Lab 5

        
          In this week's lab we explore a variety of global map projections along with their strengths and weaknesses. Since the earth is a three-dimensional object, it's not possible to project its surface onto a continuous two-dimensional surface without distortions. As a result, no map is truly equidistant in such a way that all distances between any two points on the map are of the same scale. Given that there no perfect way to project the earth's surface, many different projection methods were invented to preserve certain geometric elements at the cost of distorting the others. 

          One element of such is the shapes earth's continents. In order to preserve shapes, angles must be locally preserved. Maps that preserve angles are called conformal. In a conformal map, longitudes and latitudes must intersect at right angles, and from any given point scale should be the same in all direction. This does not necessarily mean that conformal maps have one consistent scale throughout the entire map. Most conformal maps in fact have different scales in different zones. The most popular and widely used conformal projection is the Mercator projection, in which loxodromes on the globe (line that cross meridians at a constant angle) are simply straight lines on a Mercator map. This feature proved to be very useful for nautical navigation. However, conformal projections such as the Mercator have many limitations. For example, a straight line between two points on a Mercator map is often not the shortest route (geodesic line) between those points on earth's surface. Also, area distortion worsens when moving away from the equator. As a result, Mercator maps suffers area area distortion so severe in the polar regions that most Mercator maps are clipped between 85 degree North and South.

          Of all the geographic elements, area is perhaps the most important and useful one for the application of maps. Accurate presentation of area on maps are crucial for the analysis and comparison of data regarding geographical distribution. As a result, many equal-area projections were invented for this purpose. On an equal-area map, the ratio of any two areas is always the same as the actual ratio on the globe. The preservation of area, however, comes with distortion of shape as a cost. In the maps of cylindrical equal-area projection and sinusoidal projection, shapes of continents toward polar regions seem extremely compressed in order to maintain their corresponding small surface area. Besides area, distance between two points is another important geometric factor that is preserved by many map projections.  However, as mentioned earlier, no map is truly equidistant; instead, most equidistant maps only have a limited number of lines that have the same consistent scale throughout their lengths. For example, in the Azimuthal equidistant projection only distances of straight lines that pass through the center of the map are preserved. As for the cylindrical equidistant projection, only the meridians and equator are of consistent scale. Horizontal scales rapidly increases as one moves vertically away from the equator. 

          Choosing the right map projection is all about knowing which geographic element is important for the purpose of the map and compromising between them. For example, aesthetically, conformal maps are favored for their accurate portrayal of shapes, while equal-area maps are extremely important for GIS because of their ability to accurately present the distribution of a certain attribute per unit area. However, one would be mistaken to think that every map favors just one geographic element. In fact, there are plenty of projections that attempt to compromise between different map properties by not strictly preserving any single one of them. For example, the Robinson projection, though neither conformal nor equal-area, compensate by bending meridians slightly to reduce distortion toward the poles but not enough to get rid of it completely like the sinusoidal projection.