Lecture 5

GE 161 – Geome Geometric tric Geodesy Geodesy

Introduction to Geodesy: Concepts in Geodesy

The The Geoid Geoid Geoid and and the the Height Height Height Systems Systems Lecture No. 5 Department of Geodetic Engineering University of the Philippines

a.s. caparas/06

The The True True Shape Shape of of the the Earth Earth • Recall the three surfaces in geodesy. • Since the topographic surface is highly dynamic and irregular, the sphere and the ellipsoid are used as 1st and 2nd approximation for its shape. • However, it is the geoid which gives the closest fit of the true shape of the earth. Lecture 5

Cartoon showing the ellipsoid, geoid, and topographic surface (the landmass topography as well as the ocean bathymetry).

GE 161 161 – – Geometric Geodesy

Concepts in Geodesy: The Geoid Geoid and and the Height Systems

The G tthe he Equipo E tential all The Geoid Geoid Geoid eoid and and the Equipo Equipotenti quipotentia tential Surfaces Surfaces • The geoid is a surface of constant potential energy (equipote (equipotential ntial surface) that coincides coincides with mean sea level over the oceans. • there are an infinite number of equipotential surfaces corresponding to different potential energy. • for convenience, geodesists have commonly agreed to use use a reference reference equipotential equipotential surface, and that is the geoid. Lecture 5



What What is is so so important important with with the the Geoid? Geoid? • recall that a level surface is said to be “horizontal” “horizon tal” everywh everywhere ere and is perpendicular to the plumb line, which is the vertical line that passes through the center of an optical instrument when it is leveled • an equipotenti equipotential al surface shares the the same geodetic significance of the horizontal and the plumb line with the level surface which is why so much attention is paid to it in geodesy. Lecture 5



The G th e Height He Systems The Geoid Geoid Geoid eoid and and the the the Height Height ight Syste Systems Systems ms • The coordinates of the position of a point on the surface (topographic/terrestrial) of the earth is composed of the horizontal (φ,λ) and the vertical (height). • However, the height of a point can be referred from the ellipsoid (ellipsoidal height, h), or from the geoid (orthometric height, H). • But since the point of interest is on the topographic surface and the geoid is a closer approximat approximation ion to this surface surface than the ellipsoid, then the vertical position of the point must be referred from the geoid. • Therefore it is is essential the the geoid surface be considered as reference for heights.

Lecture 5



Ge Geoi oid d Mode ling ng Geoi Ge oid d Mo Mode Modeli deli ling ng • The normal and the abnormal/anomalous gravity field of the earth.

W (x,y,z) = U (x,y,z) + T (x,y,z) “actual gr gravity fifield”

“normal gr gravity fifield”

“disturbing/anomalous gravity field”

• The actual surface surface of the geoid geoid cannot be observed observed because of this sole reason. • The only way to generate generate a geoid surfac surface e that will be used as reference is to model the normal and the anomalous gravity field accounting factors that causes the disturbing gravity field. • There several several methods for modeling modeling the geoid using different different techniques from gravity measurement to surface generation. Lecture 5



Ge Geoi oid d odel od els s Geoi Ge oid dM Mode Mo dels ls • The EGM96

The 15’ x15’ global geoid undulation undulations s produced by EGM96 (Lemoine (Lemoine et al., 1998). The undulations undulations range range from 107 m to 85 m. Black lines indicate coast lines. Concepts in Geodesy: The Geoid Geoid and and the Height Lecture 5 GE 161 161 – – Geometric Geodesy Systems

Ge Geoi oid d odel od els s Geoi Ge oid dM Mode Mo dels ls • The GPM98

Southern Europe Lecture 5



Ge Geoi oid d odel od els s Geoi Ge oid dM Mode Mo dels ls • The AusGeoid98

Lecture 5



Ge Geoi oid d odel od els s Geoi Ge oid dM Mode Mo dels ls

The OSU 89A Lecture 5

The Philippine Geoid GE 161 161 – – Geometric Geodesy


Lecture 5

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