CS 128/ES Lecture 2b1 Coordinate systems & projections

CS 128/ES Lecture 2b2 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 Lecture 2b3 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 Lecture 2b4 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 Lecture 2b5 Examples of ellipsoids Local EllipsoidsInverse flattening (1/f) Airy Australian National Clarke Clarke Everest Global Ellipsoids International GRS 80 (Geodetic Ref. Sys.) WGS 84 (World Geodetic Sys.)

CS 128/ES Lecture 2b6 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 Lecture 2b7 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 wide Some of the datums stored in Garmin 76 GPS receiver

CS 128/ES Lecture 2b8 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 Lecture 2b9 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 Lecture 2b10 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 Lecture 2b11 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 Lecture 2b12 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 Lecture 2b13 Geographical coordinates Latitude & Longitude  Both measured as angles from center of Earth  Reference planes: - Equator for latitude - Prime meridian for longitude

CS 128/ES Lecture 2b14 Parallels and Meridians Parallels: lines of latitude.  Everywhere parallel  1 o always ~ 111 km (69 miles)  Some variation due to ellipsoid (110.6 at equator, at pole) Meridians: lines of longitude.  Converge toward the poles  1 o =111.3 km at 1 o = 78.5 “ at 45 o = 0 “ at 90 o

CS 128/ES Lecture 2b15 Classes of projections a. Cylindrical b. Conical c. Planar (a.k.a. azimuthal)

CS 128/ES Lecture 2b16 Cylindrical projections Meridians & parallels intersect at 90 o Often conformal Least distortion along line of contact (typically equator) Ex. Mercator

CS 128/ES Lecture 2b17 Conical projections Most accurate along “standard parallel” Meridians radiate out from vertex (often a pole) Ex. Albers Equal Area

CS 128/ES Lecture 2b18 Planar projections A.k.a Azimuthal Best for polar regions

CS 128/ES Lecture 2b19 Complications: aspect

CS 128/ES Lecture 2b20 Complications: viewpoint

CS 128/ES Lecture 2b21 Compromise projections

CS 128/ES Lecture 2b22 Buckminster Fuller’s “Dymaxion”

CS 128/ES Lecture 2b23 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 Lecture 2b24 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 Lecture 2b25 State Plane Coordinate Zones

CS 128/ES Lecture 2b26 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 Lecture 2b27 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 Lecture 2b28 Miscellaneous Coordinate Systems Military grids Land survey grids Cadastral records Other …