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Georeferencing Concepts
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GIS differs from other information systems because they contain
spatial data.
Spatial data include coordinates defining location, shape and
extent of geographic
objects.
To use GIS effectively requires an understanding of how
coordinate systems are
established
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1. The Earth has an irregular shape which affects how we define
coordinate systems used to represent geographic features in GIS
Geodesy the science of measuring the shape of the Earth
2. A curved surface (e.g., portions of the earth) gets distorted
when represented on a flat map
Map projections transforming coordinates from a curved Earth to
a flat map
There are two major problems in mapping geographic features.
What are they?
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Model the shape of the Earth
Develop an appropriate coordinate system for representing our
area of interest on a flat map
So if we want to do a study that involves analysis of the
location, shape or extent of geographic features we need to
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Ellipsoid Spherical or geographic coordinate system Datum
Projection Units
There are five important components to model the shape of the
Earth and to develop a coordinate system for a flat map. Does
anyone know what these concepts might be?
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What is an Ellipse? An Ellipsoid?
Why is it needed?
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Ellipsoids(Source: ESRI virtual campus)
An ellipse is a 2-dimensional shape that is oval in shape. The
shape is similar to a circle but flattened.
An ellipsoid is actually a three-dimensional (mathematical)
representation of an ellipse; it is created by rotating an ellipse
about an axis.
Ellipsoids (sometimes called spheroids) provide a model of the
shape of the Earth. To georeference something in GIS, we need to
define this model.
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There are a number of standard ellipsoids (mathematical
functions) used to describe the shape of the earth. Here is the
WGS-84 ellipsoid.
(Note: ArcView refers to this as a spheroid the terms ellipsoid
and spheroid are sometimes used interchangeably even though
ellipsoid is a special type of spheroid)
Source: Peter
Danahttp://www.colorado.edu/geography/gcraft/notes/datum/datum_f.html
a
b
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WGS 84 standard used in GPS systems
Commonly used for North America:
Clarke 1866WGS 72WGS 84GRS 1980
Source: Peter
Danahttp://www.colorado.edu/geography/gcraft/notes/datum/datum_f.html
Many different ellipsoid models of the Earth since 1830
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OK. Ellipsoids mathematically model the 3-D shape of the
Earth.
Whats next?
What is a Spherical or Geographic Coordinate System?
Why is it needed?
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What is a Spherical or Geographic Coordinate System?
a reference system used to locate and measure geographic
features on the surface of a sphere-like object, like the
earth.
We need to be able to place geographic features on the
ellipsoid.
What is arguably the most widely known geographic coordinate
system?
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Longitude/Latitude System (A Spherical System)(Source: ESRI
virtual campus)
Prime meridian0 o Longitude
Equator0 o Latitude(Parallels)
Latitude range from 0to 90in the northern hemisphere, going from
the equator to the North Pole. In southern hemisphere, they range
from 0to -90, going from the equator to the South Pole.
Longitude values range from 0to 180in the eastern hemisphere,
beginning at the prime meridian in Greenwich, England, and
traveling east across Europe, Africa, and Asia. In the western
hemisphere, longitude values range from 0to -180, starting at the
prime meridian and traveling west across the Americas.
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Longitude/Latitude System(Source: ESRI virtual campus)
Spherical coordinate systems are measured in degrees, minutes,
seconds (DMS) or degrees decimal (DD).
How would you convert the above longitude into degrees
decimal?
DD = 55 + 30/60 + 30/3600 = 55.5083333
Why is DD useful? Because computers can do processing on them
they cant in DMS format
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Longitude/Latitude System(Source: ESRI virtual campus)
The network of converging long/lat lines is called a
graticule.
It cannot be called a grid because the lines dont converge in
right angles.
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OK, now weve got (1) a model of the Earths shape and (2) a
coordinate system for it.
What is a datum?
Why is this concept important?
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Datum(Source: ESRI virtual campus)
The geographic coordinate system (long, lat) is based on one
longitude location the Greenwich observatory. Other long/lat
locations need to be measured a Geodetic Survey.
A geodetic datum is a set of control points whose geometric
relationships are known, either through measurement or
calculation(Dewhurst, 1990). From these measurements we know
distance, area, direction, etc. between locations on the Earth.
Datums have two components: The reference ellipsoid A set of
survey points Both the shape of the spheroid and its position
relative to the earth are important.
Remember, the Earth is not a smooth sphere, (e.g., the Himalayan
mountains and the flat deserts), so different datums work better in
different places on the Earth.
There are two types of datums: (1) Earth-centered and (2)
Local.
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Earth-centered Datum(Source: ESRI virtual campus)
An earth-centered datum establishes the origin of the ellipsoid
at the earth's currently known center of mass.
Earth-centered datums define an X, Y, and Z, Cartesian
coordinate system with respect to the center the reference
ellipsoid
The origin of the 1983 North American Datum (NAD83) is very
close to the earth's center of mass and is the most commonly used
datum for North America. The World Geodetic System of 1984 (WGS84)
is the datum upon which GPS measurements are based.
NOTE: Some people use ellipsoid and spheroid
interchangeably!
(this is really an ellipsoid)
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Local Datum(Source: ESRI virtual campus)
A local datum is aligned so that it closely corresponds to the
earth's surface for a particular area.
An example is the 1927 North American Datum (NAD27) which uses
Meades Ranch, Kansas as the point of origin for all
measurements.
http://en.wikipedia.org/wiki/Meades_Ranch,_Kansas
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Earth-centered versus Local Datum(Source: ESRI virtual
campus)
Notice how the ellipsoid shifts, conceptually, with respect to
the Earths surface.
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Various datums fit various locations of the Earth better
See the list of datums at:
http://www.colorado.edu/geography/gcraft/notes/datum/edlist.html
Datums use different ellipsoids. If 2 maps used for GIS input
use different datums, you will run into compatibility problems
because of the different ellipsoids used (what Bolstad calls datum
shift).
For example, one dataset using the North American Datum 1927 and
another using Indian datum
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21Source: Peter
Danahttp://www.colorado.edu/geography/gcraft/notes/datum/datum_f.html
Peter Danas website shows methods to convert data using one
datum to another
http://www.colorado.edu/geography/gcraft/notes/datum/datum.html#DConv
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OK, we now have:
1. A earth model2. A geographic coordinate system3. A datum
defining where these
coordinates are on the model of the Earth
What are Map Projections and why do we need them?
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Why do we need map projections?(source: ESRI virtual campus)
We want to represent locations identified in the geographic
coordinate system and place them a flat surface (map).
Map projections transfer the spherical Earth coordinates onto a
two-dimensional (planar) coordinate system.
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What is the fundamental problem with wanting to represent a
curved surface
on a flat piece of paper?
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The fundamental problem(source: ESRI virtual campus)
Sphere graticule lines dont line up in right angles
Cartesian coordinate system lines meet in right angles
Converting a graticule to a grid results in some kind of
distortion either SHAPE, AREA, LENGTH, or DIRECTION).
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Cartesian coordinate systems, such as:
Universal Transverse Mercator (UTM) or
State Plane Coordinate System (SPCS),
are commonly used to locate features and are found on many
maps.
You convert spherical coordinates to Cartesian coordinates using
a map projection.
Why do we need map projections?(source: ESRI virtual campus)
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Using a cylinder (Cylindrical) Using a plane (Planar) Using a
cone (Conic)
What are the ways we can project the curved Earth surface on a
flat
map?
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Cylindrical projections result from projecting a spherical
surface onto a cylinder
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Cylindrical Equal-Area projections (tangent to a line of
latitude)They have straight meridians and parallels, the meridians
are equally
spaced, the parallels unequally spaced
Area is true; Shape and scale get distorted near the upper and
lower regions of the map. (Anyone see the West Wing episode on
this?)
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Transverse Mercator projections result from projecting the
sphere onto a cylinder tangent to a meridian (line of
longitude)
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The Universal Transverse Mercator (UTM) projection is used to
define horizontal, positions world-wide by dividing the surface of
the Earth into 6 degree zones, each mapped by the Transverse
Mercator projection with a central meridian in the center of the
zone
Equator
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Question on UTM projection and Distortion
UTM is a global coordinate system Common projection for data
spanning large
regions (e.g., several state plane zones) Many US federal gov
data are in UTM because
many agencies manage land spanning large areas and UTM is a well
known, standard system
UTM zones are 6 degrees wide so many studies will fit in this
that would not fit in a state plane zone (for example)
So UTM is a useful projection for broad study areas (larger than
1 state, or possibly crossing state boundaries) as long as it is
within one UTM zone.
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Equator
The Universal Transverse Mercator (UTM) projection is used to
define horizontal, positions world-wide by dividing the surface of
the Earth into 6 degree zones, each mapped by the Transverse
Mercator projection with a central meridian in the center of the
zone.
If maps are limited to the thin, vertical region near the
meridian of tangency they will be relatively free of distortion
Mercator shapes are true, but area gets distorted
(conformal).
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Question on UTM projection and Distortion
UTM is sometimes however not compatible for regional studies
that cross UTM zones.
This is because coordinate values are not continuous between
zones. The coordinate system for UTM zone 15 is different than zone
16, for example.
In other words, each UTM zone is its own projection. Combining
will result in distortion in location and shape of the objects from
a different zone than the one being used.
UTM was designed to map areas within that particular zone
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Planar Projections
(tangent case)
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Often used for air route distances.Distances measured from the
center are true. Distortion of other properties increases away from
the center point.
An example of a planar projection (tangent)
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Conic ProjectionsGenerated by projecting a spherical surface
onto a cone
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Distorts scale and distance except along standard parallels.
Areas are proportional and directions are true in limited areas.
Used in the United States and other large countries with a larger
east-west than north-south extent.
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Area, and shape are distorted away from standard parallels.
Directions are true in limited areas. Used for maps of North
America.
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Unprojected maps include those that are formed by considering
longitude and latitude as a simple rectangular coordinate system.
Scale, distance, area, and shape are all distorted with the
distortion increasing toward the poles.
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State Plane Coordinates
The State Plane Coordinate System (SPCS) uses a unique set of
projection parameters for each of the 50 states
Uses either a Transverse Mercator or Lamberts conformal conic
projection
Originally designed to provide a permanent record of land survey
monuments in the United States.
Zones, measured in feet, not meters.
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Summary
Geodesy science of modeling the shape of the earth
Map projections transformation of coordinates from a curved
Earth to a flat, paper map.
Ellipsoid 3-D model of the earth (flattened)
Spherical or geographic coordinate system system of locations on
a 3-D ellipsoid (Long/Lat)
Geodetic Datum set of measured or calculated points on the
Earth. Provides a frame of reference for measuring locations on the
Earth or places the geographic coordinate system on the
ellipsoid.
Map projections Systematic rendering of locations from a curved
Earth to a flat map surface.
The process of projecting will always distort one or more of
four spatial properties: shape, area, distance, and direction.
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Summary (source -- ESRI Virtual campus)
- The choice of map projection is important when you are working
with small (broad) scale maps, like world maps
- The choice of datum is important when working with large
(fine) scale maps, such as city maps
- When using map input for building GIS layers, you need to make
sure they are in compatible map projections.
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A final word on distortion
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Suggestions from Theobald (1999: 42) on Selecting a
Projection
If you are making a fairly detailed map, for example a city, or
requirements for accuracy is minimal, then you may not have to
worry so much about which projection to use.
If you are making a map of a regional to continental to global
scale OR are interested in precise shape, area or distance
measurements then you should choose carefully the projection.
For many study areas there is already standard projects, such as
State Plane for county or city governments or UTM for state
governments.
Three factors to consider related to accuracy: Latitude of area,
extent and theme Latitude:
Low-latitude areas (near equator) use a conical projection Polar
regions use a azimuthal planar projection
Extent Broad in East-West (e.g., the US) use a conical
projection Broad in North-South (e.g., Africa) use a
transverse-case cylindrical
projection Thematic
If you are doing an analysis that compares different values in
different locations, typically an equal-area projection will be
used.