Coordinate systems projections CS 128ES 228 Lecture 2

Coordinate systems & projections CS 128/ES 228 - Lecture 2 b 1

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 2 b 2

1. Modeling Earth’s surface n Ellipsoid: theoretical model of surface - not perfect sphere - used for horizontal measurements n Geoid: incorporates effects of gravity - departs from ellipsoid because of different rock densities in mantle - used for vertical measurements CS 128/ES 228 - Lecture 2 b 3

Ellipsoids: flattened spheres n Degree of flattening given by f = (a-b)/a (but often listed as 1/f) n Ellipsoid can be local or global CS 128/ES 228 - Lecture 2 b 4

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 Ellipsoids International 1924 297 GRS 80 (Geodetic Ref. Sys. ) 298. 257222101 WGS 84 (World Geodetic Sys. ) 298. 257223563 CS 128/ES 228 - Lecture 2 b 5

Geodids: vertical reference surfaces n Like MSL (mean sea level) extended across continents n Based on network of precise gravity measurements n Can depart from ellipsoid by as much as 60 m CS 128/ES 228 - Lecture 2 b 6

2. Then what’s a datum? n Datum: a set of reference measurements for a particular region, based on specified ellipsoid + geodetic control points n > 100 world wide Some of the datums stored in Garmin 76 GPS receiver CS 128/ES 228 - Lecture 2 b 7

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 2 b 8

Datum Smatum n NAD 27 or 83 – who cares? n One of 2 most common sources of mis-registration in GIS n (The other is getting the UTM zone wrong – more on that later) CS 128/ES 228 - Lecture 2 b 9

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 2 b 10

Properties of a map projection n Area n Distance n Shape n Direction Projections that conserve area are called equivalent Projections that conserve shape are called conformal CS 128/ES 228 - Lecture 2 b 11

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 2 b 12

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 2 b 13

Parallels and Meridians Parallels: lines of latitude. Meridians: lines of longitude. § Everywhere parallel § Converge toward the poles § 1 o always ~ 111 km (69 miles) § Some variation due to ellipsoid (110. 6 at equator, 111. 7 at pole) § 1 o =111. 3 km at 1 o = 78. 5 “ at 45 o = “ at 90 o CS 128/ES 228 - Lecture 2 b 0 14

Classes of projections a. Cylindrical b. Conical c. Planar (a. k. a. azimuthal) CS 128/ES 228 - Lecture 2 b 15

Cylindrical projections n Meridians & parallels intersect at 90 o n Often conformal n Least distortion along line of contact (typically equator) n Ex. Mercator CS 128/ES 228 - Lecture 2 b 16

Conical projections n Most accurate along “standard parallel” n Meridians radiate out from vertex (often a pole) n Ex. Albers Equal Area CS 128/ES 228 - Lecture 2 b 17

Planar projections n A. k. a Azimuthal n Best for polar regions CS 128/ES 228 - Lecture 2 b 18

Complications: aspect CS 128/ES 228 - Lecture 2 b 19

Complications: viewpoint CS 128/ES 228 - Lecture 2 b 20

Compromise projections CS 128/ES 228 - Lecture 2 b 21

Buckminster Fuller’s “Dymaxion” CS 128/ES 228 - Lecture 2 b 22

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 2 b 23

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 2 b 24

State Plane Coordinate Zones CS 128/ES 228 - Lecture 2 b 25

Universal Transverse Mercator system § Based on a cylindrical projection running from pole-pole § Distortion minimized in a N – S “strip” (zone) § Zones are 8 o wide but overlap by 1 o on each side. 60 world wide. CS 128/ES 228 - Lecture 2 b 26

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 2 b 27

Miscellaneous Coordinate Systems n Military grids n Land survey grids n Cadastral records n Other … CS 128/ES 228 - Lecture 2 b 28