GEOGRAPHIC INFORMATION SYSTEMS Lecture 11: Projected Coordinate Systems


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1 UTM Coordinate System GEOGRAPHIC INFORMATION SYSTEMS Lecture 11: Projected Coordinate Systems 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 6 o 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
2 Texas Capital Dome NAD 83, Zone 14 North 621,161 m E, 3,349,894 m N Copyright Kevin Mulligan, Texas Tech University
3 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 northsouth  to minimize distortion, these states use a transverse Mercator projection for each zone  a central meridian runs northsouth down the center of each zone in the state  in some states the zones run eastwest  to minimize distortion, these states use a Lambert conformal conic projection for each zone  the standard parallels run eastwest through the each zone in the state  in Texas, the zones run eastwest 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
4 Copyright Kevin Mulligan, Texas Tech University
5 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
6 GIST 3300 / 5300 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
7 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
8 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
9 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.
10 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)
11 Projected Coordinate Systems a) Universal Transverse Mercator (UTM) Coordinate System
12 UTM Coordinate System Why do we need the UTM coordinate system? Cartesian Coordinate System x 2,y 2 Y axis How do we calculate the distance from x 1,y 1 to x 2,y 2? x 1,y 1 X axis
13 UTM Coordinate System Why do we need the UTM coordinate system? Cartesian Coordinate System x 2,y 2 Y axis C B Pythagorean Theorem A 2 + B 2 = C 2 C = (A 2 + B 2 ) x 1,y 1 A x 2,y 1 C = (x 2 x 1 ) 2 + (y 2 y 1 ) 2 X axis
14 UTM Coordinate System Why do we need the UTM coordinate system? 35 o,100 o Y axis C B If the coordinate values are degrees, this approach doesn t work. 34 o,102 o A 34 o,100 o In this example, the longitude A = 2 o but the number of miles per degree varies with latitude. X axis
15 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
16 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 6 o of longitude
17 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
18 UTM  How does it work?  The Earth is divided into 60 zones  with each zone covering 6 o of longitude  each zone has a central meridian  for example, Zone 14  extends from 96 o W to 102 o W  the zone has a central meridian at 99 o W
19 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 99 o W 80 o N 500,000 m UTM Zone 14 N 0,0 0 o Equator 102 o W 96 o W UTM Zone 14 S Sketch not to scale Central Meridian 80 o S
20 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 99 o W 80 o N 430,000 m x,y 3,500,000 m UTM Zone 14 N easting (x) = 430,000 m northing (y) = 3,500,000 m 0,0 0 o 96 o W 102 o W Sketch not to scale 80 o S
21 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 620,000 m 99 o W 80 o N x,y 3,650,000 m UTM Zone 14 N easting (x) = 620,000 m northing (y) = 3,650,000 m 0,0 0 o 96 o W 102 o W Sketch not to scale 80 o S
22 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 99 o W x,y B 80 o N UTM Zone 14 N x,y A 620,000 m 430,000 m 0,0 0 o A = 190,000 m 102 o W 96 o W 3,650,000 m 3,500,000 m Sketch not to scale B = 150,000 m 80 o S
23 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 99 o W 80 o N 96 o W 102 o W 0 o 500,000 m UTM Zone 14 S Sketch not to scale 10,000,000 m 0,0 80 o S
24 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 99 o W 80 o N 96 o W 102 o W 595,000 m x,y 0 o UTM Zone 14 S easting (x) = 595,000 m northing (y) = 2,480,000 m Sketch not to scale 2,480,000 m 0,0 80 o S
25 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
26 UTM on Topographic Maps
27 UTM on Topographic Maps UTM Blue Ticks Full values shown in lower right and upper left on map
28 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
29 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
30 Summary Projected Coordinate Systems (UTM)  UTM is a standalone 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
31 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 x 2,y 2 latitude C B We can not calculate distances and areas if the coordinates are expressed in degrees? x 1,y 1 A x 2,y 1 longitude
32 State Plane Coordinate System Why do we need the State Plane Coordinate System?  we could use the UTM coordinate system for statewide mapping  but many states cover more than one UTM zone
33 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
34 State Plane Coordinate System How does it work? California 6 zones Texas 5 zones Comparison of State Plane and UTM Zones
35 State Plane Coordinate System To minimize distortion  states with zones that run northsouth use a Transverse Mercator projection  central meridian through the center of each northsouth zone  states with zones that run eastwest use a Lambert conformal conic project  standard parallels through the center of the eastwest zone
36 State Plane Coordinate System
37 State Plane Coordinate System  the Capital Dome in Austin
38 State Plane on Topographic Maps Full values shown in lower left and upper right on map State Plane Black Ticks
39 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
40 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
41 Summary Projected Coordinate Systems (State Plane)  State Plane Coordinate System is a standalone 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
42 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
43 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.
44 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)
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