Tuesday, August 26, 2008

Census 2000


These three maps were creating using data from the US Census (2000). The maps show the distribution of population in the continental United States in terms of race – Black, Asian and “Other.” The projection used for all three maps is the US Albers Equal Area Conic USGS, with standard parallels at 29.5° and 45.5°, appropriate for representing the conterminous 48 States. While neither shape nor scale are truly correct, distortion is minimized between the parallels. This projection was chosen because all areas are proportional to the same areas on the Earth, thus making it suitable for thematic maps since equal-area representation is maintained.


The data for percent of population of the selected race in each county is categorized into four groups using Jenks’ Natural Breaks. The Jenks’ Natural Breaks classification scheme identifies the best arrangement of values into classes, based on the inherent natural groupings in the data. Also known as the Goodness of Variance Fit, the function divides the classes where there are significant jumps in the data values, grouping similar values and maximizing the differences between classes. Jenks’ Natural Break was chosen for these maps because data distribution is explicitly considered in the method and thus appropriate for thematic maps.


Looking at the Distribution of Black Population by County in the Continental United States, the map shows that Blacks are heavily concentrated in the South, particularly the Mississippi States. In addition, Blacks are also well represented in the Mid-Atlantic, mostly in Virginia and Maryland. This region is sometimes termed the “Black Belt,” characterized by the slave plantation agriculture in U.S. history. In the Great Migration of the early 20th century, many blacks moved out of the South and into other regions of the U.S., thus, as seen in this map, blacks are also present in urban centers including Los Angeles and Oakland on the West Coast, Chicago, Detroit and New York.



According to the map of the Distribution of Asian Populations in the United States, Asian are predominantly located in on the Pacific Coast, with the majority in California and urban areas including Los Angels and San Francisco, Portland and Seattle. This can be explained by the history of Asian immigration to the U.S. since the 1800s, locating mostly in California as a result of the Gold Rush and the construction of the transcontinental railroad. There is a smaller concentration of Asians in the New England area, specifically the Washington D.C. metro area, New York and the Boston area. Additionally, Asians populations are also present in individual counties throughout the Midwest and the South, although broadly distributed.


For the Distribution of Population of “Other” Races, the map shows that the majority is heavily concentrated in the South West, including California, Arizona, New Mexico, Texas and Colorado. Other areas of concentration are in the Pacific North West – Washington State and Idaho – and in Florida, with smaller urban concentrations in the East in Chicago and New York. The U.S. Census presents race in seven categories, including White alone, Black or African American alone, American Indian and Alaska Native alone, Asian alone, Native Hawaiian and Other Pacific Islander alone, Two or more races, and Some other race alone. According to this categorization, is can be inferred that “other” races is composed of primarily Hispanic and Latino Americans, thus explaining the large concentration in the South West U.S. as historically, the area has a significant population with Hispanic/Spanish and Mexican ancestry.




Tuesday, August 19, 2008

Projections 101

A map projection takes the three-dimensional form of the Earth and represents it on a flat surface. The Earth’s surface is projected onto a developable surface such as a cylinder or cone and then “unrolled” to produce a flat plane. Depending on the shape of the developable surface, the projection can be planar/azimuthal (plane), cylindrical (cylinder) or conic (cone). No map projection can be perfect; all have distortions. However, a projection can be designed to fit specific needs, maintaining one or more these properties – true shape, true area, true distance or true direction – allowing certain distortions to be minimized.


A map that preserves shape is known as a Conformal Projection. The map scale is constant across the map and the angle between any two lines on the map is the same as the corresponding original lines on the Earth. The parallels and meridians intersect at right angles. However, the angles are only preserved at the local level and are not expected to be true beyond the intersection point.

The Mercator Projection is a cylindrical projection of the Earth, meaning that the parallels and meridians are straight and perpendicular to each other. Distances are only true along the equator and as distance away from the equator increases, the map stretches both east-west and north-south, causing the poles to be extremely distorted. According the Mercator Projection, the distance between Washington D.C. and Baghdad is approximately 8,400 miles, while the actual distance is 6,200 miles; and Antarctica appears to be larger than all other land masses combined while Greenland appears to be larger than South America. On the other hand, the east-west scale and the north-south scale remain the same relative to each other, meaning that the shapes are essentially true as well.

A typical Stereographic Projection is an azimuthal projection on a plane, where direction is true only from the center point of the projection and scale and thus distortion of areas increases away from the center point. The Gall Stereographic Projection on the other hand is a cylindrical projection that when first created, claimed to present real size proportion, having no distance, area or shape distortion. However, while area distortion is absent, in actuality, the Gall Projection contains shape and distance distortion. Antarctica and Greenland are still significantly oversized and the distance from Washington D.C. to Baghdad is approximately 5,900 miles, over 3,000 miles less than the real distance.



Equal-area Projections are projections that maintain the same proportional relationship to the corresponding areas on the Earth, although shape may not be preserved, especially at high latitudes. In the Mollweide Projection, the Earth is projected onto a 2:1 ellipse, where the equator is twice the length of the central meridian. The parallels are straight, but are compressed near the poles, while the aside from the central meridian, the meridians are projected as elliptical arcs equally spaced at the equator. This results in the elongation of shapes in the north-south direction, especially towards the poles. In addition, scale is only true along the standard parallels and according to the Mollweide Projection, the distance from Washington D.C. to Baghdad is approximately 6,600 miles.

Like the Mollweide Projection, in the Sinusoidal Projection, shapes are increasingly distorted away from the central meridian and near the poles. In the Sinusoidal Projection, the polar region is overcrowded, while the Mollweide Projection spaces the meridians, but creates more extreme angular distortion. The Sinusoidal Projection is a pseudo-cylindrical projection that preserves not only area, but distances along the horizontals. According to the projection, the distance from Washington D.C. to Baghdad is approximately 6,700 miles, which is fairly reasonable compared to the actual distance of 6,200 miles, and may have to do with the fact Washington D.C. and Baghdad are located on nearby parallels.

Equidistant Projections show distances from the center of the projection to be equidistant to any other place on the map in all directions. In the Equidistant Cylindrical Projection, all meridians are equally spaced straight vertical lines and all parallels are equally spaced straight horizontal lines. The scale is true and therefore equidistant along all the meridians, however because the poles are represented as straight lines equal in length to the equator, distortion of both shape and area increases towards the poles. According to the Equidistant Cylindrical Projection, the distance from Washington D.C. to Baghdad is approximately 4,200 miles, over 2,000 miles shorter than the actual.

In the Equidistant Conic Projection, distances are true along the meridians and one or two standard parallels, and distortion increases away from the standard parallels. In this map, areas north of the equator are well represented in direction, shape and area. According to the projection, the distance from Washington D.C. to Baghdad is approximately 6,300 miles, almost identical to the actual distance of 6,200 miles. However, the map is extremely distorted south of the equator, showing Australia as similar in size to North America.