Contour Maps: Visualizing 3-Dimensions

Contour Maps: Visualizing 3-dimensions

A contour map is a good way to represent a surface on a 2-dimensional sheet of paper. With practice, interesting information such as highpoints (maxima), lowpoints (minima) and saddles can be detected. Contour maps are a good way to “see” complicated surfaces. Below are some examples of contour maps, plus some discussion: (all topo maps are from www.mytopo.com)

Humphreys Peak, Arizona.

Note the nested behavior of the contours, all counting “up” to the summit elevation, 12,633 feet. The map shows dark contours every 200 feet, lighter contour intervals every 40 feet. The consistent spacing of the contours suggest a uniform shape to the mountain’s slopes (it’s an old extinct volcano). See the “local maximum” marked 12,089 at the bottom? Can you identify the saddle a bit to its upper left? What is the approximate elevation (z-value) of this saddle?

Mather Point, South Rim, Grand Canyon, Arizona.

Mather Point is the most popular overlook at the South Rim of the Grand Canyon, the first one you’ll come to once you enter the park. Note the broad spacing of the contours in the lower left, suggestion generally flat ground (the contours are at 40 foot intervals). Now note the multitude of intervals everywhere else – this, of course, is the canyon! Contours are never supposed to touch but in this picture the resolution seems to indicate they do. These would be the nearly vertical cliffs, while the slightly spaced-apart contouring would be the slopes between the cliffs. You can see the dramatic drop in elevation (change in z-value): Mather Point is at 7,118 feet, while less than a mile to the north-northeast is a point with an elevation of 4,968 feet, a nearly 2,200-foot drop. Pipe Spring is below 3,800 feet. Yes, the canyon drops steeply!

Arizona State University, Tempe, Arizona.

The contour lines here are in brown, but there aren’t many to be seen, suggesting our university is on mostly flat ground (the purple coloring is for man-made objects). In the lower left is a spot elevation/benchmark at the railroad tracks on Broadway road behind Tempe High School, 1,161 feet above sea level. To the right is a spot elevation/benchmark at the corner of Broadway and Rural, 1,172 feet above sea level. This is an 11-foot change in elevation (z-value) in about 1.25 miles, a very small slope indeed. It seems flat to us, but there is a very slight downhill to the west.

The Tempe Buttes – “A” Mountain can be seen at the top. These contours are crammed together tightly, suggesting a very sudden increase in elevation; these are steep little hills!

Great Salt Lake Desert, Western Utah

This exciting topographical map shows one of the flattest natural regions anywhere in the world – the Great Salt Lake Desert of Utah. Water always will settle to exact level, and when it evaporates, leaves behind a level salt field. The red box is a one-square mile “section”, used by surveyors to mark off the land (the thick red lines are Interstate-80 and the Western Pacific Railroad is also shown. This particular section is not far from the famous Bonneville Race Track, where land-speed records are set requiring a near-perfect level ground). Note the spot elevations at each corner of this section, all reading 4,218 feet above sea level. There is some variation within the box, though. The problem with a map like this is the contour spacing – they are miles apart since the gradient is so slight. Hence, mapmakers will put in more spot elevations for reference purposes.

Weather Maps

A weather map is a good example of a contour map. The colors here suggest the contouring, pinks and whites being hottest (yay, Phoenix), and reds, oranges and yellows being cooler in this example. Similarly for Dewpoints.

Scoliosis Detection

(http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=2367415)

Scoliosis is a lateral or torsional curvature of the spine. A common way to detect scoliosis is to make a “height” map of the back. A normal back would be close to symmetrical, while in patients with scoliosis, there will be asymmetry. In the above image the person’s shoulder blades jut out at different heights (a difference of nearly 15 mm) and not symmetrically with the center of the back. This imaging can be used for cases when the scoliosis may be slight and not immediately obvious to the eye.