Global Positioning System Reference
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coefficients of degrees higher than 60 or 70 due to several factors, such as the power-decay
of the gravitational field with altitude, modelling of atmospheric drag, incomplete tracking
of satellite orbits from the ground stations etc. (Rummel et al., 2002). Although the effects of
some of these limitations on the models decreased after the dedicated satellite gravity
missions CHAMP, GRACE and GOCE (GGM02, 2004; GFZ, 2006; GOCE, 2009), the new
satellite-only models still have full power until a certain degree, however rapidly increasing
errors make their coefficients unreliable at high degrees (see e.g. Tapley et al., 2005; ICGEM,
2005). Whilst, the application of combined models reduce some of the aforementioned
limitations, the errors in the terrestrial data effectively remain the same.
Theoretically, the observations, used in computation of the global models, should be
scattered to the entire earth homogenously, but it is almost impossible to realise this exactly.
As such, accuracy of quantities computed via global geopotential models, such as geoid
undulation (Equation 4), is directly connected to the quality and global distribution of
gravity data as well as to the signal power of satellite mission. The distribution and the
availability of quality gravity data therefore plays a major role in the global model-derived
values in different parts of the Earth. It may however be argued that, the various models
may not be as good as they are reported to be, otherwise the differences between them
should not be so great as they are (Lambeck & Coleman, 1983). As such, validating the
models in local scale with in situ data before using them with geodetic and geophysical
purposes is highly important (Gruber 2004). In this manner, Roland & Denker (2003)
evaluated the fit of some of the global models to the gravity field in Europe using external
data such as GPS/levelling and gravity anomalies. Furthermore, Amos & Featherstone
(2003) included astrogeodetic vertical deflections at the Earth surface in the external data for
validating the EGMs at that date in Australia. Similar evaluations were also undertaken by
Kiamehr & Sjöberg (2005), Abd-Elmotaal (2006), Rodriguez-Caderot et al (2006), Merry
(2007) and Sadiq & Ahmad (2009) in Iran, Egypt, Southern Spain, Southern Africa, Pakistan,
respectively. Satellite altimeter data and orbit parameters were also used by Klokočník et al
(2002) and Förste et al (2009) in comparative assessments of the EGMs. Erol et al (2009),
Ustun & Abbak (2010) and Yılmaz & Karaali (2010) provided some specific results on
spectral evaluation of global models and on their local validations using terrestrial data in
territory of Turkey. Motivated research conducted by Lambeck&Coleman (1983) and Gruber
(2004), we tested some of the recent global geopotential models having various orders of
spherical harmonic expansion for Turkish territory, the results of which have been recorded
later in this chapter. The listed global geopotential models in Table 1 were validated at 28
GNSS/levelling benchmarks, homogenously distributed over the country. The table
provides the maximum degrees of the harmonic expansions, the data contributed for
developing the models and also the principle references for further reading on these models.
The reference data for validations are included by Yılmaz & Karaali (2010), hence the results
from the models evaluated in both studies are comparable (see Figure 1 for the distribution
of the benchmarks).
In evaluations, the geoid heights derived from the models (Equation 4) were compared with
observations at the benchmarks, and the statistics of comparisons (see Table 2) were
investigated. In the validation results, superiority of ultra-high resolution models EIGEN-6C
(
ℓ
max
= 1420) and EGM08 (
ℓ
max
= 2190) in representing the gravity field in the region is
naturally obvious given that these models comprise information relating to full content of
gravity field spectrum. Considering the ±16.3 cm and ±17.9 cm accuracies of EIGEN-6C and
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