Transcript Map Projections

Unit 3: Understanding Coordinate Systems
Student Learning Outcomes: Students will be able to select the appropriate coordinate system for a given task
and project or re-project data acquired as needed after consulting the metadata to determine its spatial reference.
Understanding Coordinate Systems
and Map Projections
Why do I need to know this?
• GIS works with spatial data
• Data needs to be placed at a location
• Globes are great for visualization, but not practical for
many uses
• A round Earth does not fit without distortion on a flat
piece of paper
Datum
Datum
• A datum is a reference surface for measuring locations on
the earth
• A datum has two major components
• Specification of an ellipsoid
• Set of points and lines that have been surveyed and defines the
origin and orientation of latitude and longitude lines
Common Datums
• North American Datum of 1927 (NAD27)
• Used Clarke 1866 Ellipsoid
• Held fixed latitude and longitude in Kansas
• Adjusted lat/lon for ~26,000 points
• North American Datum of 1983 (NAD83)
• Successor of NAD27
• Used Earth-centered reference ellipsoid (GRS80) rather than
fixed station in Kansas
• Adjusted lat/lon for ~250,000 points
Common Datums
• World Geodetic System of 1984 (WGS84)
• Based on Doppler satellite measurements
• Based on WGS84 ellipsoid, which is similar to the GRS80
ellipsoid
• Datums do see updates and adjustments
• Both NAD83 and WGS84 have been updated multiple
times
Vertical Datums
• Vertical Datum – a reference for specifying heights
• Established through a set of surveyed control points
Vertical Datums
• Two most common vertical datums for North America
• National Geodeteic Vertical Datum of 1929 (NGVD29)
• North American Vertical Datum of 1988 (NAVD88)
Coordinates
Coordinates
• Space is important
• How can we represent this space numerically?
• 2D and 3D
3D Coordinate System
Spherical Coordinates
• 3D only
• Does not ignore curvature of Earth
• Uses two angles of rotation (Lat/Lon) and radius to
specify locations
Longitude aka Meridian
• Measures East-West
• Vary from +180° E to -180° W
20°
-150°
10°
-140°
0°
-130°
-10°
-120°
-20°
-30°
-110°
-100°
-40°
-90°
-50°
-60°
-80°
-70°
Meridians
Latitude aka Parallels
• Measures North-South
• Vary from +90° N to -90° S
North Pole 90°
80° N
70°
60°
50°
40°
30°
Equator
20°
10°
0°
10°
20°
30° S
Parallels
Spherical Coordinate Representation
• Both latitude and longitude are typically represented in two ways
• Degrees, Minutes, Seconds (DMS)
• -34°23’45.23” , +124°12’45.32”
• Decimal Degrees (DD) used by computers
• -34.395897 , 124.212589
2D Coordinate Systems
Cartesian Coordinates
• Define spatial location and extent
2D (x,y)
3D (x,y,z)
Cartesian Coordinates
• GIS data typically uses Cartesian system
• Ignores curvature of Earth
• For small areas, usually acceptable
Cartesian Coordinate Representation
• Many possible representations
• Could even make your own
• Common Representations
• State Plane Coordinate System (SPCS)
• Universal Transverse Mercator Coordinate System (UTM)
State Plane Coordinate System
• Set of 126 geographic zones
• Designed for specific regions of USA
• Useful because…
• Simple calculations
• Accurate within zones
• Comes in NAD27 and NAD83 flavors
• Coordinates represented in Feet
State Plane Coordinate System
• Each state may have multiple State Plane zones
• Provides a common coordinate reference for horizontal
coordinates over county areas while limiting error to
specified maximums
• Based on two types of map projections
• Lambert conformal conic
• Transverse Mercator
Universal Transverse Mercator
Coordinate System
• A set of 60 zones across the World
• Useful because…
• Simple calculations
• Accurate within zones
• Coordinates represented in Meters
Universal Transverse Mercator (UTM)
• Global coordinate system
• Divides Earth into zones that are 6° wide and extend from 80°S to
84°N
• Numbered from 1 to 60 heading East from 180°W
• Zones also split into North and South at Equator
• UTM is common for data and study areas that cover large
regions
• Coordinates always positive and specified in Eastings (Y), and
Northings (X)
Map Projections
Map Projections
•Short introductory video:
•http://www.youtube.com/watch?v=2LcyMemJ3dE
Map Projections
• Map Projection – systematic rendering of locations from
the curved Earth surface onto a flat map surface
• Purpose:
• Practical way to portray the Earth’s curvature on a flat surface.
• Hard to carry a globe in a pocket!
Map Projections
• Basic illustrative idea of a map project
Map (flat surface)
Ellipsoid
Light
Developable Surfaces
Developable Surfaces
• Developable Surface- Geometric surface onto which the
curved surface of the Earth is projected.
• Four geometric forms
Plane
Cylinder
Cone
Mathematical
Developable Surfaces
• Developable surfaces are placed relative to the
spheroid/ellipsoid in different locations and at different
rotations to gain the desired view and map properties.
Interaction between Developable Surfaces
and the Spheroid/Ellipsoid
• Developable surface touches spheroid/ellipsoid in either:
• Two secant lines
• One point or tangent line
Tangent
Interaction between Developable Surfaces
and the Spheroid/Ellipsoid
Tangent interaction
Secant interaction
Secant line
Map Projection Parameters
Map Projection Parameters
•
•
•
•
•
Standard Points and Lines
Projection Aspect
Central Meridian
Latitude of Origin
Light Source Location
Standard Points and Lines
Definition:
Points or lines of intersection between the developable
surface and spheroid.
Named Standard Lines:
If standard line falls a line of latitude, it is known as a
standard parallel.
If standard line falls on a line of longitude, it is known as a
standard meridian.
Standard Parallels
Why are Standard
Points and Lines Important?
Those corresponding places on the map
will have no scale distortion.
The father away from the standard point or line(s), the
greater the distortion or deformation occurs.
Secants can help minimize distortion over a large area by
providing addition control.
Projection Aspect
Definition:
Position of the projected graticule relative to ordinary
position of the geographic grid on Earth
A developable surface with the axis running from north to
south pole creates
a normal aspect
Globe Normal Axis
Normal Aspect
Non-Normal Aspect
Central Meridian
Definition:
The meridian that defines the center
of the projection.
i.e. the meridian in the center of the map
Latitude of Origin
Definition:
The Latitude that defines the center of the projection.
i.e. the latitude in the center of the map
Light Source Location
Definition:
The location of the hypothetical light source in reference to
the globe being projected.
Three Primary Positions…
Three Primary Positions
of Light Sources
Gnomonic
Stereographic
Orthographic
Map Projection Properties
Map Projection Properties
Definition:
Alterations of area, shape, distance, and direction on map
projections.
Why?
All maps contain error because of the 3D -> 2D
transformation process.
How?
Rendering a spherical surface on a plane causes tearing,
shearing, or compression of the surface.
Four Map Projection Properties
Area
Shape
Distance
Direction
Four Projection Properties
Major Properties
Area
Shape
Mutually Exclusive
Minor Properties
Distance
Direction
Cannot exist everywhere
on map
Map Distortion
• Distortions are unavoidable when making flat maps of a
globe
• Distortion may take different forms in different parts of the map
• Few points where distortions are zero
• Distortion is usually less near the points or lines of intersection
where the map surface intersects the globe
Map Distortion
• A map can show one or more – but never all – of the
following at the same time:
• True directions
• True distances
• True areas
• True shapes
Area
Equal Area Map Projection
A.K.A.
Equivalent Map Projection
Goal:
Preserve area relationships of all parts of globe
Identifying Marks:
Meridians and parallels are not at right angles.
Distance distortion is often present.
Shape is often skewed.
Area
Equal Area Map Projection
Useful for…
General quantitative thematic maps.
When it is desirable to retain
area properties.
Area
Cylindrical Equal-Area
Area
Hammer-Aitoff
Shape
Conformal Map Projection
A.K.A.
Orthomorphic Map Projection
Goal:
Preserve angles around points
and shape of small areas
Same scale in all directions from/to a point.
Identifying Marks:
Meridians intersect parallels at right angles.
Areas distorted significantly at small scales.
Shapes of large regions may be severely distorted.
Shape
Conformal Map Projection
Useful for…
Large-scale mapping.
Phenomena with circular radial patterns
(e.x. radio broadcasts, average wind directions)
Shape
Mercator Projection
Distance
Equidistant Map Projection
Goal:
Preserve great circle distances.
Distance can be held true from one to all other points, or
from a few points to others, but not from all points to all
other points.
Scale is uniform along lines of true distance.
Identifying Marks:
Neither conformal or equal area,
and look less distorted.
Distance
Equidistant Map Projection
Useful For…
General Purpose Maps
Atlas Maps
Distance
Equidistant Cylindrical
Direction
Azimuthal Map Projection
A.K.A.
True Direction
Goal:
Preserve true direction from one point to all other points.
Direction not true between non-central points.
Useful for…
Preserving direction from one point.
Direction
Azimuthal Equidistant
Map Projection
Combination of Projections
on a Single Projection
Equal Area
Conformal
Equidistant
Azimuthal
Equal Area
--
No
No
Yes
Conformal
No
--
No
Yes
Equidistant
No
No
--
Yes
Azimuthal
Yes
Yes
Yes
--
Yes denotes they can be combined
No denotes they cannot be combined
Minimum Error
Minimum Error Map Projection
A.K.A.
Compromise Map Projection
Goal:
Simultaneously minimize all
four map projection properties
Useful for…
General geographic cartography
Minimum Error
Robinson Map Projection
Organization of Cartographers for Social
Equality – West Wing Clip
http://www.youtube.com/watch?v=n8zBC2dvERM
Determining Deformation
and its
Distribution Over the Projection
Tissot’s Indicatrix


All flat maps distort shape, area, direction, or length
Tissot’s Indicatrix helps to quantify distortion and
projection properties
• Composed of infinitesimally small circles centered at points on
the Earth
• Consider the shape of the circle after projecting the map
Tissot’s Indicatrix
Interpretation:
See what happens to the circles when you project
Interpreting Tissot’s Indicatrix
Equal Area:
Circle transformed into ellipse,
but area remains the same.
Conformal:
Circle transformed as a circle,
but size varies over the map.
Conformal Projection Property
• Conformal – ellipse would remain circular, although most
likely larger or smaller than original circle
Mercator Projection
Equal Area Projection Property
• Equal Area – Circle would not have same shape, but
would have the same area as original
Flat Polar Quartic Projection
Other Projection Properties
• Equidistant – distances are true between two points
Equidistant Cylindrical Projection
Other Projection Properties
• Aphylactic – projections that distort everything
Robinson Projection
Map Projection Reference Websites
• USGS Map Projections Poster
• http://egsc.usgs.gov/isb/pubs/MapProjections/projections.html
• Radical Cartography Projection Reference
• http://www.radicalcartography.net/?projectionref
• Flex Projector
• http://www.flexprojector.com/