Coordinate systems Chapter 1: Context and Concepts What is it? Coordinate systems allow users to refer to points in two- or three-dimensional space. You may have heard of Cartesian geometry, named for the 17th-century French mathematician Descartes, the founder of analytic geometry and the Cartesian coordinate system. In two dimensions, we usually refer to two principal axes, the x (horizontal) and y (vertical). If necessary, we add the z axis for the third dimension. Points are located by referring to their position on the scales of the x and y (and z) coordinates. Diagrams usually known as scatter diagrams, or scatter plots (figure 1.10), are based on Cartesian coordinates, with their origin in the lower left corner. Things get a bit more complicated when the coordinate system is applied to the spherical shape of the Earth. Latitude/longitude For the Earth's sphere, angular measurements must be added to the x-y coordinate system. Latitude angles are measured from the center of the Earth between the Equator and poles, 90 degrees north and south, with the Equator as 0 degrees and each pole 90 degrees. Longitude angles are also measured from the center of the Earth, 180 degrees east and west of the Prime Meridian running through the Royal Naval Observatory in Greenwich, England,9 a location fixed by international agreement in 1884. So all of the United States is described in degrees north latitude and west longitude. For example, New Orleans is located at approximately 30 degrees north latitude and 90 degrees west longitude. Latitude lines are also known as parallels because they are, in fact, parallel to one another, and longitude lines are called meridians, as in "Prime Meridian." State boundaries west of the Mississippi River are predominantly made up of segments of meridians and parallels. For example, the longer western border of Oklahoma is a segment of the 100th meridian. State Plane and Universal Transverse Mercator As noted previously, appropriate map projections have been adopted for each State, yielding "Earth" projections with coordinates based on latitude and longitude, the universal reference system. But these "latitude/longitude" references, as they will be referred to, are quite cumbersome, given that they are in degrees, minutes, and seconds.10 Two principal alternative coordinate systems are found in addition to latitude/longitude: the State Plane Coordinate System and the Universal Transverse Mercator (UTM). The State Plane Coordinate System was devised for greater user convenience, with a rectangular grid superimposed over the latitude/longitude graticule, producing State plane coordinates expressed in meters, yards, or feet. In effect, this system assumes that the individual States are flat so they can be described by plane geometry rather than the spherical grid. For local applications, this use of plane geometry is acceptable because error due to failure to take Earth curvature into account is not significant over relatively small areas such as police jurisdictions. Large States are divided into zones with separate grids for each to avoid the distortion problem. Texas, for example, is divided into the North, North-Central, Central, South-Central, and South zones; Louisiana into North, South, and Coastal. Typically, the origin, or zero point, for a State plane system is placed in the southwest corner, just like the scatter plot shown in figure 1.10, to avoid the inconvenient possibility of having to express coordinates in negative numbers. The origin is also placed outside the study area for the same reason. The UTM system is used to refer to most of the world, excluding only polar regions, and consists of 60 zones, north-south, each 6 degrees of longitude wide. Each zone has a central meridian, and origins for each zone are located 500,000 meters west of the central meridian. A sample location in Texas (the capitol dome in Austin) is shown in figure 1.11. This example specifies that the dome is 621,161 meters east of the central meridian of zone 14 and 3,349,894 meters north of the Equator, the latitude of origin. The acronym NAD will appear in references to the State plane and UTM coordinate systems. NAD stands for North American Datum, a reference system that was based at a Kansas ranch in 1927. Demands for greater accuracy and more accurate surveying made possible by satellites led to a new NAD in 1983, hence the reference in figure 1.11 to NAD 83 UTM coordinates. Why we do need to worry Crime mappers using computerized data from different sources may run into a problem resulting from different data sets being digitized (assigned their x-y coordinates) in, or converted to, incompatible coordinate systems or even incompatible projections. The most frequent conflict is likely to be between latitude/longitude and State plane coordinates owing to the likelihood that locally developed data (often in State plane coordinates) will be mixed with data from more general sources, probably expressed in latitude/longitude. We saw that New Orleans is referenced as 30 degrees north latitude and 90 degrees west longitude in the latitude/longitude system. But if we refer to it using the State plane system, it is in the Louisiana South Zone, with coordinates 3,549,191 feet east of the origin and 592,810 feet north of the origin. Clearly, if we try to put the State plane data on a map set up for latitude/longitude, ugly things will happen. (What usually happens in a GIS is that the map goes blank.11) Data sets placed together on a map should have compatible projections and compatible coordinate systems. Fortunately, GIS software permits conversion from one projection to another and from one coordinate system to another, so the problem, if it does arise, is reasonably easy to fix. But if incompatibilities are not recognized at the outset, they can be quite frustrating. Positive action to check the projection and coordinate properties of a new data set is recommended because the coordinate system may not be apparent initially.