PROJECTING THE GLOBE

 

Coordinate Systems & Projections

1. What is an ellipsoid? How does an ellipsoid differ from a sphere?

A.      An ellipsoid is a sphere slightly flattened at the poles.

B.      A sphere in geometry is “The set of all points in three-dimensional space lying the same distance (the radius) from a given point (the centre), or the result of rotating a circle about one of its diameters. Now an ellipsoid is sometimes referred to as a special class of spheroid known as “oblate” spheroid. You can refer to an ellipsoid as a type of sphere.

Definition of a sphere taken from <http://www.answers.com/topic/sphere>

2. What is the imaginary network of intersecting latitude and longitude lines on the earth's surface called? 

•  The lines of constant longitude are called meridians and the lines of constant latitudes are called parallels.

3. How does the magnetic north differ from the geographic North Pole? 

•  The Magnetic north is the location towards which a compass points. The geographic North Pole is the northern pole of the Earth’s axis of rotation. For map projections and coordinate systems the geographic North Pole is the one used.

4. Why are datums important? Briefly describe how datums are developed.

·         A Datum is a reference surface. They are important because along with astronomical measurements that have been done on the earth’s surface, datums are used to specify the coordinate location of points on the surface of the earth.

·         Datums consist of two major components which are:  a specified ellipsoid from the particular area being studied and a set of points and lines that have been surveyed thoroughly with specific coordinate locations specifying horizontal positions or vertical positions on the surface of the Earth

5. What is a map projection?

• Map Projection is a systematic rendering of locations from the curved earth surface onto a flat map surface.

6. What is a developable surface?

• A developable surface is a geometric shape onto which the earth’s surface locations are projected.  Cylinder, cones and planes are the most common developable surfaces. The orientation of developable surfaces can change among projections and vice versa. Most common map projections on GIS are based on developable surfaces.

7. Which lines on the graticule run north-south, converge at the poles, and mark angular distance east and west of the prime meridian?

ü  Lines of longitude

b. The major axes

c. Parallels

d. Lines of Latitude

8. Which of the following ellipsoids is now regarded as the best model of the earth for the region of North America?

a. Clarke 1866

b. International 1924

ü  c. GRS80

d. Bessel 1841

9. Which well known coordinate system would be appropriate to use for developing and analyzing spatial data when mapping counties or larger areas? Why?

·         The State Plane Coordinate System based on two types of map projection which are Mercator and Lambert.

§  It is appropriate to use these two types of systems because distortion typically increases over large distances. This system provides a common coordinate reference for horizontal coordinates over county to multi county areas while limiting error to specified maximum values. Projection distortions are very low.

10. What is a great circle distance?

• The great circle distance is a distance measured on the ellipsoid and in a plane through the earth’s center. This planar surface intersects the two points on the earth’s surface and splits the spheroid into two halves. The formula is use to find the distance distortion caused by a projection between two points. Such calculations are approximate because we base the assumption of a spherical rather than ellipsoidal earth.  Pg96   

                 The Importance of Map Projections

Map projections are ways of transferring information from a 3 dimensional sphere to a 2 dimensional plane. This becomes important to anyone working with GIS or any other geographic system because we cannot perfectly represent a three dimensional object in two dimensions. In other words we use it to represent the earth on a flat surface.  As mention earlier, since the world is a type of spheroid when you project it on a map it will undoubtedly create some type of distortion.  When we choose a map projection it lets us control the type of distortion for the particular area of interest.  There are four characteristics that a type of projection will distort. These are shape, area, distance and direction.  For example, the Mercator and Gall Stereographic is a conformal map projection I used to create two of my maps. This type of map projection preserves shape but distorts area. This is why on the map Alaska looks bigger than Brazil. The distance from Washington DC to Baghdad is distorted because this particular projection is not preserved in that direction. Equal area projections such as Bonne (World) and Sinusoidal, preserve area but distorts shape. The proportional sizes of Brazil and Alaska are correct yet the shapes are not. The distance from Washington DC to Baghdad is approximately 6199 miles. Out of the eight map projections I used, the ones that gave me the correct miles from Washington DC to Baghdad where the Sinusoidal, Bonne and the Equidistant Conic. This is because on such projections distortion of distance is lower near that direction. It all has to do with the way you project the globe to a flat surface. This all begins when an unrolled cone or cylinder intersects the ellipsoid (The best representation of the globe so far). At the point of intersection standard “Parallel Lines” form, and the distance is less distorted here. All of this is done through a series of mathematical calculations. On the Equidistant Cylindrical map projection if you take a look the shape of the countries they look very odd. When I measured the distance between Washington DC to Baghdad it was also distorted. The reason for this is because Baghdad is not at a close distance from Washington DC. In this type of projection near distances are preserved but far away ones are distorted.

Distortions take different forms depending on which area of the map you are looking at. There are only a few places on a map where distortion is zero and where the length, direction or shape of an area is preserved. Distortion usually increases when distance increases. There is an area on a map called the “line of true scale” and this is the area where there is no distortion happening. However, as you move away from this scale all properties start to change and begin to get distorted. Among the many map projections used out there we have two that are the most commonly used. These are the Lambert Conformal Conic (LCC) and Transverse Mercator. There are a series of mathematical measurements and implications behind every single map distortion. Yet the most important thing I take from this is that choosing the right projections is up to the particular area you select to study.