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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol XXXV, Part B4. Istanbul 2004
4. NUMERICAL EXAMPLE
The study has been carried out with in 45x50 km” local region
using GPS /Levelling data. The area is in the west of Turkey
near Agean Sea, Izmir Metropolitan Region. For modeling the
geold in the area as an analytical surface, two interpolation
methods were applied. Mathematical algorithms of these two
interpolation methods have been programmed as to comprise
the computation modules of a Local Geoid Modeling software,
however, the mentioned software has not been completed yet,
on the other hand it is planed to give the final version to the
software by the year of 2005.
In the area, 181 of totally 301 GPS/ Levelling points were
decided to use as reference points (modelling benchmarks),
which contributes the computation of new points according to
appropriate interpolation method, and rest 120 GPS/ Levelling
points (testing benchmarks) were used for testing the developed
interpolation algorithms according to IDW and Kriging
Methods. During the selection of test points set topography of
the region and also keeping the homogeneous distribution of
reference points set were considered. The distribution of both
point sets can be seen in Figure 3.
REFERENCE POINTS OF IZMIR LOCAL GEOID
38.45
LATITUDE
38.35
3825 |
26.8 26.85 269 26.95 27 27.05 27.1 27.15 27.2 27.25 27.3
LONGITUDE
/\ Modeling Benchmarks
Testing Benchmarks
Figure 3. The distributions of modelling benchmarks and test
benchmarks in the area of study
(Erol and Celik, 2004).
IDW and Kriging interpolation algorithms were applied
according to developed program codes. IDW interpolation
method has a simple computation algorithm than Kriging
method. However, the most complicated part is modelling the
variogram, after that the rest of the process is similar to IDW in
that prescribed weights control the interpolation. Variogram is
an important tool to explore spatial data sets. According to
handled results:
According to IDW model and using the previously mentioned
modeling parameters, the model was tested for 121 test points.
The test was carried out by analyzing the difference between
computed geoid heights from the model and geoid heights from
measurements. As the result of these analysis, it was seen that
the model fitted the data with 43.42 cm root means square error.
This is also an indicator for usability of the model for
computing the new points.
While Universal Kriging method was applied with the same
data set, it was seen that the model fitted the data with £3.07 cm
root means square error. If these results are compared each
79
other, it can be said that Kriging method can handle the data
better than IDW.
About the computation time, the performance of both
techniques are similar each other. However, as it is mentioned
before, the algorithm of Kriging method is much more complex
than IDW for programming.
At the end of the analysis, it was decided that both interpolation
method gave reasonable results for this local area and they are
applicable for modelling the geoid of this area as an analytical
surface and to serve practical geodetic applications. On the
other hand, according to researches it mustn't be neglected that
the eligibility of a mathematical model to an area while
modeling the GPS/ Levelling geoid is strictly depends on the
properties of study area. So, it is necessary to test a developed
model that if it is appropriate for modelling the geoid of an
area, before applying the new data.
S. CONCULISON AND FUTURE WORKS
It is obvious that after GPS techniques have become wide
spread in geodetic purposes, geoid model determination for
especially use in practical applications of geodesy has an
increased importance. So, this study's main was to produce
some solutions to practical applications, such as large scale map
production, GIS applications, engineering surveying
applications etc. especially at a national level.
Therefore, to test the performances and applicability of surface
fitting methods in geoid modelling using GPS/ Levelling
measurements in a local area, this study was carried out.
In the study, two interpolation techniques, Inverse Distance
Weighting and Kriging were applied separately. In both
applications, 181 GPS/ Levelling points were used as a
reference points set for generating the model and another 121
GPS/ Levelling points as test points set were used to test the
structured models.
In the results, it has been seen that both interpolation methods
are applicable for modelling the geoid of study area as an
analytical surface; however, Kriging method fits the data better
than IDW method according to test criteria.
The computation time is similar for both methods, while the
program codes run. On the other hand, Kriging method has
much more complex computation algorithm than IDW method
has.
Local geoid models have a special importance especially for
geodetic infrastructure of Turkey. Because, regional geoid
model of Turkey hasn't got homogeneous accuracy in every
part of the Turkey. Because of that in some part of the country,
it is necessary to be supported with precise local geoid models.
Surface fitting methods are very practical with this respect;
however, it is important to assess the appropriate surface fitting
approach. So it is necessary to test the model before applying
the new points.
As the future works it is planning to program some other data
modeling techniques to add the developing geoid modelling
software. Also to combine regional geoid model and local
geoid model to create a whole and improved geoid model for
the study areas is planning.
