USGS topographical maps are useful because they show the terrain and lay of the land as well as feature like roads, structures and mines. As you read this, it would be helpful if you also had your own topographical map to refer to.

. . . What is a Topographic Map . . .

Source: http://geology.isu.edu/geostac/Field_Exercise/topomaps/topo_map.htm

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 other features (buildings, swamps, mines, etc.) that are designated on topographic maps, but which are not described in the map legend.

Topographic Mapping

Online Edition

Source: http://erg.usgs.gov/isb/pubs/booklets/topo/topo.html

The Changing Landscape of Topographic Mapping

The U.S. Geological Survey (USGS) produced its first topographic map in 1879, the same year it was established. Today, more than 100 years and millions of map copies later, topographic mapping is still a central activity for the USGS. The topographic map remains an indispensable tool for government, science, industry, and leisure.

Much has changed since early topographers traveled the unsettled West and carefully plotted the first USGS maps by hand. Advances in survey techniques, instrumentation, and design and printing technologies, as well as the use of aerial photography and satellite data, have dramatically improved mapping coverage, accuracy, and efficiency. Yet cartography, the art and science of mapping, may never before have undergone change more profound than today.

A mapping revolution is underway. New technologies are altering the production and use of traditional maps. Even more significantly, the information age has introduced a new cartographic product that is changing the face of mapping: digital data for computerized mapping and analysis.

The computer is extending mapping beyond its traditional boundaries. New applications emerge with each technological advance. At their most basic, digital data applications make it possible to display maps on a computer, even a home personal computer. At their most advanced, digital data applications stretch the definition of cartography.

This booklet examines topographic mapping and the USGS in this changing cartographic world. It describes the topographic map, its use, its history, its production, and—in light of new technology and the digital mapping revolution—its potential.

What is a Topographic Map?

Whether on paper or on a computer screen, a map is the best tool available to catalog and view the arrangement of things on the Earth's surface. Maps of various kinds—road maps, political maps, land use maps, maps of the world—serve many different purposes.

One of the most widely used of all maps is the topographic map. The feature that most distinguishes topographic maps from maps of other types is the use of contour lines to portray the shape and elevation of the land. Topographic maps render the three-dimensional ups and downs of the terrain on a two-dimensional surface.

Topographic maps usually portray both natural and manmade features. They show and name works of nature including mountains, valleys, plains, lakes, rivers, and vegetation. They also identify the principal works of man, such as roads, boundaries, transmission lines, and major buildings.

The wide range of information provided by topographic maps make them extremely useful to professional and recreational map users alike. Topographic maps are used for engineering, energy exploration, natural resource conservation, environmental management, public works design, commercial and residential planning, and outdoor activities like hiking, camping, and fishing.

Topographic Mapping and the USGS

A longstanding goal of the USGS has been to provide complete, large-scale topographic map coverage of the United States. The result is a series of more than 54,000 maps that cover in detail the entire area of the 48 contiguous States and Hawaii.

Produced at a scale of 1:24,000 (some metric maps are produced at a scale of 1:25,000), these maps are commonly known as 7.5-minute quadrangle maps because each map covers a four-sided area of 7.5 minutes of latitude and 7.5 minutes of longitude. The United States has been systematically divided into precisely measured quadrangles, and adjacent maps can be combined to form a single large map. The 7.5-minute quadrangle map series is popular as a base for maps of many different types and scales.

Because of its large land mass and sparse population, the primary scale for mapping Alaska is 1:63,360 (1 inch represents 1 mile). Each Alaska map quadrangle covers 15 minutes of latitude. The areas covered by these maps vary from 20 to 36 minutes of longitude, depending on location. There are 2,700 maps in the Alaska 15-minute quadrangle series.

In addition to the 1:24,000-scale maps, complete topographic coverage of the United States is available at scales of 1:100,000 and 1:250,000. Maps are also available at various other scales.

The amount of detail shown on a map is proportionate to the scale of the map: the larger the map scale, the more detail shown. Since 1 inch on the map represents 2,000 feet on the Earth, 1:24,000-scale maps depict considerable detail. Such large-scale maps of developed areas show features like schools, churches, cemeteries, campgrounds, ski lifts, and even fence lines. Many of these features are generalized or omitted in smaller scale topographic maps.

Other USGS map products

Topographic maps are not the only cartographic products available from the USGS. The USGS publishes and distributes a variety of special-purpose maps. Some of these are topographic-bathymetric maps, photoimage maps, satellite image maps, geologic maps, land use and land cover maps, and hydrologic maps. Each type of map has a distinct purpose and appearance and, like topographic maps, all are available to the public for the cost of reproduction and distribution. USGS maps are not copyrighted.

Information on the types of maps produced by the USGS can be found in the USGS "Catalog of Maps."

Common Mapping Scales

The USGS and the Mapping of America

Initially charged by Congress with the "classification of the public lands," the USGS began topographic and geologic mapping in 1879. Most of the early USGS mapping activities took place in the vast, largely uninhabited Western United States.

Extreme challenges awaited these mapping pioneers. Travel was arduous and costly. Many locations could be reached only by mule pack train. Furthermore, surveying and mapping instruments were crude by today's standards. Most maps were made using a classic mapping technique called planetable surveying.

Planetable surveying took great skill and, depending on the mapping site, equal daring. Carrying a planetable—essentially a portable drawing board on a tripod with a sighting device--the topographer would climb to the area's best vantage point and carefully plot on the map those features that could be seen and measured in the field. Planetable surveying remained the dominant USGS mapping technique until the 1940's, when it gave way to the airplane and the age of photogrammetry.

Mapping in the age of flight

Mapmaking entered a new era with the use of aerial photographs and the development of photogrammetry. Photogrammetry is the science of obtaining reliable information by measuring and interpreting photographs.

The use of aerial photographs for mapping was pioneered in the 1930's, when the USGS assisted the Tennessee Valley Authority in mapping its area of responsibility. This project was the first full-scale test of the use of aerial photographs in creating maps. Aerial photographs increased dramatically during World War II when its use proved crucial for gathering military intelligence. Aerial photographs and photogrammetry led to a revolution in mapmaking. This change has significantly increased map coverage and enhanced map standardization.

Making a topographic map

Producing an accurate topographic map is a long and complex process. It can take 5 years from the identification of a mapping requirement to the printing of a large-scale map like one of the USGS 7.5-minute, 1:24,000-scale quadrangle maps. This process requires a team of professionals and a series of closely coordinated steps.

A closer look at the procedures traditionally involved in topographic mapmaking demonstrates the combination of science, technology, and artistry required to produce a USGS map.

Aerial Photography

The first step in producing a topographic map is acquiring aerial photographs of the area being mapped. A pair of aerial photographs--each showing the same ground area taken from a different position along the flight line--are viewed through an instrument called a stereoscope, producing a three-dimensional view of the terrain from which a cartographer can draw a topographic map.

Most photographs used for the USGS's topographic mapping program are now obtained through the National Aerial Photography Program (NAPP). NAPP flights are flown in a north-south direction along carefully determined flight lines. It takes 10 precisely positioned NAPP aerial photographs to provide the stereoscopic coverage needed for each 7.5-minute quandrangle map.

Every aspect of the aerial photography process requires precision and meticulous planning.

• Specialized cameras are used to meet the exacting geometry needed to faithfully reproduce the stereoscopic model. Such a camera can cost more than $250,000.

• To ensure that all NAPP photographs are at a scale of 1:40,000, NAPP flights are flown at a consistent altitude above the terrain.

• Photographs must be taken when the sky is clear and with the Sun at the proper angle for the type of ground being photographed.

• Even seasonal factors must be considered. In an area of hardwood forest, for example, it is usally best to take the photographs when leaves are off the trees so that terrain features are more clearly visible.

A pair of stereoscopic aerial photographs taken over Villanueva, New Mexico, in 1984. The originals were at a scale of 1:24,000, which are reduced here. Overlapping photographs such as these can be viewed through a stereoscope, resulting in a three dimensional view of the terrain to be mapped.

Field Survey

Technology has reduced the requirement for mapping work in the field. Gone are the days of planetable surveying when the topographer sketched the map by hand. Nevertheless, the field survey still plays an important role in making and revising topographic maps. After aerial photographs are obtained, field survey work may be required to establish and measure the map's basic control points and to identify objects that need visual verification.

Survey measurements are taken carefully to establish the control points that become the framework on which map detail is compiled. Two types of control points are needed to position map features accurately. Horizontal control points identify the latitude and longitude of selected features within the area being mapped. They establish correct scale and map orientation and allow accurate positioning of the map's features. Vertical control points determine the elevation of selected points for the correct placement of a topographic map's contours.

Rigorous standards ensure USGS map accuracy

Because engineers, highway officials, land use planners, and other professionals use USGS topographic maps as tools, map accuracy is vital. Dependable maps are also important to campers, hikers, and outdoorsmen.

The National Map Accuracy Standards were developed to ensure that Federal Government maps meet the high expectations and requirements of such users. Originally issued in 1941, the National Map Accuracy Standards apply to all Federal agencies that produce maps. These standards require horizontal and vertical map precision. For example, at least 90 percent of horizontal points tested on a 7.5 minute, 1:24,000-scale map must be accurate to within one-fiftieth of an inch on the map (40 feet on the ground). Vertical testing requires that at least 90 percent of the elevations tested must be accurate to within one-half the map's contour interval. For example, on a map with a contour interval of 10 feet, tested points must be within 5 feet of the actual elevation. These and other standards of accuracy and content ensure consistency in both the detail and the appearance of maps. They also ensure compatibility among USGS maps made at different times.

What's in a Name?

Almost 2 million natural and manmade features are identified in the USGS topographic map series. These geographic names form a primary reference system essential for the communication of cartographic information. Beyond map labeling, geographic names are part of the Nation's living heritage. The origins and meanings of geographic names, derived from many languages, show national, personal, and social ingredients of life, past and present.

Some of the oldest geographic names found on U.S. maps are from Native American languages. Names like Adirondack, Chippewa, Chesapeake, Shenandoah, Choctaw, Yukon, and the names of 28 States are derived from various Native American languages. Other names reflect the European naming traditions of the early settlers. New London, Yorktown, Grover Hill, and Lancaster are derived from English; Fond du Lac, Baton Rouge, Marietta, La Salle, and St. Louis are French; El Mirage, Guadalupe, Rio Grande, San Francisco, and De Soto are Spanish names.

U. S. Geographic names are often rich in description, local color, and national history. Names like Stone Mountain, Ragged Ridge, Big Muddy River, Carmel-by-the-Sea, Grandview, and Long Island paint descriptive pictures of the places, features, and areas they represent. Last Chance, Hells Canyon, Liberty, Thief Lake, Enterprise, Rattlesnake Creek, Dread and Terror Ridge, and Paradise Flats evoke the dreams, fears, and color of the frontier.

The standardization of geographic names in the United States began late in the 19th century. The surge in mapping and scientific activities after the Civil War left the accuracy and spelling of a large number of names in doubt. This posed a serious problem to mapmakers and scientists who require nonconflicting nomenclature. The U.S. Board on Geographic Names was established in 1890 as the central authority to deal with naming conflicts. This interagency body, chaired by the U.S. Department of the Interior, helps standardize the spelling and application of geographic names on maps and documents published by the U.S. Government.

Verifying map features

Field personnel use aerial photographs to mark and verify map features. A field check is necessary because information on an aerial photograph can often be ambiguous. For example, a worker in the field can indicate the difference between a perennial stream and one that dries up at certain times of the year. This is necessary because a perennial stream would be marked with a solid line on a map while an intermittent stream is designated by either a dash-dot or lighter weight solid line on a map. People who know the local area well, such as fishermen or farmers, are excellent sources of such information.

Another important job in the field is the verification of place names and political boundaries. This work often requires looking at courthouse records and talking to local residents. It can even include a visit to the local cemetery to check the spelling of a feature that has been named after a person buried there.

Significant changes in map content on successive editions of a map of Key Largo, Florida, illustrate why maps need revision.

Compiling the map

Upon completion of the field survey, the map manuscript is compiled using stereoscopic plotting instruments. Overlapping aerial photographs are placed in a special projector connected to a separate tracing table. The projected photographs are viewed through an optical system that causes the left eye to see one photograph and the right eye to see another. The result is a three-dimensional impression of the terrain.

Map features and contour lines are traced as they appear in the stereomodel. As the operator moves a reference mark, the tracing is transmitted to the tracing table, producing the map manuscript.

Map Separates

These illustrations show a portion of a USGS topographic map (top left) and three of the six colors used to print separate features. The green layer shows areas of woodland, and the brown layer shows topographic features, including contour lines. The purple layer shows features that are added from aerial photographs and other sources, but are not field checked.

Map scribing, editing, and printing

After the map manuscript is compiled, several steps remain before a map is completed. First, a map-size film negative of the compiled manuscript is made. This negative is then photochemically reproduced on several thin plastic sheets to which a soft translucent coating (called scribecoat) has been applied. These serve as guides for scribing.

Working over a light table, the scriber then uses engraving instruments to etch the map's lines and symbols. This is done by removing the soft coating from the hard plastic guide sheet. All features to be printed in the same color on the map—such as blue for water features—are etched onto separate sheets. A map is edited several times before final scribed sheets are completed.

Type for the words on the map is selected according to standards that will ensure consistency of type sizes and styles from map to map. Type placement is important for map legibility, so type must be carefully positioned on clear plastic sheets that are overlaid on the scribed separations. Photographic negatives are made of the type for printing.

The final step before printing is the preparation of a color proof. Multiple exposures are made of the type negatives and scribed sheets. The result looks very much like a finished map. Careful editing takes place for content, legibility, accuracy, and spelling. When the final proof is approved, the map is ready for printing.

A press plate is made for each map color by exposing the appropriate scribed sheets and type negatives. Printing is done by repeated runs of the map paper through the lithographic printing press (one for each color), or one run through a press capable of printing several colors in sequence. The largest USGS press prints up to five colors of ink on a single pass.

Most of today's topographic maps were made using these techniques, but computer technology will profoundly influence the craft of mapmaking. For example, map compilation and revision will be performed from digital images. Color separates will be plotted from digital data rather than manually scribed separates. Even the type for words on the map will be positioned and plotted from digital data.

The Digital Mapping Revolution

Computer technology will not only change the way maps are made but how they are used.

Computer-assisted map production is making it easier to produce new paper maps and to revise existing ones. The USGS is responding with innovative ways of compiling map data and using them for map production. Many of the mapmaking processes described above are being changed or eliminated. Improved efficiencies in most facets of production will shorten the 4 to 5 years it takes to produce a map by traditional methods.

Widespread acceptance of computers and related technologies has accelerated the demand for mapping information in computer-compatible form. Government agencies and private businesses now require digital mapping information for their computer-based systems.

The goal of the USGS is to stay in the forefront of the technology that will modernize the production of traditional maps while responding to the growing need for data in digital form.

Digitizing data

Most of the USGS's digital map data are collected from existing topographic maps. The task is monumental.

Map digitization resembles the original map scribing process in that it requires that each feature on each map separate be located, classified, and traced. A map can have 10 or more different layers--roads, contours, boundaries, surface cover, and manmade features, for example--that require digitization. Maps can be digitized by hand, tracing each map's lines with a cursor, or automatically with scanners.

After digitizing, several editing operations remain. For example, attribute codes must be added to identify what each digitized line or symbol represents. A variety of other tasks must be performed to ensure that information is complete and correct, including matching features with adjoining files, matching features relative to each other within the file, and controlling the accuracy of attribute coding and positions.

The National Digital Cartographic Data Base

The USGS is the principal agency developing standards and coordinating other matters related to Federal digital cartographic data. The National Digital Cartographic Data Base (NDCDB) was established by the USGS to distribute digital data that meet these standards for use in map production and in automated systems.

NDCDB data provide a framework of reference for other data about the Earth and its resources. The NDCDB data consists of digital line graphs ( DLG) and digital elevation models ( DEM). DLG's are the digital representation of information typically found on a topographic map (point locations, lines and area outlines). DEM's are matrices of elevations for ground points spaced at regular distances.

Nationwide DLG coverage is complete for transportaion and hydrographic features found on 1:100,000-scale maps and for most information found on 1:2,000,000-scale maps. The 1:100,000-scale data served as the base for the Bureau of the Census Topologically Integrated Geographically Encoded Reference files--the digital representation of the Nation used in the 1990 census.

Geographic information systems

Geographic information systems (GIS) are at the forefront of the mapping revolution. A GIS makes it possible to combine layers of digital data from different sources and to manipulate and analyze how the different layers relate to each other.

With a GIS, researchers can combine geographically referenced data from the NDCDB and many other sources and perform complex analyses that have not been possible before. GIS's are being used in applications as varied as:

• Soil conservation.. The Department of Agriculture is combining DLG information with scanned photographs and field boundary data to report and analyze soil use.

• Crime solving.. Police investigators link police record systems with geographic information to analyze crime patterns and help solve cases.

• Emergency response planning. A GIS can be used to combine transportation and earth science information to help plan emergency response to a natural disaster, such as an earthquake. By merging information on the types of roads, locations of fire stations, and locations of faults, the anticipated response times of fire and rescue squads can be calculated both under normal conditions and following transportation blockages caused by an earthquake.

• Marketing. Merging sales information with digital map data can help companies target markets or present sales information in geographic terms.

Whether used in government, business, military, or a host of other applications, a GIS provides the means to examine relationships in ways never before possible.

Where do we go from here?

With today's technology, it is possible to generate personal maps on a home computer. In the near future, traffic jams may be avoided with dashboard-mounted computer mapping systems. Beyond that may lie interactive television where local news or weather reports can be chosen by touching a map on the screen.

Digital techniques will continue to influence mapmaking, enabling more rapid production of accurate, current maps. Computers can also help us manipulate data derived from traditional maps in increasingly sophisticated ways.

The first thing to notice on a topographical map is the title. It is found in the top right hand corner of the map:

The title for this particular map is, "Sunset Crater West Quadrangle." At the corner, but in smaller print is another title called Strawberry Cheater. That is the title of the next topographical map to the northeast of this one. You will find similar titles on all the corners of a topographical map as well as halfway between the corners. Use that information to find the other maps that you may need.

The next thing that you should notice on a topographical map are the numbers running all around the outside of the map. These numbers represent two grid systems that can be used to find your exact location. The first is called latitude and longitude. The exact latitude and longitude is given at each corner of that map and at equally spaced intervals between the corners. The second is called UTM's. These are the smaller bold numbers that run along the border of the map.

Latitude and longitude is the most common grid system used for navigation. It will allow you to pinpoint your location with a high degree of accuracy. Latitude is angular distance measured north and south of the Equator. The Equator is 0 degrees. As you go north of the equator the, latitude increases all the way up to 90 degrees at the north pole. If you go south of the equator, the latitude increases all the way up to 90 degrees at the south pole. In the northern hemisphere the latitude is always given in degrees north and in the southern hemisphere it is given in degrees south.

Longitude works the same way. It is angular distance measured east and west of the Prime Meridian. The prime meridian is 0 degrees longitude. As you go east from the prime meridian, the longitude increases to 180 degrees. As you go west from the prime meridian longitude increases to 180 degrees. The 180 degree meridian is also known as the international date line. In the eastern hemisphere the longitude is given in degrees east and in the western hemisphere it is given in degrees west.

At the equator, one degree of latitude or longitude represents approximately 70 statute miles. At higher latitudes the distance of one degree of longitude decreases. Latitude stays the same because they are always equally spaces apart. If you look on a globe you will see this to be the case. On the other hand , if you look on a globe you will notice that the lines of longitude get closer together as they approach the north and south poles.

Degrees are not accurate enough to find a precise location. At best, one degree of latitude and longitude would define a 70 square mile area. To over come this problem, 1 degree is divided into 60'(minutes). So if 1 degree equals 70 miles and one degree can be divided into 60' then 1' equals 1.2 miles. Dividing 1 degree into 60' allows one to calculate their position with much better accuracy. In some instances even more accuracy is needed. To do this we can divide 1' into 60"(seconds). If 1' equals 1.2 miles and we can divide it into 60", then 1" equals 0.02 miles. It it is worth taking a few seconds to memorize the following numbers. It will help you to use latitude and longitude more effectively:

If you look at the picture above you will notice the latitude and longitude in the lower right hand corner of the map. You would read it as 35 degrees 15 minutes north latitude and 111 degrees 30 minutes west longitude.

Below the title you will notice the words 7.5 minute map. This means that the map covers an area of approximately 7.5 minutes of latitude and longitude.

UTM Stands for Universal Transverse Mercator. It is another grid system that can be used to find your position. It is most commonly used in the military and for research as well as survey purposes. The UTM system divides the surface of the earth up into a grid. Each grid is identified by a number across the top called the zone number and a letter down the right hand side called the zone designator. For example, Phoenix Arizona is in UTM grid 12 S.

Every spot within a zone can be defined by a coordinate system that uses meters. Your vertical position is defined in terms of meters north and your horizontal position is given as meters east. They are sometimes referred to as your northing and easting. In the following picture you can see the northing and easting coordinates on the boarder of the topo map. They are the small bold black numbers. Along the edge of the map the first UTM shown is 3901000 meters north. On a regular topo map the dash above that number would be blue. As you go up the right hand side of the map, the next UTM is 3902000 meters north. As you go up the right hand side of the map every time you pass a the small blue dash you have gone up 1000 meters (one meter = 3.281 feet). The same applies with the UTM's across the bottom of the map.

Map scale represents the relationship between distance on the map and the corresponding distance on the ground. The scale on the topo map is found at the bottom center of the map.

Scale is represented in two different ways on a topographical map. The first is a ratio scale. The ratio scale on this map is 1:24,000. What it means is that one inch on the map represents 24,00 inches on the ground. Below the ratio scale is a graphic scale representing distance in miles, feet and meters. The graphic scale can be used to make fast estimates of distances on the map. The space between the 0 and the 1 mile mark on the scale is the distance you must go on the map to travel one mile.

One of the advantages to using a topographical map is that it shows the three dimensional lay of the land. It does this by using contour lines. A contour line is a line that connects points of equal elevation. On the topo map they appear as the brown lines.

The contour line traces the outline of the terrain at evenly spaced elevations. These are determined by the contour interval. The contour interval is found below the map scale. For this map, the contour interval is 20 feet. That means that every time you go up to another brown line the elevation increases by 20 feet and every time you go down a brown line the elevation decreases by 20 feet. In the lower left hand corner of the map there is a mountain. Notice how the contour lines define the shape of the mountain. The lines are closer together at the top of the mountain where it is steeper. The spacing between the lines decreases as the slope of the mountain decreases.

. . . Using a Topographic Map . . .

source: http://geology.isu.edu/geostac/Field_Exercise/topomaps/topo_interp.htm

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:
1) 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.

At the lower left hand corner of topographical maps there is a symbol called the magnetic declination. The symbol is used in conjunction with a compass for navigational purposes. The center line with the star above represents the direction of true geographic north. The line coming of to the right represents the direction of magnetic north, When using a compass, the needle always points to magnetic north. The symbol tells you that for the area the map covers, the magnetic compass needle will always point 13.5 degrees to the east of true geographic north. To the left of the true north line is the grid north line. This tells you how much the UTM grid and zone lines are offset from true north.

Source: http://geology.isu.edu/geostac/Field_Exercise/topomaps/mag_dec.htm 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 walk a straight line following the direction your compass needle indicates as north, you would find that you didn’t go from south to north on the map. How far your path varied from true north depends 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 below, 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). The map below shows lines of equal magnetic declination throughout the U.S. and Canada. The line of zero declination runs from magnetic north through, acrosse the western tip of Lake Superior and across the Mississippi Delta.  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.

Source: http://www.cnrhome.uidaho.edu/default.aspx?pid=68697

• REMEMBER that a compass points NOT to True North, but to Magnetic North. The difference between the two varies both according to where you are in the world, and because Magnetic North is slowly changing its position. To take accurate bearings, you need to know these variations, but even a rough idea of orientation will help you to match your map to the landscape. If you have an adjustable compass and information on the magnetic declination of your map grid from True North you can carefully match them up so that even in poor visibility, or where landscape features are beyond your horizon, you can take accurate bearings.

• MAGNETIC DECLINATION & TRUE NORTH: An important item on the map is the magnetic declination diagram shown in the margin towards the bottom left of a topographic map. This will have a star with a straight line representing the North Star and a line to the right of it or left of it depending on where you are, to denote the magnetic declination you MUST apply to correct your compass in order to use the map for true headings. Another line with a GN will also appear which represents the Geographic North. The North Star is actually offset in one direction or the other depending on where you are. The diagram is used to compute your true directions by compass on that particular map.

There are a few basic rules to follow in order to do this.

1. To change magnetic to true headings you will add East declination and subtract West declination.

2. If you want to convert from True to Magnetic you will subtract East and add West.

 

This appears confusing, so let's use a map of an area as an example.
The topo map has a declination angle at the bottom of the page which shows True North by using a star and a straight line as mentioned above. The declination for this particular area shows a 1 degree ** East declination from True North.  A reading with the compass will give a Magnetic North and if this is followed you would end up * degrees too far East. 
To convert Magnetic North on the map on the compass to coincide with True North on the map, add *degrees to whatever reading is obtained on the compass and you will be back on course.

• AZIMUTH ??? OR DIRECTION ANGLE:   What is an Azimuth? It is an angle measured in degrees in the clockwise fashion around a circle; this angle is formed by the Geo. North line and by the direction line of your walk. If you have a compass at hand, an Azimuth is the number of degrees between the colored point of the needle of your compass (taking into account the magnetic declination) and the Imaginary line which starts from the center of your compass aiming towards the object you want to reach. Ex: tree, rock etc. You can then say that this tree has such an Azimuth degree.

For example: an Azimuth of 90 means you are going East and an azimuth of 270 means you are going West. If you want to try the compass, place yourself in an open space and follow the Azimuth 45 for 20 steps then come back on your steps ALWAYS using the compass. You will then notice that you are following the Azimuth 225. You will ALWAYS notice a difference of 180 degrees.

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The Township and Range system, sometimes called the Public Lands Survey System, was developed to help parcel out western lands as the country expanded. The system takes many western states and divides them up using a base line and a principal meridian:

As you go to the east or west of the principal meridian, the range increases in that direction. If you go north or south of the base line, the township increases. This system divides the land up into townships and ranges that are 36 square miles each. In the diagram above, the square with the X in it would be defined as township 2 south (T.2S), range 3 east (R.3E). Each township and range is then subdivided into 36 sections. Each section is one mile square. Individual sections are then subdivided into half sections and quarter sections and so on. On a topo map, you will notice a grid with red lines and text crisscrossing the map. The lines represent the boarders of the various sections in the township and range of that area. In the map below you can see sections 23, 24, 26 and 25 of T.22N, R.7E.

. . . 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 1700s.  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 useful in that 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*, early surveyors established a principal meridian running north-south, and a base line running east-west. These initial survey lines served as a basis for subsequent survey lines spaced at 24 mile intervals along the eastern, western, and southern boundaries. (Why not the northern boundary as well?  hint:  Think of the relationship between latitude and longitude).  Further subdivision of these ‘squares’ led to the creation of 16 smaller squares measuring six miles on a side (see the diagram, hopefully it will clear this up). When measuring in a north-south direction, each of these squares is called a township (in some localities a township is referred to as a tier).  When measuring in an east-west direction, each of these squares is called a range.  So, a 36 square mile area located between six and twelve miles east of the principal meridian and twelve to eighteen miles north of the base line would be called township (or tier) three north, range two east (written as T3N., R2E). Each township (tier) is further subdivided into 36 smaller squares covering roughly 1 square mile.

There are many other symbols on USGS topographical maps. Here are some of the most common: