Lab 5: Projections in ArcGIS

Essentially map projection is the mathematical art of portraying a three dimensional surface onto a two dimensional plane. The reason I use the word ‘art’ is because there are inherent distortions created when this procedure is practiced, being so, the cartographer is an artist in mitigating these distortions in respect to what the map will be used for. Complex methods of abstracting a three dimensional object into a two dimensional plane are used in the form of mathematics to pinpoint where a particular spot on a globe (a latitudinal and longitudinal intersection) will lay on a flat surface in relation to another point on the said globe. What the map will be used for is immensely pertinent to how a globe is projected. For instance, a conformal projection would be used for navigation, because it maintains angular relationships; however, it wouldn’t be used to accurately view area or distances for it distorts these to a great degree. The same goes for other projection types and it should be stated that this issue can potentially create quite a problem when it comes to figuring out what is where, how far something is from something else, or what direction something is from somewhere else.

As said above, each projection has its advantages and disadvantages. Equal area map projections deal with area best, as the name implies. If you are to look at both equal area map projection below it is clear that there is close resemblance in how ‘big’ things are. Both the Hammer as well as the Sinusoidal have similar attributes, Greenland isn’t grossly over exaggerated in size (as is seen in a Mercator projection) and the continents seem very close to one another in terms of land mass. These types of maps are very good for determining how lands area changes over time. Determining how the Earth’s ice caps are shifting is a perfect example of a use for this projection as it would not alter the physical area of the ice and thus would lead to exact data results. Another use might be determining area for large boundaries; such as states, countries, lakes, etc. for the same reasons as the ice cap scenario, this is a smart map to use because it will yield accurate geometric data for area. It should also be noted that it is impossible to have a flat map that is both equal area as well as conformal. So, angular conformity is lost for the use of accurate area projection.

Equidistant maps are portrayed with measuring distance in mind. As seen by the Plate Carree map distances are true when measuring along meridians and standard parallels. However, when measuring diagonally on a Plate Carree map accuracy is diminished greatly. Equidistant maps generally only show equal distance from the point they are projected. So, for the equidistant conic map centered on the North Pole, seen below, all measurements from the North Pole would be accurate. However, when measuring two points that do not include the North Pole (i.e. Washington D.C. and Kabul) on a map similar to this, distance is distorted greatly, leading to inaccuracies. This is seen in the measurements of the two equidistant map projections; the Plate Carree being 10,110 miles and the Equidistant Conic being 6,972 miles. The interesting thing is that in this measurement the line bisects the North Pole very closely, actually giving a relatively accurate portrayal of distance if following the great circle route rather than a rhumb line route (as would be done on the Platte Carree projection). No flat map can be both equal area and equidistant.

Maps that are Conformal have exact scale in every direction and therefore parallels and meridians cross one another at right angles. This is good for showing angular accuracy and distance to some degree, but area is usually grossly distorted as one deviates from the center of the projection. In classrooms, books, magazines, and other publications around the globe people have been fed the idea that particular areas are massive in comparison to others. If you look to the Mercator projection below it’s obvious to see that Antarctica is larger than normal, I mean, can it really be larger than all of the contingents combined? Or Russia and Greenland, both vastly larger than Africa or South America, which I think most can agree is inaccurate. These maps work well geographic reference, possibly for navigation purposes, and for many things near the equator or near the center of projection, but beyond that there are large distortions that must be accounted for.

equal area