Lecture note of GEO 381/550 September 14, 2004

The purpose of this lecture is to introduce you to a variety of map projections and let you cultivate a sense of choosing the right projection suited to the need.

 

How many kinds of map projections?

 

Projection types[3] * projection properties[3]* tangent[2] * aspect[3] …

 

 

Equal-area

Conformal

Equidistant

Cylindrical

 

 

 

Conic

 

 

 

Azimuthal

 

 

 

 

Most popular choice for thematic mapping is equal-area because of the need for representing the area true to scale. Always open for customizing maps to the need (e.g. Navigational chart, proximity map, shortest path, perspective view).

Cylindrical projections

 

  • Parallels and meridians meet at the right angle; easy to construct à that’s why it has been so popular
  • The spacing of either parallels or meridians varies depending on which quality is to be preserved.

 

Mercator

o        Extend the parallel spacing in the high latitude to make the azimuth constant

o        Any straight line in Mercator maps is a rhumb line (loxodrome)

o        Areal exaggeration in high-latitude areas; In fact, Brazil is more than five times larger than Alaska à Not a good choice for statistical map of the world

 

To compensate for areal distortion, equal-area cylindrical projections have been devised.

Standard line: 0°

 

Gall

Source: http://www.colorado.edu/geography/gcraft/notes/mapproj/gif/gall.gif

Standard parallels: 45°N, 45°S

 

Other aspects for cylindrical family

 

Transverse Mercator

Standard line is central meridian

Adequate for portraying south-north extending areas

 

Universal Transverse Mercator (UTM)

Divide the world into 6 degree longitudinal strip, and then project the globe into the strip where the center of the strip becomes a standard line

 

Oblique Mercator

Good for portraying diagonally extending areas (e.g. Alaska state plane zone 1)

Equal-area pseudocylindrical projections

 

  • Unlike rectangular projections, it has rounded margin to correct for area with less  degree of shape distortion
  • Widely used for mapping world distributions

 

Sinusoidal

Horizontal parallels; sine curved meridians; awkward shape

 

Mollweide

Horizontal parallels; elliptic meridians; less distortion of shape than Sinusoidal

 

Hammer

Curved parallels; elliptic meridians, less distortion of shape than Mollweide

Conic projections

 

  • Suitable for portraying the area of large east-west extents in mid-latitude or high-latitude
  • Flexible choice of standard parallels

 

Albers equal-area conic

 

Lambert conformal conic

 

Azimuthal projections

 

  • Gives the directions or azimuths of all points on the map correctly with respect to the center
  • Azimuthal (true direction) is not an exclusive quality (i.e. comes with other qualities such as Equidistant Azimuthal, Equal-area Azimuthal, and Conformal Azimuthal)
  • The straight line from the central point to all other points is great circle (it is so between any arbitrary points in gnomonic projections)

 

Polar aspect

 

Equatorial aspect

 

  • Gnomonic: straight line between any arbitrary points is great circle; why? the location of light source; known for navigational charts for the air age in particular during the world war
  • Stereographic: conformal
  • Orthographic: provides perspective view; neither equal-area nor conformal

 

Equidistant Azimuthal                                            

 

Shows every point on the globe at its correct distance, and in its correct direction, from the center of the projection

Good choice for portraying proximity/direction to the center of map

 

Lambert Azimuthal Equal-Area

 

Well suited to mapping regions that do not have any large difference between their north-south extent and their east-west extent

Good choice for small-scale density or distributions map

Criteria for the employment of map projections (D3:49)

 

1. Projection properties

2. Deformation patterns

3. Projection center

4. Familiarity

5. Cost

Guide to the employment of projections for thematic maps in different scales

 

World in the geographic grid

Mark Equator, Prime Meridian, and International Dateline

Mark approximiate longitude and latitude of the centroid of each continent, or country

 

Table 3.1

 

1. Maps of the world in one sheet

 

Mostly derivation of pseudocylindrical family (e.g. Sinusoidal, Mollweide, Hammer)

Mercator maps for showing constant geographic direction

 

2. Maps of the hemisphere

 

Orthographic: view of earth as if from space; neither equal-area nor conformal

 

3. Maps of the continent in the mid-latitude

 

Bonne: derivation of conic family (Figure 3.3)

Albers equal-area with two standard parallels

Lambert equal-area azimuthal: Demo in ArcView

 

*Make sure the location of the continent to be mapped is centered due to the severe shape distortion edgeward

 

4. Maps of the continent in the low-latitude

 

Sinusoidal, Mollweide, Bonne

Lambert equal-area azimuthal

 

5. Maps of US

 

Albers equal-area

Lambert conformal conic

Lambert equal-area azimuthal

 

Source: http://www.colorado.edu/geography/gcraft/notes/mapproj/gif/twoproj.gif

 

Coordinate systems

 

Coordinate systems can be seen broadly as two kinds: one is spherical (unprojected) coordinate system (that is three dimensional) where latitude and longitude are used to reference the location. The other is planar (projected) coordinate system where 3 dimensional earth is transformed into 2 dimensional flat surface through projection.

Also it is possible to divide coordinate systems into global versus local. Global coordinate systems are used globally (so you can refer all regions in the world using one system such as UTM). Local coordinate systems are designed to fit a local region, so you can’t use them in other regions. (e.g., U.S. state plane, U.K. national grid)

 

Global Coordinate Systems

 

¨ Latitude Longitude (a.k.a Geographic Coordinate System)

o        Unprojected (Projection itself indicates the transformation from 3 dimensions to 2 dimension); represents the location in the three dimensional surface by longitude and latitude.

o        The Prime Meridian and the Equator are the reference planes used to define latitude and longitude.

o        The latitude of a point is the angle from the equatorial plane to the vertical direction of a line normal to the reference ellipsoid.

o        The longitude of a point is the angle between a reference plane and a plane passing through the point, both planes being perpendicular to the equatorial plane.

 

¨ Universal Transverse Mercator (UTM)

o        A kind of Transverse Cylindrical projection, but the standard line varies with the regions in the world

o        UTM zone numbers designate 6 degree longitudinal strips extending from 80 degrees South latitude to 84 degrees North latitude.

o        UTM zone characters designate 8 degree zones extending north and south from the equator.

Source: http://www.colorado.edu/geography/gcraft/notes/coordsys/gif/utmzones.gif

 

 

Local Coordinate Systems (United States)

 

¨ State Plane Coordinates

o        divides all fifty of the United States, Puerto Rico and the US Virgin Islands into over 120 numbered sections, referred to as zones. Depending on its size, each state is represented by anywhere from one to ten zones.

o        Three projections are used: the Lambert Conformal Conic for zones running east and west, the Transverse Mercator for zones running north and south, and the Oblique Mercator for one zone only, the panhandle of Alaska.

o        developed in the 1930s and was based on the North American Datum 1927 (NAD27). (NAD 27 coordinates are based on the foot.)

o        The State Plane System 1983 is based on the North American Datum 1983 (NAD83). (NAD 83 coordinates are based on the meter.)

 

Matching the map projection to the need

 

 

Equal-area

Conformal

Equidistant

Cylindrical

A1

A2

A3

Pseudocylindrical

B1

B2

B3

Conic

C1

C2

C3

Azimuthal

D1

D2

D3
  1. World population density
  2. Agricultural regions in Russia
  3. World navigational chart for mariners
  4. Navigational chart for pilots
  5. World ocean currents map
  6. Natural resources in Africa
  7. Proximity map of Buffalo
  8. Shaded relief map of South Pole
  9. Road map of Chile

Setting Map Projections in ArcView

 

When publishing geographic data, they usually come with metadata where spatial reference information is defined to which you can refer. Metadata defines coordinate system, projection (e.g., unprojected, UTM), map units (e.g., decimal degree, meters), and geodetic model (e.g. datum, spheroid) in the Spatial_Reference_Information item.

 

Example of Geographic coordinate system: (TIGER 2000)

Example of UTM: (NY Aquifer from NYDOH)

Example of Lambert Azimuthal Equal Area: (USNationalAtlas)

 

The most common form of the spatial reference is the latitude and longitude. When you add themes that are stored in geographic coordinate system, ArcView View shows the coordinates of the point you are pointing at. Just look at cursor location while you are moving around the cursor in the view area when a theme is added.

 

Decimal degree shown in the cursor location (i.e., degrees of longitude-latitude expressed as a decimal rather than in degrees, minutes and seconds) indicates the data is stored in the Latitude Longitude.

 

Choose Properties from the View menu, the Projection should be set to None because it is the unprojected coordinate system. Map units should be decimal degree. Map units are the units of the view’s display surface. For example, the data stored in UTM, the map units should be in meters as defined in the coordinate system.

In ArcView. a view's map projection can only be set if the map units of the spatial data it contains are decimal degrees.  In ArcView, you can choose the appropriate projections and play with them as long as the data is in decimal degree.

 

Display countries in different projections

a.      In a View, Add country and world30 from c:\esri\ESRIDATA\World\ by clicking

b.      In case world30 covers country, hold down the world30 to the bottom in the Table of Contents

c.      Choose Properties… from the View menu

d.      Click Projection… button

e.      Make sure Standard option box is checked on the top

f-1. Select “Projections of the World” for Category field, and select “Geographic” for Type field

f-2. Select “Projections of the World” for Category field, and select “Sinusoid” for Type field

Display U.S. in right projections

f-3. Select “Projections of the United States” for Category field, and select “Albers Equal-Area (Conterminous U.S.)” for Type field

Display South Pole in right projections

f-4. Select “Projections of a Hemisphere” for Category field, and select “Orthographic – South Pole” for Type field

Display Western New York in right projections

f-5. Select “State Plane - 1983” for Category field, and select “New York, West” for Type field

f-6. Select “UTM - 1983” for Category field, and select “Zone 18” for Type field

 

As you see from the map above, the local coordinate system is designed to minimize the distortion in the area of your interest. You should not use the local coordinate system for displaying larger area.

When your spatial data is not in decimal degrees, and you are using data from a variety of different data sources on the same view, you should make sure that all these data sources are currently stored in the same map projection. If you draw data sources that are currently stored in different map projections on the same view you may get errors and inaccurate results.