# Map Coordinates, GIS, and GPS for Enhanced 9-1-1

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2 serious understanding of the mathematics affecting the geometry of map making had not yet occurred. In 1823, mathematical research occurring simultaneously refuted Euclid s most important postulate, the Fifth. It was found that parallel lines could intersect, contrary to the Fifth Postulate. On a curved surface, such as a sphere describing the earth, parallel lines of longitude intersect at the poles. This led to the advent of non-euclidean geometry, which today includes hyperbolic geometry (where the sum of the angles of a triangle is less than 180 degrees) and elliptic geometry (where the sum of the angles of a triangle is more than 180 degrees). Map Coordinates To represent the entire surface of the earth without any kind of distortion, a map must be a sphere and this type of map is known as a globe. Using a globe, accurate measurements of distance and area are possible, and the shapes of regions are true. But a globe is not a practical map for showing a great amount of detail for a small region. For this reason, flat maps are created and used, but with flat maps, the spherical surface and coordinates of the earth cannot be accurately represented, except for very small areas where the curvature of the earth is negligible. Thus a map of the world on a flat sheet of paper does not have true shape for all regions and has cumulative measurement errors. This is because every map is a mathematical compromise among the distortions of area, shape, distance, and direction. Spherical Coordinates The spherical coordinates of a globe use a measurement grid composed of meridians of longitude and parallels of latitude. Longitude is marked 180 east and 180 west from 0 at Greenwich, England. Latitude is marked 90 north and 90 south from the 0 parallel of the equator. Any position in this location system can be accurately defined by providing degrees, minutes and seconds for both latitude and longitude. Spherical coordinates are useful for mapping large areas and the coordinate system of latitude and longitude is excellent for measuring directions, but not distances. Distance calculations with spherical coordinate measurements in small areas are very complex. During World War I, it was necessary to simplify the coordinate measurements so that accurate azimuth (direction) and range (distance) could be easily calculated with Euclidean geometry and plane trigonometry. So, a series of local plane coordinate systems were developed. Today, there are plane coordinate systems for mapping all regions of the world. The Global Positioning System (GPS) utilizes latitude and longitude to tell its user where they are on the earth, but GPS actually calculates its coordinates not in a spherical coordinate system, but rather in a Cartesian coordinate system with the origin found at the center of the earth. A GPS receiver calculates its position by measuring an x, y and z position on the earth using the earth centered earth fixed (ECEF) ordinate system and then translates these x, y and z coordinates into spherical latitude and longitude coordinates. Plane Coordinates Plane coordinate systems are flat surfaces that are tangential, or intersect a small portion of the surface of the earth. Planar coordinate systems are best used in small geographic areas and essentially treat land and water as level surfaces. To minimize mapping error in plane coordinate systems, the areas being mapped are intentionally kept small. As coordinates are measured away from the place where the flat map intersects the spherical surface of the earth, their accuracy decreases. In the United States, the state-plane coordinate system (SPCS) is the most commonly selected choice for mapping areas the size of counties. However, plane coordinate systems accumulate error in distance measurements (because the meridians on a plane coordinate system are not truly parallel, but will eventually converge - remember the refuttal of Euclid's Fifth Postulate). Thus, plane coordinate systems require adjustments to "tie" the plane to the surfaces of the earth. Changes in the "ties" to the earth's surface (geoid) occurred in the 1980s, when the North American Datum of 1927 (NAD-27) was updated with the North American Datum of 1983 (NAD-83). In some regions of the US, mapped features "moved" tens of feet. Larger areas covering many counties, or even states, are likely to be mapped with the Universal Transverse Mercator (UTM) system. Like SPCS, UTM is a plane coordinate system, but instead of the more than a hundred SPCS plane systems covering a the United States, there only a few UTM zones for the same region. Page 2 of 5

5 the coordinate of each customer could be automatically assigned Emergency Service Number (ESN) codes with a geographic information system. The map coordinates could be used by the serving telephone companies in determining accurate tax codes for each customer so that surcharge monies can be correctly collected and distributed. In the future, GPS will likely be widely available on emergency service vehicles and GPS can be used as a navigation tool to navigate to the location in question. Map coordinates could also be used to more finely geocode crime and other public safety statistics than existing computer-aided dispatch geofiles and address-based geographic information systems. The NENA recommended format for data exchange does not specify the type of coordinate that can be used in the reserved fields. Database fields of 9 bytes are reserved for each of the x, y, and z coordinates in the 512-byte record. To prevent future problems with database interchange compatibility, a choice must be made to determine standards for map coordinates and the formatting of these coordinates. It will best serve the interests of communities to use a single coordinate system that will serve the broadest range of local users. NAD 83 would be an appropriate datum and the State Plane Coordinate System is a good choice for county-level geographic information systems. However, nearly all mapping by telephone companies is in the UTM system, thus the coordinate systems between the local users and the telephone companies will not match. One possible solution that will help all organizations is to use a common coordinate system. Latitude and longitude can be translated into practically any coordinate systems used by local governments and utilities. If latitude and longitude are used in the recommended data format, then there are several choices in denoting latitude and longitude: N ddºmm ss +ddºmm ss N dd.mmss +dd.mmss N ddmm.mm +ddmm.mm N dd.dddd +dd.dddd If a choice other than latitude and longitude is to be used, such as SPCS or UTM, then more fields should be specified in the NENA Data Exchange Format. These fields will need to contain information describing the map projection, zone information, and other facts such as datums and geoids. Summary The inclusion of map coordinates with other information can help save lives and property and shorten response time. As customer demands for this type of information increase, serving telephone companies will either have to begin incorporating the coordinate information or permit emergency service providers to more easily construct and maintain their own databases. To date, there are no telephone companies that have included map coordinate information into the ALI database record, but this is likely to change as telephone companies begin to overhaul their database structures and begin to provide more responsive services to their customers. The impetus for this overhaul will also likely be a federal mandate similar to the FCC requirment to locate wireless calls using location determination technologies (LDT). Page 5 of 5

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