Lecture Notes
GIS for Civil and Environmental Engineering
Cartographic Fundamentals

1.0 MAP REVIEW

1.1 Direction

1. True (Geographical) North: A line from any point on earth to the North Pole.

2. Grid North: The artificial north used in a rectangular grid.

3. Magnetic North: A line from any point on earth to the magnetic pole.
a. Magnetic Declination: The angular divergence between true and magnetic north.

1.2 Measure of Direction

1. Azimuthal: 0^o-360^o

2. Quadrants: 0^o = N, 45^o = N 45^o E, 90^o = E, 135^o = S 45^o E, 180^o = S, 225^o = S 45^o W, 270^o = W, 315^o = N 45^o W.

1.3 Basic Metadata and Ancillary Map Data

1. Cartographer or map author(s) and addresses, e-mail, etc.
2. Souce(s) of data (with dates). Datum and projection of source(s).
3. Map projection.
4. Map datum.
5. Grid system description (if any).
6. Date of completion.
7. Map symbol description.
8. Scale.
9. Magnetic declination at date of creation.
10. North arrow(s)

1.4 Scale

1. Graphic or bar – a proportioned graphical scale.

2. Representative fraction. 1:24,000 or 1/24,000 (1' to 0.3787… mile) -- units are arbitrary, but must be consistent.

i. 1:24,000 could mean 1" = 24,000 inches, 1 cm = 24,000 cm, 1' = 24,000', etc. The units must be the same in the numerator and denominator.

ii. 1:63,360 = 1" to the mile (12*5280=63,360), or 1 cm to 1.609344 km (2.54 cm * 63,360" = 1609344 cm; 1609344 cm /100000 = 1.609344 km).

3. Large and small scale maps. For two maps of equal dimensions, where one map covers a relatively small area of the Earth's surface at high resolution and the other covers a larger area of the Earth's surface at a coarser resolution, the former will be considered large scale and the latter small scale.

1.5 Great Circles & Rhumb Lines

The shortest route between two points is found along a great circle. A great circle can be thought of as the line at which a plane, bisecting the Earth, contacts the surface of the Earth. Rhumb lines are shorter segments used to approximate a great circle in navigating. On some projections great circles are straight, on others rhumb lines are straight.

2.0 CARTOGRAPHIC BASICS

Cartography – "The art and science of representing the 3-dimensional Earth on a two dimensional plane"

First and formost - know your audience!

2.1 Feature Representation – Symbolization

GIS software gives the cartographer a wide variety of choices for the graphical representation of features. These should chosen carefully to best represent the feature or to follow standardized rules.

Some considerations in graphic presentation are:

1. Hue – generally correlative with the term "color", garish colors should be avoided. Pastels and earth tones generally work well.

2. Value – relative brightness. Bright graphics indicate importance and draw the users eye.

3. Saturation - the amount of color saturation. A hue of red that is saturated will be very red.

4. Size – large is generally thought to have relative importance and draw the users eye. Use large type sparingly.

5. Shape – can indicate specific features in a recognizable form.

6. Spacing – can be varied to fit map structure.

7. Orientation – directional arrangement of elongate graphics. Graphic orientation should generally follow the structure of the map.

8. Location – placement of graphic in relation to other graphics.

Points, Lines, & Polygons

1. Points – If using single points, they should be placed directly over the feature they represent. Points can be scaled to better represent the size of feature (graduated symbols). Points (dots) can also be used to represent density. 

2. Lines – Lines should also generally be placed directly on the features that they represent. Line weights and type should be chosen by the cartographer and standardized types should be used where possible (i.e. streams). Lines weights can be used to represent quantity (i.e. flow line maps) or statistical surfaces (isarithmic mapping).

2a. An isarithm is any trace of the intersection of a horizontal plane with a statistical surface. Z values can be mapped this way as contours.

3. Polygons – generally polygons represent areas. The proper use of patterns and fill will lead to maps that are easy to interpret. There must be enough contrast between fill and/or patterns to allow this. The use of annoying patterns should be avoided. Polygons can be used to show density and other statistics as well as Earth surface features. When using graduated polygon symbols they should be proportional.

Maintain consistency in symbolization throughout the map.

Titles, Legends, Ancillary Graphics

1. Titles, legends, and ancillary graphics, such as scale bars, north arrows, etc. should not be of a size that distracts from the map. The map should be the first thing the user sees, not the title, legend, or other ancillary graphics.

2. Legends should be simple but convey all of the information the user needs to understand the symbology. Graduated symbols can be nested, such as nested circles, when representing ordinal data.

Typography

1. Use fonts that produce type that is easy to read.

2. Orient the type to the structure of the map. On larger scale maps the type should be oriented with the upper and lower map edges. For small scale maps the type should be oriented with the parallels.

3. Never overlay type on important features.

4. Interrupt map features with type but never interrupt type. If the type must cross line work then make a block out, or, at a minimum, make sure that a space in the type is over the line. If the type is difficult to read due to background patterns or fill use a block-out.

5. Never place type upside-down.  Type should always "fall" to the right, never the left.

6. Use a larger font or bold type for important features that you want to stand-out to the user.

7. Use consistent fonts and sizes for like features.

8. Use italics for hydrologic features.

9. Curve type for elongate curved features, such as mountain ranges and rivers.

10. Use standardized typology where possible.

11. Type should be either entirely on land or on water.

12. If there is a river or boundary, keep the names of features on either side - do not cross the feature with the annotation.

13. If a feature is on a shoreline, then place the name entirely in the water.

14. Place names should be on top or on the bottom, and preferably on the top right. Map-clutter will more often then not dictate a feature's type position. Place the type where there is the least clutter and interference.

Colors and Patterns

In the age of GIS, digital mapping, and remote sensing, color theory, in some ways, is not as important as it is in traditional cartography, but in other ways it is more important. When generating computer maps cartographers have a tremendous range of color available at their fingertips. However, the proper use of color is important. Additionally, the proper use of gray scales are important when publishing in black and white.

Additive Colors

In computer cartography we are using the additive primary colors (Red, Green, Blue) rather then the subtractive primary colors (Red, Yellow, Blue). This is due to the nature of the color guns in the computer monitor. Use additive (commonly referred to as RGB) colors as follows:

1. R + G = Yellow
2. R + B = Magenta
3. B + G = Cyan
4. R + G + B = White

An absence of color equals black.

The Visible Color Spectrum

The visible color spectrum is approximated as follows:

400 – 499 nm = blue – blue green
500 – 599 nm = green – yellow - orange
600 – 699 nm = red-orange – red

In GIS the quantization level is generally 8-bits. Eight-bit data has a range from 0-255 (2⁸). 0 is black or a lack of value. 255 is the maximum value or brightness. Colors are determined from the value of the three color-guns or, in the case of ArcView, colors are created after RGB values are converted to Hue, Saturation, and Value (HSV). Hue can be thought of as the color. Saturation can be thought of as the intensity or richness of the hue, but not the brightness. The value is a range of gray-scale, from black to white, which gives brightness. For example, the following (HSV) values in ArcView, 255, 255, 255 give a brilliant red. The values 255, 65, 255 create a bright pink as the hue is maximum red, the value is maximized, but the saturation is low.

Often times, when the cartographer wishes to use color to represent a range of values, between 0–255, the data will be classified and then represented by colors ranging from short to long visible wavelengths as follows, lowest to highest: violet – blue- blue/green – green – yellow/green – yellow – orange – red.

General Color Guidelines: the following are suggestions for the use of color.

1. Blue – water, cool, positive numerical values;
2. Green – vegetation, lowlands, forests;
3. Yellow/tan – dry areas, lack of vegetation, intermediate elevation;
4. Brown – landforms (mountains, hills, etc.), contours;
5. Red – warm, important features (roads, cities, features you want to stand out, etc.).

2.2 Statistical Classification/Simplification – Choroplethic Mapping

A simple choroplethic map is uses area symbolization to represent statistical information within the area boundaries.

Equal Steps Based on the Range of the Data: this classification is based upon dividing the range of the data (range = highest minus the lowest data values) by the number of classes desired.

The following data set; 3, 5, 8, 12, 14, 15, 17, 19, 25, 27, 28, 30, 31, 35, 37, 39, if classified into 4 equal steps, would produce the following class memberships:

39 – 3 = 36
36/4 = 9;

therefore class 1 = the range between 3 and (3 + 9) -1

We must, however be sure that each class contains discrete values, the following example shows one way to achieve this:

((3+ 9) – 1) = 11; Class 1 = 3 to 11
(12 + 9) = 21; Class 2 = 12 to 20
(20 + 9) = 29; Class 3 = 21 to 29
(29 + 9) = 30; Class 4 = 30 to 39 (this class has 10 values included)

Class 1 = 3, 5, 8
Class 2 = 12, 14, 15, 17, 19
Class 3 = 25, 27, 28
Class 4 = 30, 31, 35, 37, 39

Parameters of a Normal Distribution: This classification simply uses the standard deviation of a data set for classification. Four classes, for example, could be created as follows:

Mean minus two standard deviations
Mean minus one standard deviation
Mean plus one standard deviation
Mean plus two standard deviations

On the above data set this would work thusly:

Mean = 21.56250

Standard Deviation (std. dev.) = 11.12657

mean + 1 std. dev. = 32.70907
mean + 2 std. dev.  = 43.85565
mean -1 std. dev. =  10.41593
mean -2 std. dev. = -0.73065

Therefore,  four classes consisting of,

Class 1 = 3, 5, 8
Class 2 = 12, 14, 15, 17, 19
Class 3 = 25, 27, 28, 30, 31
Class 4 = 35, 37, 39

would result.

Quantiles: this method employs the division of the number of observations by the number of classes needed. Using the above data set once again, we find that there are sixteen observations; therefore, to produce quartiles (four classes) we do the following:

Classes needed = 4
n = 16
16/4 = 4

Each class will contain four of the values.

Class 1 = 3, 5, 8, 12
Class 2 = 14, 15, 17, 19
Class 3 = 25, 27, 28, 30
Class 4 = 31, 35, 37, 39

2.3 Graduated Symbols

Another method of displaying ordinal or interval/ratio data on a map is through the use of graduated symbols. Proportional or non-proportional points, lines, or polygons may be used for this. Many methods can be used to retain proportional relationships, unless, of course, you are intentionally trying to emphasize a certain part of your data for some reason. This should be guided by the data and how you want it represented.

An example, using the above quartile classification, would be as follows considering points. First the mean of each class is found:

Class 1 = 8
Class 2 = 16.25
Class 3 = 27.5
Class 4 = 35.5

The radii of the points must then be calculated using the means. This can be done many ways. As there are four classes with four values each, you may want to keep things strictly proportional. This could be done simply by choosing a stating radius value and then adding a constant to each following value. For example:

Class 1 radius = 1 cm
Class 2 radius = 1 cm + 1 cm = 2 cm
Class 3 radius = 2 cm + 1 cm = 3 cm
Class 4 radius = 3 cm _+ 1 cm = 4 cm

This would give the map reader the impression that each change in the symbol was of equal importance, if they perceive the changes as equal. Figure 1 shows a graph displaying the relationship of the resulting circumference values in relation to the means.

Another proportional method is to simply take the square root of each mean, and use this to determine the radii of the points. This would result in the following values (rounded to the nearest unit) using the quartiles again:

Class 1 = 3
Class 2 = 4
Class 3 = 5
Class 4 = 6

The Figure 2 shows the relationship of the resulting point circumferences and the orininal means. You may or may not want to round depending on your data. The above radii would work well on a large format map if centimeters were used as units, but not on a small format map. Note the similarity in proportionality between this and the last example.

Linear graduation sometimes makes it difficult for the map reader to properly differentiate large values from small properly. The following non-linear method exaggerates the differences.

Step 1 – take the log of the data value
Step 2 – multiply the log by 0.5 or 0.57
Step 3 – take the inverse log
Step 4 - divide the inverse log by a number that results in an appropriate radius value.

Figure 3 shows a graph of the data produced using this procedure and the original means.

This method, called the Psychological Scaling Method, gives the following radii values:

Class 1 – 1.6
Class 2 – 2.4
Class 3 – 6.6
Class 4 – 7.6

when using 0.57 as the multiplier and dividing the results by 2. An example using the value from Class 1 (8) is:

Log 8 = 0.9031
0.9031 * .57 = 0.5148
Antilog 0.5148 = 3.2717
3.2717/2 = 1.6 (rounded to nearest tenth)

Radius for Class 1 = 1.6

3.1 Geoid, Ellipsoid, and Datum

GIS software, among other things, will ask for the Datum and  Ellipsoid or Spheroid in order to create properly projected maps. Ellipsoid and sphereoid are are generally used interchangeably.

1. Geoid – The irregular shape of the earth. It can be approximated by mean sea level (calculated over 19 years) over water. On land, an equipotential* surface, to which the direction of gravity is perpendicular everywhere, is used. The geoid is deformed by the Earth's rotation, which creates equatorial bulging and polar flattening. Areas over mountain ranges will appear higher than ocean surfaces. The geoid can be thought of as an undulating partial smoothing of the Earth's surface. This undulating surface is not suitable to create a horizontal plane for projections, however, it can be used in datums for vertical planes.

*Potential is defined as Potential = Force x Distance. It is described using Newton-meters (Nm). Force is described using Newtons (N). For example, if 20 N were required to compress a spring 4 meters, the resultant potential would be 80 Nm. Potential can be measured using precision gravimeters. A geoid can be developed using the elevation of each point of equal potential.

2. Ellipsoid or ellipsoid of revolution (aka spheroid) – Observations from the geoid that are transferred to the regular form that most closely approximates the geoid. An ellipsoid is a mathematical surface defined by revolving an ellipse around its minor (polar) axis. It approximates the surface of the earth without topographic undulations. A global ellipsoid has no more than 100 m difference at any point on earth from the geoid surface. The ellipsoid (Fig. 4) can be described by flattening (f)

       f = (a-b)/a

where a is the semimajor axis and b is the semiminor axis of the ellipsoid.

Figure 4. Ellipsoid showing semimajor and semiminor axes.

An ellipsoid can represent a local area as well as global.

3.  Datum -  The National Imagery and Mapping Agency (NIMA) defines a datum as follows: "A datum is defined as any numerical or geometrical quantity, or set of such quantities, which serve as a reference or base for other quantities. In geodesy, two types of datums must be considered: a horizontal datum, which forms the basis for the computations of horizontal control surveys in which the curvature of the earth is considered, and a vertical datum to which elevations are referred. In other words, the coordinates for points in specific geodetic surveys and triangulation networks are computed from certain initial quantities (datums)."

A datum is basically a mathematical model of the Earth. Datums reflect the size and shape of the earth as well as the origin and orientation of coordinate systems. Local datums are used to approximate the local surface of the earth. Datums can include aspects of both ellipsoids and geoids. For example, datum parameters for  the WGS 84 (World Geodetic System) datum include:

1.  Primary -  definition of the shape of an earth ellipsoid, its angular velocity, and the earth mass, which is included in the ellipsoid reference.

2. Secondary  - definition a detailed gravity model of the earth.  

Related Web Resources

Military

This is but a brief introduction to projections. This is just to give you an idea of how they work and their properties. Different projections are used for different purposes. There is no all-purpose projection (although there are some that are close). Therefore, projections are carefully chosen to fit specific purposes. A term to remember here is graticule, or the lines representing latitude and longitude on a map. Different projections have a variety of affects on the graticule as you'll see.

Good web resources for projections can be found at http://www.ahand.unicamp.br/~furuti/ST/Cart/CartIndex/cartIndex.html and http://everest.hunter.cuny.edu/mp/mpbasics.html please check these for more information.

3.3 Projection Properties

The first things to learn about projections are the properties. These are as follows:

1. Conformality

a. At any point on the map the scale is the same in every direction
b. Meridians and parallels intersect at right angles
c. Shapes and angles with short sides are preserved in small areas
d. The size of most areas are distorted

2. Equal Area

a. Areas on the whole map, and all subdivisions, correspond to the correlative areas on the Earth's surface.
b. No flat map can be both equal area and conformal

3. Equidistant

a. True distances are shown from the center of the projection or along a special set of lines
b. No flat map can be both equidistant and equal area

4. Direction

a. Directions are true, but generally in small areas

5. Perspective

a. Representation of three-dimensional objects and depth relationships on two-dimensional surfaces.

3.4 Projection Types and Their Properties

Azmuthal: Mathematically or geometrically projected onto a plane tangent to any point on the globe.

1. Stereographic – plane of projection from a point of tangency

a. Used by USGS for polar maps
b. Polar, oblique, or equatorial aspects (points of tangency)
c. Conformal
d. Perspective
e. Directions true from center point of projection
f. Scale increases away from center point
g. Distortion increases away from the center point
h. Any straight line through the center point is a great circle
i. Plane of projection is the opposite side of the globe from the point of tangency
j. Used for small-scale mapping – continental sized areas.

NOTE: Click on graphics to enlarge

2. Gnomonic

a. Scale increases from the center point
b. Distortion increases away from the center point
c. Perspective
d. Any straight line is a great circle
e. Plane of projection is the equator if polar aspect used
f. First known projection
g. Useful for mapping large portions of the globe

3. Azimuthal Equidistant

a. Equidistant
b. Distances and directions true only from the center point
c. Any straight line drawn through the center point is a great circle
d. Distortion of shapes and areas increase from the center point
e. Used for small-scale mapping – continental sized areas

Cylindrical Projections: mathematically projected on a cylinder tangent or secant to the surface of the Earth.

1. Mercator

a. Distances are true only along the equator and reasonably correct with 15^o of the equator
b. Tangent at the equator
c. Conformal in small areas (angles and shapes)
d. Areas and shapes of large areas are increasingly distorted away from the equator
e. Rhumb lines are straight
f. Used to map at both large- and small scale

2. Transverse Mercator

a. Distances are true along the central meridian
b. Distances, shapes, and areas are reasonably accurate within 15^o of the circle of tangency (great circle). Distortion occurs rapidly beyond this area
c. Conformal
d. Used for large-scale mapping (1:24,000 – 1:250,000)

3. Oblique Mercator

a. Line of tangency not at equator or parallel to a meridian.
b. Distances are true only along the line of tangency
c. Distances, areas, and shapes fairly accurate within 15^o of the line of tangency
d. Distortion increases away from the great circle increasing with distance
e. Conformal within a small area (shapes and angles reasonably accurate)
f. Used to map regions along a great circle

Conic Projections: Mathematically projected on a cone secant or tangent to the Earth.

1. Albers Equal Area – two secant parallels

a. Equal area – all areas on the map proportional to the same area on the Earth
b. Directions are reasonably accurate near secant line
c. Distances are true at standard parallels
d. Scale is true along standard parallels
e. USGS uses this for maps of the conterminous U.S. 48 states

3. Equidistant (simple) Conic – one line of tnagency but conceptually secant at two standard parallels

a. Directions true only along parallels
b. Directions, shapes, and areas are reasonably accurate with distortion occurring away from the standard parallels
c. Used to map mid-latitudes

4. Polyconic – mathematically based in an infinite number of cones and an infinite number of parallels

a. Directions are true only along the central meridian
b. Distances are true only along each parallel and the central meridian
c. Distortion increases away from the central meridian
d. Compromise of many properties, not conformal, equal area, or perspective
e. Used for large-scale mapping

Note: the above projection graphics are from the USGS poster Map Projections

GRIDS

State Plane

There are any number of grid systems that have been used on a local basis to maintain coordinates for surveying and map making. Most of these are outdated, as they are not standardized. Lack of standardization can create a myriad of problems when trying to use data from these grids in a GIS. In the United Stated the State Plane grid system is standardized and based on one-foot increments. Each state is broken down into one or more local state plane grids, which have names and USGS codes. The names and/or codes can be found in most GIS software manuals. In Utah there are three local state plane grids – north, central, and south. Each state also uses a specific map projection for their state plane coordinates. In Utah it is the Lambert conformal conic. Some states use the transverse Mercator.

UTM

The Universal Transverse Mercator (UTM) grid is a world standard and measured in meters. This grid is based upon 6^o wide quadrilaterals each with a central meridian. The central meridian is designated as 500,000 meters east. This value, which decreases to the west and increases to the east, is know as the easting and is always read first. Northings begin at the equator at 0, if going north, and 10,000,000 if going south. Northings are always read second. Each quadrilateral is designated at a Zone. There are 60 zones circling the earth from west to east and these are designated zones 1 – 60 in name. Zone 1 begins at 180 ^o west longitude. Zone 60 ends at 180^o east longitude. Utah is in zone 12, which has it's central meridian at 111^o west longitude.

Going south to north the quadrilaterals are 8^o in depth and have an alphabetic character designation. For instance, 80^o to 72^o south latitude is zone C.  Generally, GIS software will only need the zone number (numeric character, such as 12) and whether the area is north or south of the equator, as northings begin at the equator.

FoFor more info see: http://en.wikipedia.org/wiki/Universal_Transverse_Mercator_coordinate_system

METES & BOUNDS

Metes and bounds is an archaic system of property boundary description. To describe a boundary, a known point-of-beginning is used. All subsequent measurements relate to the point-of-beginning. The following is a "real world" example of a metes and bounds description.

Commencing North 852.28 feet and West 657.15 feet from the Southeast corner of Section 15, Township 5 South, Range 1 East, Salt Lake Base and Meridian, and running thence South 12°57'35" East 172.30 feet; thence North 89°27'02" West 125.80 feet along the North side of a concrete retaining wall; thence South 4°56'27" West 144.36 feet along the West side of a concrete retaining wall; thence North 88°49'39" West 125.02 feet along a chain link fence; thence South 1°40'26" West 103.48 feet along a chain link fence; thence North 89°50'32" West 90.26 feet along a chain link fence; thence North 89°15'18" West along an old fence 267.97 feet; thence continuing North 89°24'55" West along an old fence 612.03 feet; thence North 0°04'54" West 401.43 feet along an old fence; thence East 1198.37 feet to beginning.

We will discuses this further in class. We will also map an example using GIS in a later lab.

GIS Data Entry

When capturing data for GIS there are several ways to enter data.

1. Traditional data entry is via a digitizer tablet. We will not use this method in class, however you need to be familiar with the concepts. If using a digitizer, the technician will enter a series of tic marks or control points with known coordinates. UTM and state plane grids are good for these as is the latitude and longitude graticule. After the tics are entered, features are digitized. Upon the completion of digitizing, the data can be reprojected if need be.

2. We will use what is know as heads-up digitizing in this course. To accomplish heads-up digitizing, an image of the area of which you want to map is used to digitize points, lines, and polygons on the computer screen. To use a digital image, the image must either contain coordinate information natively (GeoTiff images for example) or an ancillary file, known as a World File in ArcView parlance, which contains this information. Once the image is loaded the coordinate information is applied to any digitized vector features.

3. You must know the datum, ellipsoid, projection and often times other projection information to reproject your maps.

4. What if no projection information is available for a map you wish to input? Welcome to the world of GIS!

METADATA

Metadata is information that keeps track of important map and data facts such as projection information, date of origin, and origin of data. Metadata is not optional, it is required for all GIS data. Without metadata a GIS data base can quicklybecome useless if the originator is not available or if they forget important information. Therefore formalized and standardized metadata schemes should be used. A simple metadata form is shown on the following page.

The Federal Geographic Data Committee (FGDC), who coordinate the National Spatial Data Infrastructure (NSDI), have developed a very complete, but very complex metadata standard for use with data in their clearinghouse program. More information can be obtained at:

http://www.fgdc.gov/index.html

Simple Metadata Example

Cartographic_Info