DEPARTMENT OF GEODETIC
ENGINEERING
Visca, Baybay City, Leyte, PHILIPPINES
Telephone: (053) 565-0600 local 1027
Email: dge@vsu.edu.ph
Website: www.vsu.edu.ph
GEng 126n – Physical Geodesy
Assessment No. 3
Name: Darlen T. Vicente
Offering No.: Y028
BSGE _2_
GEOID VS QUASIGEOID
I.
Introduction:
For years, the geodetic community is in the midst of an argument on which
among geoid and quasigeoid should be used as a reference surface for the
international height system. Most European states utilize M.S. Molodensky’s
concept of normal heights with the quasigeoid model however, the rest of the globe
rely on orthometric heights with the geoid as the zero – level.
This classical, physically featured surface which was introduced on 1873
by Listing, the geoid is determined to provide sufficient accuracy from the
measurements of the surface of the earth aside from being the most natural surface
to refer heights. In connection, it is asserted in the past 60 years the ideas of geoid
in dealing measurements kept falling into disrespect that bridges this diverse and
artificial surface called quasigeoid to enter into the scene which could be a great
substitute for computing surface data.
This report will explain the comparison between geoid and quasigeoid and
how the former had lost its punch due to advancements in the theory of geoid
computation in consideration to a knowledge increase of topographical density
anomalies.
II.
Discussion:
GEOID
QUASIGEOID
Surface of equal gravity potential (or
equipotential) that closely approximates
mean sea level. Heights with respect to the
geoid are known as orthometric heights 𝑯
and are the curved line distance between
the geoid and point of interest measured
along the plumbline.
Non-equipotential surface of the Earth’s
gravity field closely aligned to the geoid with
differences up to about 3.4 m in the
Himalayas (Rapp, 1997) and 0.15 m in
Australia (Featherstone and Kirby, 1998).
Heights with respect to the quasigeoid are
known as normal heights 𝑯* and are the
curved line distance between the quasigeoid
and point of interest measured along the
plumbline.

The Geoid
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There are an infinite number of surfaces of equal gravity potential
radiating out from the centre of mass of the Earth to outer space. The geoid is
the surface of equal gravity potential which is the best fit to mean sea level and
is denoted by 𝑊0 (units 𝑚2 𝑠 −2 ). See Figure 1 below.
Figure 1: The geoid is the surface of equal gravity potential which is the best fit
to mean sea level and is denoted by 𝑊0.
Where:
H = Orthometric Height
N = Geoid Undulation
h = Ellipsoidal Height
To approximately compute physical heights from GNSS (H), the
geometric distance between the ellipsoid and geoid (N) needs to be subtracted
from the ellipsoidal height (h).
𝑯≈ 𝒉−𝑵
Earth Geopotential Model 2008 (EGM2008) is one of the wide range of
geoid models developed for the conversion of geometric ellipsoidal heights to
physical heights which has an absolute accuracy of 20 cm.
The orthometric height system is compatible with a geoid model. An
orthometric height 𝐻 is the curved line distance between the geoid and point of
interest measured along the plumbline and computed by,
𝑯 = 𝑪/𝒈̅
where the geopotential number 𝑪 is divided by the integral mean of
gravity taken along the plumbline 𝒈̅.
Vision:
Mission:
A globally competitive university for science, technology, and environmental conservation.
Development of a highly competitive human resource, cutting-edge scientific knowledge and
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
The Quasigeoid
Recognising that evaluating 𝑊𝑝 on the geoid is practically impossible
to do, Molodensky (1945) introduced an alternative theoretical surface called
the quasigeoid. For the determination of the quasigeoid all the computations
are done, not on the geoid surface but, on the surface of the Earth.
Molodensky’s approach deals only with the external field and needs only to
know the geometry of the external field. The normal gravity is evaluated on the
surface of the telluroid.
The telluroid is a theoretical surface:
 where the normal potential gravity is equal to the true gravity potential
on the Earth’s surface i.e. 𝑈𝑝3 = 𝑊𝑝4 and on the same plumb line; and
 looks like the Earth surface except that it is displaced from the Earth
surface by the quasigeoidal height (Figure 2).
Figure 2: The telluroid is a theoretical surface where the normal potential gravity
is equal to the gravity potential of the Earth on the Earth’s surface i.e. 𝑈p3 =
𝑊p4.
Where:
H = Orthometric Height
h = Ellipsoidal Height
𝜁 = height anomaly
To compute normal heights from GNSS, the geometric distance
between the ellipsoid and the quasigeoid is known as the height anomaly 𝜁
needs to be subtracted from the ellipsoidal height ℎ.
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Development of a highly competitive human resource, cutting-edge scientific knowledge and
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Points to remember:
 Offshore, where there is no topography, the quasigeoid agrees with the
geoid.
 Onshore, it differs from the geoid by 1-2 cm in flat terrain up to 10 cm in
steep topography
The normal-orthometric height 𝑯NO is distance between the quasigeoid
and the point of interest measured along the curved normal gravity 𝜸 plumbline
and computed by,
𝑯NO = 𝑪𝜸/ 𝜸̅
In contrast to orthometric and normal height systems, which require
gravity observations to be taken along the levelling traverse in order to derive
the geopotential numbers (or normal or orthometric corrections), geopotential
numbers, 𝑪, are replaced by differences in normal potential 𝑪𝜸 (known as
normal-geopotential or spheropotential numbers) and gravity is replaced by
normal gravity (integral mean value of normal gravity taken along the normal
plumbline between the quasigeoid and point of interest) (Featherstone and
Kuhn, 2006).
III.
Conclusion:
From here, we could observe that the latter concept, in contrast to the
former will face uncertainty in the topographic density distribution while the
quasigeoid model may suffer convergence problem.
The issue in topo – density relies in this approach, but it can be resolved
to an accuracy of a few cm if the geological formation of the crust is reasonably
well known. To get the total geoid accuracy the uncertainty in the effect of
irregular topo-density must be added to the uncertainty in geoid determination
that comes from the employed approximations in the theory and the numerical
computations.
It has to be concluded that we have managed to eliminate, or at least
considerably reduce the well-understood physical difficulties encountered
when solving the classical geodetic boundary value problem while the
geometrical difficulties associated with Molodenskij’s theory remain.
IV.
References:
Anzlic Committee on Surveying and Mapping. (2021). Australian Vertical
Working
Surface
(AVWS)
Featherstone, W., and Kirby, J (1998). Estimates of the Separation Between
the
Geoid and the
Quasigeoid Over Australia. Geomatics
Research
Australasia. 68: pp. 79-90.
Sjoberg, L. (2013). The geoid or quasigeoid - which reference surface should
be preferred for a national height system?.
Vision:
Mission:
A globally competitive university for science, technology, and environmental conservation.
Development of a highly competitive human resource, cutting-edge scientific knowledge and
innovative technologies for sustainable communities and environment.
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Vanicek, P., Kingdon R., and Santos, M., (n.d). Geoid vs Quasigeoid: A Case
of Physics
Versus Geometry Vol 42:pp 101-118.
Vision:
Mission:
A globally competitive university for science, technology, and environmental conservation.
Development of a highly competitive human resource, cutting-edge scientific knowledge and
innovative technologies for sustainable communities and environment.
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