Lecture 4 - Georeferencing II

Question 1

What is a map projection?

Answer 1

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

Question 2

What is the transformation sequence for map projections?

Answer 2

1. model geoid as ellipsoid or spheroid
2. reduce scale
3. project from globe to developable surface
   - distortion is inevitable, but smaller areas will have the least distortion (larger has more distortion)

Question 3

What are map projections used for?

Answer 3

• for calculating distance, direction, and area on a flat surface

Question 4

How do map projections work?

Answer 4

• perspective projections can be constructed geometrically
• original method was ray tracing
• all projections can be represented by mathematical equations (computer generation)

Question 5

How is the amount of distortion assessed?

Answer 5

Through the use of Tissot dots - because all projects have distortion, this helps us to understand how much

Question 6

Explain Tissot’s indicatrix

Answer 6

• 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)

Question 7

What are the 3 ways of classifying map projections?

Answer 7

1. Properties
2. Physical class
3. Aspect

Question 8

What are the 3 properties?

Answer 8

1. Equal-area (aka equivalent)
2. Equidistance (scale and distance)
3. Conformity (angles and shape)
   - IMPOSSIBLE TO HAVE ALL PROPERTIES TOGETHER IN ONE MAP PROJECTION (only 1/3)

Question 9

Explain equal-area map projection

Answer 9

• 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

Question 10

Explain equidistant map projection

Answer 10

• 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)

Question 11

Explain conformal map projection

Answer 11

• 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)

Question 12

Give examples of projections with special properties

Answer 12

• 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

Question 13

What are the 3 physical classes?

Answer 13

1. Cylindrical
2. Conical
3. Azimuthal

Question 14

Explain cylindrical projections

Answer 14

• 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)

Question 15

What are some examples of cylindrical projections?

Answer 15

• 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

Question 16

Explain conic projections

Answer 16

• 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)

Question 17

What are some examples of conic projections?

Answer 17

• 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)

Question 18

Explain azimuthal projections

Answer 18

• 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

Question 19

What are some examples of azimuthal projections?

Answer 19

Correctly shows directional relationships

• gnomonic
• stereographic
• orthographic

Question 20

What are the 3 aspects?

Answer 20

1. Normal (parallel)
2. Transverse (perpendicular)
3. Oblique (other)

Question 21

Explain normal aspect

Answer 21

Main orientation of projection is parallel to the earth’s axis

Question 22

Explain transverse aspect

Answer 22

Main orientation is perpendicular to earth’s axis

Question 23

Explain oblique aspect

Answer 23

All other orientations, non-parallel and non-perpendicular

Question 24

Explain the difference between tangent and secant

Answer 24

Tangent: projection surface just touches the globe
Secant: projection surface intersects the globe

Question 25

How do you select a suitable projection?

Answer 25

1. Shape and size of area (physical)
   - small/circular = azimuthal
   - large rectangular = cylindrical
   - triangular = conic
2. Position of the area (aspect)
3. Purpose of map (property)
   Ex.
   - navigation = mercator projection
   - topographic = conformal and equidistant projections (ex. UTM)
   - distribution = equal-area (ex. lambert or albers)

Question 26

Explain importance of Universal Transverse Mercator (UTM)

Answer 26

• widely accepted projection for topographic mapping
• systematic, conformal projection, polyconic
• used in ON and CAN by govts

Question 27

How does the UTM grid work?

Answer 27

• 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

Question 28

Explain UTM quadrangles

Answer 28

• 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)