Geography Reference
In-Depth Information
poses. Geoids were almost always calculated for smaller areas because of the
complexity and cost of collecting the necessary data. With the advent of sat-
ellites, however, data collection has become much easier and geoids have
become more common. They are the reference standard when working with
global positioning systems (see Chapter 7). The geoid provides vertical loca-
tion control. Geoid positions usually refer to a reference ellipsoid for hori-
zontal location control. Differences between the ellipsoid positions and the
geoid positions are called “geoid undulations,” “geoid heights,” or “geoid
separations.” The horizontal and vertical locations of the projection surface
based on an ellipsoid can be adjusted to the irregular shape of the geoid
compared to the regular mathematical surface of an ellipsoid through geo-
detic techniques.
The Ellipsoid Model
The ellipsoid (or spheroid) is the most commonly used model for projec-
tions of geographic information and maps. It includes the noticeable distor-
tion between the length of the earth's north-south axis and its equator,
which bulges a small amount due to the centrifugal force of the earth's rota-
tion. In the simplest mathematical form, it consists of three parameters:
An equatorial semimajor axis
a
•
A polar semiminor axis
b
•
The flattening
f
•
Mapmakers and geodists have produced many ellipsoids. John Snyder
wrote that between 1799 and 1951 twenty-six ellipsoid determinations of the
earth's size were made. Each of these ellipsoids has a history and sheds light
into the science, culture, politics, and personalities involved in establishing
the ellipsoid through complicated and challenging field survey coupled with
exhaustive calculations. Ellipsoids were developed to satisfy individual ambi-
tion, to serve national goals, to make more accurate measurements, and so
on. The surveys conducted to create ellipsoids were often ambitious expedi-
tions into the remote areas of the world and continue to provide the material
for many stories. Multiple ellipsoids were developed and refined as measure-
ments improved and ellipsoids have often been specially defined for specific
areas—for example, for U.S. counties. Working with data or maps from dif-
TABLE 4.1. Ellipsoids
Name
Bessel (1841)
6,377,483.865 m
6,356,079.0 m
1/299.1528128
Clarke (1866)
6,378,206 m
6,356,584 m
1/294.98
Krassovsky (1940)
6,378,245 m
6,356,863.03 m
1/298.3
Australian (1960)
6,378,160 m
6,356,774.7 m
1/298.25
WGS (1984)
6,378,137 m
6,356,752.31425 m
1/298.257223563
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