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CARTOGRAPHIC ROOTS
MAP PROJECTIONS Thematic maps consist of both a basemap and a thematic overlay. The appearance of the basemap is dependant upon which type of projection is used. It is crucial for cartographers to understand the shape and the geometry of the Earth before working with map projections. The fact that the earth is not a perfect sphere, but flattened at the poles, complicates calculations. Today, it is referred to as a geoid (earth-shaped). Measurements have also been complicated by the many depressions and bulges found on the Earth. Cartographers also use the ellipsoid shape to describe the Earth. The current reference ellipsoid used by North American Data (1983), who decides the current reference datum, is the Geodetic Reference System (GRS83). This new projection resulted in a slight shift in latitude and longitude values. (See the datums page for a complete explanation) To simplify, most cartographic work still identifies the Earth as a perfect sphere. Coordinate Geometry focuses on location which is important to navigation and used in military operations. Currently Global Positioning Systems (GPS) are used to record precise location data. Plane coordinate geometry uses cartesian coordinate geometry with two axes, x and y. These two axes run perpendicular to one another on a plane and are marked at intervals by equally spaced lines. A point (Pxy) can be determined by using the values of x,y in conjunction with the plane value. In this system, each point can have a distinct location. Coordinate geometry is important in digitizing because the geographical points being located are laid out on a map in plane cartesian space. By contrast, Earth coordinate geometry uses angular measurements to break up the Earth into 360 degrees on a sexagesimal scale (360 degrees: one degree has 60 minutes, one minute has 60 seconds). The earth's axis of rotation, which emerges at the North pole, is a main focus of this geometry because it is based on the points of the North and South poles. The equator bisects the axis of rotation at a perpendicular angle. The North and South geographic points (poles) and the equator are the three most important parts of this system. Latitude represents a location between the equator and the north or south pole. The latitudinal plane is parallel to the equator and is valued from 0 to 90º, either North (N) or South (S). Due to the axis of rotation it is harder to find longitude values because there is no defined starting point to help determine an exact position. Longitude is measured in values between 0-180º East (E) or West (W). The Earth takes twenty four hours for a complete rotation, so any given point cycles through 360º in one day (15º/hour). Scientists decided the best way to determine a longitudinal value was to record time at one point throughout the day and determine the distance value between the local time and the point of reference. This value gave them a number in angular degrees, thus giving them a position. In 1761, John Harrison built a marine chronometer to measure longitude, which was accurate within 1.25 nautical miles. This device has been used ever since and latitude/longitude values are used by all cartographers. EMPLOYMENT OF PROJECTIONS AND THEMATIC BASE MAP COMPILATION Computer mapping has helped solve many problems related to map projections because it allows the cartographer to experiment with different options. A projection is important to the overall design of a map. It gives the map a geographical framework for all the points and areas seen on the final map. There are certain projections most accurately suited for mapping different parts of the world. Mollweide, Hammer or Boggs Projections are all examples of projections that can be used to map the whole world. The projections used for only countries or continents are different. EMPLOYMENT OF MAP PROJECTIONS 1. Thematic Maps Thematic map compilation refers to the process of constructing a new, unique map for a specific purpose with information from base maps or thematic maps (or both). This outside information comes from topographical maps, derived maps (large-scale) or small to medium-scale maps. The USGS large-scale maps are used to produce smaller-scaled ones. The accuracy of derived maps is key, so finding a reliable source is very important. There are a few items to consider when deciding on a projection for a thematic map. The projection properties need to be suitable for the current design problem. All world projections cause some shape distortion, but a projection should result in the least amount of deformities possible and those that appear should not affect the map’s purpose. The projection should allow for the map to be centered on the location of the design problem. A map needs to have both parallels and meridians that are familiar to the reader to ensure it is understood. Any cartographer has to consider cost during a project so the work hours needed to complete a map help determine which projection is most affordable. WORLD PROJECTIONS Mollweide Projections (Carl B. Mollweide) are used for mapping world distributions. This projection has curved meridians causing the lines at 90° to form a complete circle; one hemisphere is a full circle. The overall projection is an ellipse and the individual meridians are elliptical arcs. Distortion occurs mostly at the corners where the meridians and parallels meet. Since it has a good overall shape this is the projection to use if the distortion does not affect the map significantly. Similar to the Mollweide Projection is the Hammer Projection. The Hammer differs in that it has curved parallels and less distortion at the intersection of the meridians and parallels. The overall outline is the same as the Mollweide, but it is harder to construct due to the curved parallels with no true scale to match. The Hammer Projection is also good to use for mapping world distributions. The Boggs eumorphic Projection (Whittemore Boggs, 1929) is a combination of the sinusoidal and Mollweide Projections. One advantage is that it has more accurate shapes along the equator because it has equal linear scales. Visually it is easy to see the main difference of this projection because the world becomes pointed at the North and South Poles where the meridians converge. MAPPING CONTINENTS The Bonne Projection (Rigobert Bonne) "is an equal-area conical projection, with a central meridian and the cone assumed tangent to a standard parallel. All parallels are concentric circles, with the center of the standard parallel the apex of the cone. The central meridian is divided true to scale. All parallels are drawn with their lengths true to scale, and each is divided truly. The meridians are drawn through the points of division along the parallels." (Dent, 1990) This projection is used to map the larger continents: Asia, North America, South America and Australia. There is shape distortion at the northeast/northwest corners so this projection is best to use for map areas that are located only on one side of the equator. MAPPING LARGE AND SMALL COUNTRIES AT MID-LATITUDES For large and small countries at mid-latitudes either the Bonne, Lambert azimuthal equal-area or Albers equal-area Projection can be used. A Lambert azimuthal equal-area Projection causes little shape distortion so it is a good choice for countries with symmetrical shapes. This projection is developed onto a plane that is tangent to the generating globe at one point. Any point can be used, but most often the North and South Poles are used. The azimuth of any point is correct in this projection so it useful for mapping information that has an important directional relationship to the central point of the map. The Albers equal-area Projection is a conic projection with two standard parallels and has the lowest possible scale distortion for areas as large as the United States. This type of projection is good for areas with extended east-west length such as the U.S. The advantages of the Albers Projection are: a low 1.25% error in the map scale for a country the size of the U.S.; the meridians and parallels intersect at right angles; the conical shape is good for east-west lengths and for making section maps because the pieces will join together. ANOTHER SOLUTION The Gall-Peters Projection has created controversy in recent history for its unique representation. It is a combination of Gall’s work in the 1880s and Peter’s Projection from 1972. The philosophy behind creating this projection was the thought that the Mercator projection is not accurate enough because of distorted area shapes and because Europe appears too large and dominant. 2. Base Maps Base map information has to come from other sources, most often previously made maps. The USGS provides the largest percentage of maps for the U.S. To form a base map you have to generalize the current map you are working with and determine which details are unnecessary for your new map. The new map should be simplified and only contain pertinent information that focuses on your map’s theme. "Base map information serves to help readers orient the thematic information to a spatial or geographical frame of reference. The designer’s task is thus to select on those base map features that will help the reader in the context of the map’s purpose." (Dent, 1990) Examples of specific features are coastlines, lakes, rivers, stream and mountains. If specific locations are needed, it is important to include the geographic grid in your map. Generalization is a good and effective method because often too much information is supplied within a map. There are three different ways to compile your information into a base map: reduction methods, common-scale methods and one-to-one methods. Reduction methods include "lifting" or tracing selected objects from one source onto a worksheet and making the worksheet match the map scale. This method is good to use for accuracy of locations. This allows you to only trace the important information for your new base map. Common-scale methods compile information from various sources and put it into one worksheet. With this method you are able to gather information from different maps and put them all into one base map. Attention to scale is important because all of the different maps have to be set at one scale to end with an accurate final base map. The simplest method, the one-to-one method is rarely useful. This method simply involves tracing features at one scale from the source map onto a new worksheet. It is not common for all base maps to be in the same scale you are working with. For information and illustrations of the different types of projections: USGS Map Projections |
