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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
How are orthometric heights related to geopotential?
CA = ¯g HA
meaning that a geopotential number is equal to an orthometric height multiplied by the average
acceleration of gravity along the plumb line
orthometric heights
constitute the embodiment of the concept of “height above sea level”
are single-valued by virtue of their relationship with geopotential numbers and, consequently,
will produce closed leveling circuits,
do not define equipotential surfaces due to the variable nature of the force of gravity. This
could, in principle, lead to the infamous situation of water apparently “flowing uphill.” Although
possible, this situation would require a steep gravity gradient in a location with
relatively little topographic relief.
are not directly measurable from their definition. Orthometric heights can be determined
by observing differential leveling-derived geometric height differences to which are applied a
small correction, the orthometric correction
ellipsoid heights
• are single-valued (because a normal gravity potential field satisfies Laplace’s equation and is,
therefore, convex),
• do not use the geoid or any other physical gravity equipotential surface as their datum,
do not define equipotential surfaces, and
are readily determined using GPS.
H ≈ h − N
H is orthometric height, h is ellipsoid height and N is the ellipsoid height of the geoid itself, a geoid height or geoid undulation
Geopotential numbers
which gives the change in gravity potential energy between a point on the geoid and another
point of interest. The geopotential number for any place is the potential of the geoid W0 minus
the potential of that place W
Tide
Periodic changes in the shape of the Earth, other planets or their moons that
relate to the positions of the Sun, Moon, and other members of the solar system.
The gravitational force
he Moon on the Earth itself is found using Equation 2.2 on page 17:
FE = −GMmˆr
|r|^2 ,
Ocean tides affect the geoid
by redistributing the mass of the oceans, which has the following
effects. First, the redistribution of the water in the oceans creates a discernible change in the geoid.
Second, the weight of the water deforms the Earth below it, in addition to the tidal potential also
deforming the Earth
geoid height
is the geometrical separation (distance) from some reference
ellipsoid to the geoid, an ellipsoid height is the geometrical separation from some reference ellipsoid
to a point of interest, and an orthometric height is the length of the plumb line from the geoid to a
point of interest. Were plumb lines straight lines and if they were normal to the reference ellipsoid
Error sources have been grouped in three main categories:
satellite position and clock errors, signal propagation errors, and receiver error
two key pieces of information upon which GNSS positioning depends:
signal propagation time and the location of the SVs
Signal propagation time
is used to infer the range from the SVs to a receiver antenna’s phase center, and SV locations are used as the coordinates of the known points in the trilateration scheme.
the signal propagation time is biased due to an immeasurable time offset between GPS time and a receiver’s internal clock; this results in a pseudo-range rather than the actual range.
trilateration:
given three (or more) known locations and a distance from those locations to the point of interest, determine the coordinates of the point of interest
since the satellites are in motion, it does not suffice to publish a single set of coordinates for them. Instead, ephemerides are created for each SV so that the processing software can determine SV positions at the moment of transmission, which form the basis for the trilateration.
Satellite Clock Errors
GNSS satellites have onboard atomic time standards
GPS time is a weighted
average of the clocks in the controlling station on Earth and the GPS satellite clocks. Each SV
clock is monitored for its offset from GPS time, and this time bias estimate is included with the
ephemerides, both broadcast and precise, to be accounted for in the positioning software
GPS Signal Propagation Delay Errors
GNSS ranges are inferred by measuring a (biased) elapsed time from the satellite to the receiver; it is biased due to an immeasurable time offset between GPS time and a receiver’s internal clock. This elapsed time interval is scaled to be a distance by multiplying by the speed of light. GNSS signals propagate through the Earth’s atmosphere and are affected
by the ionosphere and the troposphere. Both of these atmospheric layers delay the signals, thus
introducing timing/ranging errors.
Ionosphere Delays
is a high-altitude (roughly 50 km to 1000 km above the Earth’s surface) part of the atmosphere that is composed of charged particles that have been ionized by solar radiation. It refracts rate signals
Troposphere Delays
part of the atmosphere in which weather occurs. Atmospheric density gradients of the troposphere, like the ionosphere, refract GNSS radio waves. one of the
reasons why the height component is much worse than the horizontal components in precise GPS positioning
Multipath
One of the two GNSS observables is carrier phase: “carrier” refers to the unmodulated radio signal broadcast by the SVs and “phase” refers to the total number of cycles of the carrier waves from its transmission to its reception, including a partial wavelength at the end. Multipath is the situation where GNSS radio signals arrive at the receiver via more than one path. This happens by the signal reflecting from some surface such as a chain link fence, a building, a car, or the ground
Receiver Errors and Interference
The receivers themselves cannot determine positions exactly
Electromagnetic interference and signal attenuation
The radio signals currently broadcast by the GPS satellites are relatively low power, around 50
watts. Although GNSS signals occupy a protected frequency band, nearby sources of broadband electromagnetic noise can overwhelm them
Continuous GPS Stations (C GPSS)/ CORS
Continuous GPS Stations (C GPSS) are permanently placed GPS receivers used by the academic and
research community to monitor minute changes in the shape of the earth. Continuous GPS Stations (C GPSS) refers to official
NGS stations and “C GPSS” is the generic term for Continuous GPS stations.
The predecessor to C ORS came about in the late 1980’s to provide fixed ground locations to compute more precise orbits for the satellites.
A “baseline”, or “vector”, between two receivers is derived from the differences of their 3D coordinates This is the “relative” positional relationship. The “absolute” position of either of these two receivers comes from attaching one end of the vector to a known position on a particular datum on a particular date.
static and rapid static
techniques require setting a receiver on a survey point, collecting satellite data for an appropriate amount of time and using data collected at a second receiver (either yours or a C GPSS) to compute a “baseline” or “vector” (the relative position between the two receivers)
(RTK)
real time kinematic
Antenna Height (AH)
is the vertical distance from the occupied point or station to the Antenna Reference Point (ARP)
RINEX
(Receiver Independent Exchange Format) is a
generic text file format that allows for the processing of
data from disparate GPS receivers
OPUS
The current version of OPUS determines the position of a single point
with data from a dual frequency receiver
It claims potential centimeter
(0.03 ft) accuracies at the one-sigma (s) level, under ideal conditions
OPUS currently has two processing options; OPUS-RS (Rapid Static) for
time spans of 15 minutes to 2 hours and OPUS-S (STATIC) for 2 to 48 hours
OPUS-RS
ses three to nine CORS but no more than 250 km from
your site for its solution. In addition your site must be no more than 50 km
outside of the boundary created by the exterior CORS. This means some
areas in the U.S. cannot use OPUS-RS,
Opus results
the results show positions (latitude & longitude
and Earth Centered Earth Fixed coordinates) on two datums: NAD 83
(CORS96 Adjustment) with an epoch of 2002.00; and ITRF00 with an epoch date the same as that of the survey. In addition, UTM coordinates and State
Plane Coordinates are provided (in meters). The State Plane Coordinates are
based on the NAD83 CORS96 values. The RAPID STATIC report will provide
standard deviations for each value, while the STATIC report will provide
peak to peak errors.
The standard deviation error shown on the OPUS –RS
report is the statistical
results of the simultaneous solution used to determine the position.
Generally these standard deviation values are “optimistic” meaning they
make your survey look better than it really is.
Terrestrial laser scanning (TLS)
form of light detection a nd
ranging (LIDAR), is an advanced laser-based imaging tech nology that allows for detailed mapping of terrai n at very high levels of precision.potentially hazardous landslide deposits.
Terrestrial laser scanning involves
the field deployment
of survey instrumentation that images the landscape and records three-dimensional positions and bea m attenuation. TL.) produces point-cloud position data sets tha t are clusters of millions of individual position measurements in the form of range distances a nd azimuthal and zenith angles.
Ground-based scanning-laser light detection and ranging LIDAR
technology creates
ultra high-resolution 3-D digital terrain models of earthquake damage. This new
technology allows for the rapid detailed collection of post-earthquake failure geometries
prior to modification by post-disaster recovery efforts and natural processes
Peak to peak error
shown on the OPUS-S report is the difference in the
solution from each of the three CORS used to determine the position of your
receiver. This is a direct indicator of the potential error in your solution
