Math You Need > Topographic Maps and Slopes > Constructing a topographic profile

# 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.
On the map above, the line is marked A-A' and is indicated in RED on the image below.

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).
For this profile, we've used the profile line provided and lined it up with the profile line on the map. Any blank piece of paper will do but sometimes it's just easier to use the graph paper. We've lined up the bottom of the graph paper with the profile line and marked each end with A and A'.

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.
Now that we have the paper lined up, all we have to do is make a mark and label it everytime we see a contour line cross the profile line. The image below has all of the contour lines marked with blue tick marks (and most of the contour lines are labeled except where they get really messy).

4. Take note of the highest and lowest elevation you record for later.
The highest elevation recorded on the profile is 420 ft and the lowest is 260 ft. This will become important when you need to begin to plot your profile.

5. When you have marked all of the points where a contour line crosses the paper/profile line, get a piece of graph paper (or a paper with all horizontal lines). Make sure that the graph paper 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).
Often you are given an appropriate profile graph in the problem (particularly if you have a lab manual from a national publisher). This is the case with this particular problem - you've been provided with a profile graph already. See the image in step 3 if you aren't sure what this means.

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.
We've already labeled the x axis with A-A'. In step 4, we determined the 420 is the highest elevation and 260 is the lowest. You have plenty of horizontal lines and since the contour interval is 20 ft, let's start with 200 ft and make each line 20 feet higher.
When we've finished, the elevations go from 200 to 480 - all within the range of the elevations along the profile line. For more information about how to pick a vertical scale, you can visit the vertical scale page in Idaho State's unit on Topographic maps.

Note that we have ignored the horizontal scale on this map (see the little bar scale on the bottom of the map?)
. For this map, that little bar on the map represents 3,000 ft - each little tick mark on the vertical scale of your profile is about the same size as one division on the vertical axis but we have made each tick 20 feet (not 1,000 as would be indicated by the horizontal scale). This means that in the end, the vertical scale of our profile will be extremely exaggerated (1,000 feet/20 feet = 50x vertical exaggeration). Why would geologists do this? Vertical exaggeration allows us to see even small changes in the land surface. If we kept the same vertical scale (which in some cases we do want to do), this profile would look like this (the nearly flat blue line on the bottom of this image):

It's difficult to see any variation on that particular profile, isn't it? For a discussion of vertical exaggeration and how to calculate it, see this discussion on Idaho State's website or UT Austin's page on Topographic Profiles.

7. Line up your tick marked paper with the bottom of the graph 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.
Now that we have appropriate elevations, we can transfer our elevations to the appropriate place on the plot. For example, the first elevation from left to right is 260 feet - on a vertical line, just above your tick mark for 260 feet, place a dot on the line that represents 260 feet. Then 280 feet, and so on. (If you need a reminder of how to plot points, visit the plotting points page but don't forget to come back and finish this module!!) The finished product should look like this:

8. Once you have transferred all of your tick marks to your graph, connect the dots with a smooth curve.
Remember that we're thinking about how the landscape looks. So, the tops of hills should go up above the contours that surround them and valleys go just below the contour elevations on either side. Valleys aren't flat and (in most cases) neither are hilltops. Steep sided hills have contour lines that are close together and gentle slopes have contours that are far apart - your profile should reflect these ideas. Here's the profile connected from the dots plotted in step 7:

and the profile without the dots (perhaps a better representation of the profile of the land):

• Remember that this is a profile (or slice) of the landscape; therefore, we do not connect the dots with straight line segments. Think about hills you have seen from a distance - do they go straight across at the top (yes there are some hills - called mesas - that do this but most do not, right)?
• Although the hill tops have two repeating contour lines, we do not connect the hill tops or valleys with straight lines across at the same elevation. Because there is space between them the land surface must go up or down. How much? Well, depending on the contour interval, we can make an estimation. The top of the hill cannot be higher than the next elevation marked by a topographic line. For example, on the figure above, the 40 ft contour is repeated at the top of the left hill, the profile shows the elevation going above 40 ft but not all the way to 50 ft. (the next contour line). Similarly, in the valley between the two hills, the 30 ft contour is repeated. Note that the valley floor goes below 30 ft but not all the way to 20 ft.
• A general rule of thumb is that slopes to the tops of hills will mimic the slope below (that is if they are rising gradually, it is pretty unlikely that they will suddenly dramatically change (in just a few feet). Thus, you can continue the slope on either side of the hilltop or valley until the two intersect (curve it just a little there).
• Do the best you can in connecting the dots to make it look smooth and consistent, you are interpreting all of the land surface between contour lines and each person's profile will probably look just a little different. However, the general shape should be the same.

## 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

You have completed the steps for constructing a topographic profile! Now you can move on and practice with some other data on the sample problems page.

If you would like to know more about smooth curves and topographic profiles, 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: