation 
Least-squares collocation in Gravity field addresses correlation 
between signal and noise given by gravity data, and using this 
relation predicts signal where observation is not carried out. 
The LSC represents one of the major theoretical and practical 
foundations of modern physical geodesy (Tscherning, 1986; 
Tsaoussi, 1989). 
In this paper, we used LSC to fit the EGM2008-derived geoid 
heights with geometric geoid heights calculated from 
GPS/levelling data The most important rule to apply LSC is 
that data needs to be centered before it is collocated (Moritz 
1980). In other words, trend has to be removed from the raw 
data such that mean of the data would be equal to zero 
(Forsberg et al., 2003). Procedure to remove this trend can be 
obtained by applying various trend models to raw data. 
The introduction of the GRAVSOFT package programmed by 
Forsberg et al. (2003) was a turning point in LSC application 
and adoption (Darbeheshti, 2009). In this paper, in order to fit 
geoid surface using LSC, GEOIP and GEOGRID in the 
GRAVSOFT written by Fortran 77 language are used and 
program of GCOMB is ported by C++ language and then used. 
Further details on this spherical harmonic analysis are given in 
Forsberg et al. (2003) and Darbeheshti (2009). 
3.3 MPI and OpenMP programming 
Generally, parallel programming is classified as distributed 
programming using the message-passing interface (MPI) and 
multi-core CPU-based parallel programming using the open 
multi-processing (OpenMP). 
MPI is a standardization for message passing and currently the 
de facto standard and the parallelization method for developing 
the high-performance computing (HPC) applications on 
distributed memory architecture (Message Passing Interface 
Forum, 1994; Wittwer, 2006; Chorley and Walker, 2010). The 
message-passing programming model is based on the 
abstraction of a parallel computer with a distributed address 
space where each processor has a local memory to which it has 
exclusive access (Rauber and Riinger, 2010). However, in the 
case of the communication of high volume data in the low- 
performance distributed computing environment which consists 
of low-speed network environment, MPI application's 
performance can be reduced. 
OpenMP is a standardization and an application programming 
interface (API) that supports multi-platform shared memory 
multi-processing programming. It consists of a set of compiler 
directives, library routines, and environment variables that 
influence run-time behavior (Chapman et al, 2007; Refianti et 
al., 2011). Many of the major compiler vendors (e.g. Microsoft, 
Intel, HP) support OpenMP technology. And one of advantages 
of the OpenMP technology is to allow relatively fast 
development of parallel applications through the global access 
of application memory address space (Jin et al, 2011). 
Especially, it is available in multiple operating system 
environments. However, the OpenMP technology does not 
support the distributed computing environment. 
In order to overcome this problem, researches to solve time- 
consuming problem through hybrid MPI and OpenMP approach 
which combined MPI and OpenMP have been recently 
proceeding. 
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