**LAB 3: CONTOUR MAPPING AND TOPOGRAPHIC
PROFILE**

**OBJECTIVE**:

-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**).

**I. INTERPRETING 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. RULES FOR CONTOUR LINES**

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.

**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**.

**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.

**II. DRAWING ISOLINES**

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: z_{i} is the value of the
isoline being drawn

Z_{min} is the value of the
minimum data point

Z_{max} is the value of the
maximum data point

**EXAMPLE**:

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:

50 m – 20 m 30

**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.

**III. TOPOGRAPHIC PROFILES**

**1. DRAWING A TOPOGRAPHIC PROFILE**

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.

**2. VERTICAL EXAGGERATION**

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.

**EXAMPLE**:

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:

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 (Y_{2} - Y_{1}) over a given **distance** X (X_{2}
- X_{1}). 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.

**IV. DIRECTIONS**

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.

**1. COMPASS 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**.

**2. AZIMUTH****
**

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).