Location Reference Systems GTECH 201 Lecture 06

Flattening the Earth

Historical Projections Marinus Ptolemy Mercator

Distortions Shape Area Distance Direction

Preserving Properties If two properties are to be preserved then one is always direction These properties are incompatible:

Shape Property Conformal Non-conformal

Area Property

Distance Property

Direction Property

Direction Property Mercator with rhumb line or loxodrome Azimuthal map with shortest distance

Tissot Indicatrices

Distortions Mercator Sinusoidal Equal-area cylindrical Robinson

Cylindrical Projections

Conic Projections

Planar Projections

Refining Map Projections Transverse Mercator Lambert conformal conic Albers equal area conic Lambert azimuthal equal area

Equatorial (normal) Aspect

Transverse Aspect

Oblique Aspect

Aspects for Planar Projections Polar Gnomic Stereographic Orthographic

Aspects for Planar Projections Equatorial Aspect Gnomic Stereographic Orthographic

Aspects for Planar Projections Oblique Aspect Gnomic Stereographic Orthographic

Aspects for Conic Projections Normal aspect

Polyconic Projection Hassler, 1820s US Coastal Survey

Perspective Position of the light source

Perspectives

Other Perspective Projections Lambert cylindrical equal area

Classifying Projections Cylindrical and pseudo-cylindrical

Classifying Projections Conic and pseudo-conic

Classifying Projections Planar and modified planar

Classifying Projections

Classifying Projections Cylindrical straight parallels; straight meridians Pseudo-cylindrical straight parallels, curved meridians Conic partial concentric circles for parallels; straight meridians Pseudo-conic partial concentric circles for parallels; curved meridians Planar Concentric circles for parallels; straight meridians Modified planar No common appearance of parallels and meridians

Projections Parameters Angular parameters Central meridian Latitude of origin Standard parallel Latitude of center Central parallel Linear parameters False easting False northing Scale factor

Origin of X, Y Coordinates

Central Parallel

False Easting/northing

Scale Mercator UTM

Choosing a Map Projection Conformal (shape-preserving) maps Topographic and cadastral Navigation Civil engineering Weather

Choosing a Map Projection Area-preserving maps Population density Land use Quantitative attributes

Choosing a Map Projection Scale-preserving maps no map preserves true distance for all measurements Airline distances Distance from epicenter of an earthquake Cost calculations

Rules of Thumb

Rules of Thumb

Rules of Thumb

Coordinate Systems Two ways to identify a position on a plane

Coordinate Systems .. and on a sphere

Geographic Coordinate Systems Latitude and longitude defined on a sphere

Geographic Coordinate Systems Latitude defined on a spheroid (longitude is as on a sphere)

Components of a GCS An angular unit of measure A prime meridian A datum, which includes a spheroid

Planar Coordinate Systems

Cartesian Coordinates Calculate distance A-B

Universal Transverse Mercator UTM zones

UTM Zones .. as seen from the North Pole

UTM Projections Each zone uses a custom Transverse Mercator projection with its own central meridian

Universal Polar Stereographic Fills the holes of UTM in polar regions

State Plane Coordinate System

SPC N-S zones use Transverse Mercator E-W zones use Lambert Conformal Conic Maximal scale error is 1:10,000 NAD27 or NAD83 datum

Public Land Survey System PLS are shown in purple

PLS It is used to locate areas, not points It is not rigorous enough for spatial analysis like the calculation of distance or direction It is not a grid imposed on a map projection (a system invented in a room), but lines measured on the ground by surveyors

PLS Meridians and Baselines

PLS Area Unit Hierarchy

PLS Township Sections A township is divided into 36 sections, each a square mile (640 acres) A section is divided into 160-acre quarters, which can be further divided into halves, quarters, and so on