EGM2008 EVALUATION FOR AFRICA

Charles L Merry

School of Architecture, Planning and Geomatics, University of Cape Town,

Rondebosch, South Africa. E-mail: charles.merry@uct.ac.za

1 Introduction
The Earth Geopotential Model 2008 (EGM2008) is the latest version of a series of
geopotential models developed under the leadership of the National Geospatial-
Intelligence Agency (Pavlis et al., 2008). It incorporates harmonic coefficients
derived from the GRACE satellite mission, marine gravity anomalies derived from
satellite altimetry, and a comprehensive set of terrestrial gravity anomalies. It is likely
to become the standard geopotential model used for many applications including orbit
modelling and geoid modelling. As such, it is important that it be assessed by means
of comparisons with independent or quasi-independent data sets. This paper focusses
the assessment on the continent of Africa, probably the continent for which the details
of the Earth's geopotential are least well known. This evaluation has been carried out
using three data sets:

• African Geoid Project 2007 geoid model (5' by 5' grid)

• Point gravity anomalies for southern Africa
• GPS/levelling data for 79 points in South Africa

The first two data sets are not truly independent of the EGM2008. Most of the point
gravity anomalies in the second data set also formed part of the terrestrial data used in
EGM2008. The AGP2007 geoid model (Merry, 2007) used gravity anomalies which
were also used in EGM2008, and it also used harmonic coefficients derived from
GRACE tracking data. Nevertheless, there are sufficient differences in the way the
data were used for the two data sets to provide a meaningful comparison.

2 Geoidal Heights
The AGP2007 geoidal height model uses the following data in a remove-restore
model:

• Eigen GL04C geopotential model, truncated at degree 120, tide-free system,

referenced to the WGS84 ellipsoid, a=6378137m.
• A gridded set of 5' free-air gravity anomalies, derived from three major data
sets – the holdings of the University of Cape Town (UCT) for Africa south of
8° S; the holdings of the University of Leeds for the rest of Africa (Fairhead
et al. 1988); and the KMS02 marine gravity anomaly data set from the
Danish National Survey and Cadastre (Andersen et al., 2005). Where

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 insufficient measured values existed, the Eigen GL04C field was used to
generate grid values.
• The Molodensky G1 correction term and the correction N-ζ to convert from
height anomalies to geoidal heights were computed using the gridded
anomalies and the SRTM 30" DEM (Farr and Kobrick, 2000).

EGM2008 geoidal heights for Africa, referred to the WGS84 ellipsoid in the tide-
free system, were extracted from a data set available on the NGA EGM2008 web
page (Pavlis et al., 2008). These data are on a 2.5' grid - this set was decimated to a
5' grid to enable a direct comparison with the AGP2007 model. The results are
summarised in Table 1 and Figures 1 and 2.

Difference # of points Minimum Maximum Mean Std. Dev.

EGM2008 593832 -4.58m +6.31m +0.02m 0.73m
minus AGP2007

Table 1: Difference between EGM2008 and AGP2007 Geoid Models

Figure 1: EGM2008 Geoid minus AGP2007 Geoid (metres)

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 Figure 2: EGM2008 Geoid minus AGP2007 Geoid
(contour interval: 0.5m)
(showing differences where the magnitude exceeds one metre)

The striping that is a feature of many of the GRACE models, including Eigen
GL04C used for AGP2007, is apparent in Figure 1. As mentioned in Pavlis et al.
(2008) the GRACE data have been re-processed to remove this effect from
EGM2008. Figure 2 highlights the larger discrepancies (magnitude larger than one
metre). Negative values are blue/green, positive values are in yellow/brown/purple.
The minimum discrepancy listed in Table 1 occurs in northwest Angola, in a region
where no measured gravity values were available for AGP2007. The maximum
discrepancy listed in Table 1 occurs in southern Turkey, outside the area of interest.
Looking at some of the discrepancies within Africa:

• There are large positive discrepancies in Egypt, with the maximum (+5.7m)
occurring in the Sinai region. No terrestrial data were available for AGP2007
in the Sinai region, and it could be that EGM2008 has made use of new data.
Terrestrial data are available for AGP2007 in the remainder of Egypt, and the
large positive discrepancies are unexplained.

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 • The large positive discrepancy in the southeast of Western Sahara is
unexplained. Terrestrial gravity data are available in this region.
• The small regions of positive discrepancy in northern Chad and central
Nigeria are in regions where there are no terrestrial data available for
AGP2007. Presumably such data were available for EGM2008.
• The large (-4.6m) negative discrepancy in northwest Angola is in an area
where no data were available to AGP2007. Further south, data are available,
but a negative discrepancy persists.
• The positive discrepancies in central and northern Mozambique are in areas
where no gravity data were available to AGP2007.

There are large gravity data gaps in Africa (Merry, 2007). For AGP2007 these data
gaps were filled using the Eigen GL04C model only. For EGM2008 these gaps were
filled using a combination of geopotential coefficients from GRACE and from
gravity anomalies deduced from a 30" DEM using the Residual Terrain Model
(RTM) approach (Pavlis et al., 2006). As is evident from the discussion above, the
two different approaches have yielded substantially different results for geoidal
heights in areas lacking observed terrestrial gravity data. Overall, the discrepancies
are larger than expected. A more detailed investigation would need more detailed
information regarding the terrestrial data used in EGM2008. Unfortunately there are
no GPS/levelling data sets available in the areas of the major discrepancies which
could be used to resolve these discrepancies.

3 Gravity Anomalies
The computation of AGP2007 used a 5' grid of free-air gravity anomalies. These were
interpolated from point values. Only the point values in the University of Cape
Town's holding are available for comparison (essentially south of 8° South). The
EGM2008 harmonic coefficients were used to generate a 5' grid of gravity anomalies
for southern Africa. In turn, these gridded data were used to interpolate gravity
anomalies at the data points The comparison between the two sets is summarised in
Table 2 and in Figure 3.

Difference # of points Minimum Maximum Mean Std. Dev.

Measured ∆g 157495 -132.7mgal +81.4mgal -0.8mgal 9.3mgal
minus EGM2008

Table 2: Difference between Measured and EGM2008 Gravity Anomalies

There are some interesting discrepancies between the measured gravity anomalies and
those deduced from the EGM2008 harmonic coefficients:

• With some exceptions the positive discrepancies are correlated with regions of
high or rough topography. This is especially so in Lesotho, where elevations
routinely exceed 2000m.

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 • The "peak" on the coast of Namibia correlates with the Brandberg mountain,
which EGM2008 has failed to model (no doubt due to the short wavelength
nature of the feature).
• The "peak" to the west of Lesotho corresponds to the position of the
Trompsburg gravity anomaly – like the Brandberg a short-wavelength feature.
• The linear feature on the border between South Africa and Mozambique
corresponds with a known steep gradient in the observed anomalies.
• The extensive area of positive discrepancies in Angola corresponds to a
similar discrepancy between the EGM2008 and AGP2007 geoid models. As
the discrepancy is of the order of 14mgal, the possibility exists that measured
data have not been converted from the Potsdam gravity datum to the IGSN71
gravity datum.
• There is a further positive discrepancy in the Caprivi region of northeast
Namibia. This area is virtually flat and the cause of the discrepancy has not
been identified.

Figure 3: Measured minus EGM2008 Gravity Anomalies (mgals)

Generally, within South Africa, where there is good gravity coverage, the agreement
is good. As with the geoidal heights, it is difficult to comment further upon the
discrepancies without knowing in detail what observed gravity data were used in
forming the EGM2008 model.

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4 GPS/Levelling
Precise GPS/levelling geoidal heights are few and far between in Africa. Not all data
sets are freely available, and where there are such data, there is often no information
on the quality of the data. Recently, a new GPS/levelling data set became available for
South Africa (S. Koch, personal communication, 2008). The GPS measurements have
been made at 79 benchmarks of the precise levelling network of South Africa by staff
of the Chief Directorate: Surveys & Mapping (Figure 4). The GPS co-ordinates are in
the ITRF2005 reference frame, and ellipsoidal heights refer to the WGS84 ellipsoid.
The South African height system is essentially a modified normal height system, so
for the purposes of comparison EGM2008 height anomalies were computed at these
79 points. The results are summarised in Table 3, which includes results for AGP2007
and EGM96 height anomalies.

Figure 4: GPS/Levelling Data Points – South Africa

Difference Minimum Maximum Mean Std. Dev.

GPS/levelling – EGM2008 -0.84m +0.02m -0.42m 0.17m
GPS/levelling – AGP2007 -0.92m +0.36m -0.44m 0.24m
GPS/levelling – EGM96 -0.95m +0.68m -0.24m 0.35m

Table 3: Difference between GPS/Levelling and EGM2008 Height Anomalies

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EGM2008 provides the most consistent agreement with the GPS/levelling data and is
a substantial (two-fold) improvement over EGM96. The AGP2007 result is
disappointing considering that (at least within South Africa) EGM2008 and AGP2007
used essentially the same terrestrial gravity data. It is possible that the "striping"
inherent in the underlying GL04C model used for AGP2007 may have contributed to
this comparatively poor result.

5 Conclusions
EGM2008 is a significant improvement over EGM96. Within South Africa there is a
two-fold improvement in the agreement with GPS/levelling. EGM2008 appears to be
free of the striping effect evident in geoidal heights computed from other models
based upon the GRACE mission.

There are significant small scale discrepancies with the AGP2007 geoid model, and
with the free-air gravity anomaly data in southern Africa. These discrepancies could
be due to:

• differences in the available terrestrial gravity data sets.

• differences in the way in which data gaps have been filled.

Further investigation into the sources of these discrepancies is warranted.

References
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