# 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

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 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

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 state-wide 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 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

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 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

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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