Cartography and GIS

• Understanding the way maps are encoded to be used in GIS requires knowledge of cartography

• Cartography is the science that deals with the construction, use, and principles behind maps

• A map is a depiction of all or part of the earth or other geographic phenomenon as a set of symbols and at a scale whose representative fraction is less than one to one

Earth to Globe to Map

Shape of the Earth

We think of the earth as a sphere

It is actually a spheroid, slightly larger in radius at

the equator than at the poles

Models of the Earth

The earth can be modeled as a

– sphere,

– oblate ellipsoid

– geoid

Geographic Coordinates (, z)

• Latitude () and Longitude () defined using an ellipsoid, an ellipse rotated about an axis

• Elevation (z) defined using geoid, a surface of constant gravitational potential

• Earth datums define standard values of the ellipsoid and geoid

The Spheroid and Ellipsoid• The sphere is about 40 million meters in

circumference.

• An ellipsoid is an ellipse rotated in three dimensions about its shorter axis.

• The earth's ellipsoid is only 1/297 off from a sphere.

• Many ellipsoids have been measured, and maps based on each. Examples are WGS84 and GRS80.

Earth as Ellipsoid

The Datum

• An ellipsoid gives the base elevation for mapping, called a datum.

• Examples are NAD27 and NAD83.

• The geoid is a figure that adjusts the best ellipsoid and the variation of gravity locally.

• It is the most accurate, and is used more in geodesy than GIS and cartography.

Representations of the Earth

Earth surface

EllipsoidSea surface

Geoid

Mean Sea Level is a surface of constant gravitational potential called the Geoid

Definition of ElevationElevation Z

•

Pz = zp

z = 0

Mean Sea level = Geoid

Land Surface

Elevation is measured from the Geoid

Earth Models and Datums

GeoidEllipsoid

Sphere

Sea Level

Height

Figure 2.4 Elevat ions defined with reference to a sphere, el lipsoid, geoid, or local sea level wil l al lbe different. Even location as lati tude and longitude will vary somewhat. When linking field datasuch as GPS with a GIS, the user must know what base to use.

Terrain

Geographic Coordinates

• Geographic coordinates are the earth's latitude and longitude system, ranging from 90 degrees south to 90 degrees north in latitude and 180 degrees west to 180 degrees east in longitude.

• A line with a constant latitude running east to west is called a parallel.

• A line with constant longitude running from the north pole to the south pole is called a meridian.

• The zero-longitude meridian is called the prime meridian and passes through Greenwich, England.

The most commonly used coordinate system today is the latitude, longitude, and height system. The Prime Meridian and the Equator

are the reference planes used to define latitude and longitude.

Figure 10. Equator and Prime Meridian

Map Projections

• A transformation of the spherical or ellipsoidal earth onto a flat map is called a map projection.

• The map projection can be onto a flat surface or a surface that can be made flat by cutting, such as a cylinder or a cone.

Map projections

Map Projections (contd)• Projections can be based on axes parallel to the

earth's rotation axis (equatorial), at 90 degrees to it (transverse), or at any other angle (oblique).

• A projection that preserves the shape of features across the map is called conformal.

• A projection that preserves the area of a feature across the map is called equal area or equivalent.

• No flat map can be both equivalent and conformal. Most fall between the two as compromises.

• To compare or edge-match maps in a GIS, both maps MUST be in the same projection.

No flat map can be both

equivalent and conformal.

Coordinate Systems for the US• Some standard coordinate systems

used in the United States are – geographic coordinates– universal transverse Mercator

system– military grid– state plane

• To compare or edge-match maps in a GIS, both maps MUST be in the same coordinate system.

GIS Capability

• A GIS package should be able to move between – map projections, – coordinate systems, – datums, and – ellipsoids.

Universal Transverse Mercator (UTM)

Universal Transverse Mercator (UTM) coordinates define two dimensional, horizontal, positions. Each UTM zone is

identified by a number. UTM zone numbers designate individual 6° wide longitudinal strips extending from

80° South latitude to 84° North latitude.

Alabama is in UTM Zone 16

State plane systems were developed in order to provide local reference systems that were tied to a national datum. In the United States, the State Plane System 1927 was developed in the 1930s and was based on the North American Datum 1927 (NAD_27). NAD_27 coordinates are in English units (feet).

NAD_27 State Plane Coordinate Example

STATE PLANE COORDINATE SYSTEMS

The State Plane System 1983 is based on the North American Datum 1983 (NAD_83). NAD_83 coordinates are metric.

State Plane Coordinate System Example ________________________________________________________________________

NAD_83 Latitude, Longitude of 30:16:28.82 N 97:44:25.19 W is NAD_83 Texas Central Zone

State Plane Coordinates, Easting and Northing 949465.059m, 3070309.475m______________________________________________________________________

While the NAD_27 State Plane System has been superceded by the NAD_83 System, maps in NAD_27 coordinates are still in use. Most USGS 7.5 Minute Quadrangles show several coordinate system grids including latitude and longitude, UTM kilometer tic marks, and applicable State Plane coordinates.

Each state has its own State Plane system with specific parameters and projections. Software is available for easy conversion to and from latitude and longitude. Some smaller states use a single state plane zone while larger states are divided into several zones. State plane zone boundaries often follow county boundaries.

Figure 24. State Plane Zone Example

Two projections are used in all State Plane systems, with one exception. Lambert Conformal Conic for regions with a larger east_west than north_south extentTransverse Mercator for regions with a larger north_south extent

The exception is one State Plane zone in Alaska which uses an Oblique Mercator projection for a thin diagonal area.

Also realize that using the “appropriate” projection depends on your objectives for displaying

and analyzing the map data

Distance Units: Decimal DegreesProjection: None

Undistorted distance measurement is 2451 miles

Shapes are distorted, but ArcView computes distancefrom spherical coordinates of latitude and longitude,taking the earth’s round surface into account

No projection

Distance = 3,142 miles…691 miles furtherChanging to the Mercator projection shows shapes anddirection accurately, but sacrifices distance and area.

Mercator projection

Distance = 2,238 … about 213 miles less than actualPeters Equal-Area Cylindrical projection preserves areabut sacrifices shape, distance, and direction.

Peters Equal-Area Cylindrical projection

Equidistant Conic (Coterminous U.S.)

Distance = 2,452 (almost the same as original)

Projection preserves shape and accurate east-westdistances, but sacrifices direction and area

Equidistant Conic (Coterminous U.S.)Peters Equal-Area Cylindrical projection

Mercator projectionNo projection

Distance = 2,452 (almost the same as original)

Projection preserves shape and accurate east-westdistances, but sacrifices direction and area

Distance = 2,238 … about 213 miles less than actualPeters Equal-Area Cylindrical projection preserves areabut sacrifices shape, distance, and direction.

Distance = 3,142 miles…691 miles furtherChanging to the Mercator projection shows shapes anddirection accurately, but sacrifices distance and area.

Undistorted distance measurement is 2451 miles

Shapes are distorted, but ArcView computes distancefrom spherical coordinates of latitude and longitude,taking the earth’s round surface into account