Geodesy is the branch of mathematics concerned with the size and shape of the earth and variations of the earth's gravity field. To understand where GPS coordinates come from and how to apply them to maps, it is important to understand a bit about geodesy, coordinate systems and mapping projections.
The Ellipsoid
An Ellipsoid is a smooth, mathematically perfect surface that is used to approximate the shape of the earth. The ellipsoid is very important to GPS because GPS heights are measured with respect to the ellipsoid. To determine elevation with respect to mean sea level, it is necessary to take into account the geoid.The Geoid
Obviously the earth is not smooth. Horizontal and vertical measurements made on the earth are made in the earth's gravitational field, which can distort those measurements. Therefore, it is important to know how the gravity field changes when making measurements on the earth's surface. The gravity field is dependent on the distribution of the earth's mass and some parts of the earth are more massive than others. If there is a dense mass to one side of you, down will be deflected in the direction of the mass. Therefore, down as indicated by a plumb bob isn't necessarily toward the center of the earth with enough precision for intercontinental distance measurement.A geoid is a an equipotential surface - that is, it is a field of equal value derived from the earth's gravity field and the outward centrifugal force of the earth's rotation (Thanks to Anthony Bruno of Trimble Navigation). Gravity is also purpendicular to the surface at every point. Generally, the geoid is higher over continents and lower over oceans. Because the geoid is dependent on the irregular distribution of masses in the earth, the shape of the geoid cannot be calculated, only measured.
Global positioning systems such as Navstar and Glonass calculate positions using a type of spherical coordinate system called geodetic coordinates. Geodetic coordinates are difficult to plot directly on maps. Usually you would want to convert the coordinates to a mapping projection to put it on paper.
National geodetic systems such as the North American Datum (NAD), the European Datum (ED) and the Tokyo Datum (TD) are intended to describe the shape of the earth over limited areas and are inadequate describing the shape of the earth over intercontinental distances. In the '50s, the Department of Defense began to develop a world system to which national systems could be related, creating a reference system for global navigation and measurement. These systems are improved every so often as new sets of measurements and improved data reduction techniques are developed. They include a reference ellipsoid, an ellipsoidal gravity equation, a terrestrial gravity model, a geoid and translations to other geodetic systems.
- World Geodetic System of 1960 (WGS-60)
- WGS-60 was created by consolidating world systems developed by the Army and the Air Force. Each had used different methods to determine gravimetric orientation parameters, but the results of each agreed well with the north american, european and tokyo datums
- World Geodetic System of 1966 (WGS-66)
- WGS-66 was developed by a committee composed of representatives from the Army, Navy and Air Force. Additional gravity observations and satellite data were incorporated. Ellipsoidal flattening and the semi-major axis were determined from satellite and astro-geodetic data. The basic geoid was derived from a basic free-air gravity anomaly field with detail provided for limited land areas.
- World Geodetic System of 1972 (WGS-72)
- WGS-72 was developed over a three year period and included additional sets of gravity measurements. More satellite data collected from doppler measurements, laser rangefinding and Baker-Nunn camera tracking.
- World Geodetic System of 1984 (WGS-84)
- WGS-84 is the internal reference system used by the NAVSTAR system.
- Soviet Geodetic System of 1985 (SGS-85)
- SGS-85 is the internal reference system used by the GLONASS system.
- North American Datum of 1927 (NAD27)
- NAD27 is the standard for most all USGS maps. It used the Clarke 1866 ellipsoid which fit north america fairly well, but didn't fit the rest of the world.
- North American Datum of 1983 (NAD83)
- NAD83 is the current standard for USGS maps. It uses the General Reference System of 1980 (GRS-80) ellipsoid which is nearly identical to the WGS84 ellipsoid.
The earth is round (more or less). Paper is flat! Mapping projections are methods for plotting the earth's curved surface on a flat piece of paper and there are quite a lot of them. Any plot of the earth on a flat sheet of paper will exhibit some distortion. Distortion may be minimized for some factor by drawing the map in a particular way. That is why there are a lot of them - each is intended to optimize a map in some way while allowing additional distortion in other ways.
- Universal Transverse Mercator
- State Plane Coordinate Systems
- A state plane system is a map projection system based on a particular geodetic datum. The purpose for state plane systems is to give surveyors a method for creating maps with minimal scale distortion that would be tied to a single national coordinate system.
In order to keep the scale distortion to a reasonable minimum, it was necessary to fit a map projection to a state, or sometimes a part of a state. These areas are referred to as "zones". Zones usually run along county and state boundaries. Some states are wide, some are skinny. Some are tall, others are short. The map projection for a zone is selected to best fit the zone. Zones that are short and wide, like Tennessee, are fit with a single Lambert Conical projection. States that are tall and wide, like Missouri, are broken in to several zones, each with it's own Transverse Mercator projection.
- State Plane Coordinate System of 1927 (SPCS-27)
- SPCS-27 is based on the NAD-27 system. It was designed by the U.S. Coast and Geodetic Survey in the '30s
- State Plane Coordinate System of 1983 (SPCS-83)
- SPCS-83 is based on the NAD-83 system and replaces SPCS-27.
A mathematical transformation is used to convert geodetic coordinates to x and y coordinates that are then plotted on a surface. The surface will usually be flat but not always.
Map data can take two forms. The map can be a digitized "raster" image, rather like a .GIF or .JPG file. In this form, the map is just a picture and contains no data about the map. Or, a map can take the form of a "vector" file - a database of lines, points, arcs and information about those features.National Spatial Data Infrastructure (NSDI)
The National Spatial Data Infrastructure (NSDI) is conceived to be an umbrella of policies, standards, and procedures under which organizations and technologies interact to foster more efficient use, management, and production of geospatial data. The Federal Geographic Data Committee (FGDC) has assumed leadership in the evolution of the NSDI in cooperation with state and local governments, academia, and the private sector. The FGDC maintains a clearinghouse of map data and products.TIGER Data
There are many map products now on the market that include road maps for the United States. Most, if not all of these products are based on the TIGER data set created for the U.S. Census Bureau. TIGER stands for Topographically Integrated Geographic Encoding and Referencing system. The Census Bureau's Census TIGER System supports the decennial census and sample survey programs of the Census Bureau starting with the 1990 decennial census.The TIGER data base is a disciplined, mathematical description for the geographic structure of the United States and its territories. The topological structure of the Census TIGER data base defines the location and relationship of streets, rivers, railroads, and other features to each other and to the numerous geographic entities for which the Census Bureau tabulates data from its censuses and sample surveys. It is designed to assure no duplication of these features or areas. A number of techniques were used to create the TIGER data base. These techniques include automated map scanning, manual map "digitizing," standard data keying, and sophisticated computer file matching. The Census Bureau releases periodic extracts of this data base to the public.
Free Software from NGS
The National Geodetic Survey maintains an FTP site from which their PC software and documentation may be downloaded. Source code and documentation for some of these programs is available at an extra charge. While there are many packages available, some of the most useful are:
- GEOID93
- Computes geoid height values for the conterminous United States. Displays approximately 10-cm accuracy (one sigma) between points spaced at 100 km.
- INVERSE/FORWARD3D
- Comprises four programs - Inverse which computes the geodetic azimuth and distance between two points, given their geographic positions; Forward which computes the geographic position of a point, given the geodetic azimuth and distance from a point with known geographic position; and the three-dimensional versions of these programs . INVERS3D and FORWRD3D which include the height component.
- NADCON
- Transforms geographic coordinates between the NAD 27, Old Hawaiian, Puerto Rico, or Alaska Island datums and NAD 83 values. Recommended for converting coordinate data for mapping, low-accuracy surveying, or navigation.
- SATMAP
- Facilitates the planning of GPS satellite data collection. It allows the user to view satellite windows graphically and to determine the optimal observing time for a given satellite constellation.
- SPCS83
- Converts NAD 83 state plane coordinates to NAD 83 geographic positions and conversely. Includes defining constants for NAD 83 coordinate zones. State plane coordinates are entered or computed to 1 mm accuracy, while the latitudes and longitudes entered or computed correspond to approximately 0.3 mm accuracy.
- UTMS
- Converts geographic coordinates (latitudes and longitudes) on the Clarke 1866, GRS 80/WGS 84, International, WGS 72, or any user-defined reference ellipsoid to Universal Transverse Mercator (UTM) coordinates, and vice-versa.
John Banta's Shareware Coordinate Transform
John's shareware program converts http://www.connect.net/jbanta/Chris Levin's DLG File Viewer
From Chris' Home Page:This is the Us Geological Survey DLG map file reader. It comes complete with documentation and sample files. If you like this program and you are interested in becoming involved with its continuing development please send me e-mail at levin@utw.com
Chris' DLG viewer is available at:
http://www.utw.com/~levin/cl_home.html
Vic Fraenckel's Lat/Lon to Ruler Conversion
From Vic's posting in sci.geo.satellite-nav
i wrote a program (rule2ll) in response to a series of queries as to how to get latitude and longitude off a topographic map using a ruler to measure the 'easting' and 'northing' of a point on the map. while i am not sure that this is the newsgroup where this discussion thread went on, someone might be interested in the program.email Vic at mailto:vfraenckel@wiznet.netrule2ll is a dos program. it starts with a setup where you enter the map scale (1:24000 for topos), the latitude/longitude of the SW corner of the map, the ellipsoid of the map and the input ruler units (inches or millimeters). the program then soliciates your easting and northing measurements. these are converted to lat/long using ellipsoidal earth algorithms. the program is version 0.99 and has had only limited testing but it seems to give good results. if anyone is interested in the program, it can be obtained via anonymous ftp from:
ftp://wizvax.net/pub/personal/victorf/rule2ll.zip (~180kb)
if you try it please let me know what you think. bug reports are especially useful if they contain enough detail to recreate the bug so i can fix it.
http://www.census.gov/tiger/overview.html
http://fgdc.er.usgs.gov/fgdc2.html
Mail from Anthony Bruno, Trimble Navigation (Thanks Anthony!)