# Projections. Shape (angles) Distance Direction Area. Only a sphere can retain all four properties

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1 Projections

2 Projections Map projections are attempts to portray the surface of the earth (or a portion of the earth) on a flat surface. Four spatial relationships (or properties) between locations can be distorted when the globe is projected: shape, distance, direction and area. Only a globe (a sphere) can retain all four of these relationships. Some projections minimize distortions in some of these properties at the expense of maximizing errors in others. Some projections are attempts to only moderately distort all of the spatial relationships. If you are using maps to make important decisions, you should know which projections distort which properties and to what extent. For example, a Peters projection gives accurate area calculations but inaccurate shapes, a Mercator projection maintains true direction but sacrifices area accuracy, and a Robinson projection is a compromise of all the properties. Here are some examples: The Mercator projection maintains shape and direction. The Sinusoidal and Peters projections both maintain area, but look very different from each other. The Robinson projection does not maintain any specific properties but is widely used because it makes the earth s surface and its features "look right."

3 Shape (angles) Distance Direction Area Only a sphere can retain all four properties Projections Projection is basically taking the spherical earth and flattening it out onto a 2-D map. Whenever this is done, one or more spatial relationships are distorted. We will briefly cover the projections you are likely to encounter with GPS/GIS mapping in Montana.

4 Shape and distance are maintained well Distortion increases away from the central meridian Area is distorted increasingly toward the poles UTM Projection UTM stands for Universal Transverse Mercator. Transverse Mercator projections result from projecting the spherical earth onto a cylinder tangent to (touching) a central meridian. The least distortion is where the cylinder is tangent (along the central meridian). Transverse Mercator maps are often used to portray areas with larger northsouth than east-west extent. Distortion of distance, direction and area increase away from the central meridian. A Mercator projection will retain the angles of your map, true to the angles in the real world. But, in maintaining the angles (or shapes), area is distorted. For this reason, on a Mercator projection, Mexico appears smaller than Alaska, when, in fact, Mexico has a greater land area. Greenland also looks larger than it is, and Africa looks smaller. UTM is also the name of a coordinate system, which uses the UTM projection.

5 One of the best projections for middle latitudes Used for Montana 1:24,000 USGS quads Local angles (shapes) are accurate throughout because of conformality Shape and area are distorted away from standard parallels Distance scale is correct along the standard parallels Scale is reduced between the parallels and increased beyond the parallels Lambert Conformal Conic Projection The Lambert Conformal Conic projection projects the globe onto a cone. The tangent area has the least distortion. With the Lambert Conformal Conic projection, area and shape are distorted away from standard parallels, and directions are true in limited areas. This projection is used for maps of North America. The standard parallels are lines along which the scale is as stated for the map. Most of the data you can download from the Montana State Library Natural Resource Information System (NRIS) GIS site ( is in the U.S. State Plane coordinate system which uses the Lambert Conformal Conic projection.

6 Latitude and longitude are considered as a simple rectangular coordinate system in a GIS Distance, area and shape are distorted Distortion increases toward the poles No Projection Latitude/longitude coordinates are unprojected. The reason the word unprojected is in quotes is that some people would argue that the latitude/longitude (geographic) coordinate system actually does use a projection, because it still takes the spherical earth and portrays it on a flat map. However, no specific mathematical projection is used in this process.

7 Projection Differences This diagram shows the difference between the Albers Equal Area and Lambert Conformal Conic projections in the Western world.

8 Projection Differences This diagram shows the differences among three projections of the United States.

9 Distortions may or may not be apparent Know what relationships have been distorted avoid making erroneous assumptions GIS software needs to know what projection is used, so it can store and display geographic positions accurately Why are Projections Important? Contrast stretching (histogram stretching) can help to distinguish between various features, and spatial filtering can enhance or suppress specific patterns to make what you want to see stand out.

10 2 Things to Take Away Today 1. Projections are used to convert 3D reality to a 2D map, and always cause some type of distortion (know the 4 properties that can be distorted) 2. Know what projection you are working with, so you know what properties have been distorted

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