Datums And Projections: A Brief Guide

March 1999

Scientists and resource managers often use or create data that are referenced to locations on the earth (geospatial data). Users of geospatial data need to know the coordinate system or projection the data are in so they can make accurate measurements from the data or overlay different datasets for analysis. Frequently, users or creators of geospatial data are unaware or unsure of the projection or datum geospatial data are in, or which projection to select when creating geospatial data (e.g., determining coordinates of bird nest sites with a GPS receiver). This paper is written for the scientist or resource manager who uses geospatial data occasionally and needs a quick, non-technical guide on the use of datums and projections. This paper defines important terms, presents a brief discussion on widely-used projections, suggests ways to determine what datum or projection geospatial data are in, recommends how to select the proper datum or projection for geospatial data, and proposes methods to convert between datums and projections.

Definitions

Ellipsoid – An ellipsoid is a mathematical figure generated by the revolution of an ellipse about one of its axes (DMA, 1999). The earth is not a sphere but an ellipsoid distorted by rotation about its axis, with the globe bulging at the equator and flattened at the poles. The actual amount of the flattening is about 21.5 km difference between the polar and equatorial radii (Gaus, 1999). Ellipsoidal earth models are required for accurate range and bearing calculations over long distances. For example GPS navigation receivers use ellipsoidal earth models to compute position and waypoint information. Ellipsoidal models define an ellipsoid with an equatorial radius and a polar radius. The best of these models can represent the shape of the earth over the smoothed, averaged sea-surface to within about one-hundred meters (Dana, 1999).

Datum – A datum is a mathematical model that describes the shape of the ellipsoid. The flattening is not uniform around the earth; the shape is different due to the influence of the continents and there are datums for different parts of the earth based on different measurements (Snyder, 1982).

Projection – A map or a geospatial database is a flat representation of data located on a curved surface. A projection is a device for producing all or part of a round body on a flat sheet. This projection cannot be done without distortion, so the cartographer must choose which characteristic (distance, direction, scale, area, or shape) that is to be shown accurately at the expense of the other characteristics, or compromise on several characteristics. (Snyder, 1982). Projections can be used with different datums; for example the Universal Transverse Mercator (UTM) projection could be based on the North American Datum of 1927 or North American Datum of 1983.

Geographic System – The Geographic System is not a projection, but a representation of a location on the earth’s surface using spherical coordinates as measured in latitude and longitude – the angle of a location on the earth’s surface from the earth’s center in relation to the equator and the Prime Meridian that intersects Greenwich, England. The locations in the Geographic System can be converted into other projections, but the locations represented by the Geographic System cannot be used for determining basic information such as distance or direction between two points. While the distance between degrees in latitude remain fairly constant over the earth, one degree in longitude is much longer near the equator than it is near the poles (111 km at the equator versus 19 km at 80^o North (Gaus, 1999)).

Widely Used Datums and Projections

Hundreds of different datums have been developed since Aristotle made the first estimates of the earth’s size (Dana, 1999). For many years the North American Datum of 1927 (NAD27) was the standard in the United States. NAD27 was based on the Clarke Ellipsoid of 1866, which was developed from ground survey in Europe and North America in the 19^th Century. During the 1970’s and 1980’s satellites were able to measure the ellipsoid flattening more accurately (the World Geodetic System ellipsoid of 1984 or WGS84) and a new datum was developed from these measurements called the North American Datum of 1983 (NAD83). The Global Positioning System is based on WGS84. The earth’s shape is changing and measurements are becoming more precise, and as a result new reference ellipsoids and datums are being developed: the ITRF or International Earth Rotation Service (IERS) Terrestrial Reference Frame is the latest ellipsoid that has been developed.

At least 250 different projections have been devised and described by cartographers (Gaus). Projections fall into four major classes: cylindrical, conical, azimuthal, and miscellaneous. Cylindrical projections result from projecting a spherical surface onto a cylinder while conic projections result from projecting a spherical surface onto a cone. Azimuthal projections result from projecting a spherical surface onto a plane and miscellaneous projections include systems such as rectangular latitude and longitude grids (Dana, 1999) that do not fall into the other three categories.

The Albers Equal-Area Conic Projection is based on a conic representation of a portion of the earth. It is mathematically projected on a cone conceptually secant (a plane intersecting a curve at two points) to two standard parallels. The Albers projection is used by the USGS for its state maps and all U. S. maps of 1:2,500,000 scale or smaller. It is useful for representing areas that have a predominant east-west expanse, such as the conterminous United States. All areas on the map are proportional to the same areas on a globe, directions are reasonably accurate in limited regions, and distances and scale are true only along the standard parallels.

The Lambert Conformal-Conic Projection has many of the same characteristics as the Albers Equal-Area Conic Projection. It is mathematically projected on a cone conceptually secant at two standard parallels. It is useful for representing countries or regions that have a predominant east-west expanse. It is used in the State Plane Coordinate System for North Carolina and other states. All areas on the map are proportional to the same areas on a globe, directions are reasonably accurate, and distances and scale are true only along the standard parallels.

The Lambert Azimuthal Equal-Area Projection was derived for the specific purpose of maintaining equal area. It is mathematically projected on a plane tangent (a plane touching a curve at one point) to any point on the globe. It is useful for representing areas that extend equally in all directions from center points, such as Asia, and the Atlantic Ocean. Areas are in true proportion to the globe, while direction is true only from the center point, and scale decreases gradually from the center point.

The Universal Transverse Mercator Projection is based on the Transverse Mercator projection. It is mathematically projected on a cylinder tangent to a meridian (which is transverse or crosswise to the equator). It was adopted by the military in 1947 for designating coordinates on large-scale military maps for the entire world. The world is divided into 60 east-west zones each 6^o wide in longitude. It is used by many 1:24,000 scale to 1:250,000 scale USGS quads and is useful for mapping large areas that are oriented north-south. The projection is conformal so shapes and angles within any small area (such as a USGS 7.5’ quadrangle) are essentially true.

The State Plane Coordinate System (SPCS) is not a projection, but a coordinate system that divides all 50 states into 120 zones, which are represented by different projections, based on the shape of the zone. Three projections are used: the Lambert Conic Conformal for east-west oriented zones (e.g., zones in Tennessee), the Universe Transverse Mercator for north-south oriented zoned (e.g., zones in Alabama), and the Oblique Mercator for the panhandle of Alaska.

Determining the Datum or Projection for Existing Data

Often scientists use geospatial data created by someone else, and frequently must overlay datasets that are in different or unknown datums/projections. How is the datum/projection determined? There are four methods to determine the datum/projection: 1) refer to the metadata accompanying the dataset, 2) query the dataset using your geospatial software package, 3) refer to the header file for the dataset, or 4) visually compare the dataset in question to a dataset of known datum/projection.

Metadata, or data about data, should contain information on the datum and projection of a geospatial dataset. If metadata files follows FGDC requirements, they will contain this information. Often, however, metadata are incomplete or missing altogether; in that case another method must be used.

The software used to view and manipulate the geospatial data will often allow queries to determine which datum/projection a dataset is in. For example, in ARC/INFO, the command "describe" will provide this information, if the datum/projection has been defined by the originator of that dataset. ArcView, on the other hand, will not allow the user to query the dataset to determine the projection or datum. Other software packages such as ERDAS Imagine, PCI, ENVI, or GRASS also allow the user to query the dataset to determine the datum/projection.

The header of a dataset may contain the information, if the dataset has a separate header. Headers are common for raster datasets. For example, the header of a USGS DOQQ contains the information on datum/projection, along with other information. A text editor can read the header.

When other methods fail, visually compare the dataset with a dataset of known datum/projection that has similar features in the software program. For example, a landcover vector dataset could be overlain on a DOQQ to allow comparison of features such as road intersections or permanent shorelines common to both layers. A GPS receiver that is set to a known reference system, can collect coordinates at well-defined locations, such as road intersections and those data can be overlain on the dataset in question. If these points do not align, the datasets are in different datums/projections. If the locations are approximately 200 meters apart in the north-south direction and slightly offset in the east-west direction, the difference is commonly due to the southern dataset being in NAD27 and the northern dataset in NAD83. If the datasets are hundreds or thousands of miles apart, the projections are different.

In any event, it is a good idea to visually compare a new dataset with a known dataset, even if datum/projection information exists to ensure that the information is correct.

Selecting Datums/Projections

In the conterminous Unites States NAD27 and NAD83 are the two common choices for datums. NAD27 was the standard for many years because the USGS published its topographic maps in this datum, principally the 1:24,000 scale 7.5-minute quadrangle series, which served as a reference map for many datasets. When the USGS began publishing digital data, particularly the digital ortho quarter quads (DOQQ’s), the datum used was NAD83, which provided a more accurate representation of the earth’s shape and a more accurate depiction of the location of objects on the earth. This created the problem of datasets that were generated in NAD27 that were not registered correctly to the new, more accurate, higher resolution DOQQ’s. As the DOQQ’s begin to cover significant portions of the United States, this issue has become important for many scientists and data centers who use the DOQQ’s as a base layer in their geospatial databases. In addition, datasets in NAD27 do not join together well across large regions (such as a state or a large ecoregion), due to the inaccuracies of that datum (Brown, 1999).

When creating a new geospatial dataset, it is critical to select the proper projection. Selection considerations are 1) the extent of the project area: (e.g., the world, a continent, or an ecoregion), 2) the location of the project area (e.g., polar, mid-latitude, or equatorial), and 3) the predominant extent of the project area (e.g., circular, primarily east-west axis, north-south axis, or oblique axis). If a base layer, such as DOQQ’s or USGS 1:100,000 scale maps, is used, the base layer’s projection may determine the projection. For small areas, such as a 7.5-minute quad, or a DOQQ, the UTM projection is nearly correct in every respect (USGS, no date). For continental or smaller regions in temperate zones that 1) have an east-west axis select the Lambert Conformal projection for conformal accuracy and the Albers Equal Area for areal accuracy 2) have a north-south axis select UTM for conformal accuracy, 3) have an oblique axis select the Oblique Mercator projection for conformal accuracy, and 4) have equal extent in all directions select the Polar or Stereographic Projections for conformal accuracy and the Lambert Azimuthal Projection for areal accuracy.

Conversions between Datums/Projections

The best way to convert between datums/projections is to use geospatial software’s conversion or projection commands. The algorithms used by geospatial software vary in quality, so the user must be aware of the algorithms the software uses. The best conversion programs are based on the National Geodetic Surveys NADCON (North American Datum Conversion). NADCON is a reasonably accurate (errors of less than 0.5 meters) way of converting between NAD27 and NAD83 (although there is no exact transformation between NAD27 and NAD83 because NAD27 has different errors in different parts of North America). Programs such as ARC/INFO have sophisticated commands to convert between projections and datums, while programs such as ArcView do not support conversion in their basic modules (although the Projector extension can convert coverages and shapefiles to shapefiles in different projections). Image processing software such as ERDAS Imagine and PCI also have conversion capabilities. The U.S. Army Corps of Engineers has developed Corpscon, a MS-Windows-based program which allows the user to convert coordinates between Geographic, State Plane and Universal Transverse Mercator (UTM) systems on NAD 27, NAD 83 and High Accuracy Reference Networks (HARNs). Corpscon uses NADCON to convert between NAD 27, NAD 83 and HARNs (http://crunch.tec.army.mil/software/corpscon/corpscon.html).

Another method to convert data from one projection to another, if projection information does not exist for the dataset in question, is to "rubber-sheet" the dataset to a base dataset. This is accomplished by visually connecting similar points in the two datasets and allowing the software to adjust the dataset. This is not a perfect method, but is useful if the data do not have projection information, or are not projected initially (such as a scanned aerial photograph).

Conclusions

Common errors when using or creating geospatial data are 1) to overlay datasets that are not in the same datum/projection, 2) collect field data with a GPS receiver that are in a different projection than the base data layers or to collect the data in different datums/projections on different days due to neglect or change of the settings, 3) digitize new data in an incorrect datum/projection, 4) use an inappropriate datum/projection for a project, or 5) convert datums in GPS receivers that have a poor conversion algorithm. Again, geospatial data that are in the same projection may be in different datums. It is critical to carefully check spatial datasets to ensure that they are the proper datum/projection. Useful Internet sites for more detailed information are listed in the references.

Karl Brown
Geospatial Technology Specialist
USGS Center for Biological Informatics
karl_brown@usgs.gov
303-202-4259

References

Brown, K.E. 1999. Personal communication.

Dana, P.H. 1999. Map Projection Overview. http://www.colorado.edu/geography/gcraft/notes/mapproj/mapproj_f.html.

Defense Mapping Agency. 1999. DMA Technical Manual 8358.1 Datums, Ellipsoids, Grids, and Grid Reference Systems. http://164.214.2.59/GandG/tm83581/tr83581a.htm.

Gaus, M.P. 1999. CIE 303 Geodesy, Surveying, GIS and GPS Course http://overlord.eng.buffalo.edu/ClasshomePages/cie303/index.htm.

Snyder, John P. 1982. Map Projections Used by the U.S. Geological Survey. 2^nd Edition. United States Government Printing Office, Washington, D.C. 313 pages.

U.S. Geological Survey. No date. Map Projections. Poster. U.S. Geological Survey National Mapping Division. Reston, VA.

U. S. Geological Survey. 1996. National Mapping Program Technical Instructions, Part 2, Specifications, Standards for Digital Orthophotos. U.S. Geological Survey National Mapping Division. Reston, VA, 37 pages.

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