There are two fundamental concepts that are critical to using and understanding maps: projection and scale. These elements of spatial data are critically important and conceptually difficult, and the following sections provide a background for each.

Maps are representations of the earth’s surface. This representation of space requires a spatial reference system based upon a set of geometric assumptions. A spatial reference system establishes a point of origin, orientation of reference axes, and geometric meaning of measurements, as well as units of measure. This locational information describes the position of particular geographic features on the Earth’s surface, as well as spatial relationships between features, or georeferencing.

Georeferencing is the process of establishing a relationship between the data displayed in your GIS software and its real-world location using a coordinate system. While you can locate a point on the Earth with great accuracy, representing the same point on a map is still an approximation.

Coordinates are sets of measurements related to a specific spatial reference system, e.g. pairs of distance measurements (X,Y) on independent planar reference systems, or to angular measurements from the plane of the equator and the Prime Meridian called latitude-longitude pairs. Coordinate systems allow for georeferencing. Every location in our thematic data is referenced to its corresponding location on the Earth’s surface. Coordinate systems are made up of an ellipsoid, datum, projection and units.

A common system of spatial reference is a critical element of a GIS project or map set, since it brings the different map layers into correspondence. There are two types of horizontal reference systems: geographic coordinate system and plane coordinate systems. The geographic coordinate system specifies locations on a spherical Earth; and a plane coordinate system specifies locations on a flattened Earth.

Latitude (parallels) and longitude (meridians) form an imaginary network over the earth’s surface (graticule). Degrees of latitude and longitude (Global Reference System) are used to locate exact positions on the surface of the globe; they are not uniform measures on the Earth’s surface. This rrence system measures angles from the center of the Earth, rather than distances on the Earth’s surface. Additionally, the global coordinate system (Fig. 1) is used for the curved surface of the Earth - it is not a map projection. Only at the equator does the distance of one degree of longitude approximately equal the distance of one degree of latitude.

**Fig. 1. **Global Coordinate System with main components labeled. Image Source

Degrees of latitude measure north and south of the equator (0 - 90 degrees). Latitude also represents an important measure of seasonality.

Degrees of longitude measure east and west of the Prime Meridian (0 - 180 degrees). The Prime Meridian has changed over time due to changing political fortunes and opportunities, but is currently based on Greenwich, England. Degrees of longitude also measure time, where 15 degrees of longitude is equal to one hour.

**Fig. 2. **(Above) X, Y, and Z-axes (blue) from which latitude and longitude angles (orange) are measured. Green box shows how these angles interest and locate an area on the Earth’s surface. Image Credit: Wikipedia

Because it is difficult to make measurements in spherical coordinates, geographic data is projected into **planar coordinate systems** (Cartesian coordinate systems).

You should familiarize yourself with the:

- Geographic coordinate system
- Universal Transverse Mercator system

**For more information on coordinate systems, click ****here**

The Earth is best represented by an **ellipsoid **(or spheroid). However, for small-scale maps (less than 1:5,000,000), the assumption is that a sphere can be used for the calculation as the difference between a sphere and a spheroid would not be detectable on a map. The Earth must be treated as an ellipsoid to maintain accuracy for larger-scale maps (1:1,000,000). The shape of an ellipse has two different radii. The longer axis is called the major axis and the shorter axis is called the minor axis.

The Earth has been surveyed many times to better understand its surface features. The profession that engages in this activity is called **geodesy**. Using survey monuments and **geodetic control points**, a set of numerical values are developed to serve a reference or base for mapping - a **datum**. Generally, an ellipsoid is chosen to fit one country or particular area.

There are two types of datums: earth-centered and local. An earth-centered datum has its origin placed at the earth’s currently known center of mass and is more accurate overall. A local datum is aligned so that it closely corresponds to the earth’s surface for a particular area and can be more accurate for that particular area. Because datums establish reference points to measure surface locations, they also enable us to calculate planar coordinate values when applying a projection to a particular area. Two maps using the same map projection but different datums can have very different coordinate values for the same location on the earth’s surface. *Checking the datum, as well as the projected coordinate system of a dataset is vital for matching different data sources in the same coordinate space*.

**Fig 3. **Conceptual diagram showing differences between the geoid, the variable topographic surface, and the ellipsoid designed to fit them. Image Credit: Peter H. Dana, 1994.

The most widely used global datum is the **World Geodetic System of 1984 (WGS84)**. Satellite-determined ellipsoids are starting to replace older ground-measured ellipsoids for reference calculations. All points located using GPS are tied to the 1984 datum.

**For more information on Datums, click ****here****.**

In order to map the Earth’s surface, it must be transformed from a three-dimensional surface to a two-dimensional surface. This *transformation*, using a mathematical conversion, is referred to as a map projection. Projection types or families are based upon the configuration of the plane on which the globe is projected (Fig. 4). They are:

*Geometric*(or planar/azimuthal): the spherical grid or globe is projected onto a plane*Conical:*the globe is projected on to a cone that is then “unrolled” as a flat plane*Cylindrical:*the globe is projected onto a cylinder that is wrapped around the globe and then “unrolled” onto a flat plane

**Fig. 4. **(Left to Right) Three families of projections: Geometric, Conical, Cylindrical. Note the different and unique perspectives created by each type.

*Geometric maps* are projected from a particular *perspective*. *Perspective *refers to the source of light that would project the globe onto a flat surface (Fig. 5).

*Gnomonic:*source of light is from the center of the earth*Stereographic:*source of light is a point on the opposite end of the globe*Orthographic:*source of light is from an infinite distance

**Fig. 5. **Three types of perspectives applied to geometric maps. Changing the light source changes how the map image is projected onto the planar surface.

**Distortion**

The projection distorts at least one these properties: shape, area, distance, proximity, and direction. When you are constructing a map, you should know which projections distort which properties and to what extent. Most projections are mathematically derived and are a function of mathematical relationships:

*Conformal:*preserve form or shape*Equi-distant:*distance can be measured accurately from one point to other points*Equal area:*unit area equivalent throughout map*Equi-azimuthal:*preserves angles (or directions)

**Tangency**

*Tangency *(or case) refers to the location where a projection touches or slices through the globe. Lines of tangency are where there is the least distortion on a map. Distortion increases away from the line or point of tangency. Planar projections are tangent to the globe at a single point; conical and cylindrical have a single line of tangency. *Secant case* refers to a projection surface that touches the globe along two lines. This is especially useful for very large areas.

**Fig. 6. **Examples of projections with tangent and secant cases. Red lines indicate location where project surface touches the globe (i.e. areas of known distortion).

**Aspects**

Projections can be positioned over the globe in *aspects*. *Aspects* are based upon the area of interest of the map. Aspect (along with case) can reduce distortion.

*Polar:*projection surface situated over north or south pole*Equatorial:*projection surface located over equator*Transverse:*projection surface is 90° from normal (equatorial) position*Oblique:*projection surface is anywhere between pole and equator

Naming and Selecting a Projection Names of projections should be as inclusive as possible, containing the projection creator (e.g., Mercator), the projection family (e.g., conical), and the mathematical relationship (e.g., conformal).

The job of creating a map projection has been greatly simplified due to software packages for map projections. However, the job of selecting an appropriate map projection has been made more difficult. If you try to merge data files that specify locations with different spatial reference systems, or that are based on different datums, the data files will be incompatible.

**General rules:**

- Most data as originally presented are in geographic coordinates in decimal degrees.
- The projected coordinate system is composed of the projection type, plus additional defining parameters: units (feet or meters), the central meridian, possibly a zone depending on the projections (e.g. UTM), and sometimes a
*false easting or northing*. False eastings and northings may be applied to the coordinate values so that spatial data is referenced in positive units. - For regions that are primarily East-West in extent, the Albers Equal Area or Lambert Conformal Conic are good choices for map projections. The Central Meridian should be through the middle of the region of interest, the Reference Latitude should be wherever you think the center of a coordinate systems could be (usually at the center or below the bottom of the extent of the geographic features). The two standard parallels should be located approximately 1/6 from the bottom and 1/6 from the top of the geographic extent of the mapped features.
- For regions that are primarily North-South in extent, the Transverse Mercator is a good projection choice. The Central Meridian should be through the middle of the region of interest. The Reference Latitude should be either in the middle or below the bottom of the region of interest.
- The Universal Transverse Mercator is a good choice for projection of maps of particular cities or counties.
**Consider the following when determining the projection: latitude of area, extent and theme.**

**For more information on projections:**

- Excellent figures and additional overview

*Scale* is expressed as a ratio between the distance or area on a map and the same distance or area on the earth. Map scale is commonly expressed in three ways:

- As a simple fraction (1/100,000) or ratio (1:100,000) called the
*representative fraction*(RF). In a representative fraction, the map distance is always reduced to 1. - As a written or verbal statement of map distance in relation to earth distance (1 inch equals 64 miles).
- As a graphic representation or a scale bar.
**Graphic scales remain true when maps are photographically reduced or enlarged.**

*Map* or *cartographic scale* is the proportion between a distance on a map and a corresponding distance on the ground. The relationship is expressed in the following equation:

When comparing map scales, it is helpful to remember that the* larger* the scale, the smaller the area represented and the greater amount of detail that is included. The terms large scale and small scale refer to large and small representative fractions. The smaller the denominator of a representative fraction, the larger its value, thus the larger the map scale.

*Large-scale* maps are useful for detailed information, such as location of major buildings in city plans. The *smaller* the scale, the larger the area covered and less detail presented. *Small-scale* maps allow the reader to place cities in relation to each other and can provide a regional view.

*Geographic extent* is the size of the study area. A study may be conducted at a local, regional, or global scale. The extent of your study area can affect analysis results. For example, county versus state incidence of cancer may be quite different.

*Spatial resolution* refers to the *grain* or smallest unit that is distinguishable. Map data at different scales allow for resolution of different objects. For example, a house site on a 1:24,000 scale map will not be seen on a 1:100,000 scale map. *Minimum mapping unit* (MMU) refers to the measure of detail (resolution) that discrete features are represented; MMUs may have both size and shape requirements.

*Operational scale* is where the process of interest occurs. Processes may be scale dependent – they can be detected at one scale but not another. Homogeneity and heterogeneity are affected by scale and may affect the *detectability *of a process. For example, pine bark beetle may infest individual trees in a forest – only affecting a small area; however throughout the overall forest, the loss is less detectable and the forest appears homogeneous. The relationship between process scale and observational scale needs to be understood, and in some instances a multi-scale approach may be necessary.

Accuracy is also scale dependent. The US Geological Survey’s National Map Accuracy Standard guarantees that the mapped positions of 90 percent of well-defined points (benchmarks, road intersections) on topographic maps will be within 0.02 inches of their actual positions on a map.

**Converting From one Form of Scale to Another**** **

Often when using cartographic materials it is useful to convert from one form of scale to another. If you have a good understanding of the concept of scale, the techniques are fairly simple.

- Here is an example of converting from Verbal Scale to RF. Remember, the RF has the same unit of measurement on both sides of the colon:

1 inch equals 10 miles → 1 inch = 10 miles → 1 inch = 10 miles x 12 inches/foot x 5280 feet/mile → 1 inch = 10 x 63360 inches = 633,600 inches 1:633,600

- To convert from RF to Verbal Scale you convert the fraction to familiar units of measurements; for example:

1:250,000 → 1 inch = 250,000 inches → 1 inch = 250,000 inches [d] 12 inches/foot = 20,833.3 feet → 1 inch = 20,833.3 feet [d] 5280 feet/mile = 4 miles or 1 inch = 250,000 [d] 63360 inches/mile = 4 miles 1 inch equals 4 miles. [Note: [d] = divided by]

*In ArcGIS:*

The number that ArcGIS displays in the Scale box describes the relationship between the dimensions of the view and the dimensions on earth. In order for ArcGIS to scale of your view properly in the data frame window, you need to know the map units associated with your spatial data.

One way to find out what units your spatial data is in is to add the data as a theme to an empty data frame and look at the coordinate read-out at the right hand side of the tool bar. The coordinates will be expressed in degrees, minutes and seconds if you are in the geographic coordinate system.

**RULE OF THUMB:** It is always better to reduce a map *after* analysis than to enlarge it *for* analysis.

**Additional resources for understanding scale**:

A significant source of digital data is paper maps (or *analog *representation). Digital maps are different from paper maps in several ways.

- Digital maps are numbers that explicitly describe what and where something is located. The data structure (e.g., X, Y coordinates or grid cells) affects both storage efficiency and system performance.
- Extent and grain are independent properties of a digital map. Be sure to specify both spatial extent (broad or local) and grain (coarse or fine) when describing a map.
- Spatial extent is no longer a trade off with resolution or grain. A national map can exist at a 1:24,000 scale.
- Geographic features are represented differently depending on context of display and analysis.
- Domain (or scale) of the question can change with feature abstraction.
- Variability of sampling strategy can be accounted for in the digital environment.

When considering data for GIS, both the *extent *and the *resolution *will have an affect on data volumes. Disk storage space continues to get cheaper, however the volume of data incorporated into a project is still a consideration in terms of both storage and analysis (computer processing time).

Knowing your data is critical to using spatial analysis. All spatial data are inaccurate to some degree but are generally represented in the computer with high precision.

*Accuracy:* is the closeness of results computations or estimates to true values. Spatial data is usually a generalization of the real world – we work with values that are accepted to be true. Accuracy refers to the quality of the data and the number of errors in the dataset or map.

*Precision:* refers to the level of measurement and exactness; it is the number of decimal places or significant digits in a measurement. Precision is not the same as accuracy – a large number of significant digits does not necessarily indicate that the measurement is accurate.

Positional accuracy and precision are a function of the scale at which a map (paper or digital) was created. Beware of the dangers of false accuracy and false precision, that is reading locational information from map to levels of accuracy and precision beyond which they were created. This is a very great danger in computer systems that allow users to pan and zoom at will to an infinite number of scales. Accuracy and precision are tied to the original map scale and do not change even if the user zooms in and out.

The number of significant digits required for a specific project when using Cartesian coordinates depends on two measures:

- The size of the study area (extent)
- Resolution (accuracy) of the measurement

In a computer, numbers can be stored as floating point numbers, meaning that there is no fixed number of digits before or after the decimal. In GIS, floating point numbers are single-precision (32-bit or 7 significant decimal digits) or double precision (64-bit or 15 significant decimal digits) referring to the number of digits that can be stored for a single value. Double precision requires twice the storage space, but carries more precision.

**The computer system offers more resolution than is needed by the data – meaning that the data is stored at higher precision than is justified by its accuracy.**

**Additional Resources**

There exist some excellent resources for learning more about the concepts covered in this lesson:

- ArcGIS Desktop Help: Specifying a coordinate system ; the geographic coordinate systems warning
- Any atlas, cartography text book or GIS text book