Geological Hazards Labs
Lab 1: Maps - An Indispensible Tool in Hazard Planning
Introduction
Spatial (positional) information is important to us in many ways. To find our way
from one location to another requires spatial information. Locating areas of the Earth's
surface subject to various geologic hazards also requires spatial information.
Characterization of position requires three dimensions. Typically, we represent spatial
information using a 3-dimensional globe or a two-dimensional map. Both have their own
strengths and weaknesses.
Ancient maps were works of art as well as conveyors of spatial information.
Geology is a science that is very dependent upon spatial information. Geologists
use maps for all kinds of purposes: locating transportation corridors, displaying and
interpreting geologic information, showing land ownership and uses, etc. Therefore an
understanding of spatial information and maps, in particular, is a useful and necessary
skill for a geologist. Understanding maps is also important for non-geologists. The ability
to read a road map insures a motorist will reach her destination with minimal problems.
Hikers and backpackers should know how to read and interpret a topographic map. When
you buy a house, a flood-plain map showing the location of your future property could
save you a lot of heartache and financial loss.
1 Latitude, Longitude, and Great Circles
For centuries, humans have attempted to find the best way to convey spatial
(positional) information. At first, the spatial information was conveyed in verbal form:
"Hike to the big mountain on the horizon and follow the stream to the waterfall." Clearly,
this system worked well only for limited geographical regions and for individuals
familiar with the region. As humans traveled further and further afield, a better way of
describing position was needed. Landmarks changed with time and often were interpreted
differently by different individuals. In addition, nearly 70 % of the Earth's surface, i.e. the
oceans, lack landmarks by which to navigate. What was needed was a system that would
allow one to return routinely to places visited before and to find a position easily that was
never visited before. On a sphere the best way to locate position is through a grid of
intersecting imaginary lines. By specifying the two lines that intersect at the point of
interest, the point is uniquely identified. On the Earth, this system is the longitudelatitude system and dates back to the Greeks and Egyptians. The great Greek astronomer
Hipparcuhus outlined a longitude-latitude system in the second century B.C.
Longitude and latitude lines form an intersecting grid, the graticule, that uniquely defines
the location of any point on the Earth's surface.
Latitude
To indicate position in a N-S direction, we use a series of parallel circles,
latitudes, that circle the Earth at regular intervals. The equator divides the Earth into a
Northern Hemisphere (the top) and a Southern Hemisphere (the bottom). Because the
Equator represents a unique and natural starting point, latitudes are labeled with the angle
between them and the Equator (Fig. 1a). Consequently, the Equator is 0o and the North
and South Poles are 90oN and S, respectively. Latitude lines north of the equator are
labeled N and those south are labeled S. Degrees are divided into 60 minutes (60') and
minutes into 60 seconds (60'').
2 Latitudes are parallel and never cross each other. Hence, they are also known as
parallels. On the surface, each degree of latitude is 111 km (69 mi), a minute is 1.2 km
(~1 mi), and a second approximately 30 m (~100 ft). In contrast to the distance between
the latitudes, the length of a latitude decreases systematically from the Equator to the
poles. The Equator is 40,131 km (24,937 mi) long whereas 90oN and 90oS are simply
points. In the northern hemisphere determining your latitude is simple, point one arm
toward the North Star and the other toward the horizon. Amazingly, the angle between
your arms is your latitude. A more precise measurement can be obtained by measuring
the angular height of the sun or stars above the horizon and comparing the measurement
to astronomical tables for that date. For nearly 2,000 years, it has been relatively easy to
determine latitude. Thus, one is struck by the accuracy of early maps in a north-south
direction as compared to their east-west features. This discrepancy is readily apparent on
the ancient map on the map lab Introduction page.
Longitudes
To determine east-west position, we use a series of longitudes running northsouth from the North Pole to the South Pole. Since all longitudes have the same length
and shape, there is no natural starting point as there is for latitude. By international
agreement, one longitude was arbitrarily selected as the starting point. This longitude, the
prime meridian, was the subject of controversy for a long time. Because of national
pride, different nations often used different prime meridians. This confusion was finally
resolved in 1884 when an international conference established the longitude running
through Greenwich, England as the prime meridian. Greenwich is the site of the Royal
Greenwich Observatory which has been taking astronomical measurements since 1675.
Longitudes to the west of Greenwich are labeled W and those to the east E. The two sets
of longitudes meet opposite the prime meridian at the International Dateline. The plane of
the prime meridian and International Dateline divides the Earth into a Western
Hemisphere and an Eastern Hemisphere. Unlike latitudes, longitudes are not parallel and
to do not extend all the way around the Earth. As with latitude, degrees of longitude are
divided into minutes and minutes into seconds.
3 Because they are not parallel, the distance between adjacent longitudes varies
with position away from the Equator. The largest separation occurs at the equator where
longitudes are approximately 111 km (69 mi) apart. This distance systematically
decreases toward the poles. Ultimately, at the poles, the longitudes converge and intersect
in a single point.
Unlike determining latitude, there is no natural phenomena that permits rapid and
accurate determination of longitude. Without an accurate method to determine longitude,
sailing position was determined by dead reckoning. Errors in this method would either
drive a ship onto the shore or leave a ship at sea without provisions. During the
Napoleonic wars, British losses due to shipwreck exceeded those due to hostile enemy
action. In addition, this lack of ability to measure accurately longitude resulted in poor
maps. In particular, E-W dimensions were routinely in error by large amounts. For
example, note the error in the E-W shape of North America in the map on the
4 Introduction page. From the 1500-mid-1800s, the major sea-faring nations of Europe
spent considerable effort on determining a means of accurately determining longitude at
sea. The two candidates were lunar observations (a method favored by the established
scientific community) and accurate measurements of time (a method pursued by, in
particular, one English clock maker). Among the first nations to offer a prize for
developing a means of determining longitude was Spain. With the Spanish prize still
unclaimed and a rise in British naval interests, the English Parliament offered a 20,000
pound prize for development of a method of determining longitude in 1714. An English
clock maker named John Harrison solved the problem with the development the first
chronometer in 1737. A chronometer is a very accurate timepiece that works without the
use of a pendulum and therefore keeps time on a pitching ship at sea. Because the
scientific community favored the lunar method of determining longitude, they blocked
him getting the prize. He was, however, awarded a special bounty by Parliament in 1793
after intervention by the King. By 1815, the chronometers developed by Harrison were
common on sailing ships. When the H.M.S. Beagle carrying Charles Darwin sailed in
1831 on its famous voyage, it had 22 chronometers for establishing the longitude of
foreign lands. Consequently, the quality of maps began to improve rapidly at the
beginning of the 18th century.
Great Circles
If you want to take the shortest path between two points what do you follow?
Obviously, a straight line. However, if you where to follow a straight line path between
two points on the Earth's surface you would end up traveling through the interior of the
planet. When traveling on a sphere, e.g. the Earth, the shortest distance between two
points is not a straight line but an arc along the planet's surface. A great circle is the
circle defined on the surface of a sphere by any plane passing through the center of the
sphere. Great circles divide spheres into two roughly equal size parts. (Small circles
divide spheres into unequal parts. Lines of latitude correspond to small circles.) Since
diametrically opposite longitudes are defined by planes that pass through the North and
South Poles and the Earth's center, they represent great circles. The equator is also a great
circle.
Since they lie in a plane passing through the poles and the center of the Earth, opposite
longitudes form a great circle.
5 On a sphere, the shortest distance between two points is a part or an arc of a great
circle. This arc is called a great circle route. Great circle routes are important for
airplanes and ships because they represent the shortest most economical routes to travel.
Unfortunately, most travel routes are not N-S so longitudes are generally not useful for
plotting great circle routes. Rather we need a plane defined by the Earth's center, the
origin point and the destination point on the Earth's surface. A plane defined in this
manner will define great circles oriented at some angle to the longitude lines and cut
across them. On a globe, you can determine the great circle route between two points by
stretching a string tautly between them.
Transportation routes generally follow paths oriented at an angle to the longitudes.
6 Map Projections
When dealing with spatial information, there are four properties that are important.
These are:
direction
• area
distance
• shape
The only means of accurately representing all of these properties at once for the
Earth's surface, or a large portion of it, is a globe. Unfortunately, globes are a poor way to
convey spatial information. In particular, they are inconvenient to work with and cannot
be produced at a scale sufficient to show the features important for most purposes. Image
trying to carry a globe with you on a hike in the mountains. It won't easily fit in your
backpack and it cannot be folded. Anyway, you would need a very large diameter globe
to show in detail the features you would need to navigate your way. Consequently,
humans have used maps as their primary means of conveying information for thousands
of years. Maps are two-dimensional representations of a three-dimensional world. To
make a map of the Earth's surface or a portion of it, the globe must be projected on to a
surface that is either two dimension or can be readily converted to two dimensions. This
projection always results in some distortion. No map projection can portray all four
primary spatial properties without distorting one or more. The problem is to identify what
the map is to be used for and then select a projection type that minimizes the distortion of
the properties you need most. For example, if the map is to be used for navigation, the
projection method should preserve direction and distance. On the other hand if we are
interest in calculating a nation's total cropland, our map should accurately reproduce
areas.
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Projection Types
There are three basic classes of map projections: cylindrical, azimuthal and conic.
Each has advantages and disadvantages. The type selected depends upon the purpose of
the final map.
The three basic types of map projections.
7 Within each projection type, there are several different projections. Each produces
a map with differing latitude and longitude patterns. Although the concept of map
projection is presented in a graphical context, actual projections are now done
mathematically. Each projection type has a set of complex equations used to transfer a
position from the Earth's surface to the map. Even maps developed in the 15th and 16th
centuries were mathematically based. Modern mapping techniques are still produced
mathematically, but use computers to speed and make more accurate the process of map
creation.
Cylindrical
Perhaps the easiest map projection to visualize is the cylindrical projection. The
map is produced by projecting the surface of the globe onto the inner surface of a
cylinder. The cylinder is then cut lengthwise and unrolled to produce the developed
surface or the map. Where the cylinder touches the globe is the tangent line and is the
region of least distortion. The further and further from the tangent line, the greater the
distortion. With this type of projection, areas on the globe near the cylinder axis cannot,
in fact, be projected onto the map surface. Thus, only a certain portion of the globe's
surface can be represented by these types of projections. There are three types of
cylindrical map projections: normal, transverse and oblique. For each type, the geometric
relation between the cylinder axis and the planet axis determines the position of the
tangent line on the globe.
Normal cylindrical projection
Normal cylindrical projections are produced when the axis of the cylinder and
that of the planet are parallel. In this orientation, the tangent line corresponds to the
Equator. The meridian along which the cylinder is cut determines which continents
occupy the center part of the map. For example, a cylinder cut along the Prime Meridian
will produce a map in which the Pacific Ocean occupies the central portion of the map.
8 Transverse cylindrical projection
By orienting the cylinder axis perpendicular to the planet axis, a transverse
cylindrical projection is produced. In this projection, the tangent line is oriented N-S
and passes through the poles thereby paralleling longitude lines. The longitude for the
tangent line is determined by what area of the globe will be shown in the center of the
final map.
Oblique cylindrical projection
When the cylinder and planet axes are at an angle to each other, the projection is
an oblique cylindrical projection. In this type of projection, the tangent line is oblique
to both longitude and latitude lines.
9 Conic map projection
The conic map projection can be visualized by imagining placing a paper cone
on a globe and projecting points on the globe onto the inner side of the cone. A map is
produced by cutting the cone from the apex to the base and unrolling it. Where the cone
touches the globe is the tangent line and is the region of least distortion. The further and
further from the tangent line, the greater the distortion. With this type of projection, only
one hemisphere of the globe can be represented on the final map. Thus, conic projections
produce maps that show on half of the globe's surface. There are three types of conic
map projections. For each type, the geometric relation between the cylinder axis and the
planet axis and the angle of the cone determines the position of the tangent line on the
globe. (More complex conic projection maps are created by having the cone of projection
actually pierce the globe.)
Normal conic projections
Normal conic projections are ones in which the planet axis and that of the cone
are coincident. The cone is tangent along a selected latitude determined by the angle of
the cone. On these types of maps, longitudes will consist of a series of lines radiating
from the pole. In contrast, latitudes will form arcs of circles centered on the pole.
Transverse conic projections
Transverse conic projections are produced when the cone of the axis is oriented
at right angles to the planet axis. This puts the apex of the cone over the equation. The
tangent line, as with the oblique conic projection, cuts across both latitudes and
longitudes. The pattern produced by the longitudes and latitudes are very complex.
10 Oblique conic projection
By orienting the axis of the cone at an angle to the planet axis, an oblique conic
projection is produced. On these maps, the tangent line cuts across both latitude and
longitude lines and they have no simple geometric relationship.
11 Azimuthal projections
Azimuthal projections are formed when the globe is projected onto a plane. The
plane is tangent to the globe at a single point. Distortion is least near the point of
tangency and increases outward from there. Because of the orientation of the map plane,
azimuthal projections depict only the hemisphere of the globe touching the map plane.
Normal azimuthal projection
When the map plane is tangent to the pole, a normal azimuthal projection. This
type of projection will image either the Northern or Southern hemispheres but not both.
Oblique azimuthal projection
Oblique azimuthal projections are those in which the map plane is tangent at
any point other than the poles. This type of projection produces very complex patterns of
longitude and latitudes.
12 Map components
A map must provide the user with a variety of reference information. These data
are generally provided in the margin of the map or in a legend. It allows the user to find
directions, calculate distances and identify important landforms in the area mapped. To
properly use a map, you must be able to find and correctly interpret this information.
The information necessary to interpret a map correctly is generally presented in its
margins.
Among the information provided on a map are its name, date, scale, direction and
its geographic location. The names of adjacent maps are also provided along the maps
margins.
13 Name
The name of a map allows one to identify the map for such things picking the
appropriate map and ordering it. In general, the map is named for a prominent town or
physiographic feature in the mapped region.
Data
The date of a map indicates when it was produced. In some instances a map will
have been updated later. This date of revision is also indicated on the map. The date of a
map is important because it indicates how old the information presented on the map is.
14 Direction
One of the major uses of a map is for navigating between two points. To be able to do
this, one must be able to tell how the map is oriented. In the margins of a map, three
directions are typically shown by arrows. These include:
geographic north
magnetic north
grid north
The relationship of these three north directions are indicated by a small drawing in the
margin of the map. This drawing consists of three arrows emanating from a common
point. The arrow labeled N is geographic north, MN is magnetic north and GN is grid
north.
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Geographic north
The direction of North Pole, the point where the Earth's axis of rotation intersects
the surface. The accepted norm is to have geographic north oriented toward the top of the
map.
Magnetic north
The direction toward the Earth's magnetic north. The location of magnetic north is
determined by the Earth's magnetic field and does not coincide with geographic north.
The angle between magnetic and geographic north, the magnetic declination, is generally
indicated on the map. A compass points at magnetic north not geographic. When going
into the field, one adjusts one's compass using the magnetic declination on the map. Since
the Earth's magnetic field changes with time, the magnetic declination also changes. For
really old maps, the magnetic declination shown on the map may be very different from
the true declination.
Grid north
Grid north is north arrow for the Universal Traverse Mercator (UTM) system
introduced by the U.S. Army in 1947. The UTM is a rectangular grid that spans the globe
from 80oN to 80oS. Each grid spans 6o of latitude and longitude. Starting at longitude
180o and moving east, each grid is number from 1 to 80. They are designated by a letter
moving north from 80oS. Using the UTM system, any point on the Earth's surface
between 80o N to 80oS can be represented by a simple x,y designation. Because this grid
system is rectangular and longitudes converge toward the poles, the UTM N-S lines
deviate from the longitude. The far north a map the greater the deviation. The GN arrow
on the map indicates the magnitude and direction of this deviation for the map area.
15 Map Scale
A map's scale relates the size of an object on the surface to that of the graphic
representing it on a map. Without a scale, a map is virtually useless, because there is no
way to relate distances between points or the size of features on the map to those on the
Earth's surface.
Maps are generated with a wide variety of scales to fulfill a variety of purposes. A
small-scale map shows a large portion of the Earth's surface but relatively little detail. In
contrast, a large-scale map depicts a much smaller area but in greater detail. On a map
with a scale of 1:24,000, a feature 10 km in length would be nearly 42 cm long, whereas
at 1:250,000, it would be only 4 cm long. Clearly, the choice of map scale is important in
determining the area shown by the map as well as detail.
Representation
On topographic maps, scale is illustrated at the bottom in the map's margin.
Although they convey the same information, three different mechanisms are used to
illustrate scale. These are the ratio scale and several graphic (bar) scales. Each conveys
the same information but in different ways.
Typical scale legend encountered on U.S. Geological Survey maps.
Ratio scale
Ratio or proportional scales indicate number of units of length on the Earth's
surface equals the same unit of the map. Ratio scales work for all types of units which
can be chosen by the map user. On a map with a ratio scale of 1:24,000, 1 inch on the
map equals 24,000 inches on the ground. If one chooses to work with centimeters, then 1
centimeter on the map equals 24,000 centimeters on the surface. The ratio scale of a map
is indicated in the bottom margin of the map by a ratio such as 1:24,000 or 1:62,500.
Unlike other types of scales, ratio scales cannot be used to measure distance directly on a
map.
16 A map's ratio scale is calculated knowing the distances between the same two
points on the Earth's surface and the map. For example, consider a map where the top of a
ridge and the bottom of an adjacent valley are separated by 6 miles on the ground and 2
inches on a map. The ratio scale for the map is:
Graphic scale
Graphic or bar scales show a series of bars labeled with different units of length,
e.g., feet, miles, or kilometers. The bars provide visual rulers with which to measure
distance on the map. On U.S. Geological Survey maps, the bars are drawn with 0
dividing it into ten parts. Fractional units (0.5, 1.0 km) are shown to the left of the zero,
and whole units to the right (1, 2, 3, 4, 5 km). If the map is reduced or enlarged, bar
scales will remain accurate as long as the scale bars are scaled to the same amount.
Verbal scale
Verbal scales state the relation between a unit of length on the map and another,
generally larger, unit of length on the ground. One inch equals 2000 feet and 1 cm = 1000
km are verbal scales. They are derived from proportional scales and need not be precise.
The ratio scale 1:62,500 is often expressed as a verbal scale of 1 inch equals 1 mile
because 1 mile contains 63,360 inches. If the map is reduced or enlarged, the original
verbal scale will no longer be valid.
17 Large VS. Small Scale maps
One of the most confusing things about maps for occasional users is what is
meant by large and small scale maps. The definitions of these terms is, in fact, opposite
of what one might at first think. As the scale of a map changes, the area covered and
ground detail depicted change accordingly. Thus, map scale must be selected to match
the amount of detail or area the map must display to satisfy user's needs. Projects that
need very accurate representation of the surface require maps with large scales.
Conversely, if detail is not need but area coverage is important, then a small scale map is
needed.
scale
map scale
1 mi on ground 1 in on map = area
map
= __ in on map __mi on ground covered detail
1:24,000
2.64"
0.4 mi
1:62,500
1.01"
0.98 mi
1:250,000
0.25"
3.9 mi
1:1,000,000
0.06"
15.78 mi
Based on map scale, the U.S. Geological Survey defines three classes of map
scale: large, intermediate and small. The Defense Mapping Agency uses a similar
classification scheme for scale, but defines it slightly differently from the U.S.G.S. These
scales are derived from the ratio scale of the map expressed as a fraction. The size of the
scale's denominator determines the scale of the map.
Large-scale maps
Large-scale maps have a scale sufficient to show a small portion of the Earth's
surface in great detail with excellent accuracy. The denominator of their ratio scale is
small, e.g. 1/10,000. Large-scale maps are defined by the U.S. Geological Survey as
maps with scales of 1/25,000 or larger whereas the Defense Mapping Agency defines
them as maps of 1/75,000 or greater.
On large-scale map with a scale of 1:24,000, one inch on the map represents only
2,000 feet on the ground (24,000 inch x 1 ft/12 in = 2,000 ft). Thus, a feature a quarter of
a mile in length would be represented on the map by a line 0.7 inches long. At this scale,
large buildings and individual city blocks are clearly visible. Because of their scale,
large-scale maps cover relatively limited areas of the Earth's surface, e.g. 7.5-minutes.
They are, however, able to show considerable detail thereby making them excellent for
any cartographic work that relies on very accurate detail, e.g. recreation, building siting,
etc.
18 Cheyenne, WY represented at a scale of 1:24,000.
Intermediate-scale map
Intermediate-scale maps have a scale sufficient to show most of the cultural
details, e.g. roads, and, using the appropriate contour interval, topography of a region.
The U.S. Geological Survey defines intermediate-scale maps as those with scales of
1/50,000 to 1/125,000. In contrast, the Defense Mapping Agency defines them as maps
between 1/200,000 and 1/500,000. U.S. Geological Survey intermediate scale maps are
produced as quadrangle or county maps.
Cheyenne, WY at a scale of 1:62,500.
A 1:62,500, intermediate-scale map has a scale 2.6 times greater than that of a
1:24,000 series map. On these maps, the distance on the ground represented by one inch
has increased to almost a mile (62,500 inch x 1 ft/12 in = 5,208 ft). The same quarter mile
19 feature that was 0.7 inches long on the 1:24,000 map has shrunk to a quarter of an inch.
Thus, it would be hard to show features less than this length on these scale maps. Maps at
this scale span 15-minutes of latitude and 20- to 36-minutes of longitude. Although they
often have the same detail as a 1:24,000 map, space limitations on the map sheet
commonly leads to some omission or generalized of information.
Small-scale maps
Maps with scales that cover large surface areas, but with less detail are smallscale maps. Small-scale U.S. Geological Survey maps have scales of 1/250,000 or
smaller whereas the Defense Mapping Agency defines them as maps with scales of
1/600,000 or smaller.
Cheyenne, WY at a scale of 1:250,000.
On small-scale map with scale of 1:250,000, the distance on the ground
represented by one inch has increased to nearly four miles (250,000 inch x 1 ft/12 in =
20,833 ft). A quarter mile feature on this map would be only 0.005 inches long.
Alternatively, a feature a mile wide would be only 0.25 inches on a 1:250,000 scale map.
Thus, small-scale maps are useful only for showing large parts of the Earth's surface, but
without much detail. Maps at these small scales span a degree of latitude or more. They
are useful for planning projects of large scale, e.g. transportation corridors, utility
systems, etc. Once the general course of these systems are defined, large-scale maps must
be consulted to determine specific routing at local scales.
20 Reference
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Black, J., 19-, Maps and History - Reconstructing Images of the Past
Kraak, M.J. and Ormeling, F.J., 19-, Cartography - Visualization of Spatial Data
Nelson, D., 19-, Off the Map - The Curious Histories of Place-Names
Stobel, D., and W. J.H. Andrewes, 19-, The Illustrated Longitude
Wilford, J. N., 19-, The Mapmakers
National Geographic Web site: a discussion of map projections, types of maps
and the map makers tools
The Gulf of Maine Aquarium: this page describes a simple means of studying
map projections using common everyday objects.
Online Map Creation: every want to be a cartographer? This site lets you create
your own map on-line. You get to choose the location of your map, the type of
projection used and what type of surface features to show.
Picture Gallery of Map Projections: Looking for that obscure map projection
scheme? This is the place to find it.
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