MAP PROJECTIONS Cartographic Design for GIS Geog 340

MAP PROJECTIONS Cartographic Design for GIS (Geog. 340) Prof. Hugh Howard American River College

MAP PROJECTION DEFINED

MAP PROJECTION • • Method by which Earth’s geographic coordinates are converted to projected (Cartesian) coordinates The “flattening” of Earth onto a plane Geographic Coordinates (lon, lat) Projected (Cartesian) Coordinates (x, y)

MAP PROJECTION • A great challenge faced by ancient (and modern) cartographers – Ancient Babylonians introduced the idea of scale, and 360 degrees in a circle – Ancient Greeks introduced the idea of meridians and parallels (diaphragma) – Claudius Ptolemy introduced the idea of map projections in the 2 nd century AD Claudius Ptolemy, 2 nd Century AD

MAP PROJECTION • How are projections created? – Today, most projections are created mathematically using computers – A Reference Globe is created as a scale model of Earth – A “rule” is derived that can be applied to every point on the globe

MAP PROJECTION • Projective Geometry has been used to create projections, and still serves as a conceptual explanation – A semi-transparent reference globe is fitted with a Point of Projection – Surface of reference globe is projected onto a Developable Surface – Surface is traced on developable surface

PROJECTION CLASSES (According to Projective Geometry)

PROJECTION CLASSES Classification According to Projective Geometry Developable Surface THREE CLASSES Planar Cylindrical Conic Good for: Polar regions

PROJECTION CLASSES Classification According to Projective Geometry Developable Surface THREE CLASSES Planar Cylindrical Conic Good for: Equatorial regions

PROJECTION CLASSES Classification According to Projective Geometry Developable Surface THREE CLASSES Planar Cylindrical Conic Good for: Midlatitude regions Originally developed by Claudius Ptolemy, 2 nd Century AD

PROJECTION CLASSES Classification According to Projective Geometry THREE CLASSES Planar Cylindrical Conic Mathematical Projections Some projections are developed mathematically, not according to projective geometry; developable surfaces are not involved. Pseudocylindrical, Sinusoidal, etc.

PROJECTION CASE and ASPECT

PROJECTION CASE • Case – Describes how the developable surface is positioned, relative to the reference globe – Tangent – Secant

PROJECTION CASE • Case (cont. ) – Lines of contact are Standard Lines have same scale as reference globe Distortion increases away from Standard Lines

PROJECTION ASPECT • Aspect – The orientation of the developable surface, relative to the reference globe Polar/Transverse Aspect Equatorial Aspect (Mercator) Oblique Aspect (Oblique Mercator) (Transverse Mercator)

PROJECTION CLASSES (According to Properties Preserved)

PROJECTION CLASSES Classification According to Properties Preserved • Distortion always results from the projection process – The larger the area of Earth projected, the greater the distortion – Smaller areas are subject to less distortion Large Area (strongly curved) Smaller Area (closer to flat)

PROJECTION CLASSES Classification According to Properties Preserved • Types of distortion: – Angle (shape) – Area – Distance – Direction

PROJECTION CLASSES Classification According to Properties Preserved • Projections can be classified according to the type of distortion they do not produce… • Projections can be classified by the Properties They Preserve – Angle (shape) – Area – Distance – Direction

PROJECTION CLASSES Classification According to Properties Preserved • Conformal projections: – Preserve Angles (shapes of small areas) • Equivalent (Equal Area) projections: – Preserve relative sizes of Areas • Equidistant projections: – Preserve Distances… • Azimuthal projections: – Preserve Directions…

PROJECTION CLASSES Classification According to Properties Preserved FOUR CLASSES Conformal Equivalent Equidistant Azimuthal Good for: Topographic maps Weather maps Navigational maps Conformal: Lambert Conformal Conic

PROJECTION CLASSES Classification According to Properties Preserved FOUR CLASSES Conformal Equivalent Equidistant Azimuthal Good for: Topographic maps Weather maps Navigational maps Conformal: Mercator

PROJECTION CLASSES Classification According to Properties Preserved FOUR CLASSES Conformal Equivalent Equidistant Azimuthal Good for: Thematic maps Political maps Equivalent: Eckert IV

PROJECTION CLASSES Classification According to Properties Preserved FOUR CLASSES Conformal Equivalent Equidistant Azimuthal Good for: Thematic maps Political maps Equivalent: Sinusoidal

PROJECTION CLASSES Classification According to Properties Preserved FOUR CLASSES Conformal Equivalent Equidistant Azimuthal Conformal and Equal Area projections are mutually exclusive ! No projection can be both conformal and Equal Area

PROJECTION CLASSES Classification According to Properties Preserved FOUR CLASSES Conformal Equivalent Equidistant Azimuthal Conformal and Equivalent projections are mutually exclusive No projection can be both conformal and Equivalent

PROJECTION CLASSES Classification According to Properties Preserved FOUR CLASSES Conformal Equivalent Equidistant Azimuthal Good for: Airline distance maps Seismic maps Distances are correct from the center of the projection, to all other locations (and along standard lines) Equidistant: Azimuthal Equidistant

PROJECTION CLASSES Classification According to Properties Preserved FOUR CLASSES Conformal Equivalent Equidistant Azimuthal Directions are correct from the center of the projection, to all other locations (and along standard lines) Good for: Navigational maps Azimuthal: Loximuthal

PROJECTION CLASSES Classification According to Properties Preserved Compromise Projections FOUR CLASSES Conformal Equivalent Equidistant Azimuthal Distort shape, size, distance, and direction, but distribute distortion in a way that looks natural Good for: Non-critical applications Robinson

PROJECTION CLASSES Classification According to Properties Preserved Compromise Projections FOUR CLASSES Conformal Equivalent Equidistant Azimuthal Good for: General, non-critical applications Distort shape, size, distance, and direction, but distribute distortion in a way that looks natural Van der Grinten Winkel Tripel

SELECTING an APPROPRIATE PROJECTION

SELECTING A PROJECTION • Selection of an appropriate projection requires consideration of – – – Data Symbolization method Intended audience Region of Earth Map scale Level of generalization, etc.

SELECTING A PROJECTION • John Snyder’s Guidelines provide a hierarchical mechanism for choosing projections, based on – Region to be mapped (world, hemisphere, continent or smaller) – Desired projection property (conformal, equivalent, azimuthal, equidistant) – Desired projection characteristic (class, case, aspect)

SELECTING A PROJECTION • World Map of Literacy Rates (choropleth) Preserves relative areas of enumeration units

SELECTING A PROJECTION

SELECTING A PROJECTION • Map of Russian Population (proportional symbol and dot) Preserves relative areas of enumeration units

SELECTING A PROJECTION Standard Parallels located ~1/6 from top, and ~1/6 from bottom Central Meridian located midway of E-W extent

SELECTING A PROJECTION • Map of Kansas Tornado Paths (flow) Angular relationships of paths are important No need to preserve relative areas of enumeration units

SELECTING A PROJECTION Lambert Conformal Conic

SELECTING A PROJECTION Albers Equal Area Conic Virtually no difference! The smaller the area, the less important the projection!

SELECTING A PROJECTION Lambert Conformal Conic would be the correct choice…

MAP PROJECTIONS Cartographic Design for GIS (Geog. 340) Prof. Hugh Howard American River College