GEOGRAPHIC INFORMATION SYSTEMS
Lecture 11: Projected Coordinate Systems
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 © Kevin Mulligan, Texas Tech University
Texas Capital Dome
NAD 83, Zone 14 North
621,161 m E, 3,349,894 m N
Copyright © Kevin Mulligan, Texas Tech University
State Plane Coordinate System
Why do we need the State Plane Coordinate System?
- the SPCS was designed as a state by state rectangular coordinate system
- like UTM, the system was designed to overcome the difficultly of calculating distances and areas
How it works
- the SPCS was established in the 1930’s by the U.S. Coast and Geodetic Survey
- the system was designed to facilitate surveys and mapping within a state
- the SPCS is a projected coordinate system
- like UTM, the SPCS ignores the curvature of the Earth over a small area
- each state is divided into one or more zones
- the number of zones depends upon the size of the state (some states have only one zone)
- for the largest states, Texas has 5 zones, California has 6 zones and Alaska has 10 zones
- in Texas the 5 zones are designated as North, North Central, Central, South Central and South
- each state or zone within a state is projected
- the projection used is either a transverse Mercator or a Lambert conformal conic
- a rectangular (Cartesian) coordinate system is then applied to the map area (the state zone)
- in some states the zones run north-south
- to minimize distortion, these states use a transverse Mercator projection for each zone
- a central meridian runs north-south down the center of each zone in the state
- in some states the zones run east-west
- to minimize distortion, these states use a Lambert conformal conic projection for each zone
- the standard parallels run east-west through the each zone in the state
- in Texas, the zones run east-west – so Texas uses a Lambert Conformal Conic projection
- the SPCS provides a linear accuracy of 1 unit in 10,000 (about 6 inches a mile)
- in the 1930’s, 1 in 10,000 was considered the limit of survey accuracy
- it is 4 times more accurate than UTM, which has a accuracy of 1 in 2,500 (about 2 feet in a mile)
Horizontal Datums and Units
- SPCS is usually referenced to either NAD_27 or NAD_83
- when the SPCS is referenced to NAD_27, the system was designed to use English units (feet)
- when referenced to NAD_83, the system was designed to use metric units (meters)
although these metric units are often converted to feet
- in the U.S., most cadastral and engineering applications use the SPCS in feet
referenced to either NAD_27 or NAD_83
- the easting is measured east of a line located west of the zone border
- the northing is measured north of a line located south of the zone
Describing Coordinates
- recognize that a coordinate can be replicated in different states and in different zones within a state
- to describe a coordinate, you must specify the datum, state and zone, and measurement units
- e.g. NAD 27, Texas Central Zone (4203), easting: 2,818,560 feet E, northing: 230,591 feet N
- also note that the State Plane Coordinate System is not a global coordinate system (like UTM)
- it only applies in the United States - including Alaska, Hawaii and Puerto Rico
- in other parts of the world, most countries have developed similar systems for their own use
State Plane Coordinate System on Topographic Maps (in lab)
- know how the state plane coordinate system works
- know how to find state plane coordinates on a topographic map
Copyright © Kevin Mulligan, Texas Tech University
Copyright © Kevin Mulligan, Texas Tech University
Other Projected Coordinate Systems
In addition to UTM and State Plane, there are many other projected coordinate systems in use throughout the
world. As noted earlier, many countries have systems similar to the State Plane Coordinate System. These other
projected coordinate systems are collectively known as “national grids.
- to create a national grid, the country is projected first (using the most suitable map projection for that country)
- and then an x,y, Cartesian coordinate system is overlaid on the projected map of the country
- the origin (0,0) of the coordinate system will fall outside of the country somewhere to the southwest
- this is done to make the coordinate values all positive within the country boundaries
Mapping with the United States
when mapping within the U.S. you have three basic choices:
- you can use a Projected Geographic Coordinate System (GCS)
- must be used for larger areas (e.g. the whole country or western U.S.)
- can also be used to map small areas if you set up a custom projection
- or you can use the UTM Coordinate System (UTM)
- UTM is a projected coordinate system that can be used to map small
areas anywhere in the world, so it is widely used throughout the world
- and that includes the United States
- or you can use the State Plane Coordinate System (SPCS)
- the SPCS is also a projected coordinate system
- used to map small areas - but it can only be used in the U.S.
Mapping Outside of the United States
when mapping outside of the U.S. you also have three basic choices:
- you can use a Projected Geographic Coordinate System (GCS)
- must be used for larger areas (e.g. Europe, western Australia, China)
- can also be used to map small areas if you set up a custom projection
- or you can use the UTM Coordinate System (UTM)
- UTM is a projected coordinate system that can be used to map small
areas anywhere in the world, so it is widely used throughout the world
- some small countries do not have a national grid – and only use UTM
- or you can use a National Grid (a national projected coordinate system)
- most larger countries have a system similar to the SPCS
- some smaller countries have a single grid (with no zones)
Copyright © Kevin Mulligan, Texas Tech University
GIST 3300 / 5300
Geographic Information Systems
Projected Coordinate Systems
Universal Transverse Mercator Coordinate System (UTM)
- why do we need the UTM coordinate system?
- how does it work?
- UTM coordinate system on topographic maps
State Plane Coordinate System
- why do we need the State Plane Coordinate System?
- how does it work?
- State Plane coordinates on a topographic map
Geographic Information Systems
Last lecture… coordinate systems and map projections
Geographic Coordinate Systems (GCS)
- recognize that the Geographic Coordinate System (GCS) is not projected
- the GCS might be referenced to different ellipsoids and datums
- but the data are not projected and the units are unprojected decimal degrees
Spatial Reference or Data Frame Properties Dialog
GCS unprojected
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Last lecture… coordinate systems and map projections
Projected Coordinate Systems (GCS)
- only when we apply a map projection to the data frame or the data layers
- does GCS become a projected coordinate system
Spatial Reference or Data Frame Properties Dialog
GCS projected using
North America Albers Equal Area
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Projected Coordinate Systems
1) Projected Geographic Coordinate System
- the x, y coordinate (latitude and longitude) of a feature remains the same
- but the display of the x, y coordinates (latitude and longitude) is projected
- used to minimize distortion in shape, area, distance or direction
- e.g. we apply an Albers Equal Area Conic projection to map the U.S.
Geographic Information Systems
Projected Coordinate Systems
In addition to a projected GCS, there are many other different projected coordinate
systems in use around the world.
2) Other Projected Coordinate Systems
- all other projected coordinate systems are designed to be used on
a relatively small area of the earth’s surface
- for a small area, the curvature in the earth's surface can be ignored
- the area to be mapped (zone, country, state, county) is projected first
- then, a Cartesian coordinate system is superimposed on the projected map
- x, y coordinates are expressed as feet or meters relative to a origin
a) Universal Transverse Mercator Coordinate System
b) State Plane Coordinate System
c) other national, state and county coordinate systems (grids)
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Projected Coordinate Systems
a) 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 features
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
- the Earth is divided into 60 zones - each zone covers 6o of longitude
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
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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
Projected Coordinate Systems
b) State Plane Coordinate System
Why do we need the State Plane Coordinate System?
- trying to address the same problem as the UTM coordinate system
- uses the same basic approach …
- for a small area, we can ignore the curvature of the Earth and apply
a rectangular (Cartesian) coordinate system
x2,y2
latitude
C
B
x1,y1
A
We can not calculate
distances and areas
if the coordinates are
expressed in degrees?
x2,y1
longitude
Geographic Information Systems
State Plane Coordinate System
Why do we need the State Plane Coordinate System?
System
- we could use the UTM coordinate system for state-wide mapping
- but many states cover more than one UTM zone
Geographic Information Systems
State Plane Coordinate System
How does it work?
- the SPCS system was established in the 1930’s
- by the U.S. Coast and Geodetic Survey
- system designed to facilitate surveys and mapping at the state level
- uses a rectangular (Cartesian) coordinate system over a small area
- like UTM, the SPCS ignores the curvature of the Earth within a zone
- hence the name “state plane”
- allows us to use plane geometry or plane surveying techniques
- provides linear accuracy of 1 unit in 10,000 (roughly 6 inches in a mile)
- in 1930’s, 1 in 10,000 was considered the limit of surveying accuracy
- SPCS is four times more accurate than UTM (1 linear unit in 2500)
- roughly 2 feet in a mile
Geographic Information Systems
State Plane Coordinate System
How does it work?
California
6 zones
Texas
5 zones
Comparison of State Plane and UTM Zones
Geographic Information Systems
State Plane Coordinate System
To minimize distortion
- states with zones that run north-south use a Transverse Mercator projection
- central meridian through the center of each north-south zone
- states with zones that run east-west use a Lambert conformal conic project
- standard parallels through the center of the east-west zone
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State Plane Coordinate System
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State Plane Coordinate System
- the Capital Dome in Austin
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State Plane on Topographic Maps
Full values shown
in lower left and
upper right on map
State Plane
Black Ticks
Geographic Information Systems
State Plane – Horizontal Datums and Units
United States
- because the SPCS is a coordinate system designed for use in each
of the U.S. states, it is usually referenced to either NAD 27 or NAD 83
- when referenced to NAD 27, the system uses English units (feet)
- when referenced to NAD 83, the system was designed to use meters
but English units can be used as well
- most widely used in local cadastral surveys and engineering applications
Other Parts of the World
- the State Plane Coordinate System applies only in the U.S.
- many other countries and provinces have their own system
Geographic Information Systems
State Plane – Describing Coordinates
- recognize that a single coordinate (an easting and northing) can be
replicated in different states and different state zones
- to describe a complete State Plane coordinate, you must specify:
1) the datum
2) the state and zone within the state
3) the easting and northing
4) and the measurement units (feet or meters)
Example:
NAD 27, Texas Central Zone, 2,818,560 feet E, 230,591 feet N
Geographic Information Systems
Summary …
Projected Coordinate Systems (State Plane)
- State Plane Coordinate System is a stand-alone projected coordinate system
- designed for use over a small area of the earth’s surface (zone within a state)
- we do not apply a projection because each State Plane zone is projected
- each zone is projected separately using a either a transverse Mercator or
Lambert conformal conic projection
Spatial Reference or Data Frame Properties Dialog
Geographic Information Systems
Projected Coordinate Systems
c) Other Projected Coordinate Systems
In addition to UTM and State Plane, there are many other projected coordinate
systems in use throughout the world.
Many countries have systems similar to the State Plane Coordinate System.
These projected coordinate systems are collectively known as “national grids”.
- to create a national grid, the country is projected first
- using the most suitable map projection for that country
- and then an x,y, Cartesian coordinate system is overlaid on the map
- the origin (0,0) of the coordinate system will fall outside of the country
somewhere to the southwest
- this is done to make the coordinate values (eastings and northings)
all positive within the country boundaries
Geographic Information Systems
Projected Coordinate Systems
c) Other Projected Coordinate Systems
Mapping with the United States
when mapping within the U.S. you have three basic choices:
- you can use a Projected Geographic Coordinate System (GCS)
- must be used for larger areas (e.g. the whole country or western U.S.)
- can also be used to map small areas if you set up a custom projection
- or you can use the UTM Coordinate System (UTM)
- UTM is a projected coordinate system that can be used to map small
areas anywhere in the world, so it is widely used throughout the world
- and that includes the United States
- or you can use the State Plane Coordinate System (SPCS)
- the SPCS is also a projected coordinate system
- used to map small areas - but it can only be used in the U.S.
Geographic Information Systems
Projected Coordinate Systems
c) Other Projected Coordinate Systems
Mapping Outside of the United States
when mapping outside of the U.S. you also have three basic choices:
- you can use a Projected Geographic Coordinate System (GCS)
- must be used for larger areas (e.g. Europe, western Australia, China)
- can also be used to map small areas if you set up a custom projection
- or you can use the UTM Coordinate System (UTM)
- UTM is a projected coordinate system that can be used to map small
areas anywhere in the world, so it is widely used throughout the world
- some small countries do not have a national grid – and only use UTM
- or you can use a National Grid (a national projected coordinate system)
- most larger countries have a system similar to the SPCS
- some smaller countries have a single grid (with no zones)
Geographic Information Systems