Introduction & Materials
Maps that deal with the surface changes on the earth are called topographic maps. This exercise
will look at how topographic maps are created, what information they contain, how you can use
them with a compass to get where you want to go, and how to measure the relative positions of
points of interest.
Much of the information discussed is applicable to all types of maps, but for the exercises
associated with this tutorial, the emphasis will be on information contained in a 7.5 minute
topographic map. Here is a link for USGS information regarding maps.
Required Materials:
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7.5 minute series U.S. Geological Survey topographic quadrangle map (1:24,000 scale)
and perhaps a clipboard or other flat surface on which to write in the field.
compass (capable of measuring azimuth, borrow one if necessary)
protractor (inexpensive)
graph paper (including a sharp pencil and eraser, not a pen)
field notebook (optional)
NOTE:
Your map must represent a location that is accessible to you by car, truck, llama, or whatever
means of transportation is available. Make sure it has a few sites of interest to you, such as lakes,
streams, mountains, neighborhoods, etc. (just about anything is appropriate). You can buy these
at local outfitter stores, some bookstores, your local BLM or Forest Service office or through the
U.S. Geological Survey.
Objective:
Gain an understanding of what a map is, how a map is made, and how to use a topographic map
and compass.
Requirements to complete this module:
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Read through the entire tutorial, using links to visit more extensive explanations in the
companion tutorial. Throughout the exercise, questions will be posed and answered. You
will maximize what you get out of this exercise if you work through the questions
yourself before reading the answer, but you are not required to turn in your results.
At the end of the on-line tutorial there are a series of questions in the all-important Field
Exercises. You will need to complete all of these exercises, answer the associated
questions, and turn in your results.
What is a Map?
A map is a way of representing on a two-dimensional surface, (a paper, a computer monitor,
etc.) any real-world location or object. Many maps only deal with the two-dimensional location
of an object without taking into account its elevation. Topographic maps on the other hand do
deal with the third dimension by using contour lines to show elevation change on the surface of
the earth, (or below the surface of the ocean).
The concept of a topographic map is, on the surface, fairly simple. Contour lines placed on the
map represent lines of equal elevation above (or below) a reference datum. To visualize what a
contour line represents, picture a mountain (or any other topographic feature) and imagine
slicing through it with a perfectly flat, horizontal piece of glass. The intersection of the mountain
with the glass is a line of constant elevation on the surface of the mountain and could be put on a
map as a contour line for the elevation of the slice above a reference datum.
The title of the quadrangle is printed in the upper and lower right corners of the map. In addition
to the title of the quadrangle itself, the titles of adjacent quadrangles are printed around the edges
and at the corners of the map. This allows you to easily find a neighboring map if you are
interested in an area not shown on your map. In addition there is information about the
projection and grid(s) used, scale, contour intervals, magnetic and declination.
The legend and margins of topographic quadrangles contain a myriad of other useful
information. Township and range designations, UTM coordinates, and minute and second
subdivisions are printed along the margins of the map. *Section numbers (from the PLS system)
appear as large numbers within a grid of lines spaced one mile apart. The legend also contains a
road classification chart showing different types of roads (paved, gravel, dirt, etc.).
Perhaps one of the most important sources of information on a topographic map is the date of
revision, printed to the left of the scale. Although large scale topographic features (such as
mountains) take millions of years to be formed and eroded, smaller scale features change on a
much more rapid scale.
The course of a river channel may change fairly rapidly as a result of flooding, landslides may
alter topography significantly, roads are added or go out of use, etc. Because of these changes, it
is important to have a fairly recent (or recently updated) topographic map to ensure accuracy. On
most topographic maps, the date of the initial publication will be shown, along with the most
recent revision of the map.
There are many features (buildings, swamps, mines, etc.) that are designated on topographic
maps, which are not described in the map legend. Refer to the USGS Booklet on topographic
map symbols to learn more..
Using A Topographic Map
Tips for Understanding Contour Lines
When first looking at a topographic map, it may appear somewhat confusing and not very useful.
There are a few rules that topographic contours must obey, however, and once you understand
these rules the map becomes an extremely useful and easy to use tool.
The rules are as follows:
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Every point on a contour line represents the exact same elevation (remember the glass
inserted into the mountain). As a result of this every contour line must eventually close
on itself to form an irregular circle (in other words, the line created by the intersection of
the glass with the mountain cannot simply disappear on the backside of the mountain).
Contour lines on the edge of a map do not appear to close on themselves because they run
into the edge of the map, but if you got the adjacent map you would find that, eventually,
the contour will close on itself.
Contour lines can never cross one another. Each line represents a separate elevation, and
you can’t have two different elevations at the same point. The only exception to this rule
is if you have an overhanging cliff or cave where, if you drilled a hole straight down from
the upper surface, you would intersect the earth’s surface at two elevations at the same
X,Y coordinate. In this relatively rare case, the contour line representing the lower
elevation is dashed. The only time two contour lines may merge is if there is a vertical
cliff (see figure).
Moving from one contour line to another always indicates a change in elevation. To
determine if it is a positive (uphill) or negative (downhill) change you must look at the
index contours on either side (see figure).
On a hill with a consistent slope, there are always four intermediate contours for every
index contour. If there are more than four index contours it means that there has been a
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change of slope and one or more contour line has been duplicated. This is most common
when going over the top of a hill or across a valley (see figure).
The closer contour lines are to one another, the steeper the slope is in the real world. If
the contour lines are evenly spaced it is a constant slope, if they are not evenly spaced the
slope changes.
A series of closed contours (the contours make a circle) represents a hill. If the closed
contours are hatchured it indicates a closed depression (see figure).
Contour lines crossing a stream valley will form a "V" shape pointing in the uphill (and
upstream) direction.
Reference Datum
A reference datum is a known and constant surface which can be used to describe the location of
unknown points. On Earth, the normal reference datum is sea level. On other planets, such as the
Moon or Mars, the datum is the average radius of the planet.
The term "reference datum" was used rather than ‘above (or below) the earth’s surface’ or ‘above
(or below) sea level’. The reason for this is simple once you think about it…If you use the term
‘above the earth’s surface’, what exactly does that mean? In other words, the earth’s surface
where? Similarly, although we tend to think of sea level as a constant, it is not the same
everywhere on the globe, so sea level where? and sea level when? (high tide or low) become
pertinent questions. So, to avoid these problems, a reference datum is needed that represents the
same surface or elevation at all points on the earth and that remains constant over time. An
example of a datum that could be used for the earth is a sphere with a radius equal to the average
radius of the earth.
Such a sphere would provide a constant surface to which elevations on the earth's actual surface
could be referenced. However, the earth is not a perfect sphere; the radius of the earth is greater
at the equator and less at the poles. The resulting shape is what is known as an 'oblate ellipsoid'.
By using an oblate ellipsoid as a datum for the earth we have a shape that approximates the shape
of the earth fairly well and provides a datum to which points all over the earth's surface can be
referenced (hence the term 'reference datum').
Most 7.5 minute topographic maps still in circulation use the NAD-27 (North American Datum,
1927) referencing system based on the Clarke ellipsoid of 1866. Technological advances that
allowed more precise measurements of the earth resulted in modifications of the Clarke ellipsoid,
producing the GRS-80 (Geographic Referencing System, 1980).
More recent maps commonly use the NAD-83 referencing system which is based on the GRS-80
ellipsoid. The datum used for a map is printed on the front of a map. Although the reference
ellipsoids used in the NAD-27 and NAD-83 are different, the changes are slight on large-scale
maps (scales will be discussed in greater detail later).
For a more indepth explanation of the problems associated with an elipsoid visit this site
http://kartoweb.itc.nl/geometrics/Reference%20surfaces/body.htm.
Map Projections
What is a Map?
Once a reference datum has been determined the elevation of any point can be accurately
determined, and it will correlate to the elevation of any point on the earth's surface that has the
same elevation and is using the same datum. But…how do you accurately represent the X and Y
coordinates of that point? This question leads to one of the fundamental problems of
mapmaking…how do you represent all or part of an ellipsoid object on a flat piece of paper? The
answer to this question is a bit complicated, but understanding it is fundamental to understanding
what maps actually represent (this statement will become clearer shortly).
In order to represent the surface of the earth on a flat piece of paper, the map area is projected
onto the paper. There are many different types of projections, each with its own strengths and
weaknesses.
The simplest (and easiest to visualize) example of a projection is a planar projection. To
understand this type of projection, imagine inserting a piece of paper through the earth along the
equator. Now imagine that the earth is semi-transparent and you could shine a flashlight oriented
along the (geographic) polar axis through the earth.
The resulting outline on the paper would be a map created using this type of projection (known
as a transverse azimuthal or planar projection).
There are three main types of projections, based on the shape of the 'paper' onto which the earth
is projected. The example above used an azimuthal (planar) piece of paper.
The other main types, illustrated to the right, are cylindrical and conical projections. These three
types of projections can be further modified by the way the 'paper' is oriented when it is inserted
into the earth.
In the example above, the plane was oriented along the equator, known as a transverse
orientation (hence the 'transverse azimuthal' projection). Projections may also be equatorial
(oriented perpendicular to the plane of the equator) or oblique (oriented at some angle that is
neither parallel nor perpendicular to the plane of the equator.
Map Projection Distortions
Each of the different types of projections have strengths and weaknesses. Knowledge of these
different advantages and disadvantages for a particular map projection will often help in which
map to choose for a particular project. The basic problem inherent in any type of map projection
is that it will result in some distortion of the ‘ground truth’ of the area being mapped.
There are four basic characteristics of a map that are distorted to some degree, depending on the
projection used. These characteristics include distance, direction, shape, and area. The only place
on a map where there is no distortion is along the trace of the line that marks the intersection of
our ‘paper’ with the surface of the earth.
Any place on the map that does not lie along this line will suffer some distortion. Fortunately,
depending on the type of projection used, at least one of the four characteristics can generally be
preserved.
A conformal projection primarily preserves shape, an equidistant projection primarily preserves
distance, and an equal-area projection primarily preserves area.
These image show the earth using different projections. Notice how the continents look stretched
or squashed depending on the projection. Following are some websites with more information.
http://www.colorado.edu/geography/gcraft/notes/mapproj/mapproj.html
http://erg.usgs.gov/isb/pubs/MapProjections/projections.html
http://www.soe.ucsc.edu/research/slvg/map.html
http://www.eoearth.org/article/Maps
Grid Systems
A grid system allows the location of a point on a map (or on the surface of the earth) to be
described in a way that is meaningful and universally understood. Projecting the earth’s surface
(or a portion of it) in one of the ways outlined in the Map Projections page, allows for a
representation of an area on a flat piece of paper. Once this is accomplished, it is necessary to set
up a coordinate system on the map that will allow a point to be described in X-Y space.
However, in order to describe this location in a universally understandable manner a grid system
is necessary. A simple grid is shown with the location of a point of interest that we want to
describe.
In order for a point designation on a grid to be meaningful, there must be an origin to the grid
which can be used to reference the point to. Once an origin is assigned then there is only one
correct designation for the point, and anyone looking at the grid will assign it the same value and
be able to interpret what someone else means when they describe a point located at 3,3.
A few examples of possible origins for the grid are shown. In the first example, the designation
for the point would be 3,3. In the second the designation would be 3,1, and in the third it would
be 1,1. All of these designations describe the same point and the only thing that has changed is
the origin of the grid. In order for any type of grid to be useful it is necessary for it to have an
origin and a uniform grid spacing (i.e. the distance between grid lines should remain constant).
There are several types of grids (or coordinate systems), used to divide the earth's surface. Four
of these are in common use on maps published in the United States as follows.
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Geographic . . . Uses degrees of latitude and longitude. One of the most common
coordinate systems in use.
UTM . . . Preserves shape, and allows for precise measurements in meters.
State Plane . . . Developed for local surveying, with minimal distortion.
Public Land Survey . . . This one was used in Colonial America for surveying. Not as
accurate as others.
Geographic Coordinate System
One of the most common coordinate systems in use is the Geographic Coordinate System,
which uses degrees of latitude and longitude to describe a location on the earth’s surface. Lines
of latitude run parallel to the equator and divide the earth into 180 equal portions from north to
south (or south to north). The reference latitude is the equator and each hemisphere is divided
into ninety equal portions, each representing one degree of latitude.
In the northern hemisphere degrees of latitude are measured from zero at the equator to ninety at
the north pole. In the southern hemisphere degrees of latitude are measured from zero at the
equator to ninety degrees at the south pole. To simplify the digitization of maps, degrees of
latitude in the southern hemisphere are often assigned negative values (0 to -90°). Wherever you
are on the earth’s surface, the distance between lines of latitude is the same (60 nautical miles,),
so they conform to the uniform grid criterion assigned to a useful grid system.
Lines of longitude, on the other hand, do not stand up so well to the standard of uniformity.
Lines of longitude run perpendicular to the equator and converge at the poles. The reference line
of longitude (the prime meridian) runs from the north pole to the south pole through Greenwich,
England. Subsequent lines of longitude are measured from zero to 180 degrees east or west
(values west of the prime meridian are assigned negative values for use in digital mapping
applications) of the prime meridian.
At the equator, and only at the equator the distance represented by one line of longitude is equal
to the distance represented by one degree of latitude. As you move towards the poles, the
distance between lines of longitude becomes progressively less until, at the exact location of the
pole, all 360° of longitude are represented by a single point you could put your finger on (you
probably would want to wear gloves, though). So, using the geographic coordinate system, we
have a grid of lines dividing the earth into squares that cover approximately 4,773.5 square miles
at the equator…a good start, but not very useful for determining the location of anything within
that square.
To be truly useful, a map grid must divided into small enough sections that they can be used to
describe with an acceptable level of accuracy the location of a point on the map. To accomplish
this, degrees are divided into minutes (') and seconds ("). There are sixty minutes in a degree,
and sixty seconds in a minute (3600 seconds in a degree). So, at the equator, one second of
latitude or longitude = 101.3 feet.
An alternative method of notation in the geographic coordinate system, often used for many GIS
applications (Geographic Information Systems, or GIS, is discussed in detail in another
exercise), is the decimal degree system. In the decimal degree system the major (degree) units
are the same, but rather than using minutes and seconds, smaller increments are represented as a
percentage (decimal) of a degree.
The decimals can be carried out to four places, resulting in a notation of DD.XXXX, DDD.XXX.
When using four decimal places, the decimal degree system is accurate to within ± 36.5 feet
(11.12 m).
However, because the accuracy of the fourth decimal place is often uncertain, decimal degree
coordinates are often rounded to three decimal places. This results in an accuracy of ± 364.8 feet
(111.2 m).
To give you an example of how the two systems of measurement compare, the location of Red
Hill on the Idaho State University campus in Pocatello, Idaho when expressed using minutes and
seconds is ...
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42°51’36" N, 112°25’45" W.
When using decimal degree notation this same location is written as ...
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42.8600° N, -112.4292° W.
As you can see that despite its common usage, the geographic coordinate system is not very easy
to use.
To demonstrate this, find a topographic map (or any other map that uses the geographic
coordinate system), pick a point on that map, and describe it in terms of degrees, minutes and
seconds. When you’re done with that, try it using decimal degrees. Besides the fact that the grid
on a map using the geographic referencing system is not constant from north to south, it is also
just not very easy to use. Fortunately, both problems are solved to some extent by using the
Universal Transverse Mercator coordinate system, which will be covered next.
Map Scales
Individual topographic maps are commonly referred to as quadrangles (or quads), with the name
of the quadrangle giving an idea of the amount of area covered by the map. The largest area
covered by most topographic maps used for scientific mapping purposes (i.e. geologic mapping,
habitat studies, etc.) are two degrees of longitude by one degree of latitude (see below).
A map of this size is referred to as a ‘two degree sheet’. One, two degree sheet can be divided
into four smaller quadrangles, each covering one degree of longitude and 1/2 degree of latitude
(‘one degree sheet’).
Each one degree sheet is subdivided into eight ‘fifteen minute quadrangles’, measuring fifteen
minutes of latitude and longitude.
Finally, the smallest topographic quadrangle commonly published by the U.S. geological survey
are 7.5 minute quadrangles, which measure 7.5 minutes of latitude and longitude. There are four
7.5 minute quads per fifteen minute quad, 32 per one degree sheet, and 128 per two degree
sheet.
You can determine what type of quadrangle you are looking at by subtracting the longitude
value printed in the upper (or lower) left corner of the map from the longitude printed in the
upper (or lower) right corner of the map. This can also be done using latitude values, just
remember that a two degree sheet only covers one degree of latitude and and one degree sheet
only covers thirty minutes of latitude. This information is also commonly printed in the upper
right hand corner of a map, under the title of the map.
The
sca
le
of
a
top
ographic map is here. In addition to a ratio scale, a bar scale is also shown to allow
measurement of distances on the map and conversion to real-world distances.
As alluded to above, topographic (and other maps as well) come in a variety of scales. The scale
of the map is determined by the amount of real-world area covered by the map. For example, 7.5
minute topographic quadrangles put out by the U.S. Geological Survey have a scale of 1:24,000.
This type of scale is known as a ratio scale and what it means is that one inch on the map is equal
to 24,000 inches (or 2000 ft) in the real world. Actually, it means that one of anything [cm, foot,
etc.) on the map is equal to 24,000 of the same thing on the map. Another way of writing this
would be a fractional scale of 1/24,000, meaning that objects on the map have been reduced to
1/24,000th of their original size.
Other map scales in common use for topographic maps are 1:62,500 (15 minute quadrangle),
1:100,000 (one degree sheet) and 1: 250,000 (2° sheet). The smaller the ratio is between
distances on the map and distances in the real world, the smaller the scale of the map is said to
be. In other words, a map with a scale of 1:250,000 is a smaller scale map than a 1:24,000 scale
map, but it covers a larger real-world area.
Vertical Exaggeration
Depending on why you are creating your topographic profile, you may want to use vertical
exaggeration when constructing it.
Vertical exaggeration simply means that your vertical scale is larger than your horizontal scale
(in the example you could use one inch is equal to 1000 ft. for your vertical scale, while keeping
the horizontal scale the same). Vertical exaggeration is often used if you want to discern subtle
topographic features or if the profile covers a large horizontal distance (miles) relative to the
relief (feet).
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’).
Public Land Survey System
The final grid system discussed here is the public land survey system (PLSS). Although the
geographic, UTM, state plane, and PLSS coordinate systems are the most common, there are
other coordinate systems in use today. The public land survey system is most often used on
topographic maps published in the United States and has its roots in the early surveys of North
America in the 1700's.
The PLSS system differs from the coordinate systems described above in that it is more
descriptive, and relies less on absolute measurements of location. It is a good way to give a quick
approximation of a location, but the main drawback is its lack of accuracy.
In each state (except for the original thirteen states and a few in the southwest that were
originally surveyed based on Spanish land grant boundaries), early surveyors established a
principal meridian running north-south, and a base line running east-west.
Vertical Scale
The scales discussed before only deal with the relationship between horizontal distances on the
map and horizontal distances in the real world. Because topographic maps incorporate the third
(vertical) dimension of the earth’s surface, they also have a vertical scale.
This scale is listed on a topographic map as the contour interval. The contour interval is the
vertical distance represented by consecutive contour lines on the map. In general, the smaller the
scale of the map (remember, small scale maps show a larger area of the earth’s surface) the
larger the contour interval will be. For example, the contour interval on a 7.5 minute quad is
commonly 40 feet, while on a one or two degree sheet it will often be 100 feet. In order to make
topographic maps more useful, there are exceptions to this rule of thumb.
In very flat areas, such as the plains of the midwest or the Snake River Plain, contour intervals of
one hundred, or even forty, feet may not be very useful as they will be very widely spaced. In
areas such as these, supplemental contours are often added at five or ten foot intervals
(supplemental contours appear on USGS topographic maps as dashed lines). Similarly, in very
steep mountainous areas the contours may be more widely spaced to avoid clustering of lines
into unreadable masses. The contour interval used on a topographic map is printed below the
scale in the map legend.
Regardless of the contour interval chosen, you will notice that there are at least two types of
contour lines on a topographic map. Thick contour lines, called index contours, have elevations
printed on them periodically over their length. Between each index contour are four intermediate
contours that are thinner lines than the index contours. The elevation change between the
intermediate contours is what is given in the map legend. So, if the contour interval listed in the
map legend is forty feet, each intermediate contour represents forty feet and the elevation change
between index contours is 200 feet. On many topographic maps these will be the only types of
contour lines shown.
However, as mentioned above, some maps will have supplementary contour lines representing
smaller vertical distances. If supplementary contour lines are used, they will be dashed lines and
the supplemental contour interval will be listed below the regular contour interval in the map
legend. A final type of contour that may appear on a topographic map is a line representing a
closed depression (such as a sinkhole or a crater at the top of a volcano). These contours will be
hachured (they will have small tic marks perpendicular to the main contour line), with the tic
marks pointing downslope.
Creating Topographic Profiles
A very useful exercise for understanding what topographic maps represent is the construction of
a topographic profile. A topographic profile is a cross-sectional view along a line drawn through
a portion of a topographic map. In other words, if you could slice through a portion of the earth,
pull away one half, and look at it from the side, the surface would be a topographic profile. Not
only does constructing a topographic profile aid in understanding topographic maps, it is very
useful for geologists when analyzing numerous problems.
To construct a topographic profile, you must first decide on a line that is of interest to you. This
could be an area where you want to go for a hike and want to know how steep to expect it to be,
a line that shows the maximum relief (relief is the difference in elevation between the highest
and lowest points) in the map area, or any other area in which you are interested. Once you have
determined where you want to draw your profile, use the following guidelines to construct your
profile.
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1. Pencil the line of your interest in lightly on your map, or you can put mylar over the
map and draw on it if you don't wish to mark your map. **If you use mylar, it may be a
good idea to mark the corners of the map on the mylar so you can reorient the mylar on
the map later if necessary.**
2. Place a blank piece of paper along the line you have drawn. You may want to tape the
paper to the map using drafting tape to keep them from moving relative to one another
(don’t use any other kind of tape unless you don’t mind taking some of the map off with
the tape later).
3. On both the blank paper and the map (or mylar), mark clearly the starting and ending
points of your line of section. Below these marks, write down the elevation of the
starting and ending points of your section.
4. Make a tic mark wherever the paper crosses a contour line on the map, making larger
tics for the index contours and smaller tics for the intermediate contours. Write the
elevation of the index contours below their tics on your paper…you might want to start
off writing the elevation of the intermediate contours as well to avoid confusion, but it
will soon become tedious.
Make a note of the highest and lowest points on the profile for use later. Be sure to keep track of the number of intermediate contours between
the major contours; if there are more than four intermediate contours it means that there has been a change in slope and you need to check to see
if you crossed a hill or a valley.
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5. Once you are certain you have all of the appropriate tic marks and elevations, remove
your paper from the map. Get a piece of graph paper that is at least as long as your line of
section (you can piece them together if you have to, but make sure all the grids line up).
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If you are using a map with a scale of 1:24,000 you will want to use graph paper that has
one inch grids to make your life much easier (because at a scale of 1:24,000, one inch on
the paper is equal to 2000 feet). Place your paper with the tic marks on the graph paper
(once again, you may want to tape it down) and mark the starting and ending points of
your line of section on the graph paper.
6. Draw vertical lines above your starting and ending points, these will be the boundaries
of your profile. Use the maximum and minimum elevations along your line of section to
determine how long to draw these lines. For example, if your minimum elevation is 4320
ft and your maximum elevation is 6280 ft, you will want your vertical line to be at least
two inches long. Remember that one inch equals 2000 feet on a 1:24,000 scale map. The
difference between 6280 feet and 4320 feet is less than 200 feet, so it would be possible
to draw your profile in just one inch. However, it is much easier to construct a profile if
your lowest elevation is a multiple of 2000, so you would want to start at 4000 feet and
go to 8000 feet (two inches).
7. Beginning with your starting elevation, go directly above the tic mark on your paper
and make a small dot on the graph paper at the corresponding elevation (if your graph
paper has one inch squares divided into tenths, each smaller square will represent 200
feet of elevation change; each index contour should lie along a horizontal grid line).
Make a small dot for each tic mark on your paper.
8. Connect the dots on the graph paper, and you have a topographic profile.
Calculating a Slope
Determining the average slope of a hill using a topographic map is fairly simple. Slope can be
given in two different ways, a percent gradient or an angle of the slope. The initial steps to
calculating slope either way are the same.
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Decide on an area for which you want to calculate the slope (note, it should be an area
where the slope direction does not change; do not cross the top of a hill or the bottom of a
valley).
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Decide on an area for which you want to calculate the slope (note, it should be an area
where the slope direction does not change; do not cross the top of a hill or the bottom of a
valley).
Once you have decided on an area of interest, draw a straight line perpendicular to the
contours on the slope. For the most accuracy, start and end your line on, rather than
between, contours on the map.
Measure the length of the line you drew and, using the scale of the map, convert that
distance to feet. (insert image with the line drawn on it, conversion calculation)
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Determine the total elevation change along the line you drew (subtract the elevation of
the lowest contour used from the elevation of the highest contour used). You do not need
to do any conversions on this measurement, as it is a real-world elevation change.
To calculate a percent slope, simply divide the elevation change in feet by the distance of the line
you drew (after converting it to feet). Multiply the resulting number by 100 to get a percentage
value equal to the percent slope of the hill. If the value you calculate is, for example, 20, then
what this means is that for every 100 feet you cover in a horizontal direction, you will gain (or
lose) 20 feet in elevation.
To calculate the angle of the slope, divide the elevation change in feet by the distance of the line
you drew (after converting it to feet). This is the tangent value for the angle of the slope. Apply
an arctangent function to this value to obtain the angle of the slope (hit the ‘inv’ button and then
the ‘tan’ button on most scientific calculators to get the slope angle). The angle you calculated is
the angle between a horizontal plane and the surface of the hill.
Using the example above, (click here or on image for larger picture) a hill with a 20% slope is
equivalent to an 11° slope.
Using a Compass with a Map
Pictured below are two different types of compasses. The compass at left is a Brunton compass
used by geologists and others for many specialized mapping purposes. On the right is a more
common type of compass used for general orienteering and some mapping purposes.
The features of a compass that you need to understand are found on both types of compass (and
most others as well). This section will give an overview of how to use a compass with a
topographic map to locate yourself on the map and how to get from one point on the map to
another.
Magnetic Declination
Magnetic declination is the difference between true north (the axis around which the earth
rotates) and magnetic north (the direction the needle of a compass will point). It is usually
printed on the map to the left of the scale bar at the bottom of a USGS 7.5' quadrangle. After
finding the declination on the map, you need to transfer the information to your compass before
you ever take it into the field. If you fail to do this, any readings you get from your compass will
be in error and you may wind up far from where you want to be (in other words, LOST ! ! !).
Magnetic north is determined by the earth's magnetic field and is not the same as true (or
geographic) north. The location of the magnetic north pole changes slowly over time, but it is
currently northwest of Hudson's Bay in northern Canada (approximately 700 km [450 mi] from
the true north pole). Maps are based on the geographic north pole because it does not change
over time, so north is always at the top of a quadrangle map.
However, if you were to walk a straight line following the direction your compass needle
indicated as north, you would find that you didn’t go from south to north on the map. Howfar
your path varied from true north would depend on where you started from. The angle between a
straight north-south line and the line you walked is the magnetic declination in the area you were
walking. In the example figure, if you walked 1.25 miles toward magnetic north(i.e. you
followed your compass without adjusting for magnetic declination) you would end up 1/3 of a
mile away from where you would be if you walked 1.25 miles toward true north.
Fortunately, magnetic declination has been measured throughout the U.S. and can be corrected
for on your compass (see below). This map shows lines of equal magnetic declination
throughout the U.S. and Canada.
The line of zero declination runs from magnetic north through Lake Superior and across the
western panhandle of Florida. Along this line, true north is the same as magnetic north. If you are
working west of the line of zero declination, your compass will give a reading that is east of true
north. Conversely, if you are working east of the line of zero declination, your compass reading
will be west of true north. The exact amount that you need to adjust the declination on your
compass to reconcile magnetic north to true north is given in the map legend to the left of the
map scale.
Setting Magnetic Declination on Your Compass
If you are using a Brunton compass, you set the magnetic declination by turning the declination
setting screw on the side of the compass until the reading on the graduated circle in the compass
lines up with the index pin at the top of the compass at the proper declination.
For many other types of compasses you can set the declination by simply rotating the graduated
circle on the outside of the compass until it lines up with the indicator marker at the top of the
compass at the proper declination. If neither of these methods seems to work with your compass,
check with the users manual that came with your compass, as it should have instructions on
setting the declination.
Once you have set the declination on your compass, any reading you obtain from it will be
accurate. In southern Idaho, for instance, the magnetic declination varies from roughly 14.5°E to
17°E. So, after setting the declination at 16°, when you line your compass up with 0° it will be
pointing to true north but it will appear to be 16° off from the ‘N’ printed on your compass.
A word of caution here: be sure that you set your declination in the proper direction (east in
Idaho). If you set it to 16°W rather than east, you will be off by 32° in all of your measurements,
rather than the 16° you would be off if you hadn’t adjusted it at all. To make sure you have set
your declination properly, orient your compass so that the north end of the needle is lined up
with the 0° mark on the graduated circle.
If you are located west of the line of zero declination, then the index pin or marker on your
compass should be west of the 0° marker on the graduated circle (and vice-versa if you are east
of the line of zero declination).
----- Useful links for more information ----http://www.spacecom.com/customer_tools/html/body_mag_dec.htm
USGS site with useful information about magnetic declination and your gps unit...
http://rockyweb.cr.usgs.gov/outreach/gps/compass_gps_north.html
http://www.rescuedynamics.ca/articles/MagDecFAQ.htm
Get a Bearing
A bearing is a measurement of direction between two points. Bearings are generally given in one
of two formats, an azimuth bearing or a quadrant bearing.
An azimuth bearing uses all 360° of a compass to indicate direction. The compass is numbered
clockwise with north as 0°, east 90°, south 180°, and west 270°. So a bearing of 42° would be
northeast and a bearing of 200° would be southwest, and so on.
For quadrant bearings the compass is divided into four sections, each containing 90°. The two
quadrants in the northern half of the compass are numbered from 0° to 90° away from north
(clockwise in the east, counterclockwise in the west). In the southern half of the compass, the
two quadrants are numbered away from south (counterclockwise in the east, clockwise in the
west).
Quadrant bearings are given in the format of N 40°E (northeast), S 26°W (southwest), etc.
Whenever you measure a quadrant bearing, it should always be recorded with north or south
listed first, followed by the number of degrees away from north or south, and the direction (east
or west) away from north or south. In other words, you would never give a quadrant bearing as
E 40°N or W 24°S.
Your compass may be an azimuth compass or it may be divided into quadrants. If you have an
azimuth compass and are given a quadrant bearing, you’ll have to divide it into quadrants in
your head, and the same goes for quadrant compasses if you are given an azimuth bearing.
Measuring a bearing
So, you’re in the field with your map at point A and want to get to point B…how do you
accomplish this? The first thing you need to do is determine the bearing from point A to point B.
There are two ways to go about this.
The easiest way, is to carry a protractor with you when you’re in the field. If you have a
protractor with you, place it on the map so it is oriented parallel to a north-south gridline, with
the center of the protractor on point A (or on a line drawn between points A and B). Once you
have done this, you can simply read the bearing you need to go off of the protractor.
If you don’t happen to have a protractor with you, you can determine the bearing you need using
your compass. To do this, place your compass on the map so that the edge of your compass is
oriented parallel to a north-south gridline and the center of your compass is on the line between
points A and B.
Now rotate the map and compass together until the
north arrow on the compass points to 0° on the
graduated circle. You can then approximate the
bearing you need by estimating where the line
between A and B crosses the graduated circle.
It is probably at about this point that, if you are using
a Brunton compass (and some others as well), you are
probably noticing that the ‘east’ label is on the wrong
side of the compass (west of north). You are not
hallucinating. It is that way for a reason that will
become clear in the next section, hopefully.
Going From Point "A" to "B"
Once you’ve figured out what direction you want to go, you need to figure out how to use your
compass to get you there. In the example on the previous page, you determined that the bearing
between A and B is 21° (N 21°E). All you have to do now is walk a straight line from point A to
point B at 21° and, after a little sweat, you’ll be at your destination.
To orient yourself along this path, orient your compass so that the north arrow is pointing at the
bearing you want, but in the adjacent quadrant. For example, we want to head out at a bearing of
20° (N 20°E). To do so, align the north end of the needle with 340° (N 20°W).
When you do this, the front edge of your compass is pointing 20° in the direction you want to go.
Now perhaps it is more clear why on some compasses the east and west labels appear to be on
the wrong side of the compass. If the bearing you want is N 20°E and the labels are swapped,
then when you line up with N 20°E as labeled on the compass, the compass is truly pointing
toward N 20°W.
Most compasses have some sort of sighting system built into them to allow greater accuracy in
determining where you want to go.If your compass has a sight (check your owner’s manual to
see if it has one and, if so, learn how to use it), you will orient it the same way as described
above, but you can look through the sight at the same time and find an object to walk toward.
By finding an object (such as a tree or large rock) that lies along your path you will have more
freedom to go around obstacles (such as large gullies, streams, hills, etc.) without losing track of
the direction your are travelling. Once you reach the object you were headed for, sight in on
another object along your path, repeating this process until you arrive at point B.
Finding Self on a Map
Now you know how to get from point A to point B on a map using your compass…but what if
you are not sure where exactly point A is (i.e. you are lost)? By far the easiest way to determine
where you are on a map is to pull out your pocket GPS (global positioning system receiver) and
have it give you your map coordinates. If, however, you are like a lot of people, you don’t want
to shell out a few hundred bucks for a GPS and, unless you are in an area with very little
topographic relief, you don’t need one. You can determine your position quite accurately on a
topographic map by using your compass to triangulate between three points.
The first step in triangulation is to pick three topographic features that you can see and can
identify on your map (mountains are ideal). Start with the first feature you have chosen and
determine the bearing between you and it, as outlined above. Once you have determined its
bearing, pencil in a line with the same bearing on your map that runs through the chosen feature
(once again, having a protractor would be useful).
Repeat this for the other two features, drawing lines for each. The point where the three lines
intersect on the map is where you are. Depending on how accurate your sightings were and how
accurately you drew your lines through the features, there will probably be a some error in your
location. Be sure to double check the map and reconcile it with what you see. If the lines
intersect in a valley and you are on a hill, the location is obviously off a bit on the map.
It does give a good approximation though and, by looking at your surroundings, you should be
able to figure out which hill on which side of the valley you are on. If you have an altimeter with
you, you can also use it with the triangulation to help determine your exact location more
accurately.
UTM - Universal Transverse Mercator
Geographic Coordinate System
The idea of the transverse mercator projection has its roots in the 18th century, but it did not
come into common usage until after World War II. It has become the most used because it
allows precise measurements in meters to within 1 meter.
A mercator projection is a ‘pseudocylindrical’ conformal projection (it preserves shape). What
you often see on poster-size maps of the world is an equatorial mercator projection that has
relatively little distortion along the equator, but quite a bit of distortion toward the poles.
What a transverse mercator projection does, in effect, is orient the ‘equator’ north-south
(through the poles), thus providing a north-south oriented swath of little distortion. By changing
slightly the orientation of the cylinder onto which the map is projected, successive swaths of
relatively undistorted regions can be created.
This is exactly what the UTM system does. Each of these swaths is called a UTM zone and is
six degrees of longitude wide. The first zone begins at the International Date Line (180°, using
the geographic coordinate system). The zones are numbered from west to east, so zone 2 begins
at 174°W and extends to 168°W. The last zone (zone 60) begins at 174°E and extends to the
International Date Line.
The zones are then further subdivided into an eastern and western half by drawing a line,
representing a transverse mercator projection, down the middle of the zone. This line is known
as the ‘central meridian’ and is the only line within the zone that can be drawn between the poles
and be perpendicular to the equator (in other words, it is the new ‘equator’ for the projection and
suffers the least amount of distortion). For this reason, vertical grid lines in the UTM system are
oriented parallel to the central meridian. The central meridian is also used in setting up the origin
for the grid system.
Any point can then be described by its distance east of the origin (its ‘easting’ value). By
definition the Central Meridian is assigned a false easting of 500,000 meters. Any easting value
greater than 500,000 meters indicates a point east of the central meridian. Any easting value less
than 500,000 meters indicates a point west of the central meridian. Distances (and locations) in
the UTM system are measured in meters, and each UTM zone has its own origin for east-west
measurements.
To eliminate the necessity for using negative numbers to describe a location, the east-west origin
is placed 500,000 meters west of the central meridian. This is referred to as the zone’s ‘false
origin’. The zone doesn't extend all the way to the false origin.
The origin for north-south values depends on whether you are in the northern or southern
hemisphere. In the northern hemisphere, the origin is the equator and all distances north (or
‘northings’) are measured from the equator. In the southern hemisphere the origin is the south
pole and all northings are measured from there. Once again, having separate origins for the
northern and southern hemispheres eliminates the need for any negative values. The average
circumference of the earth is 40,030,173 meters, meaning that there are 10,007,543 meters of
northing in each hemisphere.
UTM coordinates are typically given with the zone first, then the easting, then the northing. So,
in UTM coordinates, Red Hill is located in zone twelve at 328204 E (easting), 4746040 N
(northing). Based on this, you know that you are west of the central meridian in zone twelve and
just under halfway between the equator and the north pole. The UTM system may seem a bit
confusing at first, mostly because many people have never heard of it, let alone used it. Once
you’ve used it for a little while, however, it becomes an extremely fast and efficient means of
finding exact locations and approximating locations on a map.
Many topographic maps published in recent years use the UTM coordinate system as the primary
grids on the map. On older topographic maps published in the United States, UTM grids are
shown along the edges of the map as small blue ticks.
State Plane Coordinate System
The State Plane Coordinate System (SPCS) was developed in the 1930s by the U.S. Coast and
Geodetic Survey to provide a common reference system for surveyors and mappers. The goal
was to design a conformal mapping system for the country with a maximum scale distortion of
one part in 10,000, which at the time was considered the limit of surveying accuracy. The State
Plane Coordinate System (SPCS) is used for local surveying and engineering applications, but
isn't used if crossing state lines.
The State Plane grid system is very similar to that used with the UTM system, with the
exception of where the origin for the grids are located. The easting origin for each zone is
always placed an arbitrary number of feet west of the western boundary of the zone, eliminating
the need for negative easting values. The northing origin, however, is not at the equator as in
UTM, but rather it is placed at an arbitrary number of feet south of the state border.
To maintain the accuracy of one part in 10,000 and minimize distortion, large states were
divided into zones, and depending on their orientation different projections were chosen. The
three conformal projections used are listed below.



Lambert Conformal Conic... for states that are longer east–west, such as Tennessee and
Kentucky.
Transverse Mercator projection... for states that are longer north–south, such as Illinois
and Vermont.
The Oblique Mercator projection... for the panhandle of Alaska, because it lays at an
angle.
The number of zones in a state is usually determined by the area the state covers and ranges
from one to as many as ten in Alaska. Each zone has a unique central meridian.
Idaho uses a transverse Mercator projection and is divided into three zones - east, central and
west.
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Idaho East Zone: 1101 ... includes these counties: Bannock, Bear Lake, Bingham,
Bonneville, Caribou, Clark, Franklin, Fremont, Jefferson, Madison, Oneida, Power,
Teton.
Idaho Central Zone: 1102 ... includes these counties: Blaine, Butte, Camas, Cassia,
Custer, Gooding, Jerome, Lemhi, Lincoln, Minidoka, Twin Falls.
Idaho West Zone: 1103 ... includes these counties: Ada, Adams, Benewah, Boise,
Bonner, Boundary, Canyon, Clearwater, Elmore, Gem, Idaho, Kootenai, Latah, Lewis,
Nez Perce, Owyhee, Payette, Shoshone, Valley, Washington.
For more information about each state's zones visit the following site:
http://home.comcast.net/~rickking04/gis/spc.htm
The State Plane system orginally used feet as its primary unit of measure and was based on the
North American Datum of 1927 (NAD27). Because of technological advancements in measuring
the earth's size and shape some of the State Plane systems for states are being converted to North
American Datum of 1983 (NAD83), and will use meters as the primary unit of measure.
With these changes some of the states are redefining zones and primary coordinates. For instance
California changed from 7 zones to 6, Montana changed from 3 zones to 1, Nebraska changed
from 2 zones to 1.
----- Useful links for more information ----The following is an excellent site that explains state plane with an interactive map for each state.
http://www.cnr.colostate.edu/class_info/nr502/lg3/datums_coordinates/spcs.html
Utilities for converting between Geodetic Positions and State Plane Coordinates or for finding an SPC
Zone...http://geodesy.noaa.gov/TOOLS/spc.html
http://www.ngs.noaa.gov/PUBS_LIB/ManualNOSNGS5.pdf
http://www.gpsinformation.net/state-plane-mag.html
Exercise One
Purpose: Become familiar with all of the parts of your map and the information contained in
your map.
For this exercise, if you have not done so already, obtain a 1:24,000 scale map of an area near
where you live or where you would like to do field exercises. Topographic maps can be obtained
at your local BLM or Forest Service office, as well as through the U.S. Geological Survey. If
possible, choose a map that has a fair amount of topographic relief and variability, as it will
enable you to get more out of later exercises. Once you have obtained a map, answer the
following questions.
* What is the name of your quadrangle?
* What are the names of the adjacent quadrangles? (You should have eight of them)
* When was your quadrangle first made into a topographic map?
* Has it been revised?
* What datum was used to create your map?
* What is the contour interval on your map?
* Are there supplemental contours?
* What are the geographic coordinates (i.e., latitude and longitude) of the upper left-hand
corner of your map?
* What are the (UTM coordinates) of the lower right hand corner of your map?
* What is the UTM zone in which you are located?
* Pick a prominent named feature on your map and give its coordinates in PLS
coordinates. Be sure to include the name of the feature (such as Cedar Butte, Rocky Point,
etc.)
* How many different types of roads are there in your map area?
* What is the highest point in your map area?
* What is the lowest point?
* What is the total relief?
What you will be required to do to complete this exercise:
Read and work through the entire companion tutorial, using links to visit more extensive
explanations. Throughout the exercise, questions will be posed and answered. You will
maximize what you get out of the tutorial if you work through the questions yourself before
reading the answer, but you are not required to turn in your results.
At the end of the on-line tutorial there are a series of questions in the all-important "Field
Exercises" using topographic maps. You will need to complete all of these exercises, answer the
associated questions, and turn in your results.
Exercise Two
Read and work through the entire companion tutorial, using links to visit more extensive explanations. Throughout the exercise, questions will be
posed and answered. You will maximize what you get out of the tutorial if you work through the questions yourself before reading the answer, but
you are not required to turn in your results.
Purpose: Gain practical experience with locating yourself on a topographic map and calculating
your position using triangulation. Also learn some of the problems inherent in triangulation with
imprecise tools and how you can overcome these problems.
* Go into your field area (visit public lands or, if on private land, go only after obtaining
permission from the landowner ). Make your first stop somewhere that you are convinced
you know where you are (such as a prominent bend in the road, a pond, etc.).
* Locate the point on the map, mark it with a small ‘x’, and record the point in both UTM
and geographic coordinates.
* Find three other landmarks in your vicinity that you can recognize them on the map
(prominent peaks, ponds, river bends, etc.).
* Using the technique outlined in the triangulation section of the online tutorial, use these
points to triangulate your location. Be honest when you do this, as you will probably not get
it exactly right the first time. Mark your calculated position with another small ‘x’.
* Measure the distance between your true and calculated positions and convert the distance
to feet and meters, noting the direction in which your calculated position varies from your
true position.
* Repeat this process for at least three more locations in your map area.
Upon returning from the field, complete a brief write up of your results. Include information
about how far off your calculated position was from the true position. Were your errors were
systematic (direction and distance)? Did your error decrease with practice? If you had not known
exactly where you were, how could you have checked each of your calculated positions for
accuracy?
Exercise Three
Purpose: Gain an understanding of how linear 'map distances' vary from non-linear 'grounddistances', and how travel speeds vary as a result of topography and vegetation. Much of this
may seem intuitive, but it is important to get a real understanding of how these factors influence
your ability to travel, especially if you are planning a hike or estimating the time it will take you
to get from point A to point B.
Before going into the field choose two areas on the map where you can draw a straight line,
equal in distance to a mile at the scale of the map. Make one of the lines go through an area of
relatively high topographic relief and the other through an area of relatively low topographic
relief. If possible, draw your lines so they go through areas both with and without trees (trees are
represented by shaded areas on the map). If you can’t make one line go through areas with and
without trees, make one line in the trees and the other line out of the trees. Record the starting
and ending points of your profile lines using both UTM and Geographic coordinates.
Draw a topographic profile along each of your lines with no vertical exaggeration. Included on
your profile should be: a scale, vertical axis labels, and directional labels (E-W, N-S, etc.).
Using a ruler, measure the length of the line that makes up your topographic profile. Although it
will not be exact, you can estimate the total length by summing the distance between each of the
points you used to create your profile. This will give you the true 'ground distance' of your line.
For each of your profiles, what is the difference between the straight-line 'map distance' and the
true 'ground distance' in feet and meters? What is the percent difference (i.e. the ground distance
is "Z"% greater than the map distance).
Calculate the average slope for each section of your profiles (i.e. calculate the slope separately
for each uphill and downhill section of the profile).
Find a relatively flat, open section of ground near where you live where you can measure off a
mile accurately (a running track would be ideal).
Time yourself while walking one mile at your normal pace, and record your result.
Estimate, based on your time in the mile, how long you think it will take you to walk each of
your profile lines.
Go into the field and time yourself walking, in as straight a line as possible, each of your profile
lines. Note the elapsed time every time you encounter a major change in slope (at the top and
bottom of each hill).
Record your total time and, on your profile, record the amount of time it took you to complete
each uphill and downhill section.
Turn in a brief write up that includes your profiles and the answers to the questions posed
above, as well as discussing the following:






How far off from your estimated time was your actual time?
Do you think you made up as much time going downhill as you lost going uphill?
What slowed you down more, topography or vegetation?
Was it difficult to walk in a straight line?
Why or why not (discuss any difficulties encountered)?
Using your 20/20 hindsight, are there clues on the map that could have helped you choose
an easier and/or quicker route to get to your destination?
Exercise Four
Purpose: Look at an area of your map in detail to see if there is any relationship between slope
aspect (north facing, west facing, etc.), general vegetation type (you don't need to know specific
plant names, just generalities such as trees, sagebrush, grass, etc.), altitude, and topography
(steep slopes, gentle slopes, etc.).
The first step in this exercise will be to create three topographic profiles (different than the ones
used in exercise 2). In order to maximize the results of this exercise, orient at least two of the
profiles at approximately right angles to one another across ridges oriented in different directions
(they may be in different areas of the map). Try to choose areas that have significant topographic
relief (from one valley to another across a significant ridge, or across large hill or mountain) and
variations in slope angle (some steep, some gentle). If your map does not contain two ridges
oriented in different directions, draw your profiles parallel to one another but far apart and in
areas of differing relief and slope angle. Your profile should be no less than one mile long but it
may be longer; it should be long enough to demonstrate the total topographic variation in the
area.
Record the starting and ending points of your profile using UTM and geographic coordinates.
Once again, walk your topographic profiles. Note on your map any changes in vegetation type as
you encounter them (grass to sage, sage to trees, etc.). If you have a knowledge of general rock
types, note these changes as well (volcanic to sedimentary, sandstone to limestone, etc.).
After you have done this for both lines, transfer the vegetation data (and rock data if you have it)
to your profiles.
Write up your results. Include your observations about the influence (if you observe any) of:
slope aspect on vegetation, elevation on vegetation, vegetation on slope angle, slope aspect on
slope angle, and elevation on slope angle. If you have data on changes in rock type, include your
observations on its influence over the other factors as well.