Map projections

The world is like an orange … Watch video (2.5 min)

12 pieces 48 pieces (becoming like UTM zones)

What is a Map Projection? 3D Earth 2.Mercator Projection Map projection: a mathematical expression representing the 3D surface of the earth on a 2D map.                                                                                     3D Earth 2.Mercator Projection This process always results in distortion to map properties: such as area, shape, or direction. ….hundreds of projections have been developed to best suit a particular type of map. the distortion, flattening or stretching needs to be done systematically. (Watch video 3.5 min)

Literally projecting the globe onto a map … 3 of the earliest projections (by the ancient Greeks) [Gnomon = pagan sundial]

Projection Terms a. Scale Factor (SF) No map projection maintains correct scale throughout the map The distortions increase as the distance from the central point of the projection increases. SF = scale at any location / divided by the 'principal scale' e.g. if actual scale = 1:2 million and principal scale = 1:1 million then SF at that point =  1/2million divided by 1/1million  =   1/2   (0.5)

Projection Terms a. Scale Factor (SF) For example, in any projection, where every line of latitude is equal in length (whereas the relative lengths on the globe are 1 at the equator, 0.5 at 60 latitude and 0 at the Poles), SF along lines of latitude are:  at the equator SF = 1; at 60, SF =2; at 90, SF = ∞ 90 60 The SF in the other direction (along meridians) may not be the same.

Distortion increases with distance between the ‘globe’ and the surface b. Developable surface:  A two dimensional surface onto which the globe is projected Conic Cylindrical Azimuthal (planar) Distortion increases with distance between the ‘globe’ and the surface c. Standard Line:   The standard line is a line along which the scale factor equals 1 (often the point / line of contact)

d.

CONIC projections … are all ‘normal’ (e.g. Albers) They can be varied by : A: angle of the cone B: 1 or 2 standard parallels

e. Distortion: compared to the graticule: Lines of latitude are 'parallel' and evenly spaced. Meridians converge at the poles, half at 60 degrees. All grid lines cross at right angles. Scale factor is 1 in all directions. ‘Great circles’ are straight lines e.g. meridians, equator, 'straight' flight lines

Azimuthal equidistant map centred on St. John’s, NF

Projection Properties Projections may preserve shape or area, … but NOT both area and shape. a. Area A projection that maintains 'area' is   equal area (or equivalent). This is achieved by sacrificing shape: stretching in one direction to counter for earth curvature must be compensated by compaction in the other. In other words, the product of the two Scale factors at any point in the two directions (N-S and E-W) is 1.0 (e.g 1 x 1, 2 x 0.5 etc..)

b. Shape A projection that maintains shape is conformal or orthomorphic. For example a 2x2 square becomes a 1x1 or 4x4 square. Stretching in one direction is matched by stretching in the other: that is, the scale factors are equal at a point in the two directions (i.e. there is 'equal-stretching').

Mercator’s Projection 1569 - conformal All ‘straight lines’ have constant compass bearings = Rhumb lines

Lambert Equal-Area projection SF x SF (N-S, E-W) = 1 …. at any point e.g. equator 1,1 60N/S 0.5, 2

c. Distance Distances can be correct in one direction from a line, usually a standard line … or distances can be correct in all directions from a point. In these cases, the projection is termed equidistant (but only N-S) Plate Carrée projection

Distances are true N-S only

Definitions Co-ordinate System - records the location of any feature on the surface of the Earth uniquely. (Latitude/longitude) Datum - a system which allows the location of latitudes and longitudes (and heights) to be identified onto a round surface (Earth) Projection: the process of transferring the information from the surface of a 3 dimensional (3D or spherical), irregularly shaped sphere (the Earth) to a 2-dimensional (2D or flat) 'piece of paper'

Map projections – 3 major groups/techniques Conic Cylindrical Planar (azimuthal) Sub-groups based on projection orientation (normal, transverse, oblique)

Pseudocylindrical (conventional) Projections Can be called a 4th group of projections based on variations of the 3 main techniques. attempts another trade-off of shape vs. area; in the normal equatorial aspect, they are defined by: straight horizontal parallels, not necessarily equidistant and arbitrary curves for meridians, equidistant along every parallel Sinusoidal projection

Projection types/properties: How does a map show the positional relationship between two features, and their size and shape? Projection types/properties: Equal-Area (equivalent) -correctly shows the size of a feature Conformal (orthomorphic) -correctly shows the shape of features (A map can not be both equal-area or conformal – it can only be one; or the other; or neither.) Equidistant -correctly shows the distance between two features Azimuthal (True Direction) -correctly shows the direction between two features

Conic projections – 18th century The cone opens at a line of longitude the cone intersects the sphere at one or two parallels – standard lines

Conic projection with 2 standard parallels: mid latitudes Albers projections (1805) – with 2 standard parallels –coordinate systems BC: 50 and 58.5 N (central meridian 126 W = 1,000,000) Yukon: 61.67 and 68 N Alaska: 55 and 65 N Hawaii: 8 and 18 N

Canada Albers Equal Area Conic: Central Meridian: -96 Latitude Of Origin: 40 First Standard Parallel: 50 Second Standard Parallel: 70

Arc Map example

Cylindrical Projections 16th century -> Best for equatorial areas and used for world (historical) maps fill a rectangular shape Mercator (16th century) Transverse Mercator http://www.progonos.com/furuti/MapProj/Normal/ProjCyl/ProjCEA/projCEA.html

UTM zones : BC Standard line is on a selected line of longitude (meridian)

Azimuthal projections: used for polar areas - 500BC Can also be projected to centre on any point (oblique) http://www.progonos.com/furuti/MapProj/Normal/ProjAz/projAz.html Great circles= straight lines Conformal (shape) ‘View from space’ Thales Hipparchus Ptolemy

4. Conventional (pseudo-cylindrical) Projections 19th century (and 20th) These are geometrically constructed. The parallels are generally equally spaced but are made more proportional to their real length to minimize distortion. Mollweide http://www.progonos.com/furuti/MapProj/Normal/ProjPCyl/projPCyl.html

Conventional projections Generally show the whole world with least overall distortion (and are equal-area) 19th century (and 20th) E.g. Mollweide’s homolographic Tissot’s Indicatrix of distortion

Robinson projection – adopted by National Geographic in 1988 Poles drawn as lines to create better shapes http://www.mapsofworld.com/projection-maps/robinson/world-political-light.html

Interrupted version (Goode’s)

Oblique Mollweide (obliques are used sparingly) http://idlastro.gsfc.nasa.gov/idl_html_help/Pseudocylindrical_Projections.html

One more projection …. The butterfly map

one last one … the Moocator (projection humour)

You Tube videos about projections: Latitude, Longitude, and Types of Map Projections Latitude, Longitude, and Types of Map Projections Part 2