-To construct contour maps, cross-sections and calculate gradients using topographic data.

-To develop basic skills used in topographic map interpretation.

-To introduce the concept of direction (points of a compass and azimuths).

One common problem in geography is the need to portray data that have been collected to show spatial variability. The medium most commonly used is that of a map. A very effective type of map is one which uses isolines (a line that joins points of equal value). You will use many types of isoline maps in this course: isotherms (lines of equal temperature), isobars (lines of equal pressure), isohyets (lines of equal precipitation), and contours (lines of equal elevation). Later in this course, you will gain experience drawing isolines using annual precipitation (isohyets) for the island of Maui, HI (in Lab 5). In the current lab, you will learn how to draw isolines showing equal elevation (contours).


Topographic maps are scale models of the Earth's three-dimensional surface, printed on two-dimensional pieces of paper. Although length and width are easily transferred from the real world to a map, it is much more difficult to transfer the third dimension, height. Over time a number of different techniques have been developed in order to successfully show this dimension. The most commonly used method is to show height through the use of contour lines. A contour line connects all points on the map with the same elevation above sea level. An understanding of the contours on any map is possible by following a few simple rules. The objective of this and Lab 5 is to introduce you to the construction and interpretation of isoline maps.


1. Every point on a given contour line is of the exact same elevation; that is, contour lines connect points of equal elevation.

2. Contour lines always separate points of higher elevation (uphill) from points of lower elevation (downhill). One can determine which direction on the map is higher and which is lower, relative to the contour line in question, by checking adjacent elevations.

3. Contour lines always close to form an irregular circle; but sometimes part of a contour line extends beyond the mapped area, so that you cannot see the entire line.

4. The elevation between any two adjacent contour lines on a topographic map is the contour interval. Often every fifth contour line is presented as a heavier line so that you can count by five times the contour interval. These heavier contour lines are known as index contours because they generally have elevations printed on them. Whenever reporting the contour interval it is important that the units (ft, m etc.) are reported.

5. Contour lines never cross one other, except for one rare case: where an overhanging cliff is present. In such a case, the hidden contours are dashed.

6. Contour lines can merge to form a single contour line only where there is a vertical cliff.

7. Contour lines never split.

8. Evenly-spaced contour lines represent a uniform slope. Closely spaced contour lines indicate a steep slope. Widely spaced contour lines indicate a gentle slope, i.e., the spacing of the contours indicates the gradient/slope.

9. A concentric series of closed contours represents a hill.

10. Depression contours have hachure marks on the downhill side, always close, and represent a closed depression.

11. Contour lines form a V pattern when crossing streams. The apex of the V always points upstream (uphill).

12. In cases where slope orientation changes, contour lines of equal elevation will be repeated.


DATUM: An elevation from which heights are measured. In the case of topographic maps, sea level represents the zero datum from which land altitudes and sea depths are determined. Heights are referred to in meters (m) or feet (ft) above sea level (abbreviated a.s.l.).

RELIEF: The difference in elevation between two points on a map.

Local Relief: refers to adjacent hills and valleys, i.e., how high a hill is compared to its valley.

Total Relief: refers to the difference in elevation between the highest and lowest points on a map. The highest point is generally the top of the highest hill or mountain; the lowest point is usually located where the major stream of the area leaves the map, or a coastline.

SPOT ELEVATION: Precise points of elevation indicated on a map by a "x" with a number next to it. They are not marked by any feature in the field.

BENCHMARK: A special type of spot elevation, which is indicated on the map by the abbreviation B.M. United States Geological Survey benchmarks are identified in the field by a column located at the point shown on the map. On the top and bottom of the column is an engraved brass disc. The top disc can be read from the surface and the bottom disc is meant to act as a source of information if the top disc is destroyed. You can find benchmarks on the IUPUI campus, in the south-east corner of the courtyard between the old university library and education building, and by the bridge on New York street, to the west of the track stadium.


To draw isolines with precision we will use the proportional distance method. You can precisely calculate the location of an isoline between two data points (either elevation, precipitation values, atmospheric pressure measurements, etc.) as shown below:



Where: zi is the value of the isoline being drawn

Zmin is the value of the minimum data point

Zmax is the value of the maximum data point


We want to trace a contour line representing an elevation of 30 m between two points that have an elevation of 20 m and 50 m respectively. The proportional distance will thus be:

dp = 30 m – 20 m = 10 = 0.33
         50 m – 20 m    30
The second step is to multiply the dp value by the distance measured between the two points on the map. If the distance is 3 cm, you should draw the contour representing 30 m of elevation at 1 cm (0.33 x 3 cm) away from the minimum value, which is 20 m.

NOTE: An isoline will always pass between two points, one being of lower value, and the second one being of higher value than the drawn isoline value.



Topographic maps present the landscape from a vertical (overhead) point of view. Often the map user needs to know what the landscape looks like from a horizontal perspective,i.e., as though they were standing in the field looking at a vertical section through the landscape. This third dimension is illustrated using a topographic profile. Topographic profiles are a special type of cross-section and can easily be constructed following the steps outlined below.

To illustrate how the elevation changes over a distance, a cross-section may be constructed. The horizontal axis represents distance, and the vertical represents the elevation.

Practically the easiest way to do this involves taking a sheet of graph paper and lining it up between two points (along a transect).

The first step is to mark where the contours intersect the transect. These intersections indicate points where the elevation is an exact value. These values can then be plotted on the vertical axis. The values for the horizontal axis are provided by the distance along the transect and are at the same scale as the original map.

Joining up the points on this example of a cross-section presents the variation of elevation along that line. This is what we call a topographic profile.

NOTE: The term cross-section is a general term including topographic profiles and other type of profiles, like the ones your will produce using precipitation data in Lab 5.


However, when graphing distances and heights on one graph, it is necessary to report the vertical exaggeration of the cross-section. Vertical exaggeration simply means that your vertical scale is larger than your horizontal scale. Vertical exaggeration is used to add detail to a profile as if you want to discern subtle topographic features or if the profile covers a large horizontal distance (miles or km) relative to the relief (feet or meters). In the example shown on the top of the next page, you could use one centimeter is equal to 1000 m for your vertical scale, while keeping the horizontal scale the same. But in this case, you would not see the variation in relief clearly. Thus vertical exaggeration is needed to show how much the vertical scale has been exaggerated by to show the details of changes in elevation. The vertical scale of the profile can vary greatly. It will almost certainly be more detailed than the horizontal scale of the map. This difference causes an exaggeration in the vertical dimension, which is almost always necessary in the construction of a readable profile. Without vertical exaggeration, the profile may be so shallow that only the highest peaks stand out.

To determine the amount of vertical exaggeration used to construct a profile, simply divide the real-world units on the horizontal axis by the real-world units on the vertical axis.


If the vertical scale is one 1"=1000’ and the horizontal scale is 1"=2000’, the vertical exaggeration is 2x (2000’/1000’).

One unit (1 cm) on the horizontal scale represents 1000 m

One unit (1 cm) on the vertical scale represents 50 m


Thus the vertical exaggeration is:

This means that the vertical scale is 20 times more exaggerated than the horizontal scale: 20 units on the vertical scale represent the same distance/height as one unit on the horizontal scale.
NOTE: In general, profiles should be drawn with the smallest exaggeration necessary to bring out the required detail in the landscape.

You can also determine the vertical scale necessary to produce a certain amount of exaggeration. For example, if you want to draw a profile with a general exaggeration of 5x from a topographic map with a scale of 1:24,000 (1 cm = 240 m), the required vertical scale can be determined as follow:


3. GRADIENT (or slope)

Often it is of interest to know how a variable changes over a given distance. In this example on elevation, we may be interested to learn at what rate elevation changes along the river, i.e., how many feet of change in elevation per mile along the river course (the slope). Later in the course we will be concerned with other types of gradients, for example the precipitation gradient, the change in precipitation over distance which is showing precipitation patterns over regions: which parts are receiving more precipitation, which parts are more arid. You have already been shown how to calculate the gradient/slope of a graph (see Lab 1 and 2); the same form of equation is applicable for the calculation of any gradient:           


This is the change in a variable Y (Y2 - Y1) over a given distance X (X2 - X1). The easiest way to think of this is as the gradient or slope of a hill, i.e., change in height (Y) over distance (X) (Rise/Run): the larger the change in height over a given distance, the steeper the slope.


Throughout this course we will be discussing directions: The direction the wind is blowing from, the direction a river flows, etc. We will use two different ways to refer to these directions.


Compass bearings are directions using the cardinal points of the compass. This uses letters to describe the direction in terms of N,S,E,W, or various combinations of these, e.g., SE, ESE etc. Compasses point to the magnetic North. The true North is the geographic north located at the North Pole. The angle between the magnetic North and the geographic North is what we call the declination.


Azimuths are based on the 360° compass, so that due east is 090 and due west is 270. Azimuths refer to the actual numerical angle measured in degrees. These can be determined easily using a protractor. In physical geography, angles are measured clockwise from North (0°). The edges of maps are true N, S, E and W. We can then determine the direction between two points using a protractor (0° = N, 180° = S, etc.).

To make a reading with a compass, point the arrow on the base plate towards your destination. Then turn the compass housing until the red arrow on the housing lines up with the red portion of the magnetic needle. Take the reading where it says "read bearing here". The numerical value indicated there is the field azimuth, an angle in reference to magnetic north rather than true north because the earth's magnetic field causes the compass needle to align with it.

To determine the true azimuth, the angle from true north, you must add the magnetic declination (the difference in degrees between magnetic north and true north) to the field azimuth if magnetic north is east of true north, and subtract the declination if it is west of true north.

On magnetic declination diagrams from the U.S. Geological Survey topographic maps, the star representative of Polaris, the North Star, shows the direction of geographic north centered on the north rotational pole of the Earth. MN means magnetic north. The angle between these two lines is the magnetic declination. Because magnetic declination varies with time, the date at which the declination was measured is provided. GN is grid north. In the United States, magnetic declination ranges from approximately 24° east in the Pacific Northwest (Washington State) to 22° west in the northeast (in Maine).

Exercise 3

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