Lecture 4 - Georeferencing II Flashcards
What is a map projection?
A system in which locations on the curved earth’s surface are displayed on a flat sheet or surface according to some set of rules
- transforms geographic location to cartesian grid (x, y)
- basically like peeling and flattening the earth (like an orange peel)
- results in loss of info
- all maps require transformation of spherical earth to flat surface, so are very important aspect of mapping
- you can convert between map projections
What is the transformation sequence for map projections?
- model geoid as ellipsoid or spheroid
- reduce scale
- project from globe to developable surface
- distortion is inevitable, but smaller areas will have the least distortion (larger has more distortion)
What are map projections used for?
- for calculating distance, direction, and area on a flat surface
How do map projections work?
- perspective projections can be constructed geometrically
- original method was ray tracing
- all projections can be represented by mathematical equations (computer generation)
How is the amount of distortion assessed?
Through the use of Tissot dots - because all projects have distortion, this helps us to understand how much
Explain Tissot’s indicatrix
- small circles centred on earth’s surface
- look at shape after it is transformed by a given map projection to understand what kind of distortion occurs (linear, angular, and/or area)
What are the 3 ways of classifying map projections?
- Properties
- Physical class
- Aspect
What are the 3 properties?
- Equal-area (aka equivalent)
- Equidistance (scale and distance)
- Conformity (angles and shape)
- IMPOSSIBLE TO HAVE ALL PROPERTIES TOGETHER IN ONE MAP PROJECTION (only 1/3)
Explain equal-area map projection
- correctly represents area sizes on the map (proportional to ground areas)
- considerable distortion of angles and shapes on small-scale maps showing large regions
- useful for applications requiring area measurements
- ex. Lambert cylindrical equal-area projection
Explain equidistant map projection
- correctly represents distances to places
- limited: distances can only be shown true to scale from one or two points to any other point on the map or in certain directions
- equidistant along meridians and parallels (scale is correct here)
- ex. Plate Carree projection (equidistant, cylindrical)
Explain conformal map projection
- represents angles and shapes correctly at infinitely small locations and shows directions (bearings) correctly
- shapes/angles only slightly distorted as the region becomes larger
- at any point, scale is same in every direction
- useful for navigation
- ex. Mercator (conformal, cylindrical)
Give examples of projections with special properties
- Alry: minimum-error map (all scale errors are as small as possible)
- Mercator: rumb lines (lines of constant direction) are shown as straight lines
- Gnomonic: great circle paths (shortest routes between points on a sphere) are shown as straight lines
What are the 3 physical classes?
- Cylindrical
- Conical
- Azimuthal
Explain cylindrical projections
- cylinder wrapped around globe
- can be tangent to globe along great circle or secant to globe along two small circles
- normal orientation assumes cylinder tangent along equator (meridians and parallels form rectangular grid)
- distortion increases with distance from standard lines
- useful for projections of the world or regions with narrow extent in one direction (ex. tropics or Chile)
What are some examples of cylindrical projections?
- Mercator: parallels and meridians are straight lines intersecting at right angles; meridians evenly spaced; as latitude increases, area exaggeration occurs (poles)
- Transverse Mercator: distances are true only along the central meridian; distances, directions, shapes, and areas reasonably accurate within 15° of central meridian (distortion rapidly increases outside)
- Mollweide: parallels are represented by parallel straight lines while the medians are curves; equal area projection; distortion increases with distance from origin
- Robinson: compromise projection (neither conformal nor equal-area); useless other than it is visually appealing
Explain conic projections
- cone tangent to globe along one small circle or secant to globe along two circles
- apex of cone is on the globe’s axis of rotation
- meridians are radial straight lines and parallels are concentric circular arcs
- distortion increases with distance from standard lines
- useful for projections of mid-latitude regions (ex.CAN & USA - one hemisphere)
What are some examples of conic projections?
- Lambert Conformal (northern hemisphere): distances true only along standard parallels; directions reasonably accurate; distortion and area is extreme south of equator
- Albers Equal Area: all areas proportional to true areas on earth; scale true along standard parallels
- Bonne’s Equal Area: polyconic (heart shaped)
Explain azimuthal projections
- correctly shows directional relationships about projection pole (point of tangency)
- projects to a plane tangent to globe at a point or secant to globe along small circle
- normal (point is north or south pole). transverse (point on equator), oblique (point elsewhere)
- distortion increases with distance from standard point/line
- useful for polar regions
What are some examples of azimuthal projections?
Correctly shows directional relationships
- gnomonic
- stereographic
- orthographic
What are the 3 aspects?
- Normal (parallel)
- Transverse (perpendicular)
- Oblique (other)
Explain normal aspect
Main orientation of projection is parallel to the earth’s axis
Explain transverse aspect
Main orientation is perpendicular to earth’s axis
Explain oblique aspect
All other orientations, non-parallel and non-perpendicular
Explain the difference between tangent and secant
Tangent: projection surface just touches the globe
Secant: projection surface intersects the globe
How do you select a suitable projection?
- Shape and size of area (physical)
- small/circular = azimuthal
- large rectangular = cylindrical
- triangular = conic - Position of the area (aspect)
- Purpose of map (property)
Ex.
- navigation = mercator projection
- topographic = conformal and equidistant projections (ex. UTM)
- distribution = equal-area (ex. lambert or albers)
Explain importance of Universal Transverse Mercator (UTM)
- widely accepted projection for topographic mapping
- systematic, conformal projection, polyconic
- used in ON and CAN by govts
How does the UTM grid work?
- earth divided into 60 long N-S zones, each 6° wide
- numbered zones consecutively from 180° W to east
- a set of parallels divides grid into rows (labelled C to X starting south)
- zones help determine coordinates of point relative to false origin
- geocoding with UTM requires 16 digits for 1m accuracy
- ON covered by 4 UTM zones
Explain UTM quadrangles
- each UTM zone comprises 20 quadrangles
- within each quadrangle, any point located by two distances in meters: easting (east from central meridian), northing (north from equator), false easting/northing (offset added to distance east or nother of standard meridian/equator to ensure positive coordinates (makes entire system positive)
