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 (

f, l

, z)

• Latitude ( f ) and Longitude ( l ) 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

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

Definition of Elevation

Elevation Z P • z = z p z = 0 Land Surface Mean Sea level = Geoid Elevation is measured from the Geoid

Earth Models and Datums

Height Terrain Sea Level Ellipsoid Geoid Sphere Figure 2.4

Elevat ions defined with reference to a sphere, el lipsoid, geoid, or local sea level wil l al l be different. Even l ocation as l ati tude and longitude will vary som ewhat. When linking field data such as GPS with a GIS, t he user must know what base to use.

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 COORDINATE SYSTEMS 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

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 extent Transverse 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 Degrees Projection: None

No projection

Undistorted distance measurement is 2451 miles Shapes are distorted, but ArcView computes distance from spherical coordinates of latitude and longitude, taking the earth’s round surface into account

Mercator projection

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

Peters Equal-Area Cylindrical projection

Distance = 2,238 … about 213 miles less than actual Peters Equal-Area Cylindrical projection preserves area but sacrifices shape, distance, and direction.

Equidistant Conic (Coterminous U.S.)

Distance = 2,452 (almost the same as original) Projection preserves shape and accurate east-west distances, but sacrifices direction and area

No projection Mercator projection Undistorted distance measurement is 2451 miles Shapes are distorted, but ArcView computes distance from spherical coordinates of latitude and longitude, taking the earth’s round surface into account Peters Equal-Area Cylindrical projection Distance = 3,142 miles…691 miles further Changing to the Mercator projection shows shapes and direction accurately, but sacrifices distance and area.

Equidistant Conic (Coterminous U.S.) Distance = 2,238 … about 213 miles less than actual Peters Equal-Area Cylindrical projection preserves area but sacrifices shape, distance, and direction.

Distance = 2,452 (almost the same as original) Projection preserves shape and accurate east-west distances, but sacrifices direction and area