CS 128/ES 228 - Lecture 2b1 Coordinate systems & projections.

CS 128/ES 228 - Lecture 2b 1

Coordinate systems & projections


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


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


Ellipsoids: flattened spheres

Degree of flattening given by f = (a-b)/a

(but often listed as 1/f)

Ellipsoid can be local or global


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


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


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


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


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)


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.


Properties of a map projection

Area

Shape

Projections that conserve area are called equivalent

Distance

Direction

Projections that conserve shape are called conformal


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.


Geographical coordinates

Latitude & Longitude

Both measured as angles from center of Earth

Reference planes: - Equator for latitude

- Prime meridian for longitude


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


Classes of projections

a. Cylindrical

b. Conical

c. Planar (a.k.a. azimuthal)


Cylindrical projections

Meridians & parallels intersect at 90o

Often conformal

Least distortion along line of contact (typically equator)

Ex. Mercator


Conical projections

Most accurate along “standard parallel”

Meridians radiate out from vertex (often a pole)

Ex. Albers Equal Area


Planar projections

A.k.a Azimuthal

Best for polar regions


Complications: aspect


Complications: viewpoint


Compromise projections


Buckminster Fuller’s “Dymaxion”


4. Coordinate systems (grids)

Once a projection is chosen, the map needs a coordinate grid to measure location.

Common systems: State Plane

Coordinates

UTM


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)


State Plane Coordinate Zones


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.


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


Miscellaneous Coordinate Systems

Military grids

Land survey grids

Cadastral records

Other …

CS 128/ES 228 - Lecture 2b1 Coordinate systems & projections.

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