Height systems
Rudi Gens Alaska Satellite Facility Outline
y Why bother about height systems? y Relevant terms y Coordinate systems y Reference surfaces
Height systems Height y Geopotential number y Height systems
2 Why bother about height systems?
y give a meaning to a value defined for height y combination of measurements from different sources x GPS measurements vs. leveling measurements y three-dimensional calculations Height systems Height x SAR interferometry
3 Relevant terms
y spheriod x any surface resembling a sphere x an ellipsoid of revolution y ellipsoid x defined by axes, flattening and eccentricity
Height systems Height y flattening and eccentricity x characterize the deviation from a sphere
4 Geographical and geodetic coordinates
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b
a Height systems Height Geographic Geodetic latitude latitude
5 Geographical and geodetic coordinates y geographical coordinates x implying spherical Earth model y geodetic coordinates x implying ellipsoidal Earth model Height systems Height
6 Cartesian coordinates
y geodetic coordinates inappropriate for satellite imagery Æ cartesian coordinates Height systems Height
7 Approximation vs. Reality
y ellipsoid is a good approximation to the shape of the Earth but not an exact representation y Earth surface is everywhere perpendicular to the direction of gravity Æ equipotential surface
Height systems Height y true shape of the Earth is known as geoid
8 Reference surfaces
Height systems Height y three reference surfaces x topography x geoid x ellipsoid
9 Reference surfaces
Height systems Height y topography represents the physical surface of the Earth
10 Reference surfaces
Height systems Height y geoid defined as level surface of gravity field with best fit to mean sea level x maximum difference between geoid and mean sea level about 1 m
11 Reference surfaces
Height systems Height y ellipsoid defines mathematical surface approximating the physical reality while simplifying the geometry
12 Reference surfaces
Height systems Height y geoid undulation: vertical separation between geoid and reference ellipsoid x differences between ± 100 m x global root mean square of around 30 m
13 Reference surfaces
Height systems Height y vertical deflection: angle between the ellipsoid normal and the plumb line x usually resolved in a north-south component ξ and an east-west component η x angles usually amount to a few arc seconds
14 Global earth model
y geoid defined by a set of coefficients of a spherical harmonic expansion Æ global earth model y several models available x OSU91
Height systems Height x Earth Geopotential Model 1996 (EGM96)
15 Geopotential number
y different height systems can be related to each other by the geopotential number C = − = point C W0 W g dn ∫geoid
x W and W0: the potentials of gravity of a point and Height systems Height the geoid x g: gravity value x dn: leveling increment
16 Geopotential number
y different heights calculated by dividing the geopotential number by a gravity value Height systems Height
17 Heights
y dynamic height γ x constant normal gravity 0 for an arbitrary standard latitude (usually 45 degrees) x no geometrical meaning y orthometric height x natural “height above sea level” Height systems Height x measured along the current plumb line from the foot point on the geoid and the point on the surface x gravity value: mean gravity
18 Heights
y normal height x vertical distance from terrain surface to the ellipsoid reduced by the height anomaly x measured along the ellipsoidal normal x gravity value: mean normal gravity Height systems Height
19 Solution
y ellipsoid is convenient reference frame x mathematical figure x provides good approximation to the geoid y geoid better height reference system x reference to mean sea level allows to use tide gauges as height reference points Height systems Height x physical significance: ensures horizontal representation of water surfaces such lakes and seas
20 Questions Datums
y datum x describes the relationship between a particular local ellipsoid and a global geodetic reference system y coordinate system x shape and size given by the ellipsoid x position given by the fixing of the origin Height systems Height x fixing of the origin defines a datum
22 Datums
y global datums (geocentric) x Geodetic Reference System 1980 (GRS 80) x World Geodetic System 1984 (WGS 84) y local datums x North American 1927 Height systems Height
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