# Coordinate Systems. Every coordinate system has an initial reference point or origin All mapped features are represented in some coordinate system

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1 Coordinate Systems

2 Coordinate Systems A coordinate system is a 2- or 3-D reference frame used to specify locations on the earth. Many different coordinate systems exist, and each is defined by an origin, a system of coordinates laid out in a specific way, often with several zones, and always using specific units (eg. meters or feet). Coordinate systems also specify the projection and datum that are used as part of its definition. Every coordinate system has an initial reference point or origin All mapped features are represented in some coordinate system CTRS is the fundamental coordinate system of GPS. Positions are first computed in CTRS cartesian coordinates (in meters) and are then converted to latitude/longitude. Other coordinate systems will be discussed in more detail in later slides.

3 Common Coordinate Systems for GIS Work in Montana The UTM coordinate system works from 84 deg N to 80 deg S latitude. The US State Plane coordinate system works for the United States. The geographic (latitude/longitude) coordinate system works for the entire Earth.

4 Geographic Coordinate System The geographic coordinate system uses the latitude/longitude reference frame, a network of lines formed by parallels and meridians. Parallels are horizontal lines drawn east and west around the globe and equidistant from each other. Meridians are vertical lines drawn north and south on the globe perpendicular to the parallels and converging at the poles. The initial reference point, or origin, for the latitude/longitude coordinate system is the intersection between the equator and the prime meridian, which runs through Greenwich, England.

5 Location of MTSU CORS Station Radio Antenna DMS (NAD 83) Lat: N 45 40' Lon: W ' Decimal degrees (NAD 83) Lat: N Lon: W Geographic Coordinate System Coordinates are expressed in latitude, longitude and height. Latitude coordinates north of the equator are given a N or + designation. Latitude coordinates south of the equator are given a S or - designation. Longitude coordinates west of the prime meridian are given a W or - designation. Longitude coordinates east of the prime meridian are given an E or + designation. The reference units for geographic coordinates are degrees, minutes and seconds (or decimal degrees). The example in this slide shows coordinates for the MTSU CORS station radio antenna expressed both ways.

6 Degrees are Angles In this diagram, the intersection of the blue lines represents the center of the earth. Imagine you are standing at the center of the earth and you stretch your arm outward and upward at a 45 degree angle. Extend a line from your outstretched fingers to the surface of the earth. The line touches the earth s surface at 45 degrees N (or +) latitude. If you were to point down 45 degrees, you would be touching 45 degrees S ( or -) latitude. Now imagine you are standing at the center of the earth and pointing directly at Greenwich, England. You are pointing at 0 degrees longitude. As you slowly rotate your body and outstretched arm in a complete circle, the line extending from your outstretched fingers will pass through 360 degrees of longitude. Because longitude values are expressed in degrees E or W (+ or -), you will pass through 0 to 180 degrees W, and 0 to 180 degrees E. Which set you pass through first depends on which direction you rotate.

7 The intersection of the central meridian of each zone and the equator is assigned a coordinate value of x=500,000 meters and y=0 meters. A point is designated by meters E (Easting), meters N (Northing), and zone. UTM The UTM Coordinate System is a worldwide plane coordinate system, used in conjunction with the UTM projection, and originally adopted by the U.S. military in It is widely used by civilian mapping and land information organizations in many countries. The world is divided into 60 zones, each 6 in longitude wide, and extending north and south from a latitude of south 80 to north 84. Bounding meridians are evenly divisible by six, and the zones are numbered one through sixty. The equator serves as the mN (0 meters) grid line for the northern hemisphere and the mN (10,000,000 meters) grid line for the southern hemisphere to create a south to north numbering system within the zone.

8 Within each longitudinal zone the transverse mercator projection is used to give coordinates (eastings and northings) in meters The central meridian of each zone is given a false easting of 500,000 meters UTM Each UTM zone is projected independently. Note the northing coordinate at the north (10 million meters) and south (0 meters) poles. Note also that the northing coordinate at the equator is 10,000,000 m S (for the Southern hemisphere) and 0 m N (for the Northern hemisphere). So the coordinates in both the Southern and Northern hemispheres range from 0 to 10,000,000 m. - For the northings in the northern hemisphere, the origin is defined as the equator - For the northings in the southern hemisphere, the origin is defined as a point 10,000,000 meters south of the equator - The coordinates thus derived define a location within a UTM projection zone either north or south of the equator, but because the same coordinate system is repeated for each zone and hemisphere, it is necessary to additionally state the UTM longitudinal zone and either the hemisphere or latitudinal zone to define the location uniquely world-wide

9 Remember, grid lines have increasing values as you move to the east and to the north. Working with UTM coordinates can be tricky if your study area falls into more than one zone. UTM Montana is covered by three UTM zones, 11, 12, and 13, with central meridians -117, -111 and -105, respectively. Central meridian = mE (500,000 meters) Values decrease to W, increase to E MSU CORS station RTK Radio Antenna E 496, N 5,057, Zone 12 N NAD 83 UTM coordinates are referred to as Easting and Northing values. Reference units are meters. All grid zones central meridians are arbitrarily labeled mE (500,000 meters) to create a west to east numbering system within the grid zone. The west to east (left to right) grid line labels never reach the zero point as you proceed to the west (left) their values just decrease until you reach the western boundary of the zone. Conversely, as you proceed to the east (right) of the central meridian, the grid line label values increase from 500,000 meters until you reach the eastern boundary of the zone.

10

11 Established by the U.S. Coast and Geodetic Survey in the 1930's State Plane The State Plane coordinate system specifies one to five zones (due to its size, Alaska has 10 zones) for each state, using a Lambert Conformal or a Transverse Mercator projection (depending on the dominant orientation of the state, E-W or N-S, respectively). The specific projection and the size of the zone was selected to fit the geometry of the state, and to keep distortions at or below one part in 10,000. The low distortion makes the SPCS useful at the state and county levels. Coordinate units are meters Zone boundaries are typically political boundaries such as county or city lines. Montana is all in one zone: The State Plane coordinate system is referenced to the NAD83 datum.

12 Montana State Plane This is the Montana State Plane grid with the origin, standard parallels and central meridian shown. The central meridian of the zone is given a false easting of 600,000 meters. Coordinate numbers decrease to the West but never reach 0. Coordinate numbers increase to the East. This ensures that all coordinates in the zone have positive numbers. The Montana State Plane coordinate system uses a Lambert Conformal Conic projection. Along the standard parallels the scale is as stated for the map. Distortion increases away from the standard parallels. Most of the digital files available on the Montana State Library website are in State Plane coordinates.

13 Montana State Plane This diagram shows the parameters for Montana Zone 2500 with respect to the latitude/longitude graticule.

14 Montana State Plane The coordinates for the MSU GPS base station antenna are E 479,272 N 158,793 Zone: MT 2500 NAD 83 Coordinates are expressed as Northings and Eastings.

15 MSU CORS Station RTK Radio Antenna UTM E 496, N 5,057, Zone 12 N NAD 83 One Location in two Different Coordinate Systems Here is an example of the same location, expressed in two different coordinate systems. Note the differences in northings and eastings and think about how these two coordinate systems are laid out differently. State Plane E 479,272 N 158,793 Zone: MT 2500 NAD 83

16 All data in a GIS must have a correctly specified coordinate system to overlay properly How the GIS determines a layer s coordinate system Shapefiles: *.prj file TIFF files: *.tfw SID files: *.sdw or *.aux GeoTiff files: coordinate system information is embedded into the file header Specify correct coordinate system (prj file) when exporting GPS data Note: SID files are compressed TIFF files; most SID files today are compressed GeoTIFF files, with the coordinate system information embedded in the file header Why are Coordinate Systems Important? If you plan to combine GPS-collected data with other existing base layers, you must specify a coordinate system/prj file when you export your GPS data, in order for the data to be displayed properly in the GIS. Selecting a prj file defines the coordinate system, datum AND projection of the dataset, not just the projection. So the term projection file or prj file is actually a misnomer. It s not just a projection definition, it s a coordinate system, datum AND projection definition. Make sure you know what coordinate system you are using, make sure it is specified properly (by a correct prj file) and make sure all data you are displaying together have a correctly defined coordinate system in the GIS!

17 3 Things to Take Away Today 1. Coordinate systems allow us to locate an object in space and they usually specify a map projection and a datum 2. Understand how Geographic, UTM and State Plane coordinate systems are laid out 3. ArcMap reads the prj file to find out the coordinate system of a shapefile dataset (if the prj file is wrong, the data will show up in the wrong place)

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