Initial Publication Date: March 2, 2012

# How do I construct a topographic profile?Connecting points to make a smooth curve

Other parts of this resource on graphing take you through plotting points and constructing a straight line through data points. If you aren't sure how to plot points on a graph, please make sure you visit and work through the plotting points tutorial before moving on with this part of the graphing pages. This page is geared toward thinking about the shape of landscapes and pretty unique to geoscience courses. There are other instances in mathematics and graphing where a smooth curve is necessary (e.g., exponential curves, sine waves, etc.); this page is focused on a specific instance when you will construct a topographic profile from a two dimensional map.

When working data with topographic maps, topographic profiles and their construction, we often ask you to connect data points with a smooth curve. In such instances, you will be asked to plot some points and connect them with a smooth line. This is different from the plotting of a best fit line because it involves extrapolation of information from spatial data. In the case of constructing a topographic map, you must extrapolate the placement of the appropriate elevation contour. For topographic profiles, you must extrapolate the contour of the landscape (that is, whether it goes up or down) when faced with repeating elevation contours.

## When should I construct a profile?

In introductory geoscience courses, a profile is appropriate when you are asked to construct a cross-section or profile. Topographic profiles are used to understand what a topographic map is telling you in a specific area (or, you can think about it like it is giving you a "side view" of the landscape along a specific line on the map). Interestingly, many geologists are quite visual and like to have visual representations of data. Because maps are two-dimensional but represent three dimensions (that is, topgraphic maps are flat with lines that represent hills and valleys). Professional geologists use exercises such as the ones you will practice with below to help you (and us) visualize a two dimensional cross-section of what the land surface looks like (from the side) - giving you a slice of the third dimension. In other words, profiles help you to understand what a topographic map is telling us about hills and valleys along a particular line.

## How do I construct a topographic profile?

Examine the topographic map image to the left (you can click on the image to make it larger or you can download the map and a profile (Acrobat (PDF) 2.3MB Jul18 11) to try the steps below on your own). Before you start, you might want to review some of the rules about topographic maps before continuing (you can find rules at Idaho State U.'s field exercise, U. of Montana labs and U. of Memphis Topo Lab).

To construct a topographic profile, you need to find a line on a map that is interesting. In many cases, this line is given to you (often labeled something like A-A' or A-B). The line should go through some part of the map that you are interested in, so that you get useful information. The following list provides some guidelines for effectively constructing a topographic profile and uses the topographic map and profile line provided to the left (you can download a pdf of the map and profile to work from (Acrobat (PDF) 2.3MB Jul18 11)):

1. Sketch in the line on the map or locate the line that is provided.
2. Place the edge of a blank piece of paper along the line and mark the starting and ending points of the line (label them with A and A', or whatever the given line is labeled).
3. Start at one end (maybe it's the A end) and move along the edge of the paper, making a mark on the paper every time a contour line touches the edge of the paper. Make sure you label each mark with the right elevation so that you can transfer that point to the correct elevation on your profile. (If you get tired of marking every elevation contour, you can just label the index (darker) contours and the places where a contour line repeats). You may also want to mark where rivers or streams occur.
4. Take note of the highest and lowest elevation you record for later.
5. In this case, we have marked the graph paper with the appropriate lines, but you can also find a random piece of paper and mark the distances between contours on a line that you've drawn. If this is the case, you will need to find a piece of graph paper (or a paper with all horizontal lines) that is at least as long as your profile line (you can paste more than one piece together but make sure you line up the grid lines).
6. Draw a horizontal line on the graph paper that is the length of your profile line. Draw vertical lines above your starting and ending points. Label the y-axis (vertical lines) with elevations making sure that your scale goes from highest to lowest on your cross-section (see step 3). For example, if your lowest elevation is 4200 feet and your highest elevation is 7600 feet, you might want to label your axis going from 4000 to 8000 feet.
7. Line up your tick marked paper with the bottom of the graph (or use your marked graph paper) and, beginning with the elevation on the left hand side of the paper, go directly up from that tic mark to make a small dot at the corresponding elevation. Note that the point does not need to be on a vertical line on the graph paper.
8. Once you have transferred all of your tick marks to your graph, connect the dots with a smooth curve.

## Where are smooth curves used in the geosciences?

Topographic profiles are used in many applications in the Geosciences. Some of the topics where you will need to recognize and draw a topographic profile are:

• topographic maps
• earthquakes
• structural geology (and geologic cross-sections)
• glacial geology
• coastal geology
• geomorphology

## Next steps

### I am ready to PRACTICE!

If you think you have a handle on the steps above, click on this bar to try practice problems with worked answers.
Or, if you would like even more practice, you can use the links below.

## References and resources

Several universities have tutorials for how to construct a topographic profile. Here are just a few: