GEOGRAPHIC INFORMATION SYSTEMS
Lecture 9: Map Projections (cont’d)
Examples of Map Projections
- there are hundreds of standard map projections used to map the world, continents, countries and states
- you can also create your own custom map projection (so the options are limitless)
- the following examples are taken from the USGS Map Projections web site
The Globe
- a globe is a scaled physical model – not a map projection
- no distortion in shape, area, distance or direction
1) Cylindrical Projections
- Mercator Projection
- true directions – widely used for navigation (although not the shortest route)
- Miller Projection
- similar in appearance to a Mercator projection (but directions are not true)
- designed to show highest latitudes (which Mercator does not)
Copyright© 2015, Kevin Mulligan, Texas Tech University
- Transverse Mercator Projection
- line of tangency along a meridian (the central meridian)
- used for areas with a large north-south extent (e.g. Chile)
- used as the basis for the UTM coordinate system
2) Pseudo-cylindrical Projections
- Robinson Projection
- compromise projection - widely used in atlases
- it looks about right - but area, shape, distance and direction are not true
- Sinusoidal Equal Area Projection
- an equal area projection - widely used in atlases
- used to preserve relative areas on a world map
Copyright© 2015, Kevin Mulligan, Texas Tech University
3) Conic Projections
- Albers Equal Area Conic Projection
- midlatitude equal area projection (areas are correct)
- widely used to map Texas and the contiguous United States
- Lambert Conformal Conic Projection
- midlatitude conformal projection (shape of features is correct)
- widely used to map Texas and the contiguous United States
Copyright© 2015, Kevin Mulligan, Texas Tech University
4) Planer Projections
- Orthographic
- perspective views of the Earth (as it would appear from space)
- Stereographic Projection
- conformal projection (conformal means the shape of features is true)
- mostly used to map polar regions
Copyright© 2015, Kevin Mulligan, Texas Tech University
Map Projections and Coordinate Systems
- recognize that the Geographic Coordinate System is not projected
- the GCS can be referenced to many different datums (each using different ellipsoids),
but the data are not projected and the units are unprojected decimal degrees
- when we add unprojected data, ArcMap displays latitude and longitude as if latitudes are y values and
longitudes are x values in a Cartesian coordinate system (e.g. lines longitudes are parallel to one another)
- only when we apply a map projection to the data frame does the Geographic Coordinate System become a
Projected Geographic Coordinate System
Demonstration of how to apply different map projections
- right-click on Layers to open the Data Frame dialog box > Coordinate System tab.
- note the two folders…
1) Geographic Coordinate System folder – all of the Geographic Coordinate System choices in this
folder are unprojected (but they use different datums)
Unprojected Geographic Coordinate System
2) Projected Coordinate Systems folder – all of the Geographic Coordinate System choices in this
folder are projected and can be applied to map different parts of the world
Projected Geographic Coordinate System
Copyright© 2015, Kevin Mulligan, Texas Tech University
GEOGRAPHIC INFORMATION SYSTEMS
Lecture 09: UTM Coordinate System
UTM Coordinate System
Why do we need the UTM coordinate system?
- in a rectangular (Cartesian) coordinate system, with linear x and y axes, it is fairly simple to
calculate distances and areas using plane geometry (e.g. Pythagorean theorem)
- in a spherical coordinate system, these calculations are very difficult because lines of longitude
converge at the poles - and the length of a degree of longitude (in miles) changes with latitude
- the Universal Transverse Mercator Coordinate System (UTM) was designed to address this problem
- the UTM coordinate system is a projected coordinate system
- for a small area, the curvature of the Earth can be ignored and the area is treated as a flat surface
- to accomplish this, the map is projected first (using a cylindrical transverse Mercator projection)
- then, a rectangular x, y coordinate system is overlaid to describe the location of points
How it works
- in the Universal Transverse Mercator coordinate system the Earth is divided into 60 UTM zones
- each zone covers 6o of longitude - and each zone has a central meridian
- in the UTM system, each of the 60 UTM zones are projected separately
- and then the zone’s coordinate system (an x.y grid) is applied to that zone
- given that the UTM coordinate system is constructed using a transverse cylindrical map projection,
the line of tangency (where the transverse cylinder touches the globe) follows along the central meridian
- the map distortion in each zone is therefore minimal along the central meridian and it increases E and W
- within a UTM zone, the accuracy of measurements is about 1 linear unit in 2500 (about 2 feet per mile)
Northern hemisphere
- in the northern hemisphere, the origin of each zone is define by:
1) the Equator and
2) a line located 500,000 m west of the central meridian
- the easting and northing coordinates of a location are then measured as follows:
- easting: the distance east of the line located 500,000 m west of the central meridian
- northing: the distance measured north of the Equator
Southern hemisphere
- in the southern hemisphere, the origin of each zone is define by:
1) a line located 500,000 m west of the central meridian
2) a line located 10,000,000 m south of the Equator and
- the easting and northing coordinates of a location then are measured as follows:
- easting: the distance east of the line located 500,000 m west of the central meridian
- northing: the distance north of the line located 10,000,000 m south of the Equator
Horizontal Datums and Units
- the UTM coordinate system can be referenced any datum
- in the U.S. the UTM coordinate system is usually referenced to NAD_27 or NAD_83
- NAD_27 on older topographic maps - NAD_83 for most U.S. digital data
- in either case, the units (eastings and northings) are usually in meters
- in other parts of the world, UTM coordinates are usually referenced to WGS_84 in meters
Describing Coordinates
- recognize that a single coordinate (easting, northing) can be replicated 120 times (twice in each zone)
- to describe a coordinate, you must specify the datum, zone and hemisphere, and measurement units
- e.g. NAD 83, Zone 14 North, easting: 328,256 m E, northing: 3,450,586 m N
UTM on Topographic Maps (in lab)
- know how the UTM coordinate system works
- know how to find UTM coordinates on a topographic map
Copyright© 2015, Kevin Mulligan, Texas Tech University
Texas Capital Dome
NAD 83, Zone 14 North
621,161 m E, 3,349,894 m N
Copyright© 2015, Kevin Mulligan, Texas Tech University
GIST 3300 / 5300
Geographic Information Systems
Map Projections (continued)
Examples of Common Map Projections
New Topic
Projected Coordinate Systems - UTM
Geographic Information Systems
Map Projections
Geographic Information Systems
The Globe
A physical model – not a map projection
Shape – true
Area – true
Distance – true
Direction - true
Geographic Information Systems
Mercator Projection (cylindrical)
Directions are true – used for navigation
Directions do not provide the shortest route between two locations
Polar areas north or south of 85o are not present
Geographic Information Systems
Miller Cylindrical Projection (cylindrical)
Similar to Mercator – but directions are not true – not used for navigation
Polar areas north or south of 85o are present
Poles are shown as a straight line
Geographic Information Systems
Transverse Mercator Projection (cylindrical)
Distortion is minimized along a central meridian
The UTM coordinate system uses a transverse Mercator projection
Also, useful for mapping areas with a long north-south extent
Geographic Information Systems
Robinson Projection (pseudo-cylindrical)
Some distortion in shape, area, distance and direction
It looks good – used in atlases
Geographic Information Systems
Sinusoidal Equal Area Projection (pseudo-cylindrical)
Areas on the map are proportional to those on a globe
Geographic Information Systems
Albers Equal Area Conic Projection (conic projection)
Areas are true
Used to map areas in the mid latitudes (e.g. contiguous United States)
Geographic Information Systems
Lambert Conformal Conic Projection (conic projection)
Shapes are true (conformal)
Used to map areas in the mid latitudes (e.g. contiguous United States)
Geographic Information Systems
Stereographic Projection (planer projection)
Shapes are true (conformal)
Directions are true extending from the map center
Used to map polar areas of the world
Geographic Information Systems
Orthographic Projection (planer projection)
Perspective view from space
Geographic Information Systems
Geographic Coordinate Systems vs Map Projections
Geographic Coordinate Systems (GCS)
- recognize that the Geographic Coordinate System (GCS) is not projected
- the data are not projected and the units are unprojected decimal degrees
- the GCS might be referenced to different ellipsoids and datums
Spatial Reference or Data Frame Properties Dialog
GCS unprojected
Geographic Information Systems
Geographic Coordinate Systems vs Map Projections
Projected Coordinate Systems (PCS)
- only when we apply a map projection to the data frame or to the data layers
does the GCS become a projected coordinate system
Spatial Reference or Data Frame
Properties Dialog
GCS projected using
North America Albers Equal Area
Geographic Information Systems
GIST 3300 / 5300
Geographic Information Systems
Projected Coordinate Systems
Universal Transverse Mercator (UTM)
Coordinate System
- why do we need the UTM coordinate system?
- how does it work?
- UTM coordinate system on topographic maps
Geographic Information Systems
Projected Coordinate Systems
Universal Transverse Mercator (UTM) Coordinate System
Geographic Information Systems
UTM Coordinate System
Why do we need the UTM coordinate system?
Cartesian Coordinate System
x2,y2
Y axis
How do we calculate
the distance from
x1,y1 to x2,y2?
x1,y1
X axis
Geographic Information Systems
UTM Coordinate System
Why do we need the UTM coordinate system?
Cartesian Coordinate System
x2,y2
Pythagorean Theorem
Y axis
C
A2 + B2 = C2
B
C = (A2 + B2)
x1,y1
A
x2,y1
C = (x2-x1)2 + (y2-y1)2
X axis
Geographic Information Systems
UTM Coordinate System
Why do we need the UTM coordinate system?
Y axis
C
34o,-102o
A
35o,-100o
If the coordinate values
are degrees, this approach
doesn’t work!
B
34o,-100o
In this example, the
longitude A = 2o …
but the number of miles
per degree varies with
latitude.
X axis
Geographic Information Systems
UTM - How does it work?
- the Universal Transverse Mercator (UTM) coordinate system
is designed to address this problem
- for a small area, the curvature of the Earth’s surface can be ignored
- and a rectangular (Cartesian) coordinate system can be overlaid to
describe the location of points
Geographic Information Systems
UTM - How does it work?
- the Universal Transverse Mercator (UTM) coordinate system
is a projected coordinate system (the map is projected first)
- set up as a grid using a transverse cylindrical projection
Geographic Information Systems
UTM - How does it work?
- the transverse cylindrical projection is tangent to the Earth along
a line of longitude
- there is minimal distortion along this line a longitude
- the line of longitude is designated as the central meridian for a UTM zone
Geographic Information Systems
UTM - How does it work?
- The Earth is divided into 60 zones
- with each zone covering 6o of longitude
- each zone has a central meridian
- for example, Zone 14
- extends from 96o W to 102o W
- the zone has a central meridian at 99o W
Geographic Information Systems
UTM - How does it work?
- in the northern hemisphere
- the origin of each zone is defined by the Equator
- and a line located 500,000 m (500 km) west of the central meridian
99o W
80o N
500,000 m
UTM Zone 14 N
0o Equator
0,0
96o W
102o W
UTM Zone 14 S
Sketch not to scale
80o S
Central Meridian
Geographic Information Systems
UTM - How does it work?
- UTM coordinates
- easting, distance east from a line 500,000 m west of the central meridian
- northing, distance north of the Equator
99o W
80o N
UTM Zone 14 N
430,000 m x,y
easting (x) = 430,000 m
northing (y) = 3,500,000 m
3,500,000 m
0o
0,0
96o W
102o W
Sketch not to scale
80o S
Geographic Information Systems
UTM - How does it work?
- UTM coordinates
- easting, distance east from a line 500,000 m west of the central meridian
- northing, distance north of the Equator
99o W
620,000 m
80o N
x,y
UTM Zone 14 N
easting (x) = 620,000 m
northing (y) = 3,650,000 m
3,650,000 m
0o
0,0
96o W
102o W
Sketch not to scale
80o S
Geographic Information Systems
UTM - How does it work?
- Cartesian coordinate system applied to a small portion of the Earth's surface
- Earth is assumed to be flat over measured distances within a zone
99o W
80o N
x,y
UTM Zone 14 N
B
x,y
A
620,000 m
– 430,000 m
0o
0,0
A = 190,000 m
96o W
102o W
3,650,000 m
– 3,500,000 m
B = 150,000 m
Sketch not to scale
80o S
Geographic Information Systems
UTM - How does it work?
- works the same way in the southern hemisphere
- the origin of each zone is defined by a line 10,000,000 m south of the Equator
- and a line located 500,000 m west of the central meridian
99o W
80o N
96o W
102o W
0o
UTM Zone 14 S
500,000 m
Sketch not to scale
10,000,000 m
80o S
0,0
Geographic Information Systems
UTM - How does it work?
- UTM coordinates
- easting, distance east from a line 500,000 m west of the central meridian
- northing, distance north of a line located 10,000,000 m south of the Equator
99o W
80o N
96o W
102o W
0o
595,000 m
UTM Zone 14 S
easting (x) = 595,000 m
x,y
northing (y) = 2,480,000 m
Sketch not to scale
2,480,000 m
80o S
0,0
Geographic Information Systems
UTM - How does it work?
- UTM coordinate example: the Capital Dome in Austin
NAD 83; UTM Zone 14 N; 621,161 m E; 3,349,894 m N
Geographic Information Systems
UTM on Topographic Maps
Geographic Information Systems
UTM on Topographic Maps
UTM
Blue Ticks
Full values shown
in lower right and
upper left on map
Geographic Information Systems
UTM – Horizontal Datums and Units
The UTM coordinate system can be referenced to any datum
United States
- in the U.S. it is usually referenced to either NAD 27 or NAD 83
- NAD 27 on older topographic maps
- NAD 83 for most U.S. digital data and imagery
- in either case, the units (eastings and northings) are usually in meters
Other Parts of the World
- UTM coordinates are usually referenced to WGS 84 in meters
Geographic Information Systems
UTM – Describing Coordinates
- recognize that a single coordinate (an easting and northing) can be
replicated 120 times (twice in each of 60 zones)
- to describe a complete UTM coordinate, you must specify:
1) the datum
2) the zone and hemisphere
3) the easting and northing
4) and the measurement units (usually meters)
Example:
NAD 83, Zone 14 North, 621,161 m E, 3,349,894 m N
Geographic Information Systems
Summary …
Projected Coordinate Systems (UTM)
- UTM is a stand-alone projected coordinate system
- designed for use over a small area of the Earth’s surface (UTM zone)
- we do not apply a projection because each UTM zone is already projected
- each zone is projected separately using a transverse Mercator projection
Spatial Reference or Data Frame Properties Dialog
UTM Zone 14N
Geographic Information Systems