GNSS in Practical Determination of Regional Heights - Global Navigation Satellite Systems: Signal,Theory and Applications - page 131

series expansion (Equation 4), which is available in practice ( ℓ max < ∞). The other major
contributing error type is due to the noise in the coefficients themselves and termed as
commission errors. As the maximum degree ℓ max , of the spherical harmonic expansion
increases, so does the commission error, while the omission error decreases. Therefore, it is
important to strike a balance between the various errors. In general, formal error models
should include both omission and commission error types in order to provide a realistic
measure of the accuracy of the geoid heights computed from the global geopotential model.
In the following section, recently released global geopotential models using the data from
low earth orbiting missions such as CHAMP, GRACE and GOCE are exemplified and their
performances in Turkish territory investigated. Parallel to the improvements in techniques,
the new global geopotential models derived by incorporating the satellite data from these
missions are quite promising (Tscherning et al., 2000; Fotopoulos, 2003).
The other errors in the budget contributing to the N Δ g component stem from the insufficient
data coverage, density and accuracy of the local gravity data. Obviously, higher accuracy is
implied by accurate Δ g values distributed evenly over the entire area with sufficient
spacing, however there are some systematic errors such as datum inconsistencies, which
influence the quality of the gravity anomalies too. The shorter wavelength errors in the
geoid heights are introduced through the spacing and quality of the digital elevation model
used in the computation of N H . Improper modelling of the terrain is especially significant in
mountainous regions, where terrain effects contribute significantly to the final geoid model.
This is in addition to errors relating to the approximate values of the vertical gravity
gradient (Forsberg, 1994). Improvements in geoid models according to the computation of
N H , will be seen through the use of higher resolution (and accuracy) digital elevation data,
especially in mountainous regions.
2.1 Testing global geoid models
The global geopotential model used as a reference in the R-R technique has the most
significant error contribution in the total error budget of the computed regional geoid
models. Therefore employing an appropriate global model in R-R computations is of
primary importance. Likewise, in areas where regional models exist, they should be used as
they are more accurate compared to global models. However, many parts of the globe do
not have access to a regional geoid model, usually due to lack of data. In these cases, one
may resort to applying global geopotential model values (Equation 4) that best fit the
gravity field of the region. Determining the optimal global model for either, using the base
model in R-R construction of the regional geoid or estimating the geoid undulations in the
region with a relatively low accuracy, it will be necessary to undertake a comparison and
validation of the models with independent geoid and gravity information, such as
GNSS/levelling heights and gravity anomalies (Gruber, 2004; Kiamehr & Sjöberg, 2005;
Merry, 2007).
The global geopotential models are mainly divided into three groups based on the data used
in their computation, namely satellite-only (derived from the tracking of artificial satellites),
combined (derived from the combination of a satellite-only model with terrestrial and/or
airborne gravimetry, satellite altimetry, topography/bathymetry) and tailored (derived by
refining existing satellite-only or combined global geopotential models using regional
gravity and topography data) models. Satellite-only models are typically weak at