PrintWelcome to Lesson Six of this GPS/GNSS course. And this time, we'll be talking about two coordinate systems. And I have a little bit of discussion concerning heights. We've touched on that a little bit. Now these coordinate systems that we're going to discuss are plane coordinate systems based upon the fiction that the earth is flat, which, of course, immediately introduces distortion. However, much of GIS work—and GPS/GNSS work as well—is done based upon this presumption. So, it is worthwhile to spend some time discussing how the distortions are handled and some of the elements. So, we will be talking about State Plane coordinates and Universal Transverse Mercator coordinates, both plane coordinate systems. And we'll be discussing ellipsoidal heights, and geoidal heights, and orthometric heights.
In the illustration, the Lambert conformal conic projection is on the top and the Transverse Mercator projection is on the bottom.
These plane coordinates, both State Plane and UTM, are far from an anachronism. The UTM projection has been adopted by the IUGG, the same organization that reached the international agreement to use GRS80 as the reference ellipsoid for the modern geocentric datum. NATO and other military and civilian organizations worldwide also use UTM coordinates for various mapping needs. UTM coordinates are often useful to those planning work that embraces large areas. In the United States, State Plane systems based on the Transverse Mercator projection, an Oblique Mercator projection, and the Lambert Conic map projection, grid every state, Puerto Rico, and the U.S. Virgin Islands into their own plane rectangular coordinate system. And GPS/GNSS surveys performed for local projects and mapping are frequently reported in the plane coordinates of one of these systems. State Plane Coordinates rely on an imaginary flat reference surface with Cartesian axes. They describe measured positions by ordered pairs, expressed in northings and eastings, or y- and x- coordinates. The y coordinate is the northing and the x coordinate is the easting. Despite the fact that the assumption of a flat Earth is fundamentally wrong, calculation of areas, angles and lengths using latitude and longitude can be complicated, so plane coordinates persist because they are convenient. The calculations can be done with plane trigonometry. GIS coordinate systems typically are plane. As long as the extent of the coverage of the coordinate system is limited, the curvature aspect—while it leads to distortion—can be managed. It's when the flat map, the flat coordinate system, extends beyond a limited area that the distortion can get out of hand. Therefore, the projection of points from the Earth’s surface onto a reference ellipsoid and finally onto flat maps is still viable.