Gmat 2700 Geometry of Coordinate Reference Systems Alexandra Lyle Student No Session 1, 2006 The Globe Presentation by Alexandra Lyle SCHOOL OF SURVEYING & SPATIAL INFORMATION SYSTEMS, UNSW GMAT 2700 – Geometry of Coordinate Reference Systems

Gmat 2700 Geometry of Coordinate Reference Systems Alexandra Lyle Student No Session 1, 2006 ‘A map is a map’ James R. Clynch, 2006

Gmat 2700 Geometry of Coordinate Reference Systems Alexandra Lyle Student No Session 1, 2006 ‘A map is a map’ What is a map? Map show the spatial relationship between different items. Maps can be represented in various forms 2D and 3D

Gmat 2700 Geometry of Coordinate Reference Systems Alexandra Lyle Student No Session 1, 2006 ‘A map is a map’ Difference between 3D and 2D maps ‘The earth is curved and the map is flat’. 3D maps give a different visual representation of the earth to a 2D map. That is: a 3D map would give a more visually correct representation of the earth, with each of the Countries placed in perspective to each other.

Gmat 2700 Geometry of Coordinate Reference Systems Alexandra Lyle Student No Session 1, 2006 The Globe ‘… problem of representing a curved earth on flat paper. The only way to get around this problem is to use a spherical map, that is a globe.’ James R. Clynch, 2006

Gmat 2700 Geometry of Coordinate Reference Systems Alexandra Lyle Student No Session 1, 2006 The Globe Why the globe? I have one and in doing this subject I looked at it again and thought about what it is informing me about the earth: The size and shape, the relationship of water (oceans and seas) and land (countries) to each other. Problem with the globe I have: no information about the projection used. The globes details It is over 10 years old Gives information about: longitude, latitude, scale of the map, where the equator and the Greenwich Meridian is, best flight paths from one place to another, how the countries look, names of places (main cities)… many things but how accurate is it all really?

Gmat 2700 Geometry of Coordinate Reference Systems Alexandra Lyle Student No Session 1, 2006 The Globe Facts about Globes (like my one) What it looks like: It is a physical representation of the earth – in a Sphere form. You can touch it, turn it around, smell it even (if you really want to). Coordinates: latitude, longitude which are geocentric and height which is spherical. Accuracy of a globe – As the world is approximately a sphere, hence globes are good for some approximations. BUT the errors in using the spherical model can be significant.

Gmat 2700 Geometry of Coordinate Reference Systems Alexandra Lyle Student No Session 1, 2006 The Globe Accuracy of a globe continued … Distances. For the spherical computation, the radius used was the geometric average of the true radii at each end point. This gives a much better value than using one radius for all locations. For short distances, the error is small. Comparing a spherical based model (the globe) to a ellipsoid based model (maps) Function for lengths - distance. In general the errors are relative, being about the flattening of the real earth times the distance. The flattening of the earth is about 1/300. So if you need an answer more accurate that 1/300 you probably need to use the ellipsoid model. This is about 3 m per kilometer or 20 ft per mile. Latitudes - The geocentric latitude (spherical) is measured from the line to the center of the earth; the ellipsoid model uses the geodetic latitude that is always greater or equal to the geocentric latitude. The two are equal at the poles and equator and have greatest difference at 45 deg north and south. It is clear that you cannot navigate or do any quantitative work using geocentric latitude. Longitude - Geodetic and geocentric longitude are identical so the models are the same.

Gmat 2700 Geometry of Coordinate Reference Systems Alexandra Lyle Student No Session 1, 2006 Projection of the earth to the globe

Gmat 2700 Geometry of Coordinate Reference Systems Alexandra Lyle Student No Session 1, 2006 Projection What is a projection? The world is pretty much a sphere and often maps are usually not. Projection of a map is when some method (mathematical) of putting the geographic information on to a flat piece of paper. There are approximations and distortions introduced in this process – it just has to be decided what is most important about thing required in the map. There is no one best projection; different projections are better in some situations than others. What type of projection has been used for the globe An interrupted projection: looks like it is a globe that has been but out in sections. This is, it ‘ orange peel ’ version of a globe. BUT this version is not used except to illustrate the problems of flattening a globe to make a map. However there area several very common interrupted projections, such as the Goode.

Gmat 2700 Geometry of Coordinate Reference Systems Alexandra Lyle Student No Session 1, 2006 Projection Goode Projection The Goode's projection is an interrupted, equal-area, world map projection. Global regions are presented with their areas in proper proportion, with minimal interruption, and with minimal overall distortion. Developed by Goode (1925) to provide an effective alternative to presenting global areal relationships on the Mercator projection. Goode combined the Mollweide (Homolographic) and the Sinusoidal to create the Homolosine to produce the homolosine equal-area projection, a pseudo cylindrical equal area map designed to present the entire world in one view. This projection merges the Mollweide projection for higher latitudes and the Sinusoidal projection for lower latitudes. The two projections join at 40° 44'11.8" North and South; this is where the linear scale of the two projections match. The major advantage of this projection is that the continents are viewed in their proper size with respect to one another. On the other hand, direction and distance are not accurate Quick Info: Mercator: Conformal, cylindrical projection. Mercator Useful for large scale navigation. Common for world maps. Mollweide: A pseudocylindrical projection introduced in 1805, and used world maps. The outline of the world looks line an ellipse. The center meridians have only moderate distortion.

Gmat 2700 Geometry of Coordinate Reference Systems Alexandra Lyle Student No Session 1, 2006 Projection So is the globe just a 3D version of the Goode Projection or just a simple sphere projection? ?

Gmat 2700 Geometry of Coordinate Reference Systems Alexandra Lyle Student No Session 1, 2006 References James R. Clynch, Introduction to Maps, Earth Models and Maps, Projections Part I - Categories and Properties and Notes on Projections Part II - Common Projections Goode Homolosine Projection al/GoodeHomolosine/ Goode Projection Simulating the Interrupted Goode Homolosine Projection With ArcInfo