Lab 4

The following questions based on Bolstad Chapter 3, lecture, and Wikipedia.

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

An ellipsoid is a mathematical surface defined by revolving an ellipse around its minor (polar) axis. While a sphere is perfectly round an ellipsoid is slightly flattened. Due to this it is accepted as the best geometric model of the earth’s surface.

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

Geographic Coordinate System (GCS)

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

The geographic North Pole is located on the northern pole of the earth’s axis of rotation. The magnetic north is where your compass points to. They are not located at the same place, and the angular distance between them is called the magnetic declination.

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

A datum is a 3-D frame of reference that is used to determine surface locations. They have two major components. The first is a specified ellipsoid. Second, is a set of surveyed locations that specify positions on the Earth’s surface.

5. What is a map projection?

A map projection is a transformation of coordinate locations from a 3-Dimensional representation of the Earth’s surface to a 2-Dimensional one.

6. What is a developable surface?

A developable surface is a geometric shape that the Earth’s surface can be projected onto. Cones, cylinders, and planes are the most common 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?

a. Lines of longitude

b. The major axes

c. Parallels

d. Lines of Latitude

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

c. GRS80

d. Bessel 1841

C. GRS 80

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

A universal transverse Mercator (UTM) coordinate system is most useful because is divides the world into zones that are 6 degrees wide in longitude, and can contain larger areas in one zone.

10. What is a great circle distance?

A great circle distance is a distance measured on the ellipsoid and in a plane through the Earth’s center.

Map projections are important to see, understand, and analyze spatial patterns. There are several surfaces to project a map onto, but the most common are a cylinder, cone, and plane. Also, some map projections do not use a developable surface. Instead they just use a mathematical projection from an ellipsoid onto a flat surface. Distortions can be expected when taking a three-dimensional object and projecting it onto a two-dimensional surface. These distort four main properties shape, direction, area, and distance. Different projections preserve different properties, and they are categorized based on what they preserve. There are three main categories of projections: conformal, equal area, and equidistant. Conformal maps try to preserve shape and direction. It does this by preserving the angles between curves. Two examples of this are a Mercator and a Gall Stereographic projection. A Mercator projection is a cylindrical map projection that keeps linear scale constant in all directions around any point. This preserves the angles, but it distorts shape and size as move from the Equator to the poles. This can be seen in map below. The countries are all where they are supposed to be, and they all have the right shape. However, the further from the equator you get the more out of proportion they become. Greenland appears to be larger than South American which is clearly not accurate. Due to this distance is not accurate either. It is approximately 6,211 miles from Washington D.C. to Baghdad, Iraq, but with the Mercator projection it is approximately 8,407.69 miles. Another type of a conformal projection is a Gall Stereographic projection. This too preserves angles, but it's projection is based off of a sphere. In the map below  you can see an example of a Gall Stereographic projection. Notice the similarities with the Mercator projection. The counties are the right shape, but still not the right size. However, in this example they are much closer to being accurate. This can be seen in the distance from Washington D.C to Baghdad, Iraq is only 5,938.71 miles. Another category of map projections is equal area. These maps preserve area. One example of this is a Mollweide projection (see below). Notice how the countries are now all approximately the proper size. For example Greenland is no longer larger than the other continents. However, now they are not necessarily the proper shape. One place where this is apparent is around the edges of the map. They countries all appear to be distorted giving it a slightly rounded appearance.  Since the map preserves area the distance between Washington D.C and Baghdad, Iraq (6,584.28 miles) is not that far from the actual distance. Another example of an equal area projection is a Bonne projection. This is a pseudoconical projection that preserves area, but not shape or direction. Looking at the map below it is evident that neither of these are preserved. Australia is highly distorted, and the overall shape of the world is more heart-like than ellipse-like. However, again the distance between Washington D.C and Baghdad, Iraq (6,016.27 miles) is not that far from the actual distance between the two cities. The equidistant projection preserve distance over a short area. Equidistant Conic projection is an example of this. Looking at the map below you can see that area, shape, and direction are all distorted. However, the distance from Washington D.C to Baghdad, Iraq is 6.266.72 nearly the actual distance between these two cities. A Sinusoidal projection also preserves distance as a ratio between the each parallel and the cosine of the latitude. Due to this the distance in the real world is smaller than the distance displayed on the map. For example the distance between Washington D.C and Baghdad, Iraq is 6,730.50 on the map, but is actually 6,211 miles in the real world. The other properties are still distorted as you can see in the map below.