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Evaluation results of the Earth Gravitational Model
EGM08 over the Baltic countries
A. Ellmann
Department of Civil Engineering, Tallinn University of Technology, Ehitajate tee 5, Tallinn, Estonia
J. Kaminskis
Geodesy Department, Latvian Geospatial Information Agency, O.Vaciesa iela 43, Riga LV1004, Latvia
E. Parseliunas
Geodetic Institute, Vilnius Gediminas Technical University, Sauletekio al. 11, LT10223 Vilnius, Lithuania
H. Jürgenson
Estonian University of Life Sciences, Kreutzwaldi 5, Tartu, Estonia
T. Oja
Department of Geodesy, Estonian Land Board, Mustamäe tee 51, Tallinn, Estonia
Abstract. Earth’s geopotential model (EGM) in
conjunction with regional terrestrial gravity data are
often used in regional geoid determination. Thus,
significant enhancements are expected due to release
of the new high resolution Earth Gravitational
Model EGM08. Accordingly, this study evaluates
the performance of the EGM08 model over the
Baltic Sea region with emphasis to Estonia, Latvia
and Lithuania. Several different sets of the “ground
truth” data are used in the comparisons. First, the
EGM08derived height anomalies are compared
with an existing regional geoid model. The detected
discrepancies range within ± 0.3 m with a mean of 
0.02 m, whereas the standard deviation (STD) of the
discrepancies amounts to 0.08 m. The largest
discrepancies occur in the areas where only a few
data points were available either for the regional
geoid modeling or at the EGM08 compilation, or
both. Second, the freeair gravity anomalies at the
terrestrial datapoints are compared with the
EGM08derived anomalies. The STD of the
anomaly discrepancies is 2.6 mGal. Finally, the
EGM08 model is validated with respect to GPS
levelling data. The STD of detected discrepancies is
0.06 m, with a mean of 0.49 m. Thus, the EGM08
based quantities agree reasonably well with the
tested datasets. Evidently, most of the available
gravity data in the Baltic Sea region appear to be
utilised at the EGM08 construction.
Keywords: geopotential model, geoid, GPS
levelling.
_____________________________________________________
1 Introduction
A new combined Earth gravitational model EGM08
(Pavlis et al, 2008) was released to the public in
2008. EGM08 takes advantages of recent satellite,
terrestrial gravity, elevation and altimetry data. This
activity is conducted by the National Geospatial
Intelligence Agency (NGA) of the USA. The
resolution of the EGM08 is 5´ (corresponding to 9
km, i.e. to the spectral degree of ca 2160), also the
global accuracy of the EGM08 is expected to be
superior over earlier EGMs.
Regional improvements of global geoid models
can be obtained by modifying Stokes’s integral
formula (Stokes, 1849). When solving the Stokes
problem, strictly speaking, gravity anomalies over
the entire Earth are required. In practice, however,
the data availability is limited to some spatial
domain (Ω
ψ0
) around the computation point.
Modified Stokes’s formula (first proposed by
Molodenskii et al., 1960) combines local terrestrial
gravity anomalies and the EGMderived long
wavelength component of the geoid. For instance, a
generalized Stokes scheme (cf. Vaníček and
Sjöberg, 1991) can be used
( ) ( ) ( ) ( )
( )
02
0
2
0
,,
4
2
,
21
L
L
n
n
L
n
n
R
NSgRgRd
RgR
n
ψ
ψ
πγ
γ
=
Ω
=
′
Ω=∆Ω−∆ΩΩ+
+∆Ω
−
∑
∫∫
∑
(1)
where R is the mean radius of the Earth; ψ is the
geocentric angle, the modified Stokes function SL(ψ)
110
can be computed according to some algorithm (e.g.
Wong and Gore (1969); Vaníček and Kleusberg
(1987); Sjöberg (1991), among others); γ0 is the
normal gravity at the reference ellipsoid, ∆g(R,Ω) is
terrestrial gravity anomaly on the geoid, Ω denotes a
pair of geocentric coordinates (the spherical co
latitude θ and longitude λ), dΩ´ is an infinitesimal
surface element, ψ0 is the radius of the integration
cap, L is the modification degree, ∆gn are the
harmonics of the EGMderived gravity anomaly.
Due to availability, quality, and type of data, the
characteristics of an EGM vary regionally. Hence,
the performance of any EGM needs to be validated
in a regional scale by comparisons with other
external data sets that depend on the same gravity
field. Traditionally, the accuracy of the regional
geoid modelling has been assessed by using GPS
levelling points. Apparently, the computations of
new regional geoid models will also be based upon
the global EGM08 model, the testing of which is
necessary to assess its suitability for this task. In this
contribution three different sets of the “ground truth”
data are used over the three Baltic countries 
Estonia, Latvia and Lithuania. First, the EGM08
derived height anomaly is compared with an existing
regional geoid model. Second, the freeair gravity
anomalies at the terrestrial datapoints are compared
with the EGM08derived anomalies. Thereafter the
EGM08 model is validated with respect to the GPS
levelling data. The differences between a
preliminary PGM07A and the final EGM08 models
over the Baltic countries are discussed. Further
comparisons reveal that there is still some space for
further improvements of the contemporary EGMs.
Actions needed for assembling more consistant
combined geopotential models are suggestedas well.
A brief summary concludes the paper.
Note that the study results have been reported
partly in the international conference Gravity, Geoid
and Earth Observation (GGEO), held in June 2008
in Chania, Greece. Since this contribution contains
some more details, it can be considered as an
extended report of Ellmann (accepted). In addition,
this work includes further evaluation results of the
EGM08 over the Baltic countries.
2 Target area
The EGM08 performance is examined within the
following geographical boundaries: 53.83° < ϕ <
60.06°; 19.97° < λ < 28.52°, see Fig. 1. Thus, in
addition to Estonia, Latvia and Lithuania the target
area includes partly also Russia, Belarus, Poland and
Finland, together with a large portion of the Baltic
Fig. 1 Location of the target area (enclosed by the bold
rectangle). External rectangle denotes the data area borders in
the BALTgeoid04 (Ellmann, 2005) computations.
Sea. The elevation extremes are 0 m at a shoreline
and 318 m in southeast Estonia, whereas most of the
target area comprises of sea and topography below
100 m. Due to such low topography no significant
numerical differences (3 mm at most) between the
geoid and height anomaly occur over the chosen
target area.
3 Comparisons with a regional high
resolution geoid model BALTgeoid04
3.1 Regional BALTgeoid04 model
A recent Baltic geoid model was computed by
Ellmann (2004 and 2005). In his study the geoidal
heights were estimated by the least squares modified
Stokes’s formula (cf. Sjöberg, 1991).
The definition of the main computation criterias
(such as the modification limit L = 67, the radius of
the integration cap ψ0 = 2°, etc) is explained in detail
by (ibid.). An early GRACEderived („satellite
only“) GGM01s model (Tapley et al., 2004) was
used as the reference model for computing ∆gn in
Eq. (1). The resulting 1.5´x3´ geoid model is
depicted in Fig. 2. The geoidal heights in the target
area vary between 15 m and 30 m, with the regional
downslope trend from southwest toward northeast.
The geoid model is mainly smooth (with a STD of
the mean ~3 m), but it includes some local irregula
111
Fig. 2 The Baltic gravimetric geoid model BALTgeoid04
(Ellmann, 2005). Geoidal heights are given with respect to the
GRS80 reference ellipsoid. Unit is metre. The total area of
the image corresponds to 300 000 km2.
rities in the NW part of the target area. Their
location is correlated with the local anomalies of the
gravity field (cf. Ellmann, 2004, Fig. 2.3, the
anomaly range at the terrestial gravity points are also
shown in Fig. 4 of the current paper). The quality of
the BALTgeoid04 model was assessed from the
comparisons with the GPS and levelling datasets.
The same sets of the control points will also be used
for the evaluation of the EGM08derived height
anomalies, therefore some more information on
these data is spared for Section 5.
The GPSlevelling points form a surface, which is
called here the “geometric geoid model” (Ngeom = h 
H). The following STD value of the discrepancies
between the BALTgeoid04 and Ngeom were
achieved: over the whole of the Baltics 5.8 cm, in
Estonia 4.0 cm, in Latvia 6.0 cm and in Lithuania
5.7 cm, respectively. It is also concluded that the
accuracy of the BALTgeoid04 model is at least of
the same level as is the accuracy of the used control
points (Ellmann, 2005).
3.2 Accounting for the differences between
the EGM08 and GRS80 parameters
The BALTgeoid04 geoidal heights are defined with
respect to the GRS80 (Geodetic Reference System;
Moritz, 1992) ellipsoid. Also the physical constants
of the GRS80 are used for computing the normal
gravity field in the Baltic countries. Furthermore, the
GPSderived geodetic heights are reckoned from the
ETRS89 (European Terrestrial Reference System)
oriented GRS80 ellipsoid.
As is customary in geodesy, the mass of the
reference ellipsoid is chosen to be equal to the mass
of the Earth, and the origin of the reference ellipsoid
is placed at Earth’s mass centre. However, in reality
the EGM parameters may differ from the correspon
ding parameters of the adopted geodetic reference
ellipsoid. Thus, the differences between the defining
constants (i.e. gravitymass constant GM, and the
major semiaxis a of the ellipsoid versus reference
radius for the spherical EGM) of the used GGM and
adopted geodetic reference ellipsoid should be
considered. The scaling can be introduced via zonal
harmonics of the reference ellipsoid by an approach
described in Vaníček and Kleusberg (1987, Sect. 5),
see also Kirby and Featherstone (1997) and Smith
(1998). In the discussion below the EGMrelated
values will be denoted by the subscript “EGM”,
whereas the subscript “GRS” denotes the geodetic
reference ellipsoid related quantities
It should be noted that the EGM08 geopotential
model utilises GMEGM = 398600.4415⋅109 m3⋅s2,
whereas GMGRS = 398600.5⋅109 m3⋅s2. The Earth’s
gravitational potential and its derivatives (such as
the disturbing potential, gravity anomaly and geoidal
height) can be expressed in terms of an infinite
series of spherical harmonics outside the attracting
masses of the Earth. Since the EGM08 coefficients
are referred to the bounding sphere with some radius
a (the value aEGM = 6378136.3 m is adopted at the
compilation of the EGM08, whereas aGRS = 6378137
m), then the EGM derived quantities, strictly
speaking, ought be computed on the surface of the
bounding sphere (or above it). However, the gravity
field related quantities can be more or less safely
computed inside of this sphere, as long as the
evaluation point remains outside the topographic
masses. Due this, the EGMs are better suited for
computing the ground related gravity quantities,
such as the height anomaly (cf., Molodenskii et al.,
1960), rather than the geoid. Note that over the
continents the latter would require computations
inside the topographic masses.
112
3.3 The EGM08derived height anomalies
The „tidefree“ version of the EGM08 model (the
file EGM2008_to2190_TideFree.gz, retrieved from
URL:http://users.auth.gr/~kotsaki/IAG_JWG/EGM0
8_intro.html , retrieved April, 2008) contains fully
normalized, unitless spherical harmonic coefficients,
complete to degree and order 2159, plus additional
coefficients extending to degree 2190 and order
2159. The EGM08derived height anomalies ζ (at
the topographic surface, with the geocentric radius
of rt = rg + H) were computed by the following
formula:
2190
20
()
{cossin}(cos)
EGMGRS
EGM
tT
nn
EGMEGM nmnmnm
nm
tTt
GMGM
r
GMa CmSmP
rr
ζγ
λλθ
γ==
−
Ω=+
∆+
∑∑
(2)
where the normal gravity γT is referred to the surface
of the telluroid (with the geocentric radius of rT =
rGRS + H);
nm
C
and
nm
S
are fully normalised
spherical harmonic coefficients, of degree n and
order m;
(cos)
nm
P
θ
are fully normalised associated
Legendre functions. The first term on the left hand
side of Eq. (2) represents the zero degree geoid
scaling term, which is due to the difference between
the GMvalues of the EGM08 and that of the
reference elliposoid (GRS80). Using R = 6371 km
and γ = 981 Gal the zero degree geoid scaling term
becomes 0.936 m. This value will be added to the
EGM08derived height anomalies. The (residual)
zonal coeffcients
nm
C
∆ account also for the
differences between the reference radius of the
EGM08 and semimajor axis of the GRS80.
The above principles have also been realised in
the harmonic_synth_v02.f code (by Holmes and
Pavlis, version 05/01/2006, retrieved from the NGA
webpage http://earthinfo.nga.mil/GandG/wgs84/
gravitymod/new_egm/new_egm.html), which is
used in the validation of the EGM08 geopotential
model in the present study. However, the program
does not account for the influence of the zerodegree
term. Therefore, the EGM08derived quantities are
corrected for the missing zerodegree term.
Strictly speaking, Eq.(2) should also account for
the difference between the gravity potential on the
surface of the geoid (W
0
) and the normal gravity
potential on the surface of the normal ellipsoid (U0),
i.e. the term
00
WU
γ
−
−. Recall that in an ideal case
W0 = U0. Several estimates of W0 have been
proposed in the geodetic literature over the past
decades. For a recent review of the gradual
improvements see Bursa et al (2007) and references
therein. Note that many studies of the W0 rely upon
the satellite altimetry (such as TOPEX / Poseidon)
results. In this case, however, the data coverage is
not truly global, since no data from subpolar
latitudes have been included in such solutions. Some
others combine the GPS, levelling and tidegauge
data into a common solution, see e.g. Ardalan et al
(2002). Such an approach may provide the best
match with the local vertical datum over the given
study area. Both approaches can be considered being
complimentary to each other to a certain extent.
However, at the present the estimates of the W0
value can still be improved further. Therefore we
exclude the
00
WU
γ
−
− term from the present
comparisons. It is also reasonable to assume, that
there may be a certain consistency between the W0
value and the adopted set of GM and a values at the
compilation of the EGM08 model. All in all, after
the proper determination of the W0 value its
contribution can be added to the results of the
present study. Note that it will manifest only as a
simple onedimensional bias of the EGM08 derived
gravity field quantities.
The EGM08 height anomalies were computed at
the grid nodes of the BALTgeoid04 model. The
conceptual differences between the geoid and height
anomalies are well known, see e.g., Heiskanen and
Moritz (1967, Chap. 83). Recall, however, that over
the selected target area these differences are
numerically insignificant. These differences are
neglected in the following comparisons without
affecting the objectives of the present study.
3.4 The results
The discrepancies between the BALTgeoid04
model and EGM08 height anomalies (cf. Eq. (2)) at
the BALTgeoid04 grid nodes (altogether 250 x 172
points) are depicted in Fig. 3. Here we focus only on
the general features of the discrepancies. The range
of the detected discrepancies varies within ± 3 dm
over the whole target area. The largest discrepancies
are located outside the borders of Estonia, Latvia
and Lithuania. Within the borders of the three
countries the absolute range of the discrepancies
remains smaller than 15 cm. Full statistics of the
comparison can be found in Table 1 (see the last
section of this paper).
The nature of the discrepancies between the two
models appears to be quite complicated. Note that
the discrepancies in the centre of the target area
seem to possess a spectral content below degree 100.
113
Fig. 3 Discrepancies between the BALTgeoid04 model and
EGM08 height anomalies (nmax = 2190) at the BALTgeoid04
grid nodes (altogether 250 x 172 points). The discrepancies
range from 0.289 m to +0.338 m with a mean of 0.025 m.
Generally, the EGM08 height anomalies appear to be slightly
higher than the BALTgeoid04 model. Standard deviation of
the detected discrepancies amounts to 0.077 m.
It should be noted that the long wavelength
component of the GGM01s (which was used as the
BALTgeoid04 reference model, with the degree
nmax = 67) and EGM08 model is very similar. Their
long wavelength differences (both developed up to
nmax = 67, cf. Eq. (2)) do not exceed ± 4 cm over the
target area. This may indicate the presence of the
systematic biases among the terrestrial datasets used
for the computations of the BALTgeoid04 and
EGM08 model.
Alternatively, the discrepancies could either be
due to: (i) inadequate reproduction of the spectral
content of the disturbing potential from the truncated
Stokesian integration (cf. the first term on the right
hand side of Eq. (1)); (ii) deficiencies of the
harmonic analysis when determining the EGM08
spherical harmonic coefficients; or (iii) both.
All in all, within the land masses of the three
countries (Estonia, Latvia and Lithuania) the
agreement between the BALTgeoid04 and EGM08
derived height anomalies is reasonable, see Fig. 3. It
should be noted that the terrestrial data coverage
(used for the BALTgeoid04 model, see Fig 4) is
satisfactory there.
Note that the discrepancies between the
BALTgeoid04 and EGM08derived height anomaly
possess shorter wavelength features over the eastern
part (especially in SE) of the target area, where only
a few data were available for the BALTgeoid04
computations. Hence, a more complete dataset was
most likely available for the compilation of the
EGM08 over the eastern part of the target area. Also
at some offshore spots, well covered with the
terrestrial data, the range of detected discrepancies
appears to be unreasonably large. The search for an
explanation of the detected discrepancies over the
Baltic Sea prompts us to have a closer look at the
quality and coverage of the regional terrestrial data.
4 Comparisons with the historical
terrestrial gravity survey data
The gravity survey data (altogether 42559 points)
used in the current comparisons were obtained (in
2001) from the Danish National Survey and
Cadastre, the authorized holder of the Nordic–Baltic
gravity database. This international database is
created and maintained within the frame of the
activities of the Nordic Geodetic Commission. The
national contact persons deliver the data to the
database, whereas their responsibility is to ensure
the quality and internal consistency of the national
datasets.
The coverage of the terrestrial data points within
the target area is more or less satisfactory, except the
eastern part, where only a small number of gravity
points is available, see Fig 4.
Data, which are collected during several decades
with different methods and equipment and by
different nations and specifications, requires careful
analysis before further processing.
The Estonian gravity survey was performed by
the Institute of Geology at the Estonian Academy of
Sciences in 194958. The total number of Estonian
gravity survey points exceeds 4000, yielding a
density of 1 survey point per 10 km2. The accuracy
of these data is (very optimistically) claimed to be <
1 mGal. A register of Latvian and Lithuanian gravity
points is mainly reconstructed from the 1: 200 000
paper maps in conjunction with an obsolete global
topographic model. The accuracy of such data
remains unknown (Kaminskis and Forsberg, 1997).
It should be emphasised, however, that the gravity
surveys of the three Baltic countries have
historically been related to the same vertical system
and gravity datum.
114
Fig. 4 Freeair anomaly
(,)
t
gr
∆Ω
at the terrestrial data points
The anomaly values range from 73 to +44 mGal, with a mean
of 7 mGal. The STD of the anomaly values is 17 mGal. The
colors of the dots are proportional to the range of the
anomaly, cf. the colorbar.
Note that the NKG 1997 marine and Baltic Sea
1999 airborne gravity surveys have significantly
improved the data coverage over the Baltic Sea. The
accuracy of these datasets is estimated to be ~ 2
mGal (Forsberg, 2001). Aligned (mainly in EW
direction) datapoints over the Baltic Sea indicate
the location of the aerogravity survey tracks (see
Fig. 4). In addition, the marine gravity data within
the Riga Gulf and nearby Latvian coastline (aligned
in NESW direction) have been made available as
well.
An extensive analysis of NordicBaltic gravity
data is summarized in Ellmann (2001). The study
revealed the presence of some (presuambly very
small) systematic discrepancies between the used
datasets. The systematic errors in NordicBaltic
gravity datasets have also been noticed by other
authors, see e.g., Omang and Forsberg (2002),
Jürgenson (2003).
The elimination of these possible offsets is
outside of the scope of the present study, since it
requires a multilateral international involvement.
Hence, any possible inherent systematic bias
between the national datasets is simply ignored in
earlier studies and in this comparison.
The EGM08 derived freeair anomalies Δg (at the
topographic surface rt) are computed at the locations
of the NordicBaltic terrestrial gravity points by the
following formula (Heiskanen and Moritz, 1967, Eq.
2151c.):
( )
2190
22
2
0
(,)1
{cossin}(cos)
EGMGRSEGM
EGMt n
tt
n
n
EGM nmnmnm
m
t
GMGMGM
grn
rr
a
CmSmP
r
λλθ
=
=
−
∆Ω=−+−⋅
⋅∆+
∑
∑
(3)
Note that the first term on the right hand side is the
zero degree scaling term of the gravity anomaly,
which amounts to +0.144 mGal (to be added to the
EGM08derived anomalies).
Presuambly, many datasets of the Baltic Sea
region most likely do not contain the atmospheric
correction on the gravity measurements, which is
recommended by the IAG (see Moritz 1992, Sec. 5).
Fig. 5 The discrepancies between the terrestrial and EGM08
derived freeair gravity anomalies. The discrepancies
[
(,)
t
gr
∆Ω

(,)
EGMt
gr
∆Ω
] range from 18 to +18 mGal, with
a mean of 0.05 mGal. The STD of the discrepancies is 2.6
mGal. The colors of the dots are proportional to the range of
the detected discrepancies, cf. the colorbar. The black dots
denote the locations, where the absolute range of differences
exceeds 10 mGal.
115
15 10 5 0 5 10 15
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
Fig. 6 Histogram of discrepancies between the terrestrial data
and EGM08derived freeair gravity anomalies. Unit is mGal.
The total number of the points is 42559.
Recall that at the sea level this correction amounts to
+0.87 mGal. In contrast, the attraction of the
“beneath” atmospheric masses is naturally
embedded in the spaceborne gravity results.
Therefore, for the sake of consistancy of
comparisons all the terrestrial data were corrected
for the attraction of the atmospheric masses (dgatm)
by the following formula (Wenzel, 1985):
592
0.8749.9103.562510
atm
dgHH
−−
≈−⋅+⋅ (4)
where H is the height above the sea level, the results
are in mGal.
The discrepancies between the measured and
EGM08derived gravity anomalies (terrestrial minus
EGM08) vary from 18 to +18 mGal, with a mean of
+0.05 mGal, see Fig. 5. The histogram of
discrepancies is shown in Fig. 6. In general, the
EGM08derived gravity anomalies agree reasonably
well with the ground truth. However, there are some
(offshore) areas, where the discrepancies are much
larger than the regional average, see Fig. 5. This
may indicate that different (from those used in this
comparison) datasets were used (or no latest data
were available) at the compilation of the EGM08. In
particular, a relatively powerful negative anomaly
over the Gulf of Finland (at 59.5°N & 24.5°E, see
Fig. 4) remains “unnoticed” by the EGM08 data.
Other such an example is the Kuroshio lagoon at
55.5°N & 21.5°E, where the discrepancies possess a
systematic nature. Note that both areas are densely
covered with the terrestrial data. Such discrepancies
should be studied and ultimately resolved in future
gravity field and geoid modelling works.
5 Comparisons with GPSlevelling data
As is well known, intercomparison of a geoid
model, GPSderived geodetic heights, and spirit
levelled (normal or orthometric) heights at discrete
points gives a reasonable indication of the geoid
model’s accuracy. Thus the further validation of the
EGM08 model relays on nationwide sets (one for
each country) of highprecision geodetic points, for
their locations see Fig. 7.
First, the same constellation of the control points
as used at the evaluation of the BALTgeoid04
model will also be employed here. For all points the
geodetic heights from GPSmeasurements as well as
levelling heights are available. The geodetic
coordinates of the control points are related to the
respective national realization of the new European
Terrestrial Reference System ETRS89. The spirit
levelled normal heights of all points refer to the
Baltic Height System 1977 (Kronstadt tidegauge).
Fig. 7 Distribution of the Baltic GPSlevelling data
(altogether 189 points) and their differences from the EGM08
height anomalies (developed up to degree 2190). The
discrepancies [Ngeom 
EGM
ζ] range from +0.346 to +0.697 m,
with a mean of +0.493 m. The STD of the discrepancies
amounts to 0.060 m. The colors of the datapoints are
proportional to the range of the detected discrepancies (cf. the
colorbar). Unit is metre. The levellings are referred to the
Kronstadt tidegauge observations.
116
The average distance among 26 evenly distributed
Estonian control points is 50 km. The combined
error of GPSderived and spiritlevelled heights does
not exceed 23 cm, most likely. Note that the
geodetic heights are computed from the same GPS
campaign and most of these points are directly
connected to the highprecision levelling network.
The Latvian and Lithuanian datasets (53 and 110
points, respectively) are denser. However, the
accuracy of the used GPSlevelling points seems to
be rather heterogeneous.
The common Baltic geometric geoid is
represented by the sum of the three national datasets
(189 points). The numerical statistics of the detected
differences are presented in Table 1. In particular,
the mean of the differences reveals a positive offset
(+ 0.49 m) of the Kronstadt vertical datum from the
EGM08derived global geoid. Note however, that
this offset depends also on the W0 value to be
adopted in future computations. For instance, a
recent estimate W0 = 62 636 855.75 m
2
s
2 is
published by Ardalan et al (2002). Considering also
the GRS80 related U0 = 62 636 860.85 then the
term
00
WU
γ
−
− becomes +0.52 m, which should be
added to the EGM08 derived geoid model. In other
words, after implementation of the aforementioned
assumption the Kronstadt vertical datum will
practically coincide with the mean level of the world
oceans. On the other hand the Ardalan et al. (2002)
approach constrains the regional GPS, levelling and
tidegauge data (surrounding the Baltic Sea only)
into a common solutions, which may not necessarily
be representable for the whole of the globe.
The resulting STD of differences 6.0 cm
indicates almost the same level of accuracy, as it
was achieved from the BALTgeoid04 modelling
(Ellmann, 2005). Such comparisons are also
produced on a countrybycountry basis. The
corresponding statistics can be found in Table 1. In
particular, the STD of the discrepancies (after
removing the mean) as of 0.048, 0.063 and 0.048 m
were achieved for the Estonian, Latvian and
Lithuanian GPSlevelling points, respectively. Very
similar estimates were obtained also from the
comparisons with the BALTgeoid04 model
(Ellmann, 2004, Table 2.3).
Note that the Estonian GPSlevelling geoid
appears to be somewhat “higher” than the Latvian
and Lithuanian geometrical geoid models, see the
mean values (+0.56 m versus +0.48 m) in Table 1. It
should be noted that no temporal changes in the
levelled heights were considered in this study.
However, the Estonian points are affected by the
Fennoscandian postglacial rebound. Conversely, the
Latvian and Lithuanian points are mostly located
outside the landuplift zone. Since the levellings
have been performed over relatively long timespan
then the Estonian solution may be contaminated with
the landuplift effect. Thus, the used GPSlevelling
points cannot be considered as an entirely errorless
dataset.
6 Differences between the EGM08 and a
preliminary PGM07A model
As a matter of fact a Working Group (WG) was
established by the International Association of
Geodesy (IAG) for an independent and coordinated
evaluation of the EGM08 quality already in 2006. A
preliminary PGM07A model (Pavlis et al., 2007)
was released to the WG members for validation in
July 2007. The testing results were submitted to the
NGA/EGM08 development team for the ultimate
„finetuning“ of the model in October 2007. As a
result the final EGM08 model differs somewhat
from its preliminary version. The detected
discrepancies between the EGM08 and PGM07A
derived gravity quantities in the Baltic countries are
shown in Figs. 8 and 9. The differences are quite
significant, exceeding a dm level in terms of the
Fig. 8 Discrepancies between the EGM08 and PGM07
derived height anomalies (nmax = 2190). Unit is metre.
117
Fig. 9 Discrepancies between the EGM08 and PGM07
derived freeair gravity anomalies (nmax = 2190) The colours
of the dots are proportional to the range of the detected
discrepancies, cf. the colourbar. Unit is mGal. The black dots
denote the locations, where the absolute range of differences
exceeds 2 mGal
geoidal heights (a few mGal in terms of gravity
anomaly). This could be due to the subsequent
downweighting of the terrestrial data, at the same
time assigning more weight to the satellite info (priv.
comm. N. Pavlis, June 2008). In the study area the
most significant changes have taken place outside
the land masses of Estonia, Latvia and Lithuania.
As a result the accuracy of the EGM08derived
Baltic geoid model at the GPSlevelling points is
slightly worse than that of PGM07A. However, the
deterioration is just marginal, just some 23 mm in
terms of STD for each case. For instance, the STD
of the PGM07A derived Baltic geometric geoid
reached 0.058 m (cf. to that of EGM08: 0.060 m, cf.
Table 1).
Apparently, such a downweighting of the
terrestrial data has distorted the accuracy of the final
EGM08 in the Baltic Sea region. Note that the
terrestrial data coverage is rather dense in the study
area. Thus, the strategy of assigning more weight to
the satellite info at the EGM08 compilation may not
be the most optimum in such areas. Conversely, this
approach may provide better results in the areas with
sparse and less reliable terrestrial data.
7 Toward future combined geopotential
models
Intuitively, highresolution and accurate global
geoid models, such as newly released EGM08,
create tools for unification of national height
systems all over the globe. Can there be any further
improvements? The answer is affirmative, since the
geodetic community is expecting even more
promising results from the dedicated gravimetric
satellite missions. In this respect of particular
interest is the first satellite gradiometry mission
GOCE (Gravity field and steadystate Ocean
Circulation Explorer) to be launched by the
European Space Agency in 2009. This mission will
allow reaching unprecedented accuracy for
geopotential coefficients in the global scale and up
to degree and order 270 (corresponding to the spatial
resolution of 65 km). The GOCE will improve the
intermediate wavelength information of the gravity
field. However, the usage of the terrestrial data is
still unavoidable for the proper recovery of the high
degree spectrum of the gravity field.
Intuitively, for the development of global high
resolution gravity models all the terrestrial data need
to be referred to the modern gravity system, which is
based on the absolute gravity measurements. Only
such a global model will avoid drawbacks, which
originate from the usage of different gravity datums.
In other words, usage of such a global gravity
system at the compilation of the geopotential models
is a necessary precondition for the meaningful
definition of the offsets among different vertical
datums.
One of the main conclusions of the present study
was that the EGM08 derived gravity quantities agree
reasonably well with the terrestrial survey data in the
Baltic Sea region. Apparently most of the historical
terrestrial data have been utilised at the compilation
of the EGM08.
Note however, that most of the data within the
land masses of the Baltic countries have been
collected before 1990ies. Generally, the modern
gravity networks were established decades after the
historic gravity surveys. In mid 1990ies a set of
absolute gravity points was established in the Baltic
countries. After publication of the absolute gravity
measurement results (Mäkinen et al., 1996) the
national gravity networks were readjusted, see e.g.
SasUhrynowski et al. (2002) and Oja (2008). Even
though attempts were made to convert the historic
survey results into the current gravity datum, the
connections between the datasets remain still rather
loose. More specifically, at areas the discrepancies
118
between different gravity data are not random at all.
The following exercise is a clear example of this.
Most likely the gravity network points and the
results of new surveys were not accessible at the
compilation of the EGM08. For detecting the
discrepancies between the absolute gravity datum,
and the EGM08 derived gravity field the freeair
anomalies were computed at the locations of the
gravity points. Altogether 1957 new gravity points
were available for the comparisons: 424 from
Estonia, 1485 from Latvia and 48 from Lithuania.
The detected discrepancies between the newly
measured and EGM08derived gravity anomalies
(terrestrial minus EGM08) vary from 10 to +10
mGal, with a mean of +0.14 mGal, see Fig. 10. The
histogram of discrepancies is shown in Fig. 11. Such
comparisons are also produced on a countryby
country basis. The corresponding statistics can be
found in Table 1. In particular, the mean of the
discrepancies as of +0.37, +0.08 and 0.31 mGal
were achieved for the Estonian, Latvian and
Lithuanian datapoints, respectively. This shows
also, that there are some systematic biases between
the new terrestrial data and that of the EGM08. In
Fig. 10 one may detect a few regions where the dis
Fig. 10 The discrepancies between the gravity network and
new survey points and EGM08derived freeair gravity
anomalies. The discrepancies [
(,)
t
gr
∆Ω

(,)
EGMt
gr
∆Ω
]
range from 10 to +10 mGal, with a mean of 0.14 mGal. The
STD of the discrepancies is 2.0 mGal. The colours of the dots
are proportional to the range of the detected discrepancies, cf.
the colourbar. The black dots denote the locations, where the
absolute range of differences exceeds 5 mGal.
10 5 0 5 10
0
100
200
300
400
500
Fig. 11 Histogram of discrepancies between the gravity
network and EGM08derived freeair gravity anomalies. Unit
is mGal. The total number of the points is 1957.
crepancies are having the systematic nature. Clearly,
for the further improvement of the global model
accuracy the historic gravity surveys need to be
revised by the national contact persons. The results
should be made available for the future EGM
developers. This is a quite burdensome task,
requesting international and well coordinated
actions. However, this is needed for the sake of the
consistency of the global gravity data.
8 Summary and conclusions
The performance of the EGM08 model was
validated over the three Baltic countries  Estonia,
Latvia and Lithuania. Three different sets of the
“ground truth” were employed for this task.
First, the EGM08derived height anomalies were
compared with the highresolution BALTgeoid04
model. A reasonable agreement between the two
models was detected. In particular, within the
borders of Estonia, Latvia and Lithuania the absolute
ranges of the discrepancies do not exceed 15 cm.
Larger discrepancies (but not exceeding ± 3 dm) are
related to the areas where only a few data points
were available for the BALTgeoid04 modelling.
Second, the freeair gravity anomalies at the
terrestrial datapoints were compared with the
EGM08derived anomalies. This test yielded the
STD of the discrepancies ~ 2.6 mGal, which is quite
comparable with an average accuracy of the
(historical) gravity surveys in the region of interest.
Finally, the quality of the EGM08 model was
assessed with several sets of the GPSlevelling data.
It is concluded, that the overall accuracy of the
EGM08derived height anomalies in the Baltic
countries is almost of the same level as is the accura
119
Table 1. The EGM08 evaluation results.
Statistics
Type of the comparison Unit # of
points Min Max Mean STD*
BALTgeoid04 minus ζEGM
[m] 250 x 172 0.289 + 0.338 0.025 0.077
Δg(rt,Ω) ΔgEGM(rt,Ω)
Historical survey data [mGal] 42559 18.713 18.819 0.057 2.599
Modern Baltic data [mGal] 1957 8.639 +9.953 +0.136 2.046
Modern Estonian data [mGa