Post on 14-Jan-2016
Geography 70
Basic Geodesy Map Projections Coordinate Systems Scale
Locating Positions on the Locating Positions on the EarthEarth
Geographic Data
Features must be referenced to some real world location
Known as georeferencing
Geographic Data & Position
GOAL: To assign a location to all features Important elements must agree:
– ellipsoid– datum– projection– coordinate system– scale
Position/location
To determine position on the Earth, it is necessary to understand how those elements relate to one another
Begin with geodesy
What is Geodesy?
Geodesy “A branch of applied mathematics which determines by
observation and measurement the exact positions of points and the figures and areas of large portions of Earth's surface, the shape and size of the Earth, and the variations of terrestrial gravity."
What is Geodesy?
More simply, geodesy is the study of the Earth’s size and shape.
The Earth is Not Flat
Eratosthenes
(276-196 B.C.)
Measured the height of an obeliskin Alexandria and determinedthe circumference of the earth.
His measurement: 25,000 Miles
Modern Measurement: 24,860 Miles
So the Earth is Round, Right?
The Earth is Irregular
Not perfectly round due to:– Distortion due to the Earth’s
rotation– Small irregularities on the surface
such as mountains, basins, etc.– Irregularities due to variations in
gravity
The Earth is Irregular
Slightly flattened at the poles Equator bulges Southern Hemisphere slightly larger than
Northern Hemisphere
The Earth is:
A Spheroid An Ellipsoid
A Geoid
The Earth as a Sphere Geographic coordinates (latitude/longitude)
used to specify locations. Treating the Earth as a sphere is accurate
enough for small maps of large areas of the Earth(i.e. very small scale maps)
The Earth as a Sphere
Spheroid model:– short range navigation– global distance
approximations
The slight flattening at the poles result in a 20 km difference at the poles from the average spherical radius
The Earth as an Ellipsoid
Ellipsoid is a flattened sphere Ellipsoid is created by rotating a 2 -
dimensional ellipse around an axis.
The Earth as an Ellipsoid
Every ellipsoid has a semi-major (a) and semi-minor axis (b)
The amount of flattening is defined as a value f, which is calculated using the semi-axes
The Earth as an Ellipsoid
a = semi-major axis b= semi-minor axis f = ((a-b)/a) = flattening
The Earth as an Ellipsoid:WGS84 Ellipsoid
bb
aa
f = 0.003353f = 0.003353
The Earth as an Ellipsoid
Differences in Lat / Long
On a spheroid, lines of latitude (parallels) are equal distance apart
On an ellipsoid, the distance between parallels slightly increases as latitude increases
The Earth as a Geoid The only thing shaped like the Earth is the
Earth Geoid means “Earth Like” Shape is based on gravity field corrected
by the centrifugal force of the earth’s rotation.
The Earth as a Geoid Geoid -- The surface on which gravity is the
same as its strength at mean sea level Coincides with the surface to which the oceans
would conform over the entire earth if it were made only of water.
The Earth as Geoid If the Earth were completely uniform in its
geological composition, landforms and density, then the geoid would match the ellipsoid exactly
Interaction
Spheroid Ellipsoid
Geoid
Geoid
Relationship of Geoid to its reference ellipsoid
Geodetic Datum
Datum -- n. (dat - m) \ any numerical or geometric quantity which serves as a reference or base for other quantities
ee
Geodetic Datum
Geodetic datum – The information that ties an ellipsoid model to the geoid model– Horizontal datum (most common used)– Vertical datum
Horizontal Datum
Parameters of the ellipsoid – axis length– flattening value
Parameters that tie the ellipsoid to the origin point (known place on the Earth)
Components
Review
Sphere – The simplest 3D model of the earth Ellipsoid – A more accurate model that takes
into account some of the Earth’s irregularity Geoid – The most accurate, most complex
model of the Earth, taking into account the Earth’s minor variations from an ellipsoid
Datum – The information that ties an ellipsoid model to a known place on the Earth
Geodetic Control Networks Geodesists and surveyors create geodetic control
networks to precisely link a set of known locations to each other and to the ellipsoid/geoid at a datum origin.
Geodetic Control Networks
Surveyors use these known points in the control networks for surveys and mapping.
Control Points are referenced to specific datums.
Geodetic Control Network
How do surveyors and others know where these points are?
Geodetic Control Network
They mark it.
Common Ellipsoids, DatumsEllipsoid Date Semi-Major
RadiusSemi-minorRadius
Flattening Used for
Clarke 1866 1866 6,378,249.1 6,356,583.8 1/ 294.98 N. AmericaGRS80 1980 6,378,137.0 6,356,752.3 1/ 298.26 WorldWGS84 1984 6,378,137.0 6,356,752.3 1/ 298.26 World/ GPS
Datum Ellipsoid UseNAD1927 Clarke1866 Old USGS Topo maps, old
state and county surveysNAD1983 GRS80 Recent Topo maps -- a
national standardWGS1984 WGS84 Current International
Standard Datum, GPS
Geodetic Datums
The purpose of all of this is to end up with a very, very accurate map.
Not all maps needthis accuracy, but some do.
Geodetic Datums
Review
Sphere – The simplest 3D model of the earth Ellipsoid – A more accurate model that takes
into account some of the Earth’s irregularity Geoid – The most accurate, most complex
model of the Earth, taking into account the Earth’s minor variations from an ellipsoid
Datum – The information that ties an ellipsoid model to a known place on the Earth