Maps and Scales

Contents

A. Map Scale

B. Measurement Scales

C. Accuracy, Precision, and Significant Digits

D. Classification, Simplification and Symbolization of Data

---

A. Map Scale

Map scale is the relationship between a unit of length on a map and the corresponding length on the ground. We will use concepts of map scale throughout the course, so it will pay you to study this section carefully.

1. Types of Map Scales

We can relate map and ground with three different types of scale. Verbal scale expresses in words a relationship between a map distance and a ground distance. Usually it is along the lines of:

One inch represents 16 miles.

Here it is implied that the one inch is on the map, and that one inch represents 16 miles on the ground. Verbal scales are commonly found on popular atlases and maps.

The second type of scale is a graphic scale, or bar scale. This shows directly on the map the corresponding ground distance. For example:

The third type of scale is a representative fraction, or ratio scale. Compared to the first two, it is the most abstract, but also the most versatile. A representative fraction, or RF, shows the relationship between one of any unit on the map and one of the same unit on the ground. RFs may be shown as an actual fraction, for example 1/24,000, but are usually written with a colon, as in 1:24,000. In this example, one unit of any length (one mm, one cm, one inch, one foot, etc.) on the map represents 24,000 of those same units on the ground (24,000 mm, 24,000 cm, 24,000", 24,000', etc.). The RF is versatile because you are not tied to any specific units. You may work in any unit you choose, either metric, English, or other.

The RF is a called a fraction because it is just that--a fraction that shows how much the real world is reduced to fit on the map. A good comparison is often made with scale models of automobiles or aircraft. A 1/32-model of an auto is 1/32nd as large as the actual auto. In the same way, a 1:100,000-scale map is 1/100,000th as large as the ground area shown on the map.

A related idea is that of small scale versus large scale. Geographers use these terms differently than many people. A large scale map is where the RF is relatively large. A 1:1200 map is therefore larger scale than a 1:1,000,000 map. The 1:1,000,000 map would usually be called a small scale map. This is true even though the 1:1,000,000 map would show a much larger area than the 1:1200 map.

Here is a rule of thumb for size of scale by RF:

Size of Scale	Representative Franction (RF)
Large Scale	1:25,000 or larger
Medium Scale	1:1,000,000 to 1:25,000
Small Scale	1:1,000,000 or smaller

Of course, what is small or large scale is relative. I noticed a surveying text (Brinker & Wolf, 1984) that classed anything smaller than 1:12,000 as small scale -- surveyors rarely work with anything smaller than this.

The large/small scale terminology can become confusing when talking about large versus small areas. If you are talking about a phenomenon that occurs across a large region, it is tempting to say it's a large-scale phenomenon (e.g., "the forest blight is a large-scale disease"). But since the map that would show this would be small-scale, it is better to use a different term to avoid confusion. My favorite is "broad-scale."

Many maps include two or even all three types of scales. USGS topographic maps have both bar scales and RFs.

2. Converting Between Scale Types

If you are given one type of scale, you should be able to derive or construct any of the other two. This takes some practice, and some problems are included in your lab exercises. Some examples are given below.

A vital step in doing any kind of conversion that involves differing units is to include the units in the problem itself. You can then cancel the units by multiplying or dividing. This way you avoid becoming confused about which conversion factors to use and how to use them.

Verbal Scale to RF

The key here is to write the verbal scale as a fraction, then convert so that both numerator and denominator have the same units, and the numerator has a 1.

(a) Convert verbal scale of "1" to 18 miles" to RF

or 1:1,140,000.

Notice that the resulting fraction is rounded so that the RF does not imply more accuracy than the original precision warranted.

(b) Convert verbal scale of "15 cm to 1 km" to RF

or 1:6700.

In many conversions you can save steps if you remember additional equivalencies.

For example, in (a) above, we could have used the fact that 1 mile = 63,360 inches to skip a step.

Verbal Scale to Graphic Scale

Usually this is a relatively easy task if the map gives us reasonable units in the verbal scale. We can use the verbal scale like a fraction to transform the ground distance to map distance.

(c) Convert verbal scale of "1 cm to 14 km" to a graphic scale.

One centimeter is a relatively small distance, so we probably don't want our bar scale to have major divisions much smaller than this. A centimeter represents 14 km, so a division of 10 km is probably fine. Therefore we want to find how many centimeters represent 10 km.

In other words, we can represent our 10 km increment on the bar scale by measuring off 0.71 cm on the map. We'd draw the first tick at 0.71 cm, the second at 1.42 cm, and so on:

RF to Graphic Scale

This adds an extra step to the example above. We can find the map-distance equivalent of a ground distance, but we also need to be careful about choosing which ground distance we want to portray on the map. Perhaps it's easiest to choose a smaller ground distance that you can then multiply to get a reasonable bar scale.

(d) Convert an RF of 1:250,000 to a graphic scale

If we aren't sure what increments a bar scale would have for this scale, we could start out, say, with finding the map equivalent of 1 mile:

This might work fine, with one mile marked off on the map every 0.25 inch; or, we may want finer or broader increments, which we can find by dividing or multiplying the .25" as needed.

RF to Verbal Scale

Again we have to choose appropriate units to convert into. Most verbal scales are either "one inch represents ____ miles," or "one centimeter represents ___ kilometers." These are relatively easy to do, since it means only that we convert the denominator of our RF to the larger units.

(e) Convert from RF of 1:25,000 to a verbal scale, in metric

Therefore,

1 centimeter on this map represents 1/4 of a kilometer on the ground.

Graphic Scale to RF

Here we must take a measurement from the bar scale to determine the map distance that corresponds to a ground distance.

(f) Find the RF scale for the following graphic scale

By measuring with a ruler, we find that 10 kilometers measures 2.4 cm. We can use this relationship to find the RF for the bar scale:

3. Determining Scale from a Map or Photo

Some maps may come with no scale at all. Aerial photographs almost never do (unless one was painted on the ground before the photo was taken!). How can you derive a scale for use with the map or photo?

Actually the procedure is very similar to the last example above. But instead of measuring along a bar scale, you must measure the length of an object on the map or photo whose actual length you know. This might be a football field, a city block, or the Equator (if it's a world map). Often you can identify 1-mile-square sections in the US (see the account below, under Survey Systems). You may even need to go out to the location mapped or pictured and measure the distance between two identifiable objects.

Once you have the two distances, you can find the scale as above. For another example, suppose you have a map where the distance between two section-line roads is 3.5 inches on the map. We can usually assume this is one mile on the ground (there are exceptions). The RF scale is then:

One caveat (exception) for air photos is that this method assumes the two locations are at the same elevation--or that the terrain is flat. If you are using air photos, the terrain may not be flat. If there are hills, even moderate ones, the calculations can be thrown off. Keep this in mind for later in the course.

Another way to calculate scale on an unknown map or photo is to compare it to a map with a known scale. For example, suppose you have an air photo where the distance between two hills is 7.2 centimeters.You have a map of the same area at 1:24,000, and on the map the distance between the hills is 2.4 centimeters.

The answer involves a little algebra. Since the ground distance is the same on both photo and map, we can create an expression for this ground distance for both, and then put them on either side of an equation. The ground distance can be found by multiplying the map/photo distance by the scale (in this case, by the inverse of the scale--notice how this makes the units cancel correctly). We need to find, for the photo, how many ground units are represented by one unit on the photo, so we use an x for this unknown quantity and solve for it:

we can cancel the units on each side and divide by 7.2:

In other words, the RF scale for the photo is 1:8,000.

4. Determining Distance and Area from Map & Scale

Map scale isn't much use in and of itself. We can use a map's scale to determine distances and areas on the map. Compared to converting between scale types, calculating distance is simple. Area calculations are trickier, since we have to square the numbers.

Finding distance from map and scale

As an example, suppose we have a map with a scale of 1:50,000. We measure the distance along a property boundary as 1.7 cm. What is the length in the real world?

To find ground distance, we must use the map scale to convert map distance to ground distance. Notice that again we inverted the RF scale, so the units will cancel properly. Once we multiply by the scale, we need to convert the ground distance to units suitable for ground measurement--in this case, from centimeters to kilometers.

We can also calculate distance from verbal and graphic scales. With verbal scales, we use the same procedure as above with the RF. The only difference is that we have to use the units given in the verbal scale (e.g., 1 inch to 17 miles). We'd probably want to measure our map distance in the same units (in this case, inches) to make our conversion easy.

Graphic scales are probably the scales most frequently used by laypersons. You can mark off a distance on the map and compare it directly to the bar scale. You need not know how many inches or centimeters the map distance is. The main drawback of bar scales is that they are usually short compared to the map itself, and hence measuring longer distances is difficult.

Finding area measurement from map and scale

Area must be expressed in areal units, which are usually distance units squared -- cm² , mi², and so on. We must therefore used squared conversion factors when finding area from map measurements.

For example, suppose we measure a rectangular piece of property that is 3 cm by 4 cm on a map. The map is at a scale of 1:24,000. What is the area of the parcel?

The area of the parcel on the map is

on the ground.

Since this is a large number, we might want to translate to other units. There are 10,000 square meters per hectare, so the area is 69 hectares (ha) (a hectare is about 2.5 acres). Or, there are (1,000)² = 1,000,000 square meters per square kilometer, so the area is also 0.69 km².

Notice that by writing the units as part of the problem, and squaring them along with the numbers, our units cancel properly and we end up with a sensible answer.

There is another way to tackle area problems if you have distance dimensions like 3 x 4 cm to start out the problem. You can convert the distance dimensions to real-world distances first, and then multiply them to find the area. This makes the problem longer but perhaps simpler.

B. Measurement Scales

1. Definition

Any type of information on a map (or in a table, a list, a survey, etc.) can be described in terms of how pieces of the information can be related to each other. Examples of mapped information include land-use classes, road classes, city populations, and county areas.

We can think of these types of information as either categorical (or qualitative) or numerical (or quantitative). Categorical information can only be described qualitatively, whereas items of numerical information can be compared quantitatively. That is, numerical information is on a real scale, such as distance (e.g., kilometers), area (e.g., hectares), or temperature (e.g., Celsius).

• Example of categorical information:
• Land-Use categories of :
• 1= forest, 2 = grassland, 3 = urban;
• We cannot say that based on the classes, 1 + 2 = 3 !
• We can only use the numbering to describe the items qualitatively.
• Example of Numerical information, city populations:
• Springfield = 100, Harmony = 200, Centerville = 300;
• We can say that Centerville has as many people as Springfield and Harmony.

2. Four Measurement Levels

The categorical and numerical types have traditionally been further broken down, each into two levels of measurement:

Categorical information can either be nominal level or ordinal level . At the nominal level, categories simply describe different types of things, and cannot be compared to each other. Ordinal-level categories can, on the other hand, be ranked against each other.

An example of ordinal level would be road classes of interstate, primary, secondary, and primitive; although two primary roads don't make an interstate, you could say in a sense that interstates are at a higher level than the others, at least in terms of expense to build!

The land-use classes would be an example of nominal-level measurement. You probably wouldn't rank the classes against each other (unless you prefer one over the other, in which case they could be ordinal!).

Numerical information can either be interval level or ratio level . This distinction is subtle, and borders on artificial. The only difference is that ratio-level information is on a scale that includes a true zero, that is, a zero that truly represents a lack of whatever it is you're measuring.

One of the few common examples of an interval scale is temperature. You can compare two temperature readings quantitatively. For example, 20 C is 15 degrees warmer than 5 C. But the Celsius scale has an arbitrary zero point (the freezing temperature of water, or 32 F). 0 C doesn't mean a lack of temperature. For this reason, 20 C is not four times as warm as 5 C! (One temperature scale, Kelvin, does feature a true zero -- 0 K is -273 C, the temperature at which all molecular motion ceases). Fortunately, there are few examples of this on maps. You might want to include an exception for elevation, which can be below sea level, or longitude, where the 0° line (Prime Meridian) is arbitrarily drawn on the globe.

Table 2: Measurement Levels

	Measurement Level	Description	Examples
Categorical	Nominal	Simple categories; cannot rank categories	Colors; land use types; computer components
Categorical	Ordinal	Distinct categories; can rank categores in order	Road classes; flavor preferences
Numerical	Interval	Continuous scale; measure with numbers; real zero	Temperature; longitude, compass direction
Numerical	Ratio	Continuous scale; measure with numbers; real zero	Distance; weight; bank balance

Most numerical scales are ratio-level. We can compare 20 km with 10 km in any number of ways, including saying the first is twice as far as the second.

3. So What?

We will use this terminology frequently to describe the kinds of information on maps and in other sources. You will also encounter it elsewhere, I guarantee it!

Information often is translated from one level to another. The general rule is that it's easier to translate to a lower level (e.g., from ratio to ordinal) than to a higher level. In most cases, it's impossible to go legitimately to a higher level. Why bother using a lower-level scale? Often it saves space and energy to use a lower scale.

For example, if you have a table of city populations in Sonoma County (i.e., ratio level) and want to show population on a map, you could print a number next to each city name. This would preserve your ratio-level data on the map itself. A more common technique is to have a set of increasingly large symbols for the city location, each symbol indicating a range of population. These symbols would give ordinal-level information about population. This conveniently reduces the clutter on the map, but you cannot recover the original ratio-level numbers from the map.

C. Accuracy, Precision, and Significant Digits

1. Accuracy versus Precision

Some people make a distinction between accuracy and precision.

Accuracy would be how close a measured value is to the actual value.

Precision would be the number of digits reported with the value. For example, I added a thermometer to my car that shows the outside temperature to tenths of a degree (e.g., 65.2° F). The thermometer's precision is to tenths of a degree Fahrenheit. But it often seems to give readings that are too high, perhaps due to the engine's heat nearby. Its accuracy, then, might only be to within 5° F.

2. Significant Digits

Significant digits are the number of digits in a value that have real meaning and reflect the accuracy of the value or measurement. For example, a distance measurement of 45.8 km would have three significant digits. The value implies that the measurement was made to an accuracy of tenths of a kilometer. If the instrument, such as an odometer, is not accurate, the value should not include as many significant digits. Of course, if the instrument measures more accurately than this, the value should be reported with the appropriate precision.

The main point is to beware measurements with highly precise values when the accuracy could be called into question. This is especially true when converting values from one kind of scale to another. For example, if I measure a map distance as 11 inches with an ordinary ruler, then want to convert to centimeters, I find on my calculator:

(11 in.) * (2.54 cm/in.) = 27.94 cm

But 27.94 cm implies high accuracy, which I didn't have with the original measurement. The solution here is to round the answer to about the same number of significant digits as the original measurement. In this case, I should probably say the distance is 28 cm.

More example of significant digits:

• Two significant digits: 3700, 37, 3.7, 0.37, 0.0037
• Four significant digits: 19120, 19.12, 0.001912, 19.00, 0.1900

Notice that zeroes added after the decimal point imply precision equal to any other digits. Normally, zeroes to the right of other digits (e.g., 3700) are not considered significant, unless a decimal point is added and more zeroes occur to the right of it (e.g., 3700.0 implies 5 significant digits). What if we have a measurement of 1900 where the zeroes are significant? Traditionally, a bar is placed over the zeroes to indicate significance.

Another solution is to use scientific notation.

For example, 3700 with the zeroes actually being significant can be written as 3.700 x 103. This breaks the number down into the mantissa (the significant digits, here 3.700) and the exponent on the ten (here 3). In scientific notation, only one digit is placed before the decimal point in the mantissa. The exponent on the 10 indicates how many places the decimal point should be moved to restore the number to ordinary notation (in this case, three places to the right; this is equivalent to multiplying the mantissa by 1000). Negative exponents mean smaller numbers, and we shift the decimal point to the left. For example, 3.700 x 10-4 is the same as 0.0003700. Scientific notation is handy with very large or small numbers. Numbers in scientific notation can be used just like other numbers, as long as you follow the rules of exponents -- for multiplying, dividing, etc.

D. Classification, Simplification and Symbolization of Data

This is not a course in cartography, so we will not deal in detail with how data is classified and simplified for mapping, and how symbols are created to suit those data. But you should be aware that any map, including topographic maps, is the result of a lot of processing of the data behind the map. Here is a brief discussion of some elements that go into data processing for maps.

1. Classification

Maps must take the relevant data and assign it to a given number of classes, each with its own number of members. Examples are maps of land uses and of temperature. For categorical data like land uses, it is easy to overload the map reader with too many classes. Cartographers recommend a maximum of five or six different classes (for land use, these might be forest, rangeland, cropland, water, and urban). Numerical data shown on isarithmic maps (which show zones of equal values) can be somewhat more complex. For example, temperature zones can trend from 80's F to -20's F. But the data should be shown with logical symbolization (see below).

Data can be broken down into categories in three ways:

(a) Each category can have an equal number of members. For example, in a map of US population by state, we could have five categories of population, each with ten states.

(b) Each category could span an equal interval of values. In the population map, we would take the range of populations (highest state minus lowest state), and divide the range by five. Each category would be one-fifth of the overall range. In this map, categories may have different numbers of states. The highest category may only have a few states (e.g., California, New York and Texas), and other categories may have a large number of states.

(c) Finally, we could subjectively assign states to classes, perhaps by looking for "natural breaks" in population rankings. Often map-makers start out with one of the first two methods, then refine it by looking at the results and changing classes slightly. All of this should reflect the purposes of the map. Different methods can produce radically different-looking maps (see any cartography text for examples).

2. Simplification

A second major task in map-making is simplifying the information behind the map. Classification is one way of simplifying the data we use going into the map. Often this involves lowering the measurement level of the data (such as transforming ratio-level data to ordinal-level data, as in our example of city populations indicated by various circle sizes).

Another simplification task relates to the spatial aspects of the data. For example, mountainous roads may take many twists and turns. A map that shows all these curves would be cluttered and messy. We may want to generalize the road spatially to clarify things. Beware, of course, those map users who curse you for those curves they didn't expect! The cartographer's job is to simplify without distorting and misleading the map user.

Sometimes the task may necessitate eliminating features altogether. For example, a small-scale US map can show only selected cities; how do you choose which cities to include without offending too many people? I saw a US map recently that included moderate-sized cities but omitted my hometown, San Diego (now the 6th largest city in the US).

3. Symbolization

Symbolization of information is another crucial part of communicating through maps. What symbols are chosen will influence whether will people will understand, or even use, a map. Symbols should be chosen so that the intended audience will understand them. Different symbols should be used for general-purpose maps than those intended for specialists in a field.

Symbols can be placed on a continuum between intuitive and abstract. Intuitive symbols suggest to the reader what they represent. Pictographs are recognizable representations of the actual objects. For example, marshes are often shown with swampy grass symbols, or airports as planes. On the other extreme are abstract symbols with no obvious connection to what they represent. Examples are circles as cities, or streams as dotted lines. Some abstract symbols have been used so widely to represent a particular feature that, although abstract, they do connect with the object in most people's minds. A star within a circle, for instance, usually means a capital city.

Symbols can also be classed according to their dimension: point (0-dimension), line (1-dimension) or area (2-dimension) symbols. Like the other two, point symbols can convey categorical or numerical information. Examples of categorical point symbols are airports, campgrounds, springs, and quarries. Variable-sized circles for city population would be examples of numerical point symbols.

Line symbols can convey information about linear features, such as roads, railroads, and streams. Another important use of lines on maps are isolines. Isolines (also called isarithms) connect points of equal value. You'll often see these on a map of temperatures on the weather page of the newspaper. Every place along an isoline on this map has the same temperature, at least theoretically. This implies also that places between two isolines have values somewhere between the values of the surrounding lines. Without additional information, we cannot say with confidence much more about intervening values. We can estimate, or interpolate, the intervening values, for example by measuring the distance of a point from each line. There is no guarantee, of course, that our estimate is really correct, so beware such estimates from isoline maps.

An important type of isoline for this course is the elevation contour . These isolines show equal elevations, and are included on all USGS topographic maps. The contour interval is the height difference between each contour. Contour intervals on USGS maps vary depending upon the terrain. Common intervals on 1:24,000-scale maps are 20, 40 and 80 feet. A 20-foot interval would show, for example, contours at 0 (sea level), 20, 40, 60, 80, and so on.

It takes some practice to feel comfortable working with elevation contours and other isoline maps. We will have lab exercises to give you some practice with them, including visualizing terrain and constructing profiles, or two-dimensional views of how elevation changes on a line across the topographic map.

The zones between isolines are often shaded or colored to portray the information more effectively. Temperature maps in most newspapers are now in color, with warmer zones getting "warmer" colors, colder areas "cooler" colors. These shaded-isoline zones are a blend of line and area symbols.

Speaking of color and shading, let us cover one final point about map symbolization. The rules about using color and shading are different for nominal versus higher-level data (ordinal, interval, and ratio). If you are mapping nominal-level data, the categories have no particular order, and you probably want to maximize the contrast between categories. Land uses, for example, should be portrayed so that you can separate urban, suburban, forest, and pasture, or whatever categories you include on the map.

Ordinal, interval or ratio data should be mapped differently. Here there is a definite ordering of categories. To use the temperature map again, we have a trend from warm to cold in the zones we portray. We want the map reader to immediately appreciate this gradual trend in the data. Therefore we select an ordering of colors or symbols that conveys this continuous trend in the data, for example: red-orange-yellow-green-blue-violet.

Many people make the mistake of thinking they should select colors that maximize contrast between categories, even with ordinal or higher-level data. Beware this mistake! You may be able to pick out categories easily with this approach, but you destroy the impression of a trend in the data.

Projections and Survey Systems

Contents

A. Projections

B. Coordinate Systems

C. Survey Systems

---

A. Projections

1. Background

You can't squash a grapefruit peel flat without breaking it into many pieces (try it sometime). In the same way, we cannot transfer the spherical surface of Earth to a flat surface without distortion. We can create a logical way to transfer coordinates from the sphere onto a flat map. Such ways of transferring coordinates are known as projections, after the original method of transferring by literally projecting a light through a globe onto a surface. But no projection can accomplish its task without some distortion. Fortunately, we can choose to preserve certain qualities that a globe possesses. But in the process we sacrifice other qualities.

Before we project the actual Earth onto a surface, we usually simplify it. Earth isn't a perfect sphere. It's somewhat flattened at the Poles, so an ellipsoid represents Earth better (an ellipsoid is formed by rotating an ellipse around one of its axes). Actually, the diameter at the equator is only about 42.8 km more than the polar axis. But it is enough to throw off exacting measurements, like property lines.

An ellipsoid is still not perfect; the geoid is an irregular, but even closer, representation of Earth. It's the equivalent of mean sea level all over the globe. Since gravity and Earth's surface are irregular, the geoid is not a smooth surface, and can't be represented with equations easily, so it's rarely used for mapping.

A particular ellipsoid, with particular values for equatorial and polar diameters, is often used in projecting and measuring on Earth, particularly for highly accurate measuring such as in surveying. A dozen ellipsoids are in common use around the world, including:

• Clarke Spheroid of 1866, used in most of the North America. It was revised earlier this century, with the results called the North American Datum of 1927, or NAD27.
• Geodetic Reference System 1980, a new ellipsoid, is being adopted in North America to correct inaccuracies in NAD27. The resulting "datum" is called the North American Datum of 1983, or NAD83.
• International Ellipsoid, from 1924, used in most of the rest of the world (but developed in the US from US data!).

2. Methods of Projection

Many projections can be visualized as literally projecting a light source through a transparent globe onto a surface. The light source can be any number of places - at the center of the globe, at the opposite side of Earth, or out in space, for instance (see figure below for examples). The map surface onto which the projection is made can be various shapes, and can also be at various places. In all projections, the map surface touches the globe at at least one point. This is because any map is most accurate where it touches the globe; there is no distortion here. The contact point between globe and map is called the point of tangency; if it is a line, it's a line of tangency, standard line, or (if it is a parallel) standard parallel. Away from the tangent locations, the map surface gets further from the globe, and hence more distorted. Most all projections nowadays are done by computer using equations that relate lat/long to x/y coordinates on the map.

Projections may be made onto three basic shapes, with three types of projections resulting:

a. Planar

Also called azimuthal. In this case, the globe is projected onto a flat surface. The "light source" can be from several locations. Usually, the flat surface touches the globe at a single point. Most often planar projections are used for Polar regions, and the tangent point is the North or South Pole.

b. Cylindrical

Here a cylinder is wrapped around the globe, usually with the map surface touching the globe at a circle (a great circle, to be exact -- a circle whose center coincides with the center of Earth). Cylindrical projections are the only one of the three main types that can show the entire globe, and so most world maps are cylindrical.

The most famous cylindrical projection is the one named for Gerhardus Mercator, who developed it in 1569. It was valuable for early navigators, since straight lines on a Mercator map are also compass headings. Unfortunately, it greatly distorts the sizes of areas near the Poles (see section 3 below), so it should not be used as a general--purpose world map!

c. Conical

The third type of projection is made onto a cone. Usually this means contacting the globe along one of the parallels (lines of latitude), i.e., a small circle. Although we cannot use conic projections for a world map, they are excellent for continent--sized areas in the mid--latitudes. Most maps of the United States are made with conic projections.

Conic projections are usually made more accurate by "sinking" the cone part way into the globe (remember, this is all done with computers, not literally!). Then we have two lines of tangency, or two standard parallels, along which the map is extremely accurate. This two--line approach is also called the secant case, as opposed to the simple tangent case. You may see maps of the US with a statement on the bottom like: "Lambert Conformal Conic Projection, 48° and 33° Standard Parallels." The projection was developed by J.H. Lambert (1728--1777), an important figure in cartography.

d. Other

Some projections are not based on any of the above three shapes, and cannot be visualized as literally being projected. Instead, they simply have equations that tell where to plot each latitude/longitude coordinate from the globe. Some examples are the Sinusoidal and van der Grinten projections. World maps are often made with these projections, since they may have less distortion than cylindrical projections.

3. Qualities of Projections

The other major factor you need to know about a projection is the qualities about the globe that the projection either preserves or distorts. Most projections can preserve one or more of the following qualities, but none can retain all of them. Note that the projection method (planar, cylindrical, or conical) does not necessarily mean any of these qualities below are preserved or distorted. It all depends on how the projection is done.

a. Equal-Area

Some projections show all areas in true proportion to their real areas on the globe. For example, a dime placed on the map would cover the same area regardless of where placed. To show areas truly, a map must distort most of the other qualities below, at least subtlely. But if you need a general--purpose map of the world or continental area, an equal--area map, or a map that is very close to equal--area, is your best bet. Some examples: Sinusoidal, Albers Conic Equal--Area, and Lambert Azimuthal Equal--Area.

b. True Shape, or Conformality

Another important characteristic of the globe that can be distorted on a map is the shape of areas. This distortion problem is obvious on a cylindrical map that is equal--area, because the higher latitudes near the Poles have to be distorted to preserve areas. The Mercator projection is conformal, but at the expense of area. The Mercator shows Greenland almost as large as South America, when in reality it is about 1/8 the continent's size. Some people have accused developed nations (which are mostly in the higher northern latitudes) of intentionally portraying their lands as larger than developing countries (which are mostly in lower, tropical latitudes). One projection, known as the Peters projection, has been promoted as the "true" world map, since it shows countries with true areas. Peters is indeed equal--area, but does a number on shape-as one person put it, it makes the world look like it was hung on a laundry line. Many other equal--area projections are available that do a better job with shape.

c. True Scale

In no map can you use one scale accurately for the whole map. Some distortion occurs, although it is slight in many maps. Some projections can preserve true scale and distance along one or more lines. These are may be called equidistant projections. A popular planar projection for polar areas is known as the Azimuthal Equidistant, which has true scale from the central tangent point-the Pole-to any other point on the map. You could also use an Azimuthal Equidistant map centered on your location to measure distances accurately to any other place on the globe. Some map software can draw such a map for you.

d. True Direction

The last major quality of maps is direction. Maps that preserve it are called azimuthal. Most planar projections preserve true direction away from the center of the map (usually the Pole) and so azimuthal is nearly synonymous with planar projection.

e. Other Qualities

Some projections are designed to have specialized qualities. The Mercator projection is one: all constant compass headings (rhumb lines, or loxodromes) are straight lines. The Gnomonic projection is another: all great circle routes are straight lines. As you may know, great circle routes are the shortest distances between points on the globe. For example, when you fly from San Francisco to London, you don't fly along a parallel of latitude, but over the polar route; this is along a great circle. If you're flying or sailing, then, you can combine the gnomonic and Mercator maps for navigating. First you draw your route on the gnomonic map (a straight line connecting the two places), then transfer the route to the Mercator map as a series of straight segments that approximate the gnomonic line. This way, you can follow the straight segments on the Mercator map with a compass, and turn only when you need to follow the next segment. You may notice this when you're flying and the pilot periodically turns to follow these segments.

B. Coordinate Systems

How can we describe locations on Earth? If someone asks you, "where is Hawaii?", what do you tell them? You can give them directions relative to your position ("swim 2000 miles south--southwest"). Other ways are also possible, but what if you needed to pinpoint a location for people coming from many directions? Or if you wanted to record a location for later reference? Or if you had no landmarks to guide you? This is the purpose of coordinate systems. They are ways of describing locations on Earth in reference to an established grid. You have probably been exposed to the most common method, latitude/longitude, but there are many other methods in use.

1. Latitude & Longitude

The latitude and longitude system is also called the geographical grid. This grid exploits the fact that Earth is nearly a sphere, and that it spins on an axis. Looking down on the globe from above the North Pole, we can fit a circle to the rotating Earth. We could assign each location along any circle that surrounds the Pole a measurement in degrees. A circle has 360 degrees. We could use this range of numbers, going from 0° to 360°. Alas, early map--makers didn't do this, exactly. They wanted low numbers on both sides of the Prime Meridian (the 0 line). As a result, the globe is divided into hemispheres, each assigned longitude between 0° and 180°, with the addition of East or West to differentiate the halves. The lines of longitude are meridians.

To complement the east--west measurement, a north--south measurement is necessary, so that we may pinpoint locations. Since we only need to measure along one meridian, we only need to assign measures to a half--circle, or 180 degrees. Once again, it's more complicated than necessary. Rather than go from 0° at the North Pole to 180° at the South Pole (or vice--versa), the system starts with 0° at the halfway point (the Equator), and measures north and south to 90° at the Poles. Each line of latitude is a circle; these lines are called parallels (sensible, since they are parallel to one another).

With this system we can pinpoint any location on Earth. Since a degree of latitude spans about 111 km, each degree can be broken down to get more exact. A degree is composed of 60 minutes (60'), and a minute is composed of 60 seconds (60') -- just like a clock. Based on this system, SSU lies at 38° 20' 46" N, 122° 40' 30" W. If you're uncomfortable with this system, you should practice looking up locations on a globe or atlas.

Lat/long is cumbersome to use for at least two reasons. First, notice that meridians converge at the Poles. A degree of longitude decreases from about 111 km at the Equator to 0 at the Poles; 1° is about 88 km in Sonoma County. Convergence makes lat/long poor for use as a rectangular grid, where we want simple x,y coordinates for locations. Second, lat/long is not a decimal system. How far is it from 114° 34' 54" to 116° 14' 33"? Not very far, but you'd have trouble giving me the distance even in terms of degrees/minutes/seconds. For these reasons, lat/long is usually replaced by other coordinate systems, especially at the local level, for most descriptions of location. Most of these systems, including those below, use a projection of the globe onto a flat surface, onto which we can then draw an x/y grid.

2. State Plane Coordinates (SPC)

The National Geodetic Survey developed the SPC system beginning in 1933. Eventually every state was covered, with coordinates identified both on maps and on the ground, so that surveyors and cartographers could accurately identify and measure locations. The key to this system is that rather than having one coordinate system for the entire US, separate systems were assigned to smaller zones. Each zone used its very own projection and coordinate center and system. 120 zones cover the US. Within each zone, you are never far from the standard line. This way, the coordinates would be extremely accurate within each zone (less than 1 foot per 10,000 feet of measurement, in fact). The problem, of course, is that coordinates between zones don't match up, so the SPC system is not useful for small--scale (large--area) maps that include more than one zone.

Nearly all states have multiple zones, but zones never cross county lines. California has 7 zones, most extending as east--west bands; Sonoma County's zone extends to Lake Tahoe. Los Angeles County has its own zone (naturally). Each state uses either the Lambert Conformal Conic or the Transverse Mercator projection (California uses the first).

Within each zone, locations are identified by x,y coordinates in feet. Any x,y coordinate system needs an origin, that is, where the coordinates are (0,0). In order to keep all SPC numbers positive, the origin for each zone is placed off to the southwest of the actual zone covered. This origin is not the actual center of the projection (that is, where the globe "touches" the sheet projected onto). That actual center is in the middle of each SPC zone, so that coordinates are most accurate there. In short, the actual center is assigned an arbitrarily large coordinate (such as 2,000,000 feet East, 400,000 feet North), and all other coordinates are measured from there. This puts the "false origin" off to the southwest.

SPC coordinates are shown on all USGS topographic maps. Usually tick marks on the margins of the map show regular spacing of the grid, and selected marks have the actual coordinates in feet. By examining the topographic map for Cotati, we can find that the SPCs for SSU are 1,806,500' E, 246,200' N. As mentioned above, the SPC system is used widely in conducting local land surveying and public works. It can be used by the cartographer and geographer not only to identify coordinates of places, but to calculate distances between locations by use of the Pythagorean Theorem, as described in the next section.

3. Universal Transverse Mercator (UTM)

The UTM grid is similar to the SPC system, at least regarding how you use it at the local level and in being marked on all USGS topographic maps. The principal differences are that the coordinates are given in meters, not feet, and that the zones are much larger. UTM zones extend north--south, practically from Pole to Pole. The UTM grid system covers the entire globe (well, almost - except for very near the Poles).

You encountered the Mercator projection before. In the standard Mercator, the cylinder is "wrapped" around the Equator, and areas become very distorted toward the Poles. A transverse Mercator projection turns the cylinder, so that the circle of contact with the globe is around a pair of meridians. This way, the projection is very accurate on a north--south zone near the standard line. Of course, once again it distorts severely at large distances away from the meridian.

The Universal Transverse Mercator grid gets around the distortion problem by the same method as the SPC system. The UTM has many zones, each with its own projection centered on a meridian. There are 60 zones to be exact, each 6° wide (which covers Earth, 60 x 6° = 360° around). Within each zone, then, the grid is very accurate in matching true Earth distance and direction. As with the SPC system, going across zones is difficult, so the UTM is meant primarily for local and regional measurement.The UTM was adopted and thus popularized by the Army in 1947. The Army included the UTM grid on its topographic maps; later the USGS added UTM coordinates to most of its maps and photoquads. The Army numbered each 6°--wide zone around the globe from 1 to 60, starting at 180° W and going east; northern California is in zone 10. They also lettered north--south segments of each zone from A (south) to Z (north). The north--south segments aren't necessary, and so are rarely used outside the military.

Within each UTM zone, x,y coordinates can be given in meters. Like SPCs, an origin is needed, and is placed outside the zone off the southwest corner. The north--south center of the zone is arbitrarily designated as 500,000 meters east (that is, east of a false origin off to the west). "Eastings" (x--coordinates) for locations east of the center are higher than this, up to about 850,000 m E; westward the coordinates decrease, down to about 150,000 m E; the zone doesn't extend all the way to the false origin. The "northing," or north--south (y) coordinate, depends on which hemisphere you're in. For the Northern Hemisphere part of each zone, the measurement starts at the Equator with 0 and measures the number of meters north (up to about 8,800,000 m N at 80° N). In the Southern Hemisphere, the Equator is designated arbitrarily as 10,000,000 m N, and coordinates decrease as you go south toward the South Pole.

Examples: A location with coordinates 334,400 m E, 4,203,600 m N would be 334,400 meters east of the false origin, or (500,000 -- 334,400 =) 165,600 meters west of the central line. It would be 4,203,600 meters, or 4,203.6 km, north of the Equator. The UTM coordinates for SSU are: 4,243,540 m E, 528,390 m N (these are actually close to the coordinates for Stevenson 3065).

The UTM grid is shown on all recent USGS topographic maps. The latest topographic maps draw in the grid as thin black lines. All topos with the UTM have tick marks along the margin, along with values for eastings or northings next to most ticks. Except for a few values near the corners, the easting or northing value is abbreviated . For example, instead of printing "3,445,000 m N", the tick would be labeled 3445, with the thousands and meters--north assumed from the context.

The UTM grid, even if drawn in on the map, may not give us the exact coordinates for a given location. Even on 7 1/2--minute quads, the grid is only every 1,000 meters (1 km). How can you determine coordinates more precisely? The answer is called a roamer. This is simply a sheet of paper, plastic or other material that has finer distance intervals marked off that match the scale of the map. Starting from the nearest grid lines, you can measure over to the location and come close (at least within 100 m) to the actual easting and northing coordinates.

Another big advantage of the UTM (or SPC) grid is that once you have coordinates for two locations within the same zone, calculating the distance between them is simple. Just apply the Pythagorean Theorem. If the two locations are at the coordinates (x1, y1) and (x2, y2), then the distance (D) between them is:

For example, say you find coordinates for two cities: Springfield at 294,100 m E, 3,428,900 m N, and Garden City at 292,400 m E, 3,428,100 m N. The distance between them is then:

that is, the distance is 1880 meters, or 1.88 kilometers.

As you can see, the UTM grid is a very useful system for tracking Earth locations. It is used extensively in remote sensing, computerized mapping, and geographic information systems. It is worth your while to familiarize yourself with it.

C. Survey Systems

A related topic to coordinate systems is how we describe the boundaries of parcels of land. SPC or UTM coordinates are great for giving locations of points, but less so for describing area. You can describe a parcel by going from point to point--this is the first method below. But other methods are easier in some circumstances. This section covers land-description methods used in the US. An important fact about survey systems is that once land is surveyed under a given system, that's it--the description of the land stays with it permanently. Land within old Spanish Land Grants in California still retain their descriptions based on the original survey.

1. Metes-and-Bounds

Early settlers in the Thirteen Colonies used the same method for dividing and describing land as they had in the Old World (especially England). This system is known as metes__-and-bounds. The idea is very simple: a land parcel is described based on going from one point to another, in a polygon that encompasses the parcel. For example, a legal description might read:

"Commencing from a point one-half mile upstream from Smith Bridge on Jones Creek, proceed northeast 500 feet to Spring Hill, then northwest to the large oak tree, then southwest to the large rock in the middle of Jones Creek, then along Jones Creek to the origin."

The first settlers in an area naturally claimed the best land, and set up boundaries that encompassed that land. Most of the time, this worked alright, and in a sense it shapes human use of the land according to the landscape itself, rather than imposing an artificial pattern on the land.

But metes-and-bounds surveys are liable to create problems. Since surveys were done as land was claimed, overlapping claims often resulted--with lengthy court battles ensuing. Even today, land titles are more difficult to verify in areas surveyed by metes-&-bounds. A bigger problem is that the boundary markers (oak tree, big rock) eventually are obliterated, with the boundaries becoming ambiguous. One measure to help has been to replace landmarks with exact compass directions and distances (also known as "Coordinate Geometry"). The description above might be replaced with:

"Commencing from a point one-half mile upstream from Smith Bridge on Jones Creek, proceed N 45° E 500 feet, then N 50° W 324 feet, then S 35° W to Jones Creek, then along Jones Creek to the origin."

A final problem with metes-&-bounds was that the US government wanted to sell off land in the West quickly, in order to raise cash (no income taxes back then). A system was needed that could quickly and rationally divide up the land, allowing for sales without a lot of legal wrangling. The US Public Land Survey, described below, became the US answer to the problem.

2. Spanish Land Grants

The Spanish, and later Mexicans, ruled California and much of the Southwest for about 300 years. They too parceled out land for use by colonists (with little regard to Native occupation, of course). The methods of description were very similar to metes-and-bounds. Much of the land was given or sold to large landowners for ranchos as Spanish Land Grants. These land grants usually focused on water resources, which are scarce in the West; sometimes the system is called Spanish Riparian (riparian means relating to watercourses).

Much of the better land in California ended up in one of these land grants. Remember, once allocated, land continues to be described under its original survey, permanently. Even after California became part of the US, and land grant claims were honored (though sometimes exchanging hands under questionable deals). The land grants have be subdivided since then, but evidence still can be found in property descriptions, and on USGS topographic maps. For instance, some land grants in Sonoma County were Rancho Cabeza de Santa Rosa, Petaluma Rancho, and Rancho Cotate. These labels, along with their boundaries, can be found on topos for Sonoma County.

3. Other Irregular Surveys

Other survey methods were used in certain parts of the US. In Louisiana and other areas settled by the French, long-lots were used. The land along important lanes of commerce, usually rivers, was divided into narrow strips extending back into the interior. This resulted in a series of long but narrow plots of land that are still evident on topo sheets of Louisiana, coastal Texas, and Mississippi River towns, even as far upstream as Wisconsin.

4. The US Public Land Survey (PLS)

The majority of the land in the US is described under the US Public Land Survey (PLS) System. After independence, the US wanted to dispose quickly of lands in the West (at that time, land between the 13 Colonies and the Mississippi River). Some form of logical, orderly system was inevitable, but the exact form took time to shape. Thomas Jefferson and others eventually worked out a rational, rectangular (squarish) survey, called the Public Land Survey (PLS) system, which was enacted under the Northwest Land Ordinance of 1785 (with later revisions).

The PLS starts out by establishing an x,y coordinate system for a given area. The north-south line is called a principal meridian, and the east-west line a baseline. Each baseline is given a unique name, so that each land parcel can be identified by that name. The area described based on a principal meridian/baseline pair varies from a small part of a state (e.g., eastern Ohio, northwestern California), to several states (e.g., the Fifth Principal Meridian covers most of Arkansas, Missouri, Iowa, Minnesota, and most of the Dakotas).

California has three principal meridian/baseline pairs: the San Bernardino Meridian (southern California), Mt. Diablo Meridian (most of northern California), and the Humboldt Meridian (northwestern corner of the state).

The initial point is the intersection of the principal meridian and baseline. From this point, townships are marked off east/west and north/south. Each township is 6 miles on a side, or 36 square miles. Townships are designated on the east-west direction as being a certain number of Ranges east or west of the principal meridian. The township is also a certain number of Townships north or south of the baseline (note the dual use of the term township, as an area and as a coordinate). For example, the township that is just on the northeast corner of the initial point is Township 1 North, Range 1 East, usually abbreviated T. 1 N, R. 1 E. Or T. 3 S, R. 2 W would be the third township south of the baseline and two townships to the west.

Each township had to be divided, since few people could afford 36 mi². The division was into 36 sections, one square mile each. Rather than using an x,y system here, the sections were simply numbered consecutively from 1 to 36, starting in the northeast corner and snaking around the rows, with 36 at the southeast corner.

Most land purchases were for less than one section; the Homestead Act of 1863 allowed people to receive one-quarter section if lived on by the claimant. Sections can be broken down into halves or quarters, each part designated by a compass direction. If divided in half, we have either east/west halves, or north/south halves. If divided into quarters, we have the NE, NW, SW, and SE quarters. Quarters can be broken down further if necessary, for example we might have the NE quarter of the SE quarter.

A square mile contains 640 acres, so a quarter section has 160 acres, a quarter-quarter 40 acres, and so on. The typical Midwestern farm used to be a quarter section, or 160 acres. Farms have been consolidated over the past several decades, so the typical farm occupies closer to a square mile, especially in California.

A complete property description must include all of these breakdowns into township, section, and fraction of section (if less than an entire section). A typical property description in a PLS area might read:

E 1/2 of SE 1/4, Sect. 22, T. 87 N, R. 34 E, 6th Principal Meridian

USGS topographic maps indicate PLS townships and ranges along the margins. Section and township lines are shown on the map itself with red lines, and sections are numbered in red. You will no doubt notice on some topos that the PLS townships and sections end abruptly in some part of the map. This is common around Santa Rosa. This is because these non-PLS lands were in Land Grants before 1846, when California became part of the US. Remember, once surveyed, never again.

The PLS has had a dramatic impact on the American landscape. Since all land is divided into squares, the landscape itself looks very square. You'll notice this when flying over the middle part of the US, where topography does not interfere with its effects as much. It also contributed to the isolation of farm families in the 19th Century, who lived on their own square farms far from neighbors. Contrast this to French surveyed-lands, where people live much closer together. Our survey system no doubt contributed to the ideal of American individualism.

A final note about the PLS--it's far from a perfect system. There are many irregularities, which are especially noticeable in certain regions. Section and township lines are not always exactly north/south and east/west, and sections are sometimes less than a full square mile (they're then called government lots, or fractional lots). The irregularities derive from several sources:

• Meridians converge to the north, so as surveyors moved north, townships didn't match up with those further south. Often east-west correction lines were set up, along which townships were re-aligned. You'll notice this effect when driving north or south along a country road and you have to take a sudden turn right or left, then turn north/south again after a short distance.
• Surveying in wet or mountainous terrain is difficult, and lines often went astray. Once set up, however, the errors were kept, and lines remained askew.
• Surveyors were paid by the number of sections surveyed, so hurried surveyors weren't always careful surveyors.
• Some surveyors simply weren't careful, or were even staggering-drunk on the job.

Because of these irregularities, the PLS is not a great system for computerized map coordinates when you want a regular x,y grid. Use the UTM or SPC grid instead.

5. Other Rectangular Surveys

Some states weren't touched at all by the PLS: the original 13 Colonies (and subsequent split-offs: West Virginia, Vermont, Maine), Tennessee, Kentucky, and Texas. Some New England towns used a modified rectangular survey when settled. Some of the states had considerable land left to dispose of in the 19th Century, and developed their own rectangular survey for these lands. Texas, in particular, used several variations on a rectangular survey, some of which used Spanish units. These rectangularly-surveyed areas look like PLS areas as you travel over them, even though officially they're not.

Topographic Map Interpretation

Contents

A. Physical Features

B. Cultural Features

C. Conclusion

---

Everything up to now can be applied to topographic maps as well as other kinds of maps and information. The rest of this discussion focuses specifically on how you can use topographic maps to extract information about the landscape. Both physical and cultural features are often discernible from topographic maps. This section draws many ideas from a course handbook titled "The Language of Maps," by my advisor at the University of Minnesota, Phil Gersmehl.

The US Geological Survey has published many different kinds of maps, including several series of topographic maps. Only a few series are in common use. The 7 1/2-minute quadrangles, which have a scale of 1:24,000, are the most popular. These detailed maps are supplemented by the 1:250,000-scale series. A third series, the 15-minute quad at 1:62,500, was popular but discontinued by the USGS for mysterious reasons (probably because the detailed 1:24,000 maps had to be done, and the 1:62,500s would duplicate some of their uses). The 1:100,000-scale metric series is a recent addition, and is now complete for the US. All of its maps show features in metric, for example elevation is in meters.

Table : USGS Topographic Map Series

Series	Scale	Lat. x Long	Area (mi2)	Paper Size
7-1/2 Minute	1:24,000	7-1/2' x 7-1/2'	49-70	22" x 27"
15-Minute	1:62,500	15' x 15'	197-282	17" x 21"
Metric	1:100,000	30' x 1ª	3,173-4,334
1:250,000	1:250,000	1ª x 2ª	6,346-8,669	24" x 34"
1:1,000,000	1:1,000,000	4ª x 6ª	73,734 x 102,759	27" x 27"

A. Physical Features

In addition to this section, see also the discussion of contour lines and slopes above under Symbolization in Part I. You may also want to read (or reread) a text @ecoatlas.GIS.physical geography or geology to help in understanding the terms and concepts here.

1. Landforms

Contour lines and other map symbols can give you clues about the geology and geomorphology that underlies the landscape. In general, rocks differ in their resistance to weathering and erosion, and these differences are reflected in the landscape. Some examples:

Fault lines.

Some faults can sometimes be seen on a map where streams have been offset to the left or right along a line, then continue downstream. These are strike-slip, or transform, faults, where one section of the crust is sliding past another. California's San Andreas and associated faults are examples of transform faults. In other faults, one section of the crust slides under another. These normal or reverse faults are usually less visible unless considerable uplift has occurred. Death Valley is the result of a pair of normal faults letting the valley floor downward several thousand meters.

Cuestas and hogbacks. These are the result of a block of terrain being tilted upward at one end. The result is a gradual upward slope with a cliff at the uplifted end. Good examples of these can be found in the desert Southwest.

Volcanoes.

In contrast to most hills, volcanoes are usually much rounder, so that contour lines around them are circular. This is especially true for stratovolcanoes, the most violent and prominent volcanoes. Examples are Mt. Shasta in California and Mt. Rainier in Washington. Some volcanic eruptions are gentler and form gentler hills or even broad plateaus. These flows are more difficult to detect from the topographic map, unless the USGS adds a dotted pattern that indicates a lava flow.

Wave Action.

Waves are very efficient at cutting back into cliffs. The waves crash against the base of the cliff and undercut the cliff. Eventually a chunk of cliff topples into the sea. But waves don't cut down much below sea level, especially where the rock along the shore is relatively hard. The result is that wave action can create a long wave-cut platform or terrace along the shore. These platforms are often visible on coastal maps.

If the coast is uplifted, this flat wave-cut (or marine) terrace can be high and dry above the ocean. The California coast has been rising relative to the sea over the past several hundred thousand years. In many areas a series of terraces are visible on maps and in person. The Sea Ranch, along the coast in northern Sonoma County, is built on a marine terrace.

Glaciation.

Glaciers can occupy either mountainous or flat terrain, and result in corresponding alpine or continental glacial features. Many kinds of features can result, so I'll mention only a couple of examples. For alpine glaciation, the ice will occupy a valley and hollow out its sides and head. This turns the valley from V-shaped to U-shaped, with steep sides and flat bottom. Small lakes may form in the valley, known as tarns. As it excavates into the mountain at the head of the valley, another glacier may be doing the same on the other side of the mountain. This results in a sharp ridge, or arete. If three glaciers surround and erode a mountain, they may form a three-sided peak, known as a horn (the Matterhorn is the best-known example). California's Sierra Nevada was covered by glaciers during the last glacial peak (about 15,000 years ago), and many of these features remain as evidence.

Continental glaciers, or ice sheets, produce different landforms. The most striking is where the glacier's front has remained stationary for a long period. The glacial ice will be moving forward toward the front, carrying rock and debris in the ice. The ice melts at the front and leaves the debris as a moraine. Moraines are hilly ridges perhaps a mile wide and up to several hundred miles long. They may have a hundred feet of local relief (vertical elevation change). The ridges contain many depressions that fill with water. If you see a map with irregular hills and many small lakes, glaciation may be the cause. Ice sheets covered most of the upper Midwest, down to about the Missouri and Ohio Rivers. Nearly all of Minnesota's 10,000 lakes were formed by glaciers. California didn't have any continental glaciation to speak of--only alpine.

Karst.

Another type of area with irregular terrain, sometimes with many lakes, is known as karst. Karst forms in limestone and other rock that easily dissolves in water. The water dissolves both the surface and the subsurface. Caves result below the surface--most caves are formed in limestone rock (Carlsbad Caverns, Mammoth Cave, etc.). But the surface may also show the result of being dissolved: sinkholes (small depressions) and disappearing streams (where a stream suddenly vanishes) are evidence. Karst is common in Indiana, Kentucky, Arkansas, Missouri, and Florida (where houses have been swallowed by sinkholes). California has a small area of karst in the Marble Mountains, in the extreme northern part of the state.

Winds.

Winds rarely shape the landscape enough to show on topographic maps. The exception is in areas with accumulations of loose sand, which wind can move effectively. Sand may accumulate in deserts, along shores, or where the bedrock is sandstone. The wind usually shapes the sand into dunes. There are many types of dunes, mostly due to different wind speeds and directions. Often the wind is consistent enough from one direction to line up the dunes, so a linear pattern shows up on the topographic map. Streams are usually absent or rare, since water flows into and through the dunes easily. Topographic maps usually show sand dunes with a distinctive dotted pattern. Large sand seas are found in the Nebraska Sand Hills, White Sands National Monument, and southeastern California.

Mass movement.

Gravity affects all events on Earth, but it is the defining force in mass movement. Landslides, rockfalls, and slumps are all examples of mass movement. When a slope becomes too steep for the cohesive forces retaining it, it gives way. The reasons for gravity overcoming the slope can include uplift from a fault, an earthquake, a stream undercutting a slope, burning of vegetation that holds the slope, or excavation by humans. Small mass movements may be too small and temporary to be visible on a topographic map. Large landslides and slumps may be evident, especially in certain areas where they are frequent. Mountains are good candidates. Sonoma County is also prime terrain, as winter rains saturate hills that have been overgrazed, undercut or built upon.

2. Drainage Patterns

The terminology of drainage patterns is not particularly useful in and of itself. But drainage patterns can suggest what is happening with the underlying geology and landscape.

Dendritic.

The "normal" pattern of stream drainage is called dendritic, since it looks like a tree's roots or branches. This pattern occurs when no strong geological factor controls the drainage network.

Meandering.

A stream that has had a chance to erode for a long period tends to widen its path across a large floodplain, and meander back and forth across the floodplain. These streams usually flood periodically and fill their floodplain. While unwise to build on the floodplain, the land is usually flat and fertile, and tempting for short-sighted settlers. These streams are often channelized into straight courses. This rids the local area of water quickly but creates even more flooding downstream.

Braided.

Some streams in floodplains have many small channels that merge and separate downstream. Braided streams are most common where the water flow is variable (e.g., deserts or mountains) and the stream bed is mostly sand and gravel.

Trellis & Rectangular.

These patterns are where streams flow in straight segments and turn at sharp angles. Usually this results from sedimentary bedrock controlling the direction of streams along the surface. Good examples of trellis drainage are found in eastern Pennsylvania, where folded sedimentary rocks cause streams to flow at right angles to each other.

Radial.

Radial drainage occurs around circular hills and mountains, with streams radiating out in all directions. This would be typical around a volcano.

Centripetal.

The opposite of radial, here streams drain inward toward a central basin. The basin usually has a dry or saline lake and has no outlet--a sign of arid conditions.

Deranged.

Streams have no organized pattern. Some drain externally toward major rivers, others may drain internally. This is usually a sign of continental glaciation, or possibly sand dunes or karst.

Artificial.

Human-caused modifications of streams include channelized streams (straighter than any normal stream), canals, drainage ditches (may be a sign of natural wetlands), reservoirs (which not only have a dam, but usually a more indented shoreline than a natural lake), and levees.

3. Vegetation

USGS topo maps often contain some indication of vegetative cover, but not always. Older maps lack this information, and some kinds of vegetation aren't indicated.

Forest and woodland.

USGS maps indicate forest or woodland (area with trees but not continuous canopy cover) by a uniform green tint. The size, orientation and shape of tree cover can tell us about climate and land use. Types of cover patterns include:

• Treeline forests, in higher elevations where cold climate prevents trees from growing any higher;
• Moisture-favorable forests, in canyons, ravines, on slopes away from the Sun (especially north slopes), or up slopes in arid lands;
• Dry-land forests, on drier islands in wetlands; good examples may be seen in Florida's Everglades, in "mahogany hammocks";
• Landslides or avalanche chutes, where falling rock or snow keeps areas clear of mature trees;
• Human-caused forest patterns, including clearcuts with sharp edges in otherwise forested land; bottomland forests in wet areas where the surrounding land has been cleared; and woodlots, shelterbelts and windbreaks around farms and ranches.

Orchards and vineyards.

USGS topos give these distinctive patterns of regular dots. It is interesting to examine where these have been placed on the terrain--usually up above the valley floor slightly to avoid cold-air drainage that occurs at night.

Scrub.

Scrub or shrub vegetation has an irregularly-dotted pattern. Chaparral vegetation in California normally has this pattern, although it is not always mapped. Chaparral is a sign of Mediterranean climate, that is, mild, wet winters and warm, dry summers. Soil is also a factor. For example, in our area, soils that dry out thoroughly in summer are more likely to harbor chaparral.

Wetland vegetation.

USGS topographic maps have distinctive symbols for wooded wetland (also called swamp), nonforested marsh, and mangroves. Mangroves are shrub or small tree-sized plants that grow directly in warm salt water along tropical and subtropical coasts. Florida and other Gulf Coast states have many mangrove areas, although many have been cleared for development.

B. Cultural Features

1. Transportation Patterns

Besides the types of roads listed in the key for topographic maps (primary, secondary, light-duty, unimproved), look also at the placement of the road. It may follow along elevation contours, even if the route is circuitous--an indication of steep terrain, relative to the amount of traffic carried. Heavily-traveled routes tend to get straightened.

Other areas may have roads that follow flat terrain, and cross steep slopes only when connecting level areas. The flat areas are either valley floors, with few roads going over mountains, or mesas or interfluves, where the flat land is dissected by streams. The Appalachians are good places to find transportation along valleys. A glance at a road map of eastern Pennsylvania will indicate that valleys and hills trend from southwest to northeast. Southern California has good examples of mesas, most of which are marine terraces formed long ago and since lifted above the sea.

Grid patterns are the rule where areas were surveyed before settlement, as in most lands under the Public Land Survey system. Roads in these areas often follow the square grid regardless of terrain.

Don't overlook other kinds of transportation, such as railroads, canals, and trails. These often indicate something about the history or land use of an area. A map with many railroads, for example, likely says the area was important during the early 20th Century. You also may notice corridors that used to be railroads--often shown as "old railroad grade." Many of these are being converted to foot trails or bicycle paths. Canals for transportation are rarely built nowadays, but were popular in the 19th Century.

2. Rural Settlement

Rural housing.

Rural houses and buildings are usually shown on topographic maps as small black squares. Rural settlement patterns usually reflect the original land survey. Regions surveyed under the PLS started out with a very dispersed settlement pattern. Homes were scattered on farms and ranches, usually no more that four per square mile. Areas surveyed under irregular survey systems (metes-and-bounds, land grants, etc.) tend to have homes more clustered, or along roads that went through or around land parcels. Land in long-lot surveys typically has houses closely spaced along a few main roads or rivers, with few houses elsewhere.

Service facilities.

Along major transportation routes in rural areas, small settlements sprung up to service travelers and their vehicles. These settlements concentrated at railroad stations in the 19th and early 20th Centuries. As the automobile became the primary means of transporting people in the mid-20th Century, service facilities became more dispersed along highways. With travel more concentrated on interstate highways, facilities and settlements are once again becoming more concentrated, this time at major exits on interstates.

Urban invasion.

Many rural areas have been "invaded" by urbanites for summer or weekend homes, or even long-distance commute homes. Lakes and rivers are popular places, especially in more arid regions of the West. Campgrounds, resorts, and other tourist facilities have expanded rapidly in the past few decades. A dense pattern of these indicate either a nearby metropolitan area (such as Sierra Nevada resort areas), an unusually popular location (such as Yosemite or Redwood parks), or a wealthy clientele (such as Aspen or Vail).

3. Urban Development

The patterns of streets and facilities in urban areas can suggest much about the function and history of the city. Often you must investigate the particular groups that settled the area to fully appreciate the patterns. The myriad groups who immigrated to the US brought their own traditions of land-use. Of particular influence were the English, French, German, and Spanish. Subtle influences of others, such as Native Americans or Asians, can sometimes be detected.

Irregular street patterns.

Early in our history, streets were laid out according to the major trading routes and the shape of the land. This produced an irregular pattern, especially in smaller towns.

Regular grid patterns.

Most cities adopted regular grids for streets to make surveying and development easier. This is particularly true in PLS areas. At first, street grids were oriented with respect to the major transportation line, even if the line went northwest-southeast. Later, most street grids were oriented north-south and east-west. The changing pattern can be seen in many cities as they grew outward from the center.

Irregular patterns, again.

In the past few decades, the regular grid of street became associated with uniform houses and middle-class lifestyles. Wealthy people (and some who want to look like they are) like to distinguish themselves from ordinary folk, and have used winding, irregular streets for their housing to do so. This also goes along with the trend in the US for wealthy people to live in hills above the city; regular grids would be difficult here anyway.

Industrial areas are often visible on topographic maps as clusters of larger buildings, and may help discern the area's function. Economic geographers often divide industries into raw materials-oriented, such as gravel pits and food processing plants; those in manufacturing, which often cluster together where power, labor or transportation is available; and market- and service-oriented, which cluster where customers are, for example bottling plant, shopping malls and strip developments.

4. Place-names

Place-names often give clues about the area's history or occupants. Often this can suggest a series of different groups in an area, or sequent occupance in geographic jargon. In California, of course, many names reveal the Spanish and Mexican presence--which is both historical and continues today. Town names are not the only clue. Other words were applied to places and have stuck, sometimes as more reliable than city names. For example, I doubt many of these communities were founded by Spanish-speakers: Del Mar, Tierrasanta, San Anselmo, El Cerrito, San Carlos and Rancho Mirage. On the other hand, words like verde, agua, mesa, arroyo, iglesia, and oso occur on maps as part of other names and indicate early settlement by the Spanish. Laguna lake is redundant--laguna means lake in Spanish--and the name may reveal an early Spanish presence.

Other groups settled throughout the US, and even California. Groups including French, German, Czech, Swedish, Norwegian, Danish, Irish, Polish, Chinese, Korean, Japanese, and recently Vietnamese and Hmong have established place-names. The Russians colonized the northwestern coast of North America in the early 19th Century, and some place-names remain even where few Russians do (Sitka, Petersburg, Soldotna, Andreanov Islands, etc.). Sebastopol, however, is a later revision having nothing to do with the Russian city other than the name itself.

5. Mining

Mining operations disturb local areas, sometimes severely. Topographic maps often show mining pits with a distinctive shading pattern (see Topographic Map Symbols brochure). Gravel pits and quarries also receive a point symbol. We could also include oil and gas wells here, indicated on topo maps; presence of many such wells suggest a major contribution to the local economy. Oftentimes other clues also reveal mining, especially past mining: irregular contours that do not match the general trend of the landscape, unexpected depressions shown by contours, and rail lines or roads dead-ending in the area. Large mines, such as strip mines in the Appalachians and open-pit copper mines in Arizona show these features prominently on topo maps.

C. Conclusion

Topographic maps can be a rich source of information about a landscape, even absent other information. It is a good idea to use collateral information, such as histories or geographies of an area, before sharing your conclusions with friends and relatives. Remember, maps are representations of reality, not reality itself!

Conversion Constants

Contents

Using conversion constants

Converting from Imperial units

Converting from Metric units

Converting from Geographic units

United State Survey Foot

Additional Equivilants

---

Using conversion constants

The following is a list of conversion constants that can be utilized in converting from one measurement system to another. The measurement system to be converted should be multiplied by the associated conversion constant. For example, to convert feet to centimeters, multiply feet by the conversion constant of 30.48 (27 feet x 30.48 = 822.96 centimeters).

Converting from Imperial units

Multiply	by	to obtain
acres	0.4046856	hectares
acres	43560.0*	square feet
acres	4046.856	square meters
acres	0.0015625*	square miles
acres	4840.0*	square yards
feet	30.48*	centimeters
feet	0.0003048*	kilometers
feet2	0.3048	meters
feet (U.S. survey foot)	0.304800609601**	meters
feet	0.00018939394	miles
feet	304.8*	millimeters
square feet	0.000022956	acres
square feet	929.0304*	square centimeters
square feet	0.09290304*	square meters
square feet	0.00000003587	square miles
inches	2.54*	centimeters
inches	0.0254*	meters
inches	0.000015782	miles
inches	25.4*	millimeters
inches	0.027777778	yards
square inches	6.4516*	square centimeters
square inches	0.00064516*	square meters
square inches	645.16*	square millimeters
miles	160934.4*	centimeters
miles	5280.0*	feet
miles	63360.0*	inches
miles	1.609344*	kilometers
miles	1609.344*	meters
vmiles	1760.0*	yards
miles	1.15077945	nautical miles3
square miles	640.0*	acres
square miles	27878400.0*	square feet
square miles	2.589988110647	square kilometers
yards	914.4*	millimeters
yards	91.44*	centimeters
yards	0.0009144*	kilometers
yards	0.9144*	meters
yards	0.000568182	miles
square yards	0.000206611	acres
square yards	0.83612736*	square meters
square yards	0.0000003228305	square miles

Converting from Metric units

Multiply	by	to obtain
centimeters	0.03280839895	feet
centimeters	0.3937007874	inches
centimeters	0.00001*	kilometers
centimeters	0.01*	meters
centimeters	0.000006213711922	miles
centimeters	10.0*	millimeters
centimeters	0.01093613298	yards
square centimeters	0.001076391042	square feet
square centimeters	0.15500031	square inches
hectares	2.471054073	acres
hectares	107639.1042	square feet
kilometers	1000000.0*	millimeters
kilometers	100000.0*	centimeters
kilometers	1000.0*	meters
kilometers	1093.613298	yards
kilometers	3280.839895	feet
kilometers	39370.07874	inches
kilometers	0.6213711922	miles
square kilometers	247.1054	acres
square kilometers	10763910.42	square feet
square kilometers	0.386102158496	square miles
meters	100.0*	centimeters
meters	3.280839895	feet
meters	3.280833333331	feet (U.S. survey foot)
meters	39.37007874	inches
meters	0.001*	kilometers
meters	0.0006213711922	miles
meters	1000.0*	millimeters
meters	1.093613298	yards
square meters	0.0002471054	acres
square meters	10.76391042	square feet
square meters	0.0000003861003	square miles
millimeters	0.1*	centimeters
millimeters	0.003280839	feet
millimeters	0.03937007874	inches
millimeters	0.000001*	kilometers
millimeters	0.001*	meters
millimeters	0.0000006213711922	miles
millimeters	0.001093613298	yards
square millimeters	0.00001076391042	square feet

Converting from Geographic units

Multiply	by	to obtain
degrees	1.111111111	grads
degrees	0.017453292	radians
grads	0.9*	degrees
grads	0.015707963	radians
radians	57.2958	degrees
radians	63.6620	grads

United State Survey Foot

In 1959, the directors of the National Bureau of Standards and the United States Coast and Geodetic Survey agreed on a redefinition of the inch-centimeter relationship. This redefinition defined 1 inch as equal to 2.54 centimeters, exactly, or 1 foot as equal to 0.3048 meters, exactly. However, their agreement stipulated that the older value for 1 meter equaling 39.37 inches, exactly, be retained for identifying the U.S. survey foot. One of the reasons for this retention was that the State Plane Coordinate Systems, which are derived from the national geodetic control network, are based on the relationship of 1 meter equaling 39.37 inches, exactly. The difference between these two values for the foot is very small, two parts per million, which is hardly measurable but not trivial when computational consistency is desired. Fundamental survey units, such as rods, chains, statute miles, acres, sections, and townships, all depend on the relationship of 1 meter equaling 39.37 inches, exactly. The following list represents the corrected values (or U.S. survey values), using the 39.37-inch conversion value:

Multiply	by	to obtain
acres	0.4046873	hectares
acres	10.0*	square chains
acres	43560.0*	square feet
acres	4046.873	square meters
acres	0.0015625*	square miles
acres	160.0*	square rods
chains	66.0*	feet
chains	100.0*	links
chains	20.11684	meters
chains	0.0125*	miles
chains	4.0*	rods
square chains	0.1*	acres
s quare chains	0.04046873	hectares
square chains	4356.0*	square feet
square chains	404.6873	square meters
square chains	0.00015625*	square miles
square chains	16.0*	square rods
feet	0.01515152	chains
feet	1.515152	links
feet	0.304800609601**	meters
feet	0.00018939394	miles
feet	0.06060606	rods
square feet	0.00002295684	acres
square feet	0.000009290341	hectares
square feet	0.00000003587006	sections
square feet	0.0002295684	square chains
square feet	0.09290341	square meters
square feet	0.00000003587006	square miles
square feet	0.003673095	square rods
square feet	0.0000000009963907	townships
hectares	2.471044	acres
hectares	24.71044	square chains
hectares	107638.7	square feet
hectares	10000.0*	square meters
hectares	0.003861006	square miles
hectares	395.3670	square rods
links	0.01*	chains
links	0.66*	feet
links	0.2011684	meters
links	0.000125*	miles
links	0.04*	rods
meters	0.04970960	chains
meters	3.280833333331	feet
meters	4.970960	links
meters	0.0006213699	miles
meters	0.1988384	rods
square meters	0.0002471044	acres
square meters	0.0001*	hectares
square meters	0.0000003861006	sections
square meters	0.002471044	square chains
square meters	10.76387	square feet
square meters	0.0000003861006	square miles
square meters	0.03953670	square rods
square meters	0.000000010725	townships
miles	80.0 *	chains
miles	5280.0*	feet
miles	8000.0*	links
miles	1609.347	meters
miles	320.0*	rods
square miles	640.0*	acres
square miles	258.9998	hectares
square miles	1.0*	sections
square miles	6400.0*	square chains
square miles	27878400.0*	square feet
square miles	2589998.0	square meters
square miles	102400.0*	square rods
square miles	0.027777778	townships
rods	0.25*	chains
rods	16.5*	feet
rods	25.0*	links
rods	5.029210	meters
rods	0.003125*	miles
square rods	0.00625*	acres
square rods	0.002529295	hectares
square rods	0.0625*	square chains
square rods	272.25*	square feet
square rods	25.29295	square meters
square rods	0.000009765625*	square miles
sections	27878400.0*	square feet
sections	2589998.0	square meters
sections	1.0*	square miles
sections	0.027777778	townships
townships	36.0*	sections
townships	1003622400.0*	square feet
townships	93239945.0	square meters
townships	36.0*	square miles

Additional Equivilants

width of township	6 miles
1 township	36 sections
1 mi2 (usually)	1 section
1 mi2	27,878,400 ft2
mean polar radius of Earth	6373 km or 3960 mi
Earth radius at Pole (Clarke Ellipsoid)	6,356.6 km
Earth radius at Equator (Clarke Ellipsoid)	6,378.2 km

* Constants are exact.

** A coordinate system in U.S. survey feet may be converted to a coordinate system in meters by scaling the system to a scale factor of 0.304800609601. An exact conversion can be accomplished by multiplying U.S. survey feet by the fraction 1200/3937.

¹ A coordinate system in meters may be converted to a coordinate system in U.S. survey feet by scaling the system to a scale factor of 3.28083333333. An exact conversion can be accomplished by multiplying meters by the fraction 3937/1200.

² The foot is one-third of the Imperial standard yard, which is defined to be 0.9144 meters, exactly. Thus the foot is defined as 0.3048 meters, exactly.

³ Represents the international nautical mile and also the U.S. nautical mile. The international nautical mile is defined to be 1852 meters, exactly. However, the U.K. nautical mile is defined to be the average distance on the earthís surface subtended by one minute of latitude, thus being 6080 feet, exactly, or 1853.184 meters, exactly.

Bibliography

Brinker, R.C. and Wolf, P.R. 1984. Elementary surveying. 7th edition. New York: Harper & Row.Gersmehl, Philip. 1989. Student manual for The Language of Maps. Dept. of Geography, University of Minnesota.

Johnson, H.B. 1976. Order upon the land: The U.S. rectangular land survey and the upper Mississippi River country. London: Oxford University Press.

Muercke, Phillip C. 1978. Map use: Reading, analysis, and interpretation. Madison, Wis: JP Publications.

Robinson, A.H., Sale, R.D. & Morrison, J.L. 1978. Elements of cartography. 4th edition. New York: John Wiley.

Snyder, John P. 1982. Map projections used by the U.S. Geological Survey. 2nd edition. Geological Survey Bulletin 1532. Washington, DC: US Government Printing Office.

U.S. Department of the Army. 1958. Universal Transverse Mercator Grid. TMS 241-8. Washington, DC.