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 PROCESS most projections are combinations of the following characteristics: characteristic of earth features that are maintained shape of the projection plane (developable shape) aspect of the projection plane points or lines of tangency or secancy location of the false ‘illumination source’

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 shapes, distances and areas are badly distorted

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 Area Distance Direction Shape Equal-Area No Yes Equidistant Azimuthal Conformal

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

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 depends on: purpose for which the data is to be used property in which distortion is minimized extent and location of area

CHOOSING PROJECTION steps: size of area of interest small area has little distortion, any projection. latitude of area of interest low-latitudes – cylindrical mid-latitudes – conical polar latitudes - planar

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

SCALE

SCALE size of an object on a map compared to the actual object on the ground may not be the same in all directions from a point

SCALE TYPES Verbal scale describes the scale in words i.e. “one centimeter represents one kilometer” commonly found on popular atlases and maps

SCALE TYPES Visual scale (bar scale or graphic scale) graphically illustrates relationship between map distance and ground distance. one end can be divided most common remains correct if reduced or enlarged

SCALE TYPES Visual scale (bar scale or graphic scale)

SCALE TYPES Representative Fraction (RF) ratio (proportion) between map distance to earth distance i.e. 1:50,000 most versatile; not tied to any specific units

SCALE FACTOR Representative Fraction Globe distance Earth distance = Map Scale: (e.g. 1:24,000) Map Projection: Scale Factor

SCALE FACTOR stated scale is correct only at selected points statement of relation between given scale and actual scale value i.e. SF of 2.000 would mean that actual scale is twice the principal scale

LARGE VS SMALL SCALE large scale: show a small area with a large amount of detail. small scale: show a large area with a small amount of detail all relative

DETERMING SCALE use map scale to convert map distance to ground distance. for verbal and RF scales - multiply by the scale, then convert the ground distance to units suitable for ground measurements. i.e. we have a map with a scale of 1:50,000. We measure the distance along a property boundary as 1.7 cm. What is the length in the real world? for graphic scales – mark off a distance on the map and compare it directly to the bar scale.

TRANSFORMING SCALES Verbal to RF write verbal scale as a fraction then convert so that both numerator and denominator have the same units and numerator has a 1 i.e. convert verbal scale “1 cm represents 100 km” to RF RF to Verbal i.e. convert from RF of 1:25,000 to verbal scale, in metric

TRANSFORMING SCALES Graphic Scales and RF/Verbal take the measurement from the bar scale to determine the map distance and corresponding ground distance. i.e. 10 km on ground measures 2.4 cm on map. use method for verbal scale to RF conversion.