Lab 13A: Map Skills II

Ian Saunders and Stuart MacKinnon

This lab addresses the fundamentals of how to specify direction and then focuses on the three-dimensional nature of the landscape as expressed in topographic maps – maps which show the three-dimensional landscape by means of contour lines. It builds on the material that was covered in Lab 12, such as deriving locations and distances from a map, so be sure that you are familiar with that material before starting this lab.

Nearly every land surface on Earth is composed of slopes (even if, at first glance, they appear to be flat). The direction in which a slope faces is known as its aspect (in other words, it’s the direction down the slope). It is the infinite number of combinations of slopes and aspects that make up the physical landscape.

This lab is about how to use topographic maps to gain an appreciation of the three-dimensional landscape from a two-dimensional map. We will seek answers to such questions as: In which direction are we looking/going? How high is the land here? How steep is that slope? What profile shape is that hillside? How do we interpret topographic profiles?

Learning Objectives

After completion of this lab, you will be able to:

  • Specify directions using the three principal types of azimuth;
  • Understand how to use contours to determine elevation and slope;
  • Interpret topographic profiles;
  • Use Google Earth to find directions and elevations, and generate topographic profiles.



We are all familiar with the points of the compass (Figure 13.1, left). These allow us to specify general directions, but are insufficient to define specific values. For this we use an azimuth, which is the angle measured clockwise from north (Figure 13.1, right). The term bearing is often used synonymously with azimuth, although there are also some other uses of the term, so “azimuth” will primarily be used here. Therefore, north has an azimuth of 0°, northeast is 45°, east is 90°, and so on. The range of azimuth values is 0° to 359°.

Figure 13.1. Compass points (left) and azimuths (right). Source: Ian Saunders, CC BY-NC-SA.

Although conceptually simple, defining an azimuth is made a little more problematic because there are three different north arrows to choose from! These are:

  1. True North: this is the straight-line direction to the Geographic North Pole (GNP). This is also equivalent to following a meridian. An azimuth referenced from True North is called a True Azimuth. Since the GNP is a fixed point on Earth, a True Azimuth for any particular location will never vary.
  2. Grid North: this is the straight-line direction that runs northwards parallel to the UTM grid on a NTS map. An azimuth referenced from Grid North is a Grid Azimuth. At most locations, the UTM grid will vary slightly from the latitude-longitude grid, and therefore there is usually a small difference between True North and Grid North.
  3. Magnetic North: this is the direction towards the North Magnetic Pole (NMP), and is the same direction that a magnetic compass needle points towards. An azimuth referenced from Magnetic North is a Magnetic Azimuth. The Earth’s magnetic field is dynamic and always changing its position, and therefore the location of the NMP is always moving. This means that a magnetic azimuth that is correct this year will be slightly incorrect next year. The difference between True North and Magnetic North varies widely.

In reality, the Grid North arrow may be to the west or to the east of the True North arrow and, likewise, the Magnetic North arrow may be to the west or to the east of the True North arrow. All combinations are possible, and are location-dependent.

Figure 13.2. A declination diagram. Source: Ian Saunders, CC BY-NC-SA.

When converting between different types of azimuth, we need to have information about where the three North arrows are —this is typically provided by a declination diagram (although some mapping agencies provide the information verbally). Shown at right is an example, using made-up values of True North and Magnetic North:

The difference between True North and Magnetic North is known as the magnetic declination. In the example shown in Figure 13.2, this is 14° W. We must specify “West” or “East” to avoid ambiguity; in this case, it is “West” because the Magnetic North arrow lies to the west of True North.

The difference between Grid North and Magnetic North is known as the grid declination. In Figure 13.2, this is 17° W. Again, we must specify “West” or “East” to avoid ambiguity; in this case, it is “West” because the Magnetic North arrow lies to the west of Grid North. Grid declination is necessary when converting between magnetic compass bearings and grid azimuths, which is a very useful field skill.

The difference between Grid North and True North is known as the grid convergence angle. In Figure 13.2, this is 3° E.

Figure 13.3. Deriving azimuths.Source: Ian Saunders, CC BY-NC-SA.

How do we apply this knowledge? Let’s use the same declination diagram as above, and assume that the direction from A to B is 75° True. Portraying things visually help us see how the different azimuths can be derived:

In Figure 13.3 we can see that the angle between Grid North and the A-B direction is slightly smaller than that between True North and A-B – in fact, it is 3° smaller and therefore the Grid Azimuth is 75°–3° = 72°. Similarly, we can see that the angle between Magnetic North and the A-B direction is 14° larger than that between True North and A-B, so the Magnetic Azimuth is 75°+14° = 89°. So, the direction from A to B can be specified as any or all of: 75° True, 72° Grid, or 89° Magnetic.

When using azimuths in a real-world situation, we need the actual declination diagrams from the study area (preferably the latest edition). Figures 13.4 and 13.5 show additional examples from Canadian 1:50,000 NTS maps (diagrams have been simplified for purposes of clarity).

Figure 13.4b Declination Diagram from St. John’s. Source: Natural Resources Canada, Open Government License-Canada.View source.
Figure 13.4a Declination Diagram from Victoria. Source: Natural Resources Canada, Open Government License-Canada.View source.


Notice that the date of the magnetic information is given, and the rate of change in it. This allows us to calculate the grid declination for the current year. For example, we can see (Figure 13.4a) that the grid declination in Victoria, BC, was 19° 38′ E in 2000, and it was decreasing by 5.9′ annually. So, in 2020 the value is 19° 38′ E minus the accumulated changes in the intervening years, which amount to: (2020-2000) \times 5.9′ = 118′. Therefore, the 2020 value of the grid declination at Victoria is 17° 40′ E.

Figure 13.5. Part of NTS 1:50,000 map sheet 82N05 (Glacier) 3rd edition. Elevation units are in feet. Source: Natural Resources Canada, Open Government License-Canada.View source.

Height Datums and Units

When talking about how high a land surface is, we need a reference level, sometimes referred to as the height datum (not to be confused with a geodetic datum, which is an issue that we don’t need to discuss here). Hereafter, we will use the term elevation to define the height above (or, sometimes, below) a height datum. A standard convention in topographic maps is to define elevation relative to the mean sea level.

In all cases where elevation is involved, be careful to check what units are being used. The units of elevation are typically feet or metres. See the map’s legend to find out. (Note that older editions of a particular map sheet might use feet, but later editions of the same map sheet might use metres. Always check!)

Spot Heights and Bench Marks

One of the simplest ways to indicate the elevation of land on a map is to use a spot height, which is simply the elevation of a particular point (e.g. the summit of a hill or mountain). Many spot heights are determined from aerial photographs, rather than being surveyed on the ground. Occasionally, you may also see a bench mark shown on a map. These are points that have been surveyed, perhaps as part of construction projects such as highways or rail lines. Locations that have been surveyed for the purposes of map making or town planning (for example) are known as horizontal control points. Many horizontal control points will have a small metal marker affixed to the ground.

Figure 13.6. Examples of a spot height (elevation = 1377), a bench mark (elevation = 1256), and a horizontal control point (elevation = 8622). Note: elevation units may be feet or metres – you’ll need to check the map. Sources: (left) NTS 1:50,000 map sheet 82E14 (Kelowna) 4th edition (right) and NTS 1:50,000 map sheet 92H01 (Ashnola River) 2nd edition. Natural Resources Canada, Open Government License-Canada.







Contour Lines

Contour lines (or simply contours) on a topographic map are the most common way of showing the three-dimensional landscape. With practice, a geographer can easily visualise the landscape from a two-dimensional map sheet—a valuable skill.

Contours are lines that connect points of equal elevation. One way of envisaging this is to imagine a valley filled with water. If you drew a line along the shoreline, it would be a contour line. If you dropped the lake level by, say, ten metres and again drew a line along the shoreline you would have a second contour line. Repeating this exercise again and again would leave you with a landscape covered in horizontal lines all ten vertical metres apart (known as the contour interval). You have just made a topographic map! (In reality, contours are typically derived by a combination of ground surveys and analyses of aerial photographs.)

If we follow the hypothetical procedure for deriving 10-metre contours outlined above, it will be obvious that in very flat areas, a contour interval of ten metres will probably not allow you to pick up the subtleties of the landscape. On the other hand, in a mountainous region a contour interval much greater than ten metres would be advisable, otherwise there would be so many contours that nothing else could be mapped! So, always check the contour interval of the topographic map you’re using. It will normally be found in the map’s legend. You will also normally find that contour interval increases as map scale decreases.

A map’s contours allow us to derive some fundamental pieces of information: how high we are (our elevation), the steepness (or gradient; see below) of the slope, the slope’s profile shape, and the overall relief of the landscape. The usual use of the term “relief” is to qualitatively describe the range of elevations found in a given area (known as relative relief). A “high-relief landscape” is one in which there is a great difference between the low and high elevations, such as in mountain ranges. Conversely, a “low-relief” landscape such as a plateau has little elevation range. Don’t confuse “relief” with “elevation.” We might have a “high-elevation low-relief landscape” just as easily as a “low-elevation low-relief landscape”.

Types of Contours

There are several different types of contours that are good to know about:

  1. Index contours. Typically, every fifth contour is a bolder line than the regular contour. This is especially useful in high-relief terrain because it allows us to find elevations from the map without having to count every single contour: we can go up/down the mountainside by jumping from one index contour to the next.
  2. Approximate contours. These are similar to regular and index contours but are drawn using a short-dashed line. This indicates that the exact elevation of the surface was difficult to determine and/or may vary in time.
  3. Auxiliary contours. If a map shows low-relief terrain adjacent to high-relief terrain, extra contours with a smaller contour interval are sometimes used in the low-relief area to provide more topographic detail. On NTS maps, these are depicted as long-dashed brown lines.
  4. Depression contours (Figure 13.7, left). These indicate where the land inside a closed-loop contour is lower (i.e., a depression—or hollow—in the surface). The contour line has small hachure marks that face downhill, into the depression.
  5. Cliff symbol (Figure 13.7, right). Okay, so this is not an actual contour line, but it is worth adding to our list. When slopes get very steep and become cliffs, it may be difficult or impossible to use contours, so a symbol is used instead. The tightly-spaced hachure marks indicate the way the cliff faces.
Figure 13.7 Left: Depression contours indicate that terrain within the contour is a depression. Right: Cliff symbols indicate a cliff face. Source: Ian Saunders, CC BY-NC-SA.

Interpreting Contour Lines

When interpreting contour lines, there are several key points to remember:

  1. A contour always separates land that is higher from land that is lower.
  2. All contours are single, continuous lines. They do not split or cross over each other.
  3. A closed-loop contour always indicates that there’s higher ground inside the loop, unless it is a depression contour.
  4. On Canadian NTS maps, the convention is that contour labels are oriented to indicate which is uphill. Look carefully at Figure 13.5, for example: along the Illecillewaet River valley at the bottom of the figure, you can see two contour labels on either side of the valley, 3800 and 4200. Uphill is the direction above the top of the number if you were reading it normally.
  5. If you see contours form a “V” pattern along a watercourse, the “V” always points upstream. If you’re at a sharp ridge, such as a glacial arete or a large lateral moraine for example, the “V” pattern in the contours points downhill. Figure 13.5 has several good examples: note the contours along Cougar Brook (at the bottom of the figure) where the “V” pattern points uphill, toward the creek’s headwaters. Just to the east of there, examine the contours at Napoleon Spur—the “V” pattern points down the ridge crest.

Deriving Slope Gradients from Maps

There are several different ways of expressing slope gradient, and all of the most common ones are based on the ratio of horizontal and vertical distances between two points (the classic “rise over run” situation):

Figure 13.8. Fundamental elements of a slope. Source: Ian Saunders, CC BY-NC-SA.

To find the slope we need two values: the horizontal distance between points A and B, and the elevation difference between them. The horizontal distance (\Deltax) is found by measuring it on the map and using the map’s scale to convert to real-world distance (i.e. exactly what you were doing in Lab 12). The vertical distance between A and B (\Deltaz) is the elevation difference between them, which can be found by interpolating from contours and/or spot heights.

With this information we can derive the slope’s gradient expressed as:

  1. A fraction (i.e. rise\divrun) or a ratio (i.e. rise:run); in the latter, it is the convention that the rise is expressed as the number one. Example: if rise = 70 m, and run = 560 m, then the slope steepness is (70\div560) = 0.125, or 70:560 = 1:8 (which might also be referred to as a “1 in 8” slope).
  2. A percentage: simply, the fraction expressed as a percentage. Example: using the same rise and run as above, we get: (70\div560)\times100 = 12.5%.
  3. An angle (\Theta in Figure 13.7): applying trigonometry, \Theta (degrees) = tan-1 (rise\divrun). Example: using the same rise and run as above, we get: tan-1 (70\div560) = 7.1°. If you don’t have a calculator with trigonometric functions, you can use an online arctan calculator like this one to find the inverse tangent. You will need to calculate (70\div560) as an input for this particular calculator.

Notice that in Figure 13.8 the horizontal distance separating A and B (i.e. \Deltax) is not the actual ground distance. The true distance from A to B is along the hypotenuse of the triangle in Figure 13.8. For small slope gradients the difference between A-B distance and \Deltax is negligible, but in steep terrain the A-B distance will be significantly longer than \Deltax.

Finally, when deriving slope steepness from a map you must measure \Deltax along a line that is perpendicular to the contours. This gives the true slope, equivalent to the fall line—think of the direction that water would run down a slope: it would move down the steepest, most direct path, and not deviate along lower-angled routes. In Figure 13.9, true slopes are shown with red arrows. Notice how the red arrows cut across contours at a 90º angle. All other lines crossing the contours represent a false slope (blue arrows), which will always be less than the true slope. On simple slopes, you may be able to measure \Deltax along a straight line, but realise that the line of true slope will often be curved, as in Figure 13.9.

Figure 13.9. Examples of true (red) and false (blue) slopes. Arrows point downhill. Source: Ian Saunders, CC BY-NC-SA. Base map: Natural Resources Canada, Open Government License-Canada.View source.

Topographic Profiles

A topographic profile (Figure 13.10) is a cross-sectional diagram through the landscape, which helps us envisage the nature of the terrain. A profile line might be a simple straight line (which generates a simple profile), or a series of straight lines connected at angles to each other (which generates a compound profile), or more or less any other continuous line, straight or curved. If we used a profile line that cross all of the contours at right-angles, we would have a transverse profile. The longitudinal profile of a river is a transverse profile familiar to geomorphologists and hydrologists.

Figure 13.10. Topographic profile of the length of the Trans Canada Highway shown in Figure 13.5. Source: Google Earth, used in accordance with Google Earth guidelines.

Topographic profiles are commonly employed to simply show the ups and downs along a particular line (often used in depicting the slopes along a hiking trail). They may also be a bit more complicated and show the subsurface geology, such as the way rock strata tilt and/or fold beneath Earth’s surface.

It is common to find that topographic profiles are vertically exaggerated (stretched in the vertical direction) to better depict the subtleties of the terrain. Vertical exaggerations of up to about 3x are common; anything more than this tends to make every little bump in the landscape look like hills and mountains!

Vertical exaggeration is determined as follows:

VE = (vertical scale / horizontal scale)

Vertical Exaggeration Sample Calculation (Try It!)

Interpreting the Landscape

The value of topographic maps in allowing us to see the three-dimensional landscape on a two-dimensional map sheet cannot be underestimated. It is a valuable skill, but one that for most people does not come easily. Practice, practice, practice! Here are a few exercises that compare what you see on a map sheet to what is visible in Google Earth.

Lab Exercises

The following lab exercises provide some practice at applying the concepts discussed above. You will need a ruler, calculator, and an internet connection to download a map and access Google Earth. Some of the exercises may be easier if you are able to print the relevant portion of the map. It is assumed that you have successfully completed Lab 12. It also assumed that you can convert between metres and feet. The exercises should take you 1½ to 3 hours to complete.

Supporting Material Links

How to Find True Slope Along Topographic Profiles

Google Earth Procedures

Downloading NTS Topographic Maps


EX1: Directions

  1. Refer to Figure 13.5.

a. From the declination diagram shown, derive the grid declination for the current year.

b. Assume that you travel through the Connaught Tunnel, from the SW end to the NE end. On the map, the tunnel is at angle 34° from the UTM grid. Derive all three azimuths. When calculating the magnetic azimuth, use the current year’s grid declination that you found in 1(a). Round off all final answers to integers.

i. Grid azimuth:

ii. True azimuth:

iii. Magnetic azimuth:

c. Assume that you are at the motel at Rogers Pass and see an interesting-looking mountain peak but don’t know which one it is. You take a compass bearing of 282°. Use this information and your grid declination from 1(a) to determine which mountain peak you are looking at.

  1. Use Google Earth and go to the Alexandra Bridge at 18T4447205031067.

a. If you cross the bridge from its west side (in Hull, Quebec) to the east side (in Ottawa, Ontario), what is your direction? (Google Earth provides True Azimuths).

b. From your location, what is the tall landmark you can see at 141° True?

EX2: Elevation & Contours

All questions in Exercise 2 refer to Figure 13.5.

  1. Study the map and determine the following, making sure to use the correct units:

a. The contour interval

b. The interval between the index contours.

  1. Noting that 1 m = 3.281 feet, estimate:

a. The elevation (in metres) of Ursus Major Mountain.

b. The elevation (in metres) of Rogers Pass.

c. Which of the two estimates, 4(a) or 4(b), is probably the least accurate? Why?

  1. Find the Tupper Glacier. The long-dashed lines across the glacier are approximate contours. Why has the cartographer chosen to depict the surface topography of the glacier using this type of contour?
  2. Find the creek at 585807—it appears to simply stop! (And, no, it is not a cartographic error.) What happens to it? Hint: interpret the nearby contour lines.

EX3: Slope Gradients

  1. Find the average gradient between the historic site at Rogers Pass (the diamond symbol at 642818) and the summit of Mount Cheops at 616812. You can assume that a straight line between these two points is the true slope. Express the slope steepness as:

a. A ratio of 1:n.n

b. A percentage

c. An angle in degrees

  1. The Connaught Tunnel, which carries a rail line beneath Rogers Pass, is about 8080 metres in length. Its northeast portal is at an elevation of 3600 feet. The southwestern portal is at approximately 644797 in Figure 13.5. Derive the average slope of the tunnel as an angle in degrees expressed to two decimal places.

EX4: Topographic Profiles

  1. Below is a topographic profile of a short hiking trail in the Okanagan region of BC. It is posted at the trailhead so that hikers can see what’s in store for them.
    Figure 13.11 Topographic profile of the Bitterroot Loop trail. Source: Rose Valley Regional Park kiosk information, used here with permission from the Regional District of Central Okanagan.

a. The trail looks very steep in places, but this might be due to the vertical exaggeration. Determine the VE to find out. Hint: you can measure the lengths of each axis from the screen and apply the generic scale formula from Lab 12 to find the scales of the vertical and horizontal axes.

b. Determine the average gradient between point 1 (“Trail Start”) and point 3 (highest point). Express the slope steepness as:

i. A ratio of 1:n

ii. A percentage

iii. An angle in degrees

c. Now that you have done these calculations, do you think the trail is very steep? Why/why not?

  1. Figure 13.12 combines a topographic profile of part of the Rocky Mountains near Banff, Alberta with information about the rock layers and geologic structures present.
    Figure 13.12. Topographic profile and geologic cross-section of part of the Rocky Mountains near Banff, Alberta. Source: Ian Saunders, CC BY-NC-SA. Adapted from Geological Survey of Canada Map 1294A.

a. Determine the vertical exaggeration.

b. Assume that the topographic profile in the Sulphur Mountain area runs along the strike of the strata, which means that the slope of the strata shown in the figure represents the angle at which the rock layers are tilting (the dip slope). Use Figure 13.12 to determine the true dip angle of the rock layers at the top of Sulphur Mountain.

EX5: Interpreting the Landscape

The value of topographic maps in allowing us to see the three-dimensional landscape on a two-dimensional map sheet cannot be underestimated; it is a valuable skill, but one that for most people does not come easily. Practice, practice, practice! Here are a few exercises that compare what you see on a map sheet to what is visible in Google Earth.

  1. Figure 13.5 shows includes some good examples of landforms made by alpine glaciation (see the list below). Use Google Earth to zoom in and explore these features. Carefully observe the size and shape of each feature and how it appears on the map. Then, for each of 11(a)- 11(d), give the grid reference of another example of the landform seen in Figure 13.5. Note: You can find a review of structures formed from glacial erosion (horns, arêtes, and cirques) here. More information about glacial deposits like lateral moraines can be found here.

a. The glacial horn or pyramidal peak of Mount Sifton (616872)

b. The arêtes that radiate from Mount Sifton’s summit

c. The cirques, such as those immediately to the N and NW of Mount Sifton’s summit

d. The lateral moraine at 607873

  1. Use Google Earth to generate a topographic profile across the Illecillewaet River valley shown in Figure 13.5. Construct the profile between ~625806 and ~639782 and describe the cross-sectional shape of the valley.
  2. Download NTS 1:50,000 map sheet 92J08 (Duffey Lake) 2nd edition. The following grid references locate common glacial landforms. Using only the map, identify as many as you can.

a. 379755

b. 392768

c. 377770

d. 397748

e. 426828

f. 444734

Reflection Questions

  1. Many people rely on their GPS receiver to provide locational and directional information. But GPS receivers can go wrong, or get broken or lost. In 3 to 5 sentences, explain how you would use a map and compass to find your way when the high-tech equipment is no longer an option.
  2. You want to hike to the top of a mountain but it looks steep and you want to find the easiest (least-steep) route. You open up Google Earth and know that you can get elevation values for the top of the mountain and a number of points along the base of the mountain. Using the ruler tool for horizontal distances, explain how you could determine the slope of the route options and find the best route?
  3. A Google Earth topographic profile is a quick and easy tool for looking at topography of interest. Give an example of how could you see yourself using this tool outside of this course.

Supporting Material

Back to Lab Exercises

How to Find True Slope Along Topographic Profiles

Unless the vertical exaggeration of the profile is 1.0 (i.e. horizontal and vertical scales are the same), slope gradients will not be realistic. They will have to be derived by finding the rise and run of a tangent as shown by the following example (a hiking trail in BC).

Figure 13.13 Vertically exaggerated topographic profile of a hiking trail. Source: Ian Saunders, CC BY-NC-SA.

Assume that we want to find the true slope gradient at point X.

Step 1. Draw a tangent through the topographic profile (the sloping dashed line).

Step 2. Find the rise (\Deltaz) and run (\Deltax) of the line. Here \Deltaz = 800 m and \Deltax = 1150 m.

Step 3. Slope gradient = tan-1(\Deltaz\div\Deltax) = tan-1(800\div1150) = 35°. Note how the slope of the dashed-line tangent is much steeper in Figure 13.13 than 35° because of the vertical exaggeration of the profile.

Google Earth Procedures

To derive an azimuth: Tools-Ruler and in the pop-up box select Line. Mouse-click once to start a line, then click a second time to end the line. The True Azimuth is shown as the Heading.

To generate a topographic profile: ToolsRuler and in the pop-up box select Path and check the Show Elevation Profile box. Mouse-click once to start a line. Every successive click adds a node to the path. Use Clear to end the process.

Downloading NTS Topographic Maps

If you don’t know the map sheet’s number: access the GeoGratis web site and select the Geospatial Product Index. You can then zoom in or out of the map and the map codes will appear. For example, zoom in on Vancouver. You will first see 92 appear, then a grid with letter codes, and then number-letter-number codes which are the 1:50,000 map IDs; downtown Vancouver is map sheet 92G06. You may get access to the maps directly from here, but if not go to the next step.

If you know the map sheet’s number: Use GeoGratis’s ftp site. You will probably find that the canmatrix_geotiff versions are the easiest to use. These are scanned versions of the original NTS map sheets.

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