Sometimes we wish to preserve the shape of environmental features on a map. In special cases this shape is a circle on the ground, or a phenomenon that spreads outward in circular ring-like fashion from a source area. A special class of projections makes it possible to capture the circular character of these features.

Ranges and Positions
Most circles on the earth are created when something extends outward a specified distance from a central point. Radio, television, and cellular telephone signals all exhibit this characteristic. Similarly, an airplane can only fly a limited number of miles or hours from an airport before it runs out of fuel. In each case the effective range is a circle on the ground.

To illustrate the range of something, we need to choose a projection on which ground circles are preserved as circles on the map. Conformal projections have this special property if the circles are relatively small. But since we cannot preserve both shape and area on the same map projection, circles of constant ground size will plot in different sizes from one part of a conformal map to another. The azimuthal family of projections will preserve a circle of any size as long as the projection is centered on that circle. But this means that circles with centers elsewhere will not plot as circles on most of these projections. Only on the Stereographic projection will all circles on the ground plot as circles on the map.

Modern navigation and positioning instruments are commonly based on measuring the time it takes an electronic signal to reach your location from several ground stations or satellites of known position. By converting signal transit time to distance traveled, you can determine your range to each transmitting source.

In the case of ground stations, if we know we are located somewhere along each of two range circles, we must be where the two circles intersect. Thus, if lost in a storm while sailing, we can use the distances to two known shore transmitting stations, as provided by electronic navigation instruments, to plot our location on a map (Figure 12-1). Notice how the range circles intersect at our location; the map helps us to visualize as well as compute. When signals are being received from satellites, we now have a third dimension and must deal with intersecting spheres. The same principles apply in both cases, however, since the intersection of a satellite range sphere with the earth sphere is a circle.

Rings of Activity
The distribution of landscape forms created by environmental processes on spherical earth can be difficult to visualize. The pattern of earthquake and volcanic activity around the earth illustrates this point. A thoughtless choice of map projection that pays no attention to the geographical character of the phenomenon being mapped might look like Figure 12-2. The geometry of this map provides little insight into process and structural relations and, as a result, the pattern shown is complex and confusing. The band of intense tectonic activity known as the "Ring of Fire" surrounding the Pacific Ocean is apparent but its understanding is obscured more than enhanced by this map.

To choose a projection well, we must take advantage of what is known about a phenomenon. In this case, tectonic activity is said to be associated with the slow breakup of a single ancient land mass centered approximately at the present location of the southern tip of Africa, and the subsequent drift of the pieces (tectonic plates) holding the continental "islands" that make up the surface layer of the earth. It is believed that tectonic activity is greatest along the leading edge of the continental plates as they move outward from the position of the original landmass. Thus, if we choose an Azimuthal Equidistant projection and center it on the tip of South Africa, we obtain a most revealing pattern of tectonic activity (Figure 12-3). The intensely active "Ring of Fire" becomes an encompassing circle that coincides with the forward-moving edge of the continents. We might even visualize ship-like continents plowing slowly through the earth's crust, creating zones of instability.

A related example of ring-like diffusion phenomena further illustrates the importance of projection choice. Shock waves generated by earthquake activity in the "Ring of Fire" can cause a huge water wave called a tsunami to be propagated across the Pacific Ocean surface. On occasions tsunamis have caused severe property damage and loss of life in coastal areas at great distance from an earthquake site. If our aim is merely to visualize the path taken by a tsunami, maps based a wide variety of projections will suffice. But in this circumstance we might want to go beyond visualization. Clever choice of projection can actually turn the map into a powerful nomographic tool for geographical analysis.

Consider, for example, the fate of residents living in coastal lowlands on the island of Hawaii. When a tsunami is caused by an earthquake occurring somewhere in the Pacific basin, they would like to know how big a water wave has been generated and how long it will be before this wave hits their shores. Since the wave will travel across the ocean surface at a nearly constant rate of speed, the important thing to know is distance to the earthquake site. An Azimuthal Equidistant projection centered on Hawaii and marked off to the Pacific Ocean rim with equally spaced tsunami travel time lines admirably serves this purpose (Figure 12-4). A glance at the map would suffice to determine the estimated time of arrival of the potentially dangerous water wave, regardless of its origin in the basin. Preparations can be made accordingly.

Chapters: 1 2 3 4 5 6 7 8 9 10 11 12 Contents