GRAPHICACY

Literacy refers to the ability to read, write, and use words. Geographers often find it more efficient to convey concepts by using maps and diagrams.  Graphicacy refers to the ability to effectively use, interpret, and make maps and diagrams. The sciences regularly use diagrams. A graphically literate person should recognize the shortfalls and advantages of different types of diagrams. A graphically literate person can “read” images.

Maps are a specific type of image.  Maps show how data and characteristics change across space. All geographic data has a spatial component. It must have some type of location information associated with the data.  A column graph showing two or more cities and their corresponding burglary rates is a valid graphical depiction of geographic data.  The geographic location data is each of the cities.  However, as you plot more and more cities on the column graph, it becomes more difficult to read.  Good graphics should make it easier for the user to get the desired information.  Plotting several dozen, or several thousand, cities on a single column graph would become incomprehensible.  A map is much easier to read.

MODELS

Maps are models of reality.  As models, they simplify and generalize the actual situation.  Map makers, called cartographers, must decide on the intended purpose of the map in order to determine what data is necessary to achieve the intended purpose.  Data that is unnecessary or distracting should be removed. For instance a highway map of an entire state will not show individual trees because the trees are not necessary for determining the routes along roadways.

SCALE (Distance)

Scale is the degree of generalization of a map.  There are three ways of indicating map scale: verbal scale, representative fraction, and graphical scale. The verbal scale is an old form, rarely used since about WWII.  It is simply writing the scale in words: “One inch is approximately six miles”.

The representative fraction (RF) scale is mathematically consistent across the map. To use the RF scale, you must have a ruler. The RF scale is written as a ratio (1:24,000) where there first number is always ‘1’ and is the distance measured with a ruler on the map.  Multiply that number by the second number (in the example it’s 24,000) to find the true ground distance.  Remember to consider significant figures when using the RF scale. The result is the actual ground distance between the two points, with the same units as you used with the ruler.  Notice the RF scale has no units in it, so whichever units you use when measuring on the map (mm or cm or inches) is the same units on the ground.

The third scale is a graphical scale.  This is especially common in the era of photo copiers. If a paper map is photographically enlarged or reduced, but the graphical scale is included in the same process, then the graphical scale is still accurate whereas the verbal and RF scales are no longer accurate after enlarging or reducing.

To use a graphical scale, a ruler may be used, but it’s not necessary.  Any piece of paper will work. Place the edge of the paper along a line between the two points of interest and mark their locations on the edge of the paper.  Now bring the paper to the graphical scale and note where the two points align on the scale.

Different maps have different scales.  Maps are either large scale or small scale. There is no predefined limit where small scale shifts to large scale.  It is a relative term.  One map is smaller scale compared to (in relation to) a second map.  Larger scale maps show less area in more detail than smaller scale maps. This is easier to explain using the RF scale.  A map of RF scale 1:2 shows more detail than a map with scale 1:4.  The first map is a larger scale than the second map. Mathematically, 1/2 is greater than 1/4. When we talk about large- and small-scale maps and geographic data, then, we are talking about the relative sizes and levels of detail of the features represented in the data. In general, the larger the map scale, the more detail is shown. Photographs and images do not have consistent scale throughout the entire displayed area.  This can be corrected mathematically so that a single scale is correct.  The correction, called orthorectification, alters the image so it appears as if the map user is directly overhead of all points on the map rather than overhead of one point and viewing other points from a slight angle.  USGS topographic maps are developed from images that have been orthorectified.

AREA

The area on the map relates to area on the ground based on the map scale. The USGS makes several series of maps using standard scales and there are inexpensive tools that you can buy to quickly estimate area on those standard map scales.

As with so many of life’s problems, you probably won’t know the answer before you start. But often you can find a region of possibilities. From basic geometry you know there are formulas for finding the area of regular shapes such as squares, circles, and polygons. Even if you’ve forgotten what the formulas are, you know they exist. The difficulty with natural shapes on maps is they are regular polygons and those formulas won’t work.

There are many methods for estimating the area of irregular shapes, but most of them work on the idea of finding the area of a simple shape such as a square or rectangle and fitting those in the irregular shape.

Find the maximum possible and an approximate minimum area for the shape.

The maximum area. Create a regular polygon (square, rectangle, maybe a circle) that is larger than the irregular shape. In the figure to the right, we are estimating the area of the circle. We can see that area of the circle is smaller than the area of the large square because the circle is entirely within the large square.  A maximum area of the circle is 1.5 in x 1.5 in = 2.25 in². Note: the large square doesn’t have to touch the circle, but getting it closer will narrow your error range.

Now find a minimum. First you know the shape exists in space because it’s shown on the map. The area will certainly greater than zero. But you can do better. Put another, smaller, regular shape entirely within the irregular shape. Here the dark blue square is entirely within the circle. You know the area of the circle is greater than 1 in x 1 in = 1 in². NOTE: I wouldn’t spend too much time on the minimum. I’d probably find the maximum then move on the the next step of using small squares.

To get a better estimate of the area of the irregular shape, use smaller squares! In this example the small squares are 0.1 in x 0.1 in. = 0.01 in². As drawn, even with the smaller squares, we know we will under estimate the area of the circle because all of the squares fit inside the circle and there’s still white space visible and none of the light blue is covered. There might be a situation where it’s important to know that you’ve under estimated the area. In another situation you may want to be sure you’ve over estimated (you don’t want to run out of sod for the lawn) so you would make sure there’s no white area visible by adding more small squares.

If you want a good estimate, but aren’t concerned if you’re either over- or underestimating, then draw small squares along the edge of the circle so some squares are more within the circle and others are more outside the circle and estimate when you have an entire square’s worth.  Three squares that are each only 1/3 within the circle will add up to 1 full square.

How small is too small? Once again it depends on the map scale, what your needs are, and the precision of other measuring tools. If you’re drawing squares by hand even the thickness of the pencil might be a large portion of the area of the small circles. That’s bad.

Here’s an actual lake estimate:

Maximum area. McDougal lake is entirely within the square that measures 1 in x 1.25 in on the map. The scale is 1:18,000 or 1in = 0.2mi.

Convert from map length and area to ground area:

One side of the rectangle is: 1 in = 0.2 mi on the ground

The side of the rectangle is: 1.25 in x 0.2 mi/in = 0.25 mi on the ground

Ground area covered by the rectangle is 0.2 mi x 0.25 mi = 0.05 mi²

Ground area: 0.05mi² x 640ac/mi² = 32 acres (in the USA acres is a common unit of measuring surface area).

We now know the area of the lake is less than 32 acres.

In the image below, each small square is 0.1 in x 0.1 in  so 0.02 mi x 0.02mi = 0.0004 mi² x 640ac/mi² = 0.256 ac (about 1/4 acre per square).

Each square with a blue dot is entirely water. There are 40 of them: 40 squares x 0.256ac /square = about 10 acres.

Each square with an orange dot has some water and some land. I estimate they are equivalent to about 31 fully water squares: 31 sq x 0.256 ac/sq =  7.9 acres.

In the image to the right the blue square and blue dot is 100% water. One of the orange squares is nearly all water while the other orange square is nearly all land. Estimate one as 90% water and the other as 10% water and you have one square at 100% water.

Total lake area estimate: 7.9 acres + 10 acres = 17.9 acres.

A second method (or check your work):

In the image with the small squares and dots, there are 10 rows of squares and 12.5 columns (the far right column is half-width), for 10 x 12.5 =125 squares.

We counted a total of 40 + 31 = 71 squares of water. 71 water squares/125 total squares x 32 acres = 18.2 acres of water. It’s not exactly the same due to some rounding, but both estimates are valid.

Based on my personal knowledge of lakes in the mapped region, this seems like a plausible approximation.

DIRECTION

Direction is one of the three key concepts in geography. When I would fill in as a bus dispatcher, drivers would occasionally call or radio to ask for directions. After a few calls, I got to know which drivers preferred to use street and building names and which drivers preferred to use compass directions and distances. Both methods work. Both drivers picked up and delivered passengers just fine.

Relative directions use local landmarks that presumably will be known or obvious to the person receiving the instructions. An example might be “Turn left at the tallest building in town. No other building comes close to its height.” That example includes an obvious landmark, (the tallest building), and a relative direction (left). ‘Left’ is a relative direction because a person arriving at the building from the opposite direction would turn right instead of left.

Absolute directions use compass directions such as north, south, east, west. Technically, even those directions are relative to the earth’s magnetic poles and and axis of rotation, but we won’t quibble with that. From the previous example, the word ‘left’ could be changed to ‘north’.  With that change, everyone knows to turn north at the building and you don’t need a second set of instructions for people arriving at the building from different directions. But you do need to know which way is north!

With the proper tools, and if your needs demand it, you can provide compass directions to fractions of a degree of arc just like degrees of latitude and longitude are divided into minutes and seconds or into decimal fractions of a degree. However, your tools such as the map scale and manufacturing tolerances of the compass or surveying instruments must be up to the task of such precision.

If you’re finding directions on a map, you don’t truly need a compass. A protractor will work for an estimate within a few degrees when using a 1:24,000 scale map. Set your protractor on the map with the 0° marker aligned with the north direction of the map. On the map, draw a line connecting the two points you’re interested in.  Put the center of the protractor on one point, or anywhere along that line, but maintain the orientation of the protractor so 0° is still parallel to north. Read where the line intersects the numbers, the degrees, on the protractor.  The line could intersect the protractor at two locations. Think which direction you’re determining. You may want to start goin 135° (southeast) but if you reverse your direction, you be going 315° (northwest).

Once you’re outdoors, you’ll need a compass. Find north so the red arrow on the compass overlaps the printed arrow on the rotating housing of the floating arrow.  That housing has degree marks written on it. With one hand hold the housing to keep the arrows aligned. With the other hand rotate the base of the compass (usually transparent) until the direction arrow on the base aligns with the degree direction you want to follow. Walk the direction of the large arrow on the base while keeping the magnetic arrow hovering over the arrow in the housing.

Compass Directions: Azimuth or Bearing

There two methods to write a compass bearing, Azimuth or Bearing

A compass AZIMUTH is where due north is always 0° and values increase clockwise. Due east is 90°, due south is 180°, due west is 270°. The maximum possible value for AZIMUTH is 360°, which is also due north, but is usually labeled as 0°. It’s understood that due north is always the starting point and values always increase clockwise, therefore there’s no need for including a direction (north south east west) in the azimuth. The yellow compass above has an azimuth of 135°

In a compass BEARING, N or S is given first, then a degree to an adjacent cardinal direction (E or W) is given second. Example: A direction of 70° has a BEARING  of N70°E. The dominant cardinal direction is N but you go east, specifically 70°. Bearing: N70°E is correct. E 20°N is wrong. As azimuth that bearing is written: 70°

SYMBOLS

Maps contain symbols to represent different portions of reality. Common types of symbols are point, line, and area symbols.

All three classes of symbols have variations that are better able to indicate changes in either quantity or quality of the represented characteristic.  Quantity is often shown by changing the size of the symbol.  If a circle represents a town, a larger circle indicates a larger population.  To show different types of features (changes in quality), the shape of the symbol is changed.  A circle can be a town, a small airplane represents an airport, and an anchor could be a harbor. Color intensity (shading) is often used for quantitative change, but changes in color hue (red or green) generally indicate a change quality.

As the scale and generalization of maps change, some symbolic representations of reality might change.  For instance a small scale map of Iowa that is printed in a notebook would probably use a point symbol to indicate the location of cities.  But a map of Des Moines, IA on the same size piece of paper would use an area symbol for the entire city.

MAP TYPES

Scales and symbols are used in all types of maps.  Maps are broadly categorized as either reference maps or as thematic maps.  Reference map display a broad range of characteristics and try to give equal value to all of them.  Topographic maps are a type of reference map that depict the lay of the land, including elevation and water bodies. Thematic maps often ignore the topography and landforms to better show other characteristics.

POINTS OF VIEW

Most maps are probably drawn in map view. (Stunning statement!) This is the overhead, from above, view. It’s a good choice for showing how a characteristic changes or moves horizontally. US State highway maps are drawn in map view.

A profile view shows the vertical change of a characteristic. When you stand on the ground and look at buildings from the base to the roof, you’re looking at their profile.

Isolines are also approximations of reality.  A weather map of the entire state seems to tell you what the temperature is at all points.  In fact, the temperature was measured only in a few locations and estimates of the temperature for all other points are indicated with the isolines.  Isolines indicating temperature are called isotherms.  The same process is used to make topographic maps.  The USGS has a large number of points with known elevation and location.  Using these points, called benchmarks, as a starting point, contours are drawn to indicate the slope of the land surface.

Examples of Thematic Maps

THEMATIC MAPS

The two maps shown above are both thematic maps.  Neither map shows landforms.  The map on the left shows how languages were distributed spatially across North America, while the map on the right is showing how crime rates vary by state. They are both good maps.  The language map uses color well because no single color stands out as more significant, all colors have the same shade indicating that all languages have similar importance.  However, the map reader must beware that languages don’t change as abruptly as the the map might indicate.  As you move from southern Minnesota to northern Minnesota, don’t expect an abrupt change in spoken languages from Sioux to Algic.  Although such an abrupt change is possible, it isn’t necessarily the case.

The craft brewery map is good because it uses shades of a single color and the data has been processed properly.  The map shows how a single data set (Craft Breweries per capita) changes so it uses a single color in different shades.  People naturally associate darker shades with more of a value so the dark blue indicates that the Pacific Northwest has a more breweries per capita.  The cartographer also processed the data to improve comparisons among states with different populations and population density. Good choropleth maps such as this use preexisting political boundaries (countries, states, counties) and show data in forms such as breweries per consistent number of people (per capita) or as per consistent unit of area (per mi² ).

Summary

Maps are models that simplify and generalize the real world.  The amount of generalization is the scale of the map. Good use of map symbols can improve the interpretation of the map.  There are broad categories of maps that are better suited to demonstrating broad categories of data.