What are map projections?


 Myron Evans
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1 Page 1 of 155 What are map projections? ArcGIS 10 Within ArcGIS, every dataset has a coordinate system, which is used to integrate it with other geographic data layers within a common coordinate framework such as a map. Coordinate systems enable you to integrate datasets within maps as well as to perform various integrated analytical operations such as overlaying data layers from disparate sources and coordinate systems. What is a coordinate system? Coordinate systems enable geographic datasets to use common locations for integration. A coordinate system is a reference system used to represent the locations of geographic features, imagery, and observations such as GPS locations within a common geographic framework. Each coordinate system is defined by: Its measurement framework which is either geographic (in which spherical coordinates are measured from the earth's center) or planimetric (in which the earth's coordinates are projected onto a twodimensional planar surface). Unit of measurement (typically feet or meters for projected coordinate systems or decimal degrees for latitude longitude). The definition of the map projection for projected coordinate systems. Other measurement system properties such as a spheroid of reference, a datum, and projection parameters like one or more standard parallels, a central meridian, and possible shifts in the x and ydirections. Types of coordinate systems There are two common types of coordinate systems used in GIS: A global or spherical coordinate system such as latitude longitude. These are often referred to
2 Page 2 of 155 as geographic coordinate systems. A projected coordinate system based on a map projection such as transverse Mercator, Albers equal area, or Robinson, all of which (along with numerous other map projection models) provide various mechanisms to project maps of the earth's spherical surface onto a twodimensional Cartesian coordinate plane. Projected coordinate systems are sometimes referred to as map projections. For a conceptual overview, see Georeferencing and coordinate systems. Coordinate systems (either geographic or projected) provide a framework for defining realworld locations. In ArcGIS, the coordinate system is used as the method to automatically integrate the geographic locations from different datasets into a common coordinate framework for display and analysis. ArcGIS automatically integrates datasets whose coordinate systems are known All geographic datasets used in ArcGIS are assumed to have a welldefined coordinate system that enables them to be located in relation to the earth's surface. If your datasets have a welldefined coordinate system, then ArcGIS can automatically integrate your datasets with others by projecting your data on the fly into the appropriate framework for mapping, 3D visualization, analysis, and so forth. If your datasets do not have a spatial reference, they cannot be easily integrated. You need to define one before you can use your data effectively in ArcGIS. The spatial reference or coordinate system is metadata. It describes the coordinate framework that the data is already using. Caution: When you define the coordinate system for a dataset using the Define Projection tool or the dataset property page, you are updating the metadata to identify the current coordinate system. The dataset's extent and coordinate values will not change. The dataset must already be using the coordinate system. To change a dataset's coordinate system, including its extent and values, use the Project or Project Raster tools. What is a spatial reference in ArcGIS? A spatial reference in ArcGIS is a series of parameters that define the coordinate system and other spatial properties for each dataset in the geodatabase. It is typical that all datasets for the same area (and in the same geodatabase) use a common spatial reference definition. An ArcGIS spatial reference includes settings for: The coordinate system The coordinate precision with which coordinates are stored (often referred to as the coordinate resolution) Processing tolerances (such as the cluster tolerance) The spatial or map extent covered by the dataset (often referred to as the spatial domain) Learning more about coordinate systems Here is a series of links to help you learn more about applying map projections and coordinate systems in your work. Learning more about map projection and coordinate system concepts
3 Page 3 of 155 Concept To understand geographic coordinate systems and latitude longitude To understand projected coordinate systems To learn which map projections are supported To learn about datums To learn about spheroids and spheres To choose a map projection To learn about the geodatabase spatial reference. Map projection and coordinate system tasks Where to go for more information See What are geographic coordinate systems? See What are projected coordinate systems? See List of supported map projections See Datums See Spheroids and spheres See Choosing a map projection See the Geodatabase Spatial Reference. Common coordinate system and map projection tasks in ArcGIS Here is a series of links to guidance on how to perform a number of common coordinate system tasks in ArcGIS. Defining the coordinate systems, reprojecting, and transforming datasets Common task Where to go for more information To define the spatial reference for a new dataset in the geodatabase To record the coordinate system of an existing dataset To define the coordinate system for external raster and image files To project feature, rasters, and image data layers To identify an unknown coordinate system Coordinate system definition and projection See An overview of spatial references in the geodatabase See the "Define Projection" tool in An overview of the Projections and Transformations toolset See Defining or modifying a raster's coordinate system See An overview of the Projections and Transformations toolset See Identifying an unknown coordinate system Datum transformation and rubbersheeting Common task Where to go for more information To learn transformation concepts To transform and rubbersheet data layers To georeference unregistered raster data To georeference unregistered CAD data Data transformation tasks See Geographic transformation methods See Performing spatial adjustment See Changing the geographic coordinates of a raster dataset: georeferencing See Georeferencing a CAD dataset Working with Vertical Coordinate Systems Common task To learn vertical coordinate system concepts Where to go for more information See What are vertical coordinate systems?
4 Page 4 of 155 To define a vertical coordinate system for a feature class Working with vertical coordinate systems See Defining_feature_class_properties What existing coordinate systems and transformations are available? Object type Where to go for more information Geographic or vertical coordinate systems Projected coordinate systems See geographic_coordinate_systems.pdf See projected_coordinate_systems.pdf Geographic (datum) transformations What existing coordinate systems and transformations are available? See geographic_transformations.pdf About map projections Geographic transformation methods What are geographic coordinate systems? What are projected coordinate systems? Projection basics for GIS professionals Coordinate systems, also known as map projections, are arbitrary designations for spatial data. Their purpose is to provide a common basis for communication about a particular place or area on the earth's surface. The most critical issue in dealing with coordinate systems is knowing what the projection is and having the correct coordinate system information associated with a dataset. There are two types of coordinate systems geographic and projected. A geographic coordinate system uses a threedimensional spherical surface to define locations on the earth. It includes an angular unit of measure, a prime meridian, and a datum (based on a spheroid). In a geographic coordinate system, a point is referenced by its longitude and latitude values. Longitude and latitude are angles measured from the earth's center to a point on the earth's surface. The angles often are measured in degrees (or in grads). Learn more about geographic coordinate systems. A projected coordinate system is defined on a flat, twodimensional surface. Unlike a geographic coordinate system, a projected coordinate system has constant lengths, angles, and areas across the two dimensions. A projected coordinate system is always based on a geographic coordinate system that is based on a sphere or spheroid. In a projected coordinate system, locations are identified by x,y coordinates on a grid, with the origin at the center of the grid. Each position has two values that reference it to that central location. One specifies its horizontal position and the other its vertical position. Learn more about projected coordinate systems. When the first map projections were devised, it was assumed, incorrectly, that the earth was flat. Later the assumption was revised, and the earth was assumed to be a perfect sphere. In the 18th century, people began to realize that the earth was not perfectly round. This was the beginning of the concept of the cartographic spheroid.
5 Page 5 of 155 To more accurately represent locations on the earth's surface, mapmakers studied the shape of the earth (geodesy) and created the concept of the spheroid. A datum links a spheroid to a particular portion of the earth's surface. Recent datums are designed to fit the entire earth's surface well. These are the most commonly used datums in North America: North American Datum (NAD) 1927 using the Clarke 1866 spheroid NAD 1983 using the Geodetic Reference System (GRS) 1980 spheroid World Geodetic System (WGS) 1984 using the WGS 1984 spheroid Newer spheroids are developed from satellite measurements and are more accurate than those developed in the 19th and early 20th centuries. You will find that the terms "geographic coordinate system" and "datum" are used interchangeably. Learn more about datums. The coordinates for a location will change depending on the datum and spheroid on which those coordinates are based, even if using the same map projection and projection parameters. For example, the geographic coordinates below are for the city of Bellingham, Washington, using three different datums: Datum Latitude Longitude NAD NAD WGS A principle of good data management is to obtain the coordinate system information from the data source providing the data. Do not guess about the coordinate system of data because this will result in an inaccurate GIS database. The necessary parameters are the following: Geographic coordinate system (Datum) Unit of measure Zone (for UTM or State Plane) Projection Projection parameters Projection parameters may be required, depending on the map projection. For example, the Albers and Lambert conic projections require the following parameters: 1st standard parallel 2nd standard parallel Central meridian Latitude of origin False easting False northing Unit of measure You can define a coordinate system for data with the Define Projection tool in the Data Management toolbox. If the data has a coordinate system definition, but it does not match the typical coordinate system
6 Page 6 of 155 used by an organization, you can reproject the data. You can reproject data in a geodatabase feature dataset, feature class, shapefile, or raster dataset using the Project tool or Project Raster tool in the Data Management toolbox. Identifying an unknown coordinate system The geoid, ellipsoid, spheroid and datum What are map projections? The geoid, ellipsoid, spheroid and datum, and how they are related The geoid is defined as the surface of the earth's gravity field, which is approximately the same as mean sea level. It is perpendicular to the direction of gravity pull. Since the mass of the earth is not uniform at all points, and the direction of gravity changes, the shape of the geoid is irregular. Click on the link below to access a website maintained by the National Oceanographic & Atmospheric Administration (NOAA). The website has links to images showing interpretations of the geoid under North America. To simplify the model, various spheroids or ellipsoids have been devised. These terms are used interchangeably. For the remainder of this article, the term spheroid will be used. A spheroid is a threedimensional shape created from a twodimensional ellipse. The ellipse is an oval, with a major axis (the longer axis), and a minor axis (the shorter axis). If you rotate the ellipse, the shape of the rotated figure is the spheroid. The semimajor axis is half the length of the major axis. The semiminor axis is half the length of the minor axis. For the earth, the semimajor axis is the radius from the center of the earth to the equator, while the semiminor axis is the radius from the center of the earth to the pole. One particular spheroid is distinguished from another by the lengths of the semimajor and semiminor axes. For example, compare the Clarke 1866 spheroid with the GRS 1980 and the WGS 1984 spheroids, based on the measurements (in meters) below. Spheroid Semimajor axis (m) Semiminor axis (m) Clarke GRS WGS Spheroid comparison A particular spheroid can be selected for use in a specific geographic area, because that particular spheroid does an exceptionally good job of mimicking the geoid for that part of the world. For North America, the spheroid of choice is GRS 1980, on which the North American Datum 1983 (NAD83) is based. A datum is built on top of the selected spheroid, and can incorporate local variations in elevation. With the spheroid, the rotation of the ellipse creates a totally smooth surface across the world. Because this doesn't reflect reality very well, a local datum can incorporate local variations in elevation.
7 Page 7 of 155 The underlying datum and spheroid to which coordinates for a dataset are referenced can change the coordinate values. An illustrative example using the city of Bellingham, Washington follows. Compare the coordinates in decimal degrees for Bellingham using NAD27, NAD83 and WGS84. It is apparent that while NAD83 and WGS84 express coordinates that are nearly identical, NAD27 is quite different, because the underlying shape of the earth is expressed differently by the datums and spheroids used. Datum Longitude Latitude NAD NAD WGS Geographic coordinates below are for the city of Bellingham, Washington using 3 different datums The longitude is the measurement of the angle from the prime meridian at Greenwich, England, to the center of the earth, then west to the longitude of Bellingham, Washington. The latitude is the measurement of the angle formed from the equator to the center of the earth, then north to the latitude of Bellingham, Washington. If the surface of the earth at Bellingham is bulged out, the angular measurements in decimal degrees from Greenwich and the equator will become slightly larger. If the surface at Bellingham is lowered, the angles will become slightly smaller. These are two examples of how the coordinates change based on the datum. Datums Projection basics for GIS professionals Spheroids and spheres Identifying an unknown coordinate system Coordinate system information is usually obtained from the data source, but not always, as with legacy data. The technique described below helps identify the correct coordinate system. If the coordinate system is unknown, you will receive this warning message when trying to add the layer to ArcMap: The following data sources you added are missing spatial reference information. This data can be drawn in ArcMap, but cannot be projected. The term coordinate system can refer to data expressed in decimal degrees, or a projected coordinate system expressed in meters or feet. The term projection, or PRJ, is an older term that is also used, but it is not as precise. If a data source has a defined coordinate system, ArcMap can project it on the fly to a different coordinate system. If data does not have a defined coordinate system, ArcMap cannot project it on the fly. ArcMap simply will draw it. If you change the data frame's coordinate system, all layers that have coordinate systems will be projected on the fly to the new coordinate system. If you set the data frame's coordinate system and the data with a known coordinate system lines up with the unknown data, the data frame's coordinate system is that of the unknown data's. Steps: 1. Start ArcMap with a new empty map and add the data with the unknown coordinate
8 Page 8 of 155 system. The data must not have a defined coordinate system. For shapefiles, it must not have a PRJ file. 2. Rightclick the layer name in the table of contents, click Properties to open the Layer Properties dialog box, select the Source tab, then examine the extent of the data. If the coordinates, which are shown in the Extent box, are in decimal degrees, such as between longitude 180 and +180 and latitude 90 and +90, you need to identify the geographic coordinate system (datum) used for the data (such as North American Datum (NAD) 1927 or NAD 1983). Note: If you have data that has a coordinate system called GCS_Assumed_Geographic_1, this is not the data's correct coordinate system. The GCS_Assumed_Geographic_1 coordinate system definition was created to permit ArcMap to guess at the coordinate system for data that has coordinates in decimal degrees. You should determine the correct geographic coordinate system for the data. If the data is in the United States and shows an extent in which the coordinates to the left of the decimal are six, seven, or eight digits, the data is probably in a zone of the State Plane or Universal Transverse Mercator (UTM) coordinate systems, which are projected coordinate systems. Learn about geographic coordinate systems Learn about projected coordinate systems 3. If the unknown data lies within the United States, add comparison data to ArcMap. You can find comparison data in the Reference Systems folder of your ArcGIS installation. The default location is C:\Program Files\ArcGIS\Desktop10.0. Navigate to the Reference Systems folder and add the file usstpln83.shp. 4. In the table of contents, rightclick Layers > Properties, then click the Coordinate System tab. 5. In the Select a coordinate system section, expand Predefined > Projected Coordinate Systems > State Plane. a. One by one, expand the folders, click a State Plane projection file, then click Apply. The Geographic Coordinate Systems warning box may appear to warn you that the layer's geographic coordinate system is not the same as the data frame's geographic coordinate system. This may cause offsets from a few meters to several hundred meters. A geographic (datum) transformation can reduce the offsets. You can set a transformation from this dialog box, or you can also examine the transformation information: i. Click the Transformations button on the Coordinate System tab. ii. Verify that the appropriate transformation method was applied in the Using dropdown menu. For example, use NAD_1927_To_NAD_1983_NADCON to go between NAD 1927 and NAD 1983 in the lower 48 states, and use the applicable state or regional file for transforming to High Accuracy Reference Network (HARN). Repeat, assigning different State Plane zones until the usstpln83.shp file snaps into place and the data with the unknown coordinate system appears in the
9 Page 9 of 155 correct place within the proper state. Note: Additional PRJ files for some states are available in the State Systems, County Systems, and National Grids folders. If your data is in one of the regions listed in these folders, you should also test these PRJ files. b. Click the OK button on the Data Frame Properties dialog box. c. Verify the correct place by zooming in to the layer and using the Identify tool on the state where the data is drawn. If the data does not line up after testing the State Plane options, perform the same steps above using the UTM PRJ files. 6. Expand the UTM folder. 7. One by one, expand the folders, click a UTM projection file, then click Apply as discussed above to identify a State Plane projection. It will be useful for you to first identify what UTM zone your data should be in. For a map of UTM zones, search the Web for UTM zone map. One link is UTM Grid Zones of the World compiled by Alan Morton. Coordinates in UTM meters on the NAD 1983 datum and coordinates for the same point on the WGS 1984 datum in the continental United States are within onehalf meter from each other. Data in the UTM coordinate system referenced to the NAD 1983 datum is approximately 200 meters north of the same data referenced instead to the NAD 1927 datum. There may be a slight shift either east or west between data on these two datums, but an approximate 200meter difference in the northing is diagnostic. The 200meter difference is comparatively slight; therefore, it is essential that you use accurate comparison data to determine whether the correct datum is NAD 1927 or NAD 1983 for data in the UTM projection. 8. When the correct coordinate system is found, write down its location and name so that you can define the data's coordinate system using the Define Projection tool. When the coordinate system is identified and defined, the data will line up in ArcMap with other data added to the ArcMap session, provided that the correct datum transformation was specified. If the above steps do not line up the data in ArcMap, the data is in a custom coordinate system. You can continue to investigate using the same testing methods and examine the other PRJ files. But you will most likely have to do more research on your data to define the correct coordinate system. Projection basics for GIS professionals Converting Degrees Minutes Seconds values to Decimal Degree values The following is the simple equation to convert Degrees, Minutes, and Seconds into Decimal Degrees.
10 Page 10 of 155 DD = (Seconds/3600) + (Minutes/60) + Degrees The conversion must be handled differently if the degrees value is negative. Here's one way: DD =  (Seconds/3600)  (Minutes/60) + Degrees In the instructions below you will convert one field in a table of latitude or longitude values in Degrees, Minutes, and Seconds to Decimal Degrees using the Field Calculator. The code is in VBA, but is easily converted to other programming languages. It is assumed that the Degrees, Minutes, and Seconds are stored as a string (text), with spaces between the numbers and not containing any symbols. For example the data would be stored as: where 25 is degrees, 35 is minutes, and 22.3 is seconds. The output will be stored in a number field. Steps: 1. Add the table to ArcMap. 2. Rightclick the table in the table of contents and click open. 3. Click the Options button and click Add Field. 4. Type "Lat2" in the Name field. 5. Click the Type dropdown arrow and click Double from the list. If "Lat2" is already used as a field name, select a name that is not used. 6. Click OK. 7. Rightclick the Lat2 field and click Field Calculator. 8. Click Yes if presented with a message box. 9. Check the Advanced check box. 10. Paste the following code into the expression box: Dim Degrees as Double Dim Minutes as Double Dim Seconds as Double Dim DMS as Variant Dim DD as Double DMS = Split([Latitude]) Degrees = CDbl(DMS(0)) Minutes = CDbl(DMS(1)) Seconds = CDbl(DMS(2)) If Degrees < 0 Then DD = (Seconds/3600)  (Minutes/60) + Degrees Else DD = (Seconds/3600) + (Minutes/60) + Degrees End If In the sixth line, beginning with 'DMS...' the text within the brackets [ ] should be the name of the field holding the latitude values. Replace the word Latitude in the code with
11 Page 11 of 155 the name of the field (in your table) that stores the DMS latitude values in the table. 11. Paste the following code into the 'Lat2 =' box at the bottom of the dialog box. CDbl(DD) 12. Click OK. 13. Repeat steps 3 through 12 for the longitude values. What are geographic coordinate systems? A geographic coordinate system (GCS) uses a threedimensional spherical surface to define locations on the earth. A GCS is often incorrectly called a datum, but a datum is only one part of a GCS. A GCS includes an angular unit of measure, a prime meridian, and a datum (based on a spheroid). A point is referenced by its longitude and latitude values. Longitude and latitude are angles measured from the earth's center to a point on the earth's surface. The angles often are measured in degrees (or in grads). The following illustration shows the world as a globe with longitude and latitude values. In the spherical system, horizontal lines, or east west lines, are lines of equal latitude, or parallels. Vertical lines, or north south lines, are lines of equal longitude, or meridians. These lines encompass the globe and form a gridded network called a graticule. The line of latitude midway between the poles is called the equator. It defines the line of zero latitude. The line of zero longitude is called the prime meridian. For most geographic coordinate systems, the prime meridian is the longitude that passes through Greenwich, England. Other countries use longitude lines that pass through Bern, Bogota, and Paris as prime meridians. The origin of the graticule (0,0) is defined by where the equator and prime meridian intersect. The globe is then divided into four geographical quadrants that are based on compass bearings from the origin. North and south are above and below the equator, and west and east are to the left and right of the prime meridian.
12 Page 12 of 155 Latitude and longitude values are traditionally measured either in decimal degrees or in degrees, minutes, and seconds (DMS). Latitude values are measured relative to the equator and range from  90 at the South Pole to +90 at the North Pole. Longitude values are measured relative to the prime meridian. They range from 180 when traveling west to 180 when traveling east. If the prime meridian is at Greenwich, then Australia, which is south of the equator and east of Greenwich, has positive longitude values and negative latitude values. It may be helpful to equate longitude values with X and latitude values with Y. Data defined on a geographic coordinate system is displayed as if a degree is a linear unit of measure. This method is basically the same as the Plate Carrée projection. Learn more about the Plate Carrée projection Although longitude and latitude can locate exact positions on the surface of the globe, they are not uniform units of measure. Only along the equator does the distance represented by one degree of longitude approximate the distance represented by one degree of latitude. This is because the equator is the only parallel as large as a meridian. (Circles with the same radius as the spherical earth are called great circles. The equator and all meridians are great circles.) Above and below the equator, the circles defining the parallels of latitude get gradually smaller until they become a single point at the North and South Poles where the meridians converge. As the meridians converge toward the poles, the distance represented by one degree of longitude decreases to zero. On the Clarke 1866 spheroid, one degree of longitude at the equator equals km, while at 60 latitude it is only km. Because degrees of latitude and longitude don't have a standard length, you can t measure distances or areas accurately or display the data easily on a flat map or computer screen. Tables of the supported geographic coordinate systems, datums, and so on are available in a geographic_coordinate_systems.pdf file in the ArcGIS Documentation folder. This illustration shows the parallels and meridians that form a graticule. Datums Fundamentals of vertical coordinate systems North American datums Spheroids and spheres What are projected coordinate systems? Spheroids and spheres The shape and size of a geographic coordinate system's surface is defined by a sphere or spheroid.
13 Page 13 of 155 Although the earth is best represented by a spheroid, it is sometimes treated as a sphere to make mathematical calculations easier. The assumption that the earth is a sphere is possible for smallscale maps (smaller than 1:5,000,000). At this scale, the difference between a sphere and a spheroid is not detectable on a map. However, to maintain accuracy for largerscale maps (scales of 1:1,000,000 or larger), a spheroid is necessary to represent the shape of the earth. Between those scales, choosing to use a sphere or spheroid will depend on the map's purpose and the accuracy of the data. Definition of a spheroid A sphere is based on a circle, while a spheroid (or ellipsoid) is based on an ellipse. A spheroid, or ellipsoid, is a sphere flattened at the poles. The shape of an ellipse is defined by two radii. The longer radius is called the semimajor axis, and the shorter radius is called the semiminor axis. The semimajor axis, or equatorial radius, is half the major axis. the semiminor axis, or polar radius, is half the minor axis. Rotating the ellipse around the semiminor axis creates a spheroid. A spheroid is also known as an oblate ellipsoid of revolution. The following graphic shows the semimajor and semiminor axes of a spheroid. The semimajor axis is in the equatorial plane, while the semiminor axis is perpendicular to the equatorial plane. A spheroid is defined by either the semimajor axis, a, and the semiminor axis, b, or by a and the flattening. The flattening is the difference in length between the two axes expressed as a fraction or a decimal. The flattening, f, is derived as follows: f = (a  b) / a The flattening is a small value, so usually the quantity 1/f is used instead. These are the spheroid parameters for the World Geodetic System of 1984 (WGS 1984 or WGS84):
14 Page 14 of 155 a = meters b = meters 1/f = The flattening ranges from 0 to 1. A flattening value of 0 means the two axes are equal, resulting in a sphere. The flattening of the earth is approximately Another quantity that, like the flattening, describes the shape of a spheroid is the square of the eccentricity, e 2. It is represented by the following: Defining different spheroids for accurate mapping The earth has been surveyed many times to better understand its surface features and their peculiar irregularities. The surveys have resulted in many spheroids that represent the earth. Generally, a spheroid is chosen to fit one country or a particular area. A spheroid that best fits one region is not necessarily the same one that fits another region. Until recently, North American data used a spheroid determined by Clarke in The semimajor axis of the Clarke 1866 spheroid is 6,378,206.4 meters, and the semiminor axis is 6,356,583.8 meters. Because of gravitational and surface feature variations, the earth is neither a perfect sphere nor a perfect spheroid. Satellite technology has revealed several elliptical deviations; for example, the South Pole is closer to the equator than the North Pole. Satellitedetermined spheroids are replacing the older groundmeasured spheroids. For example, the new standard spheroid for North America is the Geodetic Reference System of 1980 (GRS 1980), whose radii are 6,378,137.0 and 6,356, meters. The GRS 1980 spheroid parameters were set by the International Union for Geodesy and Geophysics in Because changing a coordinate system's spheroid will change all feature coordinate values, many organizations haven't switched to newer (and more accurate) spheroids. Datums North American datums What are geographic coordinate systems? Datums While a spheroid approximates the shape of the earth, a datum defines the position of the spheroid relative to the center of the earth. A datum provides a frame of reference for measuring locations on the surface of the earth. It defines the origin and orientation of latitude and longitude lines. Learn more about spheroids and spheres. Whenever you change the datum, or more correctly, the geographic coordinate system, the coordinate values of your data will change. Here are the coordinates in degrees/minutes/seconds (DMS) of a control point in Redlands, California, on the North American Datum of 1983 (NAD 1983 or NAD83):
15 Page 15 of Here's the same point on the North American Datum of 1927 (NAD 1927 or NAD27): The longitude value differs by approximately 3 seconds, while the latitude value differs by about 0.05 seconds. NAD 1983 and the World Geodetic System of 1984 (WGS 1984) are identical for most applications. Here are the coordinates for the same control point based on WGS 1984: Geocentric datums In the last 15 years, satellite data has provided geodesists with new measurements to define the best earthfitting spheroid, which relates coordinates to the earth's center of mass. An earthcentered, or geocentric, datum uses the earth's center of mass as the origin. The most recently developed and widely used datum is WGS It serves as the framework for locational measurement worldwide. Local datums A local datum aligns its spheroid to closely fit the earth's surface in a particular area. A point on the surface of the spheroid is matched to a particular position on the surface of the earth. This point is known as the origin point of the datum. The coordinates of the origin point are fixed, and all other points are calculated from it. The coordinate system origin of a local datum is not at the center of the earth. The center of the spheroid of a local datum is offset from the earth's center. NAD 1927 and the European Datum of 1950 (ED 1950) are local datums. NAD 1927 is designed to fit North America reasonably well, while ED 1950 was created for use in Europe. Because a local datum aligns its spheroid so closely to a particular area on the earth's surface, it's not suitable for use outside the area for which it was designed. Learn more about North American datums. North American datums Spheroids and spheres What are geographic coordinate systems?
16 Page 16 of 155 North American datums The two horizontal datums used almost exclusively in North America are NAD 1927 and NAD Learn more about datums. NAD 1927 NAD 1927 uses the Clarke 1866 spheroid to represent the shape of the earth. The origin of this datum is a point on the earth referred to as Meades Ranch in Kansas. Many NAD 1927 control points were calculated from observations taken in the 1800s. These calculations were done manually and in sections over many years. Therefore, errors varied from station to station. NAD 1983 Many technological advances in surveying and geodesy electronic theodolites, Global Positioning System (GPS) satellites, Very Long Baseline Interferometry, and Doppler systems revealed weaknesses in the existing network of control points. Differences became particularly noticeable when linking existing control with newly established surveys. The establishment of a new datum allowed a single datum to cover consistently North America and surrounding areas. The North American Datum of 1983 is based on both earth and satellite observations, using the Geodetic Reference System (GRS) 1980 spheroid. The origin for this datum was the earth's center of mass. This affects the surface location of all longitude latitude values enough to cause locations of previous control points in North America to shift, sometimes as much as 500 feet compared to NAD A 10year multinational effort tied together a network of control points for the United States, Canada, Mexico, Greenland, Central America, and the Caribbean. The GRS 1980 spheroid is almost identical to the World Geodetic System (WGS) 1984 spheroid. The WGS 1984 and NAD 1983 coordinate systems are both earthcentered. When originally published in 1986, NAD 1983 and WGS 1984 could be considered coincident. That is no longer true. WGS 1984 is tied to the International Terrestrial Reference Frame (ITRF). NAD 1983 is tied to the North American tectonic plate to minimize changes to coordinate values over time. This has caused NAD 1983 and WGS 1984 to drift apart. Generally, coordinates in WGS 1984 and NAD 1983 are around one to two meters apart. GPS data is actually reported in the WGS 1984 coordinate system. However, if any type of external control network is being used, such as the Continuously Operating Reference Stations (CORS) service, the GPS coordinates are relative to that coordinate system, not WGS HARN or HPGN There was an ongoing effort at the state level to readjust the NAD 1983 datum to a higher level of accuracy using stateoftheart surveying techniques that were not widely available when the NAD 1983 datum was being developed. This effort, known as the High Accuracy Reference Network (HARN) previously the High Precision Geodetic Network (HPGN) was a cooperative project between the National Geodetic Survey (NGS) and individual states. Currently, all states except Alaska have been resurveyed, and transformation grid files for 49 states and five territories have been published. Control points that have been adjusted are labeled in the National Geodetic Survey database as NAD83 (19xx) or NAD83 (20xx) where xx represents the year of adjustment. Some points have been adjusted several times, and the year may not be the same as the original HARN readjustment. NGS has never released transformations to convert
17 Page 17 of 155 between an original HARN and later readjustments. Other NAD 1983 readjustments NGS maintains a reference network of CORS stations. This set of control points is labeled as NAD 1983 (CORS96), and the points are tied to the ITRF through a transformation. Other geodetic control points are labeled with the adjustment year. Recently, NGS performed a national readjustment. All existing control points except the CORS stations were updated and are now labeled NAD 1983 (NSRS2007). The official name of the readjustment is National Spatial Reference System (NSRS) of For most of the United States, the differences between HARN coordinates and NSRS2007 are a few centimeters. Because of this, no standardized transformations have been calculated and published to convert between NAD 1983 (NSRS2007) and earlier realizations of NAD More information is available on the NGS Website. Other United States datums Alaska, Hawaii, American Samoa, Guam, Puerto Rico and the Virgin Islands, and some Alaskan islands have used other datums besides NAD New data is referenced to NAD 1983 or one of its readjustments. Canada Several readjustments occurred in Canada prior to the adoption of NAD A national adjustment, called NAD 1927 DEF 1976 (commonly called MAY76), and a regional adjustment for Quebec, NAD 1927 CGQ77, were carried out. The maritime provinces conducted a separate adjustment and defined the Average Terrestrial System of 1977 (ATS 1977). In the 1980s, Canada joined the United States to define NAD Since then, Canada has readjusted its control network, and the reference system is now known as NAD 1983 (CSRS). CSRS stands for Canadian Spatial Reference System. An excellent paper with more details is by Don Junkins and Gordon Garrard. Learn more about geographic transformation methods. Datums What happens to features at +/180 (dateline)? Data in a geographic coordinate system is treated, in a sense, as twodimensional, at least to the point that there are edges, just as in a projected coordinate system. Generally, the edges are at  180/+180 for the east west extents, and /+90 for the north south extents. These extents are called the "horizon" of the coordinate system. When ArcMap displays data in a geographic coordinate system, it is shown as twodimensional. Part of the reason for this is that there is a discontinuity at the +180 and 180 meridians. Although they represent the same line, they are relatively far apart mathematically. Identifying and handling features that cross this discontinuity would have a performance impact. In a geodatabase, a feature that crosses an edge will be clipped to the horizon. If you are editing features in ArcMap, the data frame's coordinate system will affect what happens to a feature that crosses the +/180 line. If the data frame is using a geographic coordinate system, that is, the +180
18 Page 18 of 155 and 180 lines are separated, a feature that crosses outside the horizon will be clipped to the horizon. If the data frame is using a projected coordinate system, with the +/180 line inside, a feature that crosses it will be split into multiple parts. Some clients instead use a or 360 to 0 longitude range, although this does just move the issue to the Greenwich meridian. It's also possible to store data in a projected coordinate system that is centered in the Pacific, but again, that will mean that there is a "break" somewhere else in the world. GCS_Assumed_Geographic_1 The GCS_Assumed_Geographic_1 coordinate system definition was created for ArcGIS 8 to permit ArcMap to infer the coordinate system for certain shapefiles when the coordinate system is undefined. The shapefile's extent must have values that look like decimal degrees. For instance, if longitude, or x, values are between 180 and +180, ArcMap "assumes" the coordinate system is in degrees and assigns GCS_Assumed_Geographic_1. ArcMap then can project the data on the fly, although there are no valid geographic (datum) transformations. The coordinate system is not permanently attached to the shapefile. If you look at the shapefile's metadata, the coordinate system is undefined. In version 9.2, GCS_Assumed_Geographic_1 was removed. Shapefiles, even if their extents fit decimal degrees, will have an unknown coordinate system in ArcMap. Shapefiles that did line up, because they were projected on the fly before, will no longer line up with datasets in other coordinate systems. If you have a shapefile that no longer lines up in version 9.2, check its coordinate system. Occasionally, data has been defined with the GCS_Assumed_Geographic_1 coordinate system. If you see that a shapefile or other data type displays the GCS_Assumed_Geographic_1 coordinate system, take steps to identify the data's true coordinate system. What are projected coordinate systems? A projected coordinate system is defined on a flat, twodimensional surface. Unlike a geographic coordinate system, a projected coordinate system has constant lengths, angles, and areas across the two dimensions. A projected coordinate system is always based on a geographic coordinate system that is based on a sphere or spheroid. In a projected coordinate system, locations are identified by x,y coordinates on a grid, with the origin at the center of the grid. Each position has two values that reference it to that central location. One specifies its horizontal position and the other its vertical position. The two values are called the x coordinate and ycoordinate. Using this notation, the coordinates at the origin are x = 0 and y = 0. On a gridded network of equally spaced horizontal and vertical lines, the horizontal line in the center is called the xaxis and the central vertical line is called the yaxis. Units are consistent and equally spaced across the full range of x and y. Horizontal lines above the origin and vertical lines to the right of the origin have positive values; those below or to the left have negative values. The four quadrants represent the four possible combinations of positive and negative X and Y coordinates.
19 Page 19 of 155 When working with data in a geographic coordinate system, it is sometimes useful to equate the longitude values with the X axis and the latitude values with the Y axis. Lists of the supported projected coordinate systems are available in a projected_coordinate_systems.pdf file in the ArcGIS Documentation folder. About map projections Projection types About map projections Whether you treat the earth as a sphere or a spheroid, you must transform its threedimensional surface to create a flat map sheet. This mathematical transformation is commonly referred to as a map projection. One easy way to understand how map projections alter spatial properties is to visualize shining a light through the earth onto a surface, called the projection surface. Imagine the earth's surface is clear with the graticule drawn on it. Wrap a piece of paper around the earth. A light at the center of the earth will cast the shadows of the graticule onto the piece of paper. You can now unwrap the paper and lay it flat. The shape of the graticule on the flat paper is different from that on the earth. The map projection has distorted the graticule. A spheroid can't be flattened to a plane any more easily than a piece of orange peel can be flattened it will rip. Representing the earth's surface in two dimensions causes distortion in the shape, area, distance, or direction of the data. A map projection uses mathematical formulas to relate spherical coordinates on the globe to flat, planar coordinates. Different projections cause different types of distortions. Some projections are designed to minimize the distortion of one or two of the data's characteristics. A projection could maintain the area of a feature but alter its shape. In the graphic below, data near the poles is stretched.
20 Page 20 of 155 The following diagram shows how threedimensional features are compressed to fit onto a flat surface. Map projections are designed for specific purposes. One map projection might be used for largescale data in a limited area, while another is used for a smallscale map of the world. Map projections designed for smallscale data are usually based on spherical rather than spheroidal geographic coordinate systems. Conformal projections Conformal projections preserve local shape. To preserve individual angles describing the spatial relationships, a Conformal projection must show the perpendicular graticule lines intersecting at 90degree angles on the map. A map projection accomplishes this by maintaining all angles. The drawback is that the area enclosed by a series of arcs may be greatly distorted in the process. No map projection can preserve shapes of larger regions. Equal area projections Equal area projections preserve the area of displayed features. To do this, the other properties shape, angle, and scale are distorted. In Equal area projections, the meridians and parallels may not intersect at right angles. In some instances, especially maps of smaller regions, shapes are not obviously distorted, and distinguishing an Equal area projection from a Conformal projection is difficult unless documented or measured. Equidistant projections Equidistant maps preserve the distances between certain points. Scale is not maintained correctly by any projection throughout an entire map. However, there are in most cases, one or more lines on a map along which scale is maintained correctly. Most Equidistant projections have one or more lines in which the length of the line on a map is the same length (at map scale) as the same line on the globe, regardless of whether it is a great or small circle, or straight or curved. Such distances are said to be true. For example, in the Sinusoidal projection, the equator and all parallels are their true lengths. In other Equidistant projections, the equator and all meridians are
21 Page 21 of 155 true. Still others (for example, Twopoint Equidistant) show true scale between one or two points and every other point on the map. Keep in mind that no projection is equidistant to and from all points on a map. Learn more about the Sinusoidal projection Learn more about the Twopoint Equidistant projection Truedirection projections The shortest route between two points on a curved surface such as the earth is along the spherical equivalent of a straight line on a flat surface. That is the great circle on which the two points lie. Truedirection, or Azimuthal, projections maintain some of the great circle arcs, giving the directions or azimuths of all points on the map correctly with respect to the center. Some Truedirection projections are also conformal, equal area, or equidistant. Projection types What are projected coordinate systems? Projection types Because maps are flat, some of the simplest projections are made onto geometric shapes that can be flattened without stretching their surfaces. These are called developable surfaces. Some common examples are cones, cylinders, and planes. A map projection systematically projects locations from the surface of a spheroid to representative positions on a flat surface using mathematical algorithms. The first step in projecting from one surface to another is creating one or more points of contact. Each contact is called a point (or line) of tangency. A planar projection is tangential to the globe at one point. Tangential cones and cylinders touch the globe along a line. If the projection surface intersects the globe instead of merely touching its surface, the resulting projection is a secant rather than a tangent case. Whether the contact is tangent or secant, the contact points or lines are significant because they define locations of zero distortion. Lines of true scale include the central meridian and standard parallels and are sometimes called standard lines. In general, distortion increases with the distance from the point of contact. Many common map projections are classified according to the projection surface used: conic, cylindrical, or planar. Learn more about the conic projection. Learn more about the cylindrical projection. Learn more about the planar projection. Projection types illustrated Each of the main projection types conic, cylindrical, and planar are illustrated below. Conic (tangent)
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