Introduction to Geodesy

1
Lecture 5

• Introduction to Geodesy

Geodesy is a 21st Century science making use of
the most advanced space measurement and computer
technologies.
2
What you should know by the end of this lecture

• What is Geodesy
• Applications of Geodesy
• How do we define the shape of the Earth
• Geodetic datums and map projections used in
  Australia
• An appreciation of the Earths gravity field and
  international time systems

3
What is Geodesy?

• Geodesy is the study of
• The size, shape and motion of the earth
• The measurement of the position and motion of
  points on the earth's surface, and
• The study of the earth's gravity field and its
  temporal variations
• Types of Geodesy
• terrestrial or classical geodesy
• space geodesy
• theoretical geodesy

4
So how did Geodesy get started?

• It began with the idea of a spherical Earth

About 500BC Pythagoras claimed kai thu ghu
stroggulhu
The Earth is round
5
Then what...

• Eratosthenes (276 - 195BC) made the first attempt
  to compute the dimensions of the Earth.
• He noticed that at the summer solstice (ie sun
  directly overhead) the suns rays were reflected
  vertically from a deep well in Syene, Egypt.At
  the same time, at Alexandria, the suns rays were
  measured at an inclination of 7o 12 from the
  vertical

6
The diagram
S distance from Alexandria to Syrene
Sphere radius r circumference C 2?r
S r.Z r S / Z
but assumes Alexandria and Syrene on same meridian
7
The results

• Syene not exactly on Tropic of Cancer. Therefore
  Sun not
• directly overhead.
• Syene and Alexandria not on same meridian
• Distance between Syene and Alexandria not
  accurately
• known (10 too long)
• Earth not exactly spherical

Final result gave circumference of the Earth as
16 too big.
8
Is that it?

• After Columbus and de Gama discovered earth was
  not flat
• Fernel, 1525 observed the elevation of the sun in
  Paris and Amiens using astro tables and odometer,
  1 error
• Newtons laws of motion determined the earth was
  a oblate ellipsoid.

9
more...

• Bouguer discovered regional gravity variations
  due to the non uniform density of the earth
• Clairaut and Stokes relationships between gravity
  measurements and the flattening of the earth
• Laplace, Gauss and Bessel, deviation of the plumb
  line

10
So why do we study Geodesy

• Geophysics and Oceanography
• Meteorology, astronomy and physics
• Geology
• Crustal dynamics
• Astronomy

Geodesy serves as a foundation for the mapping
and referencing of all geospatial data, it is a
dynamic application of scientific methods in
support of many professional, economic and
scientific activities and functions, ranging from
land titling to mineral exploration from
navigation, mapping and surveying to the use of
remote sensing data for resource management from
the construction of dams and drains, to the
interpretation of seismic disturbances.
Applications
11
Earth and ocean tides affect both the shape of
the ocean surface and the gravity field. Their
measurement and interpretation may therefore be
regarded as essential to geodesy as well as to
geophysics and oceanography.
12
Refraction of electromagnetic waves in the
Earths atmosphere affects geodetic measurements
that are made at various wavelengths of the
electromagnetic spectrum, as so the interest of
geodesists overlap with those of the
meterologist, astronmer and ionospheric
physicist.
13
The study of the gravity field by surface
measurements and by satellite methods is of
direct relevance to geology since it reveals the
existence of otherwise inaccessible structures at
various depths inside the Earth. An accurate
knowledge of the geoid is also required in
satellite altimetry to allow the identification
of the undulations of the ocean surface caused by
currents and wind.
14
Local, regional and global movements of the
earths crust result in changes in the positions
of geodetic reference points, and so geodesy
contributes to the study of crustal dynamic, a
term used to study the relationship between
earthquakes and plate tectonic motion. The space
geodetic techniques of satellite laser ranging,
radio interferometry and GPS are providing direct
determinations of the current rates of motion of
the earths crustal plates.
15
A knowledge of the orientation of the earth with
respect to a space fixed reference frame is
necessary for interpreting many type of
astronomical observations. Thus the study of
Geodesy is of fundamental importance to
astronomy. Moreover variations in the rotation
rate and the orientation of the rotation axis
provide valuable data on the interior of the
earth and about the interactions between the
crust, oceans and atmosphere. These studies
apart from providing useful data for geophysics,
oceanography, and meteorology, are of
significance to theories of the origin and
evolution of the earth-moon system. They may
also provide a measure of the possible variations
in the constant of gravity.
16

• survey and mapping
• precise relative positions eg oilfields
• satellite positioning and navigation
• earthquake prediction
• engineering - relocation of drilling rigs,
  construction of long tunnels and canals,
  deformation monitoring
• Location of mineral, oil and ore deposits
• flood risk management
• Scale of universal time for global navigation

17
Geodesy in Australia

• Australian Land Information Group (AUSLIG)
• CSIRO
• Universities
• Australian Academy of Science
• International Association of Geodesy (IAG)

18
Shape of the Earth

• Over limited area treat earth as a plane - simple
• Sometime as as a sphere - spherical trigonometry
• geoid
• Forces generated by the Earths rotation
  flatten the Earth into an ellipse

.
19
Relationship Between Different Surfaces
Earth An irregularly shaped planet we have to
work on. Geoid An equipotential surface (a
fancy way of saying the pull of gravity is equal
everywhere along the surface) which influences
survey measurements and satellite orbits. A
plumb bob always points perpendicular to the
geoid, not to the center of the earth.
Ellipsoid An ellipse which has been rotated
about an axis. This provides a mathematical
surface on which we can perform our
calculations. The shape of the ellipsoid is
chosen to match the geoidal surface as closely
as possible.
20
(No Transcript)
21
(No Transcript)
22
Relationship between the Geoid and Ellipsoid
geoid - spheroid separation N h - H
H orthometric height approximated by AHD above
the geoid h spheroidal height above the
spheroid N geoid height above the spheroid
23
Deflection of the Vertical

• Instrument set up perpendicular to the geoid.
  Because we work with the spheroid. Difference is
  the deflection of the vertical. This can be
  neglected if small.
• deflections are unique for each spheroid,
  depending on the fit of the ellipsoid to the
  geoid should be less than 1
• Varies continuously with position due to local
  variations in the geoid
• are related to the differences between astronomic
  and geodetic coordinates

24
Coordinate Systems

• Plane Coordinates
• local, possible arbitrary
• z axis vertical throughout
• right handed system
• bearings relative to y axis
• ignores shape of earth
• x,y,z

25
The most commonly used coordinate system today is
the latitude, longitude, and height system. The
Prime Meridian and the Equator are the reference
planes used to define latitude and longitude.
26
The geodetic latitude of a point is the angle
from the equatorial plane to the vertical
direction of a line normal to the reference
ellipsoid. The geodetic longitude of a point
is the angle between a reference plane and a
plane passing through the point, both planes
being perpendicular to the equatorial plane.
The geodetic height at a point is the distance
from the reference ellipsoid to the point in a
direction normal to the ellipsoid.
27
Cartesian Coordinate System
28
Map Grid Coordinates

• derived from geodetic coordinates
• transform 3D to 2D
• scale and line distortions present
• survey observables require corrections
• map projections

29
Introduction

• The aim of a map projection is to represent the
  Earths surface or mathematical representation of
  the Earths surface on a flat piece of paper
  with a minimum of distortion.
• Recall
• Spheroidal Earth can be approximated to a plane
  over small areas with minimal distortion
• As the area of the spheroid becomes greater then
  the distortion becomes greater

30
The Problem
P
Q
P
Y
?
?
Q
X
We can say that x f1(???) y f2(???)
Therefore, the coordinates on the plane have a
direct functional relationship with latitude and
longitude. It follows that should be a one to
one correspondence between the earth and the
map. However 1) some projections may not be able
to show the whole surface of the Earth. 2) some
points may be represented by lines instead of
points This is because the spheroid has a
continuous surface whereas a plane map must have
a boundary.
31
Projection surfaces

• developable surfaces
• geometric or mathematical
• gnomonic, stereographic, orthographic

32
Map projections are attempts to portray the
surface of the earth or a portion of the earth on
a flat surface. Some distortions of conformality,
distance, direction, scale, and area always
result from this process. Some projections
minimize distortions in some of these properties
at the expense of maximizing errors in others.
Some projection are attempts to only moderately
distort all of these properties.
Conformality When the scale of a
map at any point on the map is the same in any
direction, the projection is conformal.
Meridians (lines of longitude) and parallels
(lines of latitude) intersect at right angles.
Shape is preserved locally on conformal or
orthomorphic maps. Distance -
equidistant A map is equidistant
when it portrays distances from the center of the
projection to any other place on the map.
Direction - azimuthal A map preserves
direction when azimuths (angles from a point on a
line to another point) areportrayed correctly in
all directions. Scale
Scale is the relationship between a distance
portrayed on a map and the same distance on the
Earth. Area - equal-area When a map
portrays areas over the entire map so that all
mapped areas have the same proportional
relationship to the areas on the Earth that they
represent, the map is an equal-area map.
33
When the cylinder upon which the sphere is
projected is at right angles to the poles, the
cylinder and resulting projection are
transverse.
When the cylinder is at some other,
non-orthogonal, angle with respect to the
poles, the cylinder and resulting projection is
oblique.
34
The Universal Transverse Mercator UTM
The Universal Transverse Mercator projection is
actually a family of projections, each having in
common the fact that they are Transverse Mercator
projections produced by folding a horizontal
cylinder around the earth. The term transverse
arises from the fact that the axis of the
cylinder is perpendicular or transverse to the
axis of rotation of the earth. In the Universal
Transverse Mercator coordinate system, the earth
is divided into 60 zones, each 6 of longitude in
width, and the Transverse Mercator projection is
applied to each zone along its centerline, that
is, the cylinder touches the earth's surface
along the midline of each zone so that no point
in a given zone is more than 3 from the location
where earth distance is truly preserved.

• unit of length is the metre
• an ellipsoid is adopted as the shape and size of
  the earth
• coord obtained by a TM of f and l of points on
  the ellipsoid
• the true origin of coords is the intersection of
  the equator and the central meridian of a zone
• a central scale factor of 0.9996 is superimposed
  on the central meridian
• for points in the northern hemisphere, E and N
  coords are related to a false origin 500,000m W
  if the true origin and for points in the southern
  hemisphere, E and N are related to a false origin
  500,000m W and 10,000,000m S of the true origin
• the projection has 60 zones, 6o wide in
  longitude, beginning with zone 1 having a central
  meridian of 177oW, numbered consecutively
  eastwards, ending with zone 60 with a central
  meridian of 177oE
• the latitude extent of each zone is 80oS and 84oN

35
AMG and MGA

• The AMG and MGA are both systems of rectangular
  coordinates based on TM projections of f and l
  related to the AGD and GDA.
• closely corresponds with the UTM grid used
  globally
• coordinates in metres
• zones are 6 wide (1/2 degree overlap)
• zones numbered from zone 49 with central
  meridian 111E to zone 57 with central meridian
  159E
• central scale factor k0 0.9996
• origin of each zone is the intersection of
  central meridian with the equator

• false origin S 10 000 000m, W 500 000
• coordinates described in Easting (E) and
  Northing (N)

36
WGS84 cartesian to AMG
Note height transformed by hWGS84 - N HAHD
37
Geodetic Datums

• numerical or geometrical quantity or set of
  quantities which serve as a reference or base for
  other quantities
• The adopted coordinates (after and adjustment of
  measurements comprise the datum)
• The spheroid is a simple geometrical reference
  surface to which the coordinates are referred
• horizontal or vertical, datums
• regional or global different best-fitting
  reference spheroids have been defined in
  different parts of the world because of the
  undulating geoid. Eg. the Australian National
  Spheroid.

NB Difference between spheroid and datum
38
Geodetic Datums

• consists of f, l or an initial origin the
  azimuth for one line the parameters of the
  reference ellipsoid and the geoid separation at
  the origin. The deflection of the vertical and
  geoid-spheroid separation are set to zero at an
  origin point eg Johnson in Australia
• geodetic latitudes and longitudes depend on both
  the reference spheroid and coordinate datum
• often the spheroid is implicitly linked to the
  datum, so it has become common to use the datum
  name to imply the spheroid and vice versa eg
  WGS84
• the orientation and scale of the spheroid is
  defined using further geodetic observations
• horizontal and vertical

39
Geodetic Datums

• Local/regional datum
• Approximates size and shape of the earth on a
  local, regional scale
• geometrical centre of the spheroid not
  necessarily coincident with geocentre
• well suited to surveying over the areas they were
  defined for - inadequate for global satellite
• surveying systems.

40
Regional Spheroids and Datums

• once the best-fitting spheroid is adopted, all
  geodetic observations are reduced to this
  spheroid, adjusted in a least squares sense,
  which forms the geodetic datum.

eg the Australian Geodetic Datum (AGD) is based
on ANS
41
Global Spheroids and Datums

• satellite geodesy provides us with spheroids that
  are geocentric, where their geometrical centre
  corresponds with the Earths centre of mass since
  the satellite orbits are close to the geocentre
• orientation achieved by aligning its minor axis
  with the Earths mean spin axis at a particular
  epoch eg WGS84
• a modern global network of accurately coordinated
  ground stations comprises a global datum called
  the International Earth Rotation (IERS)
  International Terrestrial Reference Frame (ITRF)

42
Global Spheroids and Datums

• ITRF is positioned relative to the geocentre
  using a variety of space geodetic techniques,
  such as Satellite Laser Ranging (SLR), Very Long
  Baseline Interferometry (VLBI) and GPS.
• The ITRF is considered to be a more reliable
  datum than WGS84 and will form the backbone of
  the GDA 10cm difference between them
• Datum and spheroid must be specified to define
  horizontal position not just f, l
• Without this information a single point can
  refer to different positions