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geodesy
science of measuring the shape of the earth, and map projections, the transformation
of coordinate locations from the
Earth’s curved surface onto flat maps.
the geoid
Differences in the density of the Earth
cause variation in the strength of the gravitational
pull, in turn causing regions to dip or
bulge above or below a reference ellipsoid
his undulating shape is called
a geoid.
elevation
is typically defined as the distance
above a geoid. This height above a geoid is
also called the orthometric height (Figure 3-
9). Heights above an ellipsoid are often
referred to as ellipsoidal height
geoidal height and geoidal
separation.
The difference between the ellipsoidal
height and geoidal height at any location,
parallels and meridians
Lines of constant longitude are
called meridians, and lines of constant latitude
are called parallels. Parallels run parallel
to each other in an east-west direction
around the Earth. The meridians are geographic
north/south lines that converge at
the poles.
magnetic declanation
compass will usually point east or west of geographic north, defining an angular difference in direction to the poles. This angular difference is called the magnetic declination
horizontal datums
datum is a reference surface. a geodetical datum consist of two components: ellipsoid with spherical or cartesian coordinate system and origen, second,
well-surveyed points that allow us to
specify a reference frame, including an origin
or starting point
bench marks
precisely surveyed points
vertical dantum
used as a reference for specifying
heights.
Establishing vertical datums also requires
estimating the strength and direction of the
gravitational force near the surface of the
Earth
Leveling survey
are among the oldest
methods for establishing a vertical point.
Distances and elevation differences are precisely
measured from an initial point to other
points, establishing height differentials
Early surveys used an approach known as spirit leveling. Horizontal rods were placed between succeeding leveling posts across the landscape to physically measure height differences (Figure
map projections
is a systematic rendering of locations from the curved Earth surface onto a flat map surface. may be viewed as sending rays of light from a projection source (Figure 3-29). Rays radiate from a source to intersect both the ellipsoid surface and the map surface
A projection center
“light” source location
must also be specified,
most often placed at one of three locations.
The projection center may be at the
center of the ellipsoid (a gnomonic projection),
at the antipodal surface of the ellipsoid
(diametrically opposite the tangent point, a
stereographic projection), or at infinity (an
orthographic projection).
The Lambert conformal conic
LCC
projection may be conceptualized as
a cone intersecting the surface of the Earth,
with points on the Earth’s surface projected
onto the cone. The cone in the Lambert conformal
conic intersects the ellipsoid along
two arcs, typically parallels of latitude, as
shown in Figure 3-37 (top left). These lines
of intersection are known as standard parallels.
Distortion decreases towards the
standard parallels, and increases away from
these lines. Those farther away tend to be
more distorted.
One property of the Lambert conformal
conic projection is a low-distortion band
running in an east-west direction between
the standard parallels
Distortion is controlled by the placement
and spacing of the standard parallels,
the lines where the cone intersects the globe.
The transverse Mercator
is another common
map projection. This map projection
may be conceptualized as enveloping the
Earth in a horizontal cylinder
commonly intersects the Earth ellipsoid
along a single north-south tangent, or along
two secant lines
secants is often called
the central meridian. The central meridian
extends north and south through transverse
Mercator projections.
band of low distortion, but this band runs in
a north-south direction. Distortion is least
near the line(s) of intersection
Distortion increases
markedly with distance east or west away
from the intersection line
Universal Transverse Mercator Coordinate System (UTM)
The Universal Transverse Mercator
(UTM) coordinate system is another standard
coordinate, distinct from the State Plane
system. The UTM is a global coordinate system,
based on the transverse Mercator projection.
The UTM system divides the Earth into
zones that are 6 degrees wide in longitude
and extend from 80 degrees south latitude to
84 degrees north latitude. UTM zones are
numbered from 1 to 60 in an easterly direction,
starting at longitude 180 degrees West
(Figure 3-42). Zones are further split north
and south of the equator
UTM distances
Distances in the UTM system are specified
in meters north and east of a zone origin
(Figure 3-44). The y values are known as
northings, and increase in a northerly direction.
The x values are referred to as eastings
and increase in an easterly direction.
Zone easting coordinates
are all greater than zero because the
central meridian for each zone is assigned an
easting value of 500,000 meters. This effectively
places the origin (E = 0) at a point
500,000 meters west of the central meridian.
All zones are less than 1,000,000 meters
wide, ensuring that all eastings will be positive.
The equator is used as the northing origin
for all north zones. Thus, the equator is
assigned a northing value of zero for north
zones
South zones have a false northing value
added to ensure all coordinates within a zone
are positive. UTM coordinate values
increase as one moves from south to north in
a projection area.
For UTM south zones, the northing
values at the equator are set to equal
10,000,000 meters, assuring that all northing
coordinate values will be positive within
each UTM south zone
height means:
a geometric separation versus hydraulic head.
Leveling
is a process by which the geometric height difference along the vertical is transferred from
a reference station to a forward station.
differential leveling height
differences differ from orthometric height
differences by the amount that surface gravity differs from gravity along the plumb
line at that geopotential.
heights derived from uncorrected differential leveling
• are readily observed by differential leveling,
• are not single-valued by failing to account for the variability in gravity,
• will not, in theory, produce closed leveling circuits, and
• do not define equipotential surfaces. Indeed, they do not define surfaces in the mathematical
sense at all.
Orthometric heights
are the natural ‘heights above sea level,’ that is, heights above the geoid. They thus have an unequalled geometrical and physical significance
“The distance between the geoid and a point measured along the plumb line and taken positive upward from the geoid
Related to gravity in addition to being a geometric quantity
plumb line
A line perpendicular to all equipotential surfaces of the Earth’s gravity field that intersect with it
depends on gravity in two ways. First, the curve begins at the geoid. Second, plumb lines remain
everywhere perpendicular to equipotential surfaces through which they pass so the shape of the
curve is determined by the orientation of the equipotential surface
