Spatial Technologies-Mapmaking and GIS

Coordinates and projections.

THE WORLD IS not flat, this we know. Representing our round world on a flat map has always been difficult, and GIS practitioners today face the same challenges as cartographers did hundreds of years ago. To map the world more accurately, GIS uses a variety of geographic coordinate systems and projections. The basic idea behind geographic coordinates is to convert a 3D sphere or spheroid into a flat map.

Spheres and Spheroids

While we know the earth is not flat, it's also not round. It's actually an ellipsoid that bulges at the equator and flattens out at the north and south poles. A sphere is based on a circle, while a spheroid is based on an ellipse. Different spheroids are used because what works best for one region is not necessarily the best for another.

One of the fundamental principles behind GIS is that all data and maps are connected to the real world. In the real world, every object has a specified location relative to its surroundings. Geographic coordinates tie features on a map to their actual location on the surface of the Earth.

Data is created in a geographic, projected or local coordinate system. Geographic coordinate systems are typically used for maps with a scale smaller than 1:5,000,000. At this scale, the earth is treated as a sphere because the difference between a sphere and a spheroid is not detectable. Projected coordinate systems are used for larger scale maps where accuracy is of greater concern. If you need a high level of accuracy and plan to take precise measurements off your GIS map, make sure to use a projected coordinate system to minimize distortions.

Local coordinate systems assume the earth is flat. For simple maps that use latitude and longitude coordinates, most GIS programs simply draw them as if they were planar x,y coordinates. For small areas or projects where accuracy is not as important, this approach works fine, but for larger areas this oversimplification can result in significant errors. Many CAD files are created in a local coordinate system that assigns a value of 0, 0, 0 to the origin because this makes it easier to create site-scale drawings. When CAD files are imported into GIS, the coordinate system must be transformed into one with real-world coordinates.

Geographic Coordinate Systems

A GCS (geographic coordinate system) uses a 3D spherical surface to define the locations of features on the earth. Each geographic coordinate system consists of an angular unit of measure, a prime meridian and a datum. There are a staggering number of GCSs available. To select the best one for a particular project, start by selecting the country where the data is located. If you select North America, for example, ESRI's ArcMap offers 27 different options to choose from.

The most common datums used in the United States are NAD (North American Datum) 1927, NAD 1983 and WGS (World Geodetic System) 1984. A datum is a simple point, line or surface used as a reference in surveying and mapping. A datum defines the origin and orientation of the latitude and longitude lines of a spheroid relative to the center of the earth. Latitude refers to lines that run east to west, and longitude refers to north-to-south lines. Longitude and latitude can be used to locate a position on the earth, but they cannot be used for consistent measurements because they don't have a standard length. The length of each measurement changes as you move away from the equator.

Each datum has a point of origin, and all measurements are calculated from this particular point. In many ways it's similar to using a benchmark, for those familiar with traditional surveying methods. Local datum is used because particular spheroids are the best fit for a particular section of the earth's surface. For example, Alaska, Hawaii, Puerto Rico and the Virgin Islands also use local datums.

NAD 1927, NAD 1983 and WGS 1984 each use a different spheroid definition to help create more accurate maps. For large-scale maps, the standard spheroid in the United States used to be Clarke 1866. Today, newer spheroids developed from satellite measurements are more accurate.

NAD 1983 has become the de facto U.S. standard. The standard digital orthophoto produced by the USGS (U.S. Geological Survey), for example, is referenced to the NAD 1983 and cast on the UTM (Universal Transverse Mercator) projection. Much of the data available from the USGS and other national agencies is still in NAD 1927 format—many organizations have not translated their data to NAD 1983 because of how long it takes to do so. WGS 1984 has become more popular in recent years and is the standard for worldwide data. Google Earth (figure 1), most aviation charts and the U.S. Armed Forces use WGS 1984.

Figure 1. Google Earth uses the WGS 1984 coordinate system for all of its data.

There have also been efforts to improve the NAD 1983 datum. One effort, led by the NGS (National Geodetic Survey), is a series of GPS surveys called HARNs (high-accuracy reference networks) that are intended to provide the level of accuracy needed for even local surveys. HARN surveys have an accuracy of approximately 0.05 meters. All of the U.S. has been resurveyed using HARN, but not all of this information is currently available.

Projected Coordinate Systems

When mapping larger areas, the actual shape of the earth must be taken into account. All maps have some degree of distortion in distance, shape, area and direction. By selecting the map projection that best fits your given situation, you can help minimize the level of distortion.

Project coordinate systems use spheroids because they are more accurate at representing the shape of the earth for large-scale maps. Today, spheroids defined via the use of satellites are replacing the older ground-measured spheroids. In North America, for example, the Geodetic Reference System of 1980 has replaced the Clarke 1866 spheroid.

Projected coordinate systems are defined on a flat, 2D surface and have constant lengths, angles and areas. Locations are identified by x,y coordinates on a grid, with the origin at the center of the grid. A map projection mathematically recalculates the coordinates on a sphere to minimize distortions that occur when it's converted to a flat map.

There are many different map projections, each designed for a specific purpose. Users select a map projection based on the location and scale of the area to be mapped, the shape of the area and the specific spatial properties that are most important to preserve. Many common map projections are classified by the type of projection surface being used, such as conic, cylindrical and planar.

Some projects use a combination of these surfaces, while others don't closely resemble any. Map projections designed for small-scale data are usually based on spherical geographic coordinate systems.

Projections

Some of the more common projections are UTM, State Plane coordinate system, Lambert Conformal projection and Transverse Mercator projection. In the United States, the most commonly used projected coordinate systems are UTM and State Plane.

UTM is a system of plane coordinates based on 60 north-south trending zones that circle the earth, each with a longitude width of 6°. It is a specialized application of the Transverse Mercator projection. UTM coordinate systems provide a constant distance relationship anywhere on the map, and this makes it easier to consistently measure distances. UTM systems are also easy to read because they are measured in meters, use decimals instead of minutes and seconds, and don't use negative numbers.

The State Plane coordinate system is based on zones drawn state by state on transverse Mercator and Lambert projections. The State Plane divides the country into more than 120 different zones. State Plane was developed in the 1930s to provide a consistent mapping system for large-scale projects and is still used extensively by many state and local governments. It's much more accurate than UTM for small areas, but not as effective for larger mapping projects. State Plane systems use the Transverse Mercator, Lambert Conformal Conic and Oblique Mercator for projections of different parts of the country.

The Lambert Conformal projection was first introduced in the late 1700s, but did not become popular until used by the French in World War I. It's widely used for large-scale mapping projects.

Transverse Mercator is a cylindrical projection that is very accurate at the equator, but becomes less so the farther you move away.

Translating

If all of your data is stored in the same coordinate system, all information aligns the way it should without any additional effort on your part. Unfortunately, that doesn't happen very often. If you work with geospatial data from different datums, the difference may be as much as a kilometer, and that is acceptable only at the broadest of scales.

For a recent GIS project, the original data I needed was in six different coordinate systems. When you combine data that uses different geographic coordinate systems, you get some degree of error in the final results (figure 2). Because of that, all data in a given project has to be translated into one consistent set of coordinates.

Figure 2. For this project, all data was in NAD 1927, expect for the Digital Ortho Quad from USGS, which was in NAD 1983. There is a noticeable discrepancy between the lake (light blue) and the DOQ.

Programs such as ESRI's ArcMap are usually capable of aligning data layers of various coordinate systems on-the-fly if the coordinate systems are defined correctly. ESRI's ArcCatalog includes an ArcToolbox Project Tool that can change the coordinate system of specific data. For other translations, grid-based methods are typically used because they are accurate and much easier to use than some other methods. I recently printed a list of translations available and was shocked to find it ran to nine pages! The NGS publishes grids that are used to convert between older geographic coordinate systems, including NAD 1927 to NAD 1983.

Essential Accuracy

For GIS professionals, cartographers and anyone else interested in preparing accurate maps, an understanding of geographic coordinate systems and projections is essential. Standards used today continue to evolve and may be replaced by more accurate systems as technology continues to improve.

IN THIS ARTICLE

ESRI, ArcMap • www.esri.com
National Geodetic Survey • www.ngs.noaa.gov
USGS • www.usgs.gov

James L. Sipes is the founding principal of Sand County Studios in Seattle, Washington, and senior associate with EDAW in Atlanta, Georgia. Reach him at jsipes@sandcountystudios.com.