MAP PROJECTIONS AND SCALE OUTLINE: scale definition types of scale projection definition projection properties and classification choosing a map projection
PROJECTIONS
THE GLOBE Advantages: most accurate map latitude and longitude lines Disadvantages expensive to make cumbersome to handle and store difficult to measure not fully visible at one
PROJECTIONS Flat Map Curved Earth process of transforming earth’s spherical surface to a flat map while maintaining spatial relationships. Curved Earth Flat Map
PROJECTIONS projection process involves stretching and distortion
PROJECTIONS no matter how the earth is divided up, it can not be unrolled or unfolded to lie flat (undevelopable shape).
PROJECTION PROPERTIES properties in which distortion is minimized when producing a map Area equal area or equivalent area sizes are correct everywhere on map shapes greatly distorted
PROJECTION PROPERTIES Distance equidistant distance is correct in all directions from a point i.e. equidistant projection centered on Winnipeg would show the correct distance to any other location on the map, from Winnipeg only distorting area and/or direction
PROJECTION PROPERTIES Equidistant
PROJECTION PROPERTIES Direction azimuthal compass bearing is maintained in all directions only from a point – focal point shapes, distances and areas are badly distorted
PROJECTION PROPERTIES all distances measured from the center of the map along any longitudinal line are accurate; an example of a polar azimuthal equidistant projection can be seen on the United Nations flag
PROJECTION PROPERTIES Shape conformal shape maintains its shape across the map distorting area latitude and longitude cross at right angles used for navigation
PROJECTION PROPERTIES Tissot’s Indicatrix convenient way of showing distortion size and shape of the indicatrix will vary from one part of the map to another Mercator projection Equal-Area projection
PROJECTIONS made by projecting a globe onto a surface – developable surface distortion is least where developable surface touches the earth accomplished by use of geometry and mathematics Mercator:
PROJECTION CLASSIFICATION Tangent case – shape just touches the earth along a single line or at point. Secant case – shape intersects or cuts through earth as two circles.
PROJECTION CLASSIFICATION Conical globe sits under a cone, touching along pre-selected line of latitude projection developed by cutting cone lengthwise and unrolling
PROJECTION CLASSIFICATION normal case: parallels – concentric circular arcs, meridians – straight equally spaced lines
PROJECTION CLASSIFICATION Lambert conformal conic projection Albers equal-area conic projection
PROJECTION CLASSIFICATION Conical Distortion
PROJECTION CLASSIFICATION Conical Polyconic – envelopes globe with an infinite number of cones, each with its own standard parallel
PROJECTION CLASSIFICATION Cylindrical projected onto a cylinder which is also cut lengthwise and unrolled
PROJECTION CLASSIFICATION Cylindrical evenly spaced network of straight, horizontal parallels and straight vertical meridians (grid like)
PROJECTION CLASSIFICATION
PROJECTION CLASSIFICATION Cylindrical Distortion projection of the entire world, significant distortion occurs at the higher latitudes parallels become further apart and poles can not be seen
PROJECTION CLASSIFICATION Cylindrical Distortion sizes of Greenland vs. Africa Mercator Projection True size
PROJECTION CLASSIFICATION Cylindrical straight line between any two points follows a single direction called a rhumb line useful in construction of navigational charts
PROJECTION CLASSIFICATION Planar/Azimuthal portion of earth’s surface is transformed from a perspective point to a flat surface
PROJECTION CLASSIFICATION Planar/Azimuthal perspective point/light source Light rays
PROJECTION CLASSIFICATION Planar/Azimuthal true direction only between center and other locations most often used to map polar regions
PROJECTION CLASSIFICATION NORMAL TRANSVERSE OBLIQUE
CANADA PROJECTED Cylindrical Conic Planar
PROJECTION CLASSIFICATION Pseudo map projections Pseudocylindrical pseudoconic and pseudocylindrical projections - have curved meridians instead of straight ones
PROJECTION CLASSIFICATION Pseudo map projections modified projections - changes have been made to reduce the pattern of distortion or add more standard parallels modified to reduce the distortion in the size of areas
PROJECTION CLASSIFICATION Pseudo map projections individual or unique projections – can not be easily related to one of the three developable geometric forms Goode’s Projection
CHOOSING PROJECTION shape of area of interest: E-W extent: conic or cylindrical N-S extent: cylindrical square or circular: planar purpose: navigation – planar or cylindrical world distributions – cylindrical specific locations - planar
COMMON PROJECTIONS Albers Equal-Area Conic equal area, secant conical projection (two standard parallels) resembles earth graticule
COMMON PROJECTIONS Mercator cylindrical, conformal projection angular relationships are preserved parallels and meridians appear as straight lines parallels are farther apart with increased distance from equator
COMMON PROJECTIONS Mercator change in N-S scale exactly offset change in E-W direction (shapes preserved) scale is true at equator or at two standard parallels equidistant from equator all rhumb lines appear as straight lines, while great circle arcs are not (except equator and meridians) used primarily for navigation and large scale maps
COMMON PROJECTIONS Transverse Mercator cylindrical, conformal projection similar to Mercator except the axis of projection cylinder is rotated 90o from polar axis scale is true along central meridian or along two straight lines equidistant from and parallel to central meridian used to portray areas with larger N-S than E-W extent.
COMMON PROJECTIONS Lambert Conformal Conic conformal, secant conical projection with two standard parallels possesses true shape of small areas with area distortion concentric parallels (increasing intervals) and equally-spaced straight meridians
COMMON PROJECTIONS
COMMON PROJECTIONS
COMMON PROJECTIONS Mollweide pseudocylindrical, equal-area projection N-S scale is decreased in high latitudes, increased in low latitudes; opposite in E-W direction parallels are straight, spaced closer together from equator
COMMON PROJECTIONS Polar Stereographic directions are true from center point conformal projection: over a small area, angles in the map are the same as the corresponding angles on Earth's surface meridians are straight and radiating; parallels are concentric circles shows only one hemisphere
COMMON PROJECTIONS Polar Stereographic preserves circles - all great and small circles are shown as concentric arcs or straight lines scale true only where the central parallel and meridian cross used in polar aspect for topographic maps of polar regions, regions that are circular in shape
COMMON PROJECTIONS Eckert IV Equal Area pseudocylindrical and equal-area scale is true along the parallel at 40:30 North and South
COMMON PROJECTIONS Robinson developed to minimize appearance of angular and area distortion distorts shape, area, scale and distance in an attempt to balance errors of projection properties
COMMON PROJECTIONS Robinson based on tables of coordinates not mathematical formulae overall effect – more than 75% of earth is shown with less than 20% departure from true scale size used for thematic and reference maps
OTHER PROJECTIONS Berghaus Star
OTHER PROJECTIONS Sanson-Flamsteed
OTHER PROJECTIONS Conoalactic
OTHER PROJECTIONS Hammer
OTHER PROJECTIONS Eisenlohr
OTHER PROJECTIONS Gall Stereographic Cylindrical
OTHER PROJECTIONS Cassini