a line of equal value, drawn to show the shape of something. In geology, contours are used to show the shape of the land surface (elevation contours) and in many other applications using a wide variety of data types.
the value difference between adjacent contours
a contour made bold or colored differently from other contours. For large maps with many contours, if you don't use index contours, it can look like a "sea of spaghetti," making it difficult to see features. But by making every fifth contour bold, as an example, you eyes will look to the bold index contours for the general shape, and you will look at the regular contours when you need to see details. The index contour interval is just the alternation, or spacing, of the index contours (e.g., "every 5th contour set to a bold index contour" would be set by an index contour interval of 100, if the regular contour interval is 20).
a line of equal elevation, e.g., the 100 foot (above sea level) contour, on a topographic map
the value difference between adjacent elevation contours, e.g., 25 feet would be the contour interval between 50 and 75 foot contour lines
the plane or surface from which values are measured, e.g., sea level for elevation contours
the level of the world ocean, projected under the land surface of continents (Well, Death Valley and a couple of other inland places are actually below sea level, but usually sea level is below the level of the land.)
a map showing the "lay of the land" -- the shape of the land surface. Topographic maps can be any size, but most are the standard 7 1/2 minute quadrangle maps made by the United States Geological Survey. A 7 1/2 minute quadrangle map is 7 1/2 minutes of latitude along the y axis (bottom to top) and 7 1/2 minutes longitude along the x axis (left to right). A topographic quadrangle map, "topo" for short, will have the scale of the map and the contour interval labeled along the bottom.
Any data that is spatially located can be contoured (spatial, for "in space," usually two-dimensional space, with each item of information located on a map or graph). For maps, the spatial location is given by the x and y location of data points. The x and by can be coordinates measured in latitude in longitude, meters, feet, etc. Each data item, in addition to its location given by x and y position, contains some observation. In geology, the most common type of data is for elevation, with each data point containing x, y, and z values, where z gives the elevation at each point. Traditionally, surveyors went out and surveyed the elevation at various points across the landscape, and recorded the x, y, and z for each surveyed elevation point. More recently, instruments on airplanes and satellites have been used to provide x, y, z elevation points for mapping.
But, in addition to elevation, the observation at each point can be any one of a wide variety of things in geology and related sciences:
In each example above, independent observations or measurements of something would be made at different places and recorded, along with the x and y locations of the places. Usually the observations or measurements are recorded as numbers. So, a dataset would consist of x, y, and z values for a number of points, like this:
On a map, we locate points by their x and y values. Let's pick the point with the greatest z value, 345. This point has an x map coordinate of 278 and a y map coordinate of 342, which we use to plot the point:
And, when we do the same for the rest of the points, with z values plotted in red and x, y map coordinates plotted in black, we see our map with all points plotted:
When data points are plotted on a map by their x and y locations, and the value for the observation at each point is plotted, as above, the map can be contoured to show how the values vary across the map. Without contouring, the map may be difficult to interpret, as one would have to look carefully at the values at the various points and try to see patterns in variation across the map. Contours help that visualization. But first, lets look at the map with just the z values posted (the x and y coordinates are just for location, and normally aren't plotted):
So, the task at hand is to draw contours through the points. We'll step through the process in the methods section.