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CS 128/ES 228 - Lecture 2b 1
Coordinate systems & projections
CS 128/ES 228 - Lecture 2b 2
Overview of the cartographic process
1. Model surface of Earth mathematically
2. Create a geographical datum
3. Project curved surface onto a flat plane
4. Assign a coordinate reference system
CS 128/ES 228 - Lecture 2b 3
1. Modeling Earth’s surface
Ellipsoid: theoretical model of surface - not perfect sphere - used for horizontal measurements
Geoid: incorporates effects of gravity - departs from ellipsoid because of different rock densities in mantle - used for vertical measurements
CS 128/ES 228 - Lecture 2b 4
Ellipsoids: flattened spheres
Degree of flattening given by f = (a-b)/a
(but often listed as 1/f)
Ellipsoid can be local or global
CS 128/ES 228 - Lecture 2b 5
Examples of ellipsoids
Local Ellipsoids Inverse flattening (1/f)
Airy 1830 299.3249646
Australian National 298.25
Clarke 1866 294.9786982
Clarke 1880 293.465
Everest 1956 300.8017
Global EllipsoidsInternational 1924 297
GRS 80 (Geodetic Ref. Sys.) 298.257222101
WGS 84 (World Geodetic Sys.) 298.257223563
CS 128/ES 228 - Lecture 2b 6
Geodids: vertical reference surfaces
Like MSL (mean sea level) extended across continents
Based on network of precise gravity measurements
Can depart from ellipsoid by as much as 60 m
CS 128/ES 228 - Lecture 2b 7
2. Then what’s a datum?
Datum: a set of reference measure-ments for a particular region, based on specified ellipsoid + geodetic control points
> 100 world wideSome of the datums stored in Garmin 76 GPS receiver
CS 128/ES 228 - Lecture 2b 8
North American datums
Datums commonly used in the U.S.:
- NAD 27: based on Clarke 1866 ellipsoid centered on Meads Ranch, KS - NAD 83: based on GRS 80 ellipsoid
centered on center of mass of the Earth
CS 128/ES 228 - Lecture 2b 9
Datum Smatum
NAD 27 or 83 – who cares?
One of 2 most common sources of mis-registration in GIS
(The other is getting the UTM zone wrong – more on that later)
CS 128/ES 228 - Lecture 2b 10
3. Map projections
A reminder: the Earth is not flat!
Producing a perfect map projection is like peeling an orange and flattening the peel without distorting
a map drawn on its surface.
CS 128/ES 228 - Lecture 2b 11
Properties of a map projection
Area
Shape
Projections that conserve area are called equivalent
Distance
Direction
Projections that conserve shape are called conformal
CS 128/ES 228 - Lecture 2b 12
Two rules:
Rule #1: No projection can preserve all four properties. Improving one often makes another worse.
Rule #2: Data sets used in a GIS must be in the same projection. GIS software contains routines for changing projections.
CS 128/ES 228 - Lecture 2b 13
Geographical coordinates
Latitude & Longitude
Both measured as angles from center of Earth
Reference planes: - Equator for latitude
- Prime meridian for longitude
CS 128/ES 228 - Lecture 2b 14
Parallels and Meridians
Parallels: lines of latitude.
Everywhere parallel
1o always ~ 111 km (69 miles)
Some variation due to ellipsoid (110.6 at equator, 111.7 at pole)
Meridians: lines of longitude.
Converge toward the poles
1o =111.3 km at 1o
= 78.5 “ at 45o
= 0 “ at 90o
CS 128/ES 228 - Lecture 2b 15
Classes of projections
a. Cylindrical
b. Conical
c. Planar (a.k.a. azimuthal)
CS 128/ES 228 - Lecture 2b 16
Cylindrical projections
Meridians & parallels intersect at 90o
Often conformal
Least distortion along line of contact (typically equator)
Ex. Mercator
CS 128/ES 228 - Lecture 2b 17
Conical projections
Most accurate along “standard parallel”
Meridians radiate out from vertex (often a pole)
Ex. Albers Equal Area
CS 128/ES 228 - Lecture 2b 18
Planar projections
A.k.a Azimuthal
Best for polar regions
CS 128/ES 228 - Lecture 2b 19
Complications: aspect
CS 128/ES 228 - Lecture 2b 20
Complications: viewpoint
CS 128/ES 228 - Lecture 2b 21
Compromise projections
CS 128/ES 228 - Lecture 2b 22
Buckminster Fuller’s “Dymaxion”
CS 128/ES 228 - Lecture 2b 23
4. Coordinate systems (grids)
Once a projection is chosen, the map needs a coordinate grid to measure location.
Common systems: State Plane
Coordinates
UTM
CS 128/ES 228 - Lecture 2b 24
State Plane Coordinate System Older system – usually based on Clarke 1866
ellipsoid and NAD 27 datum
Goal: distortion < 1 part in 10,000
Each state divided into either E-W or N-S zones, depending on its orientation. Most use either Transverse Mercator or Lambert Conformal projections (Alaska, New York, and Florida use both)
Only exception: Alaska panhandle (uses Oblique Transverse Mercator)
CS 128/ES 228 - Lecture 2b 25
State Plane Coordinate Zones
CS 128/ES 228 - Lecture 2b 26
Universal Transverse Mercator system
Based on a cylindrical projection running from pole-pole
Distortion minimized in a N – S “strip” (zone)
Zones are 8o wide but overlap by 1o on each side. 60 world wide.
CS 128/ES 228 - Lecture 2b 27
UTM coordinates
Coordinates are based on an arbitrary origin at equator and 500,000 m west of central meridian
E-W position: “easting”N-S position: “northing”
NYS has 3 zones – most state-wide datasets use zone 18
CS 128/ES 228 - Lecture 2b 28
Miscellaneous Coordinate Systems
Military grids
Land survey grids
Cadastral records
Other …