The Nature of Geographic Information

16. Nearly Spherical

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Geographic space is nearly spherical. The fact that the Earth is nearly, but not quite, a sphere poses some surprisingly complex problems for those who wish to specify locations precisely.

World map showing the differences in elevation between a
geoid and a reference ellipsoid.
Figure 1.17.1 Differences in elevation between a geoid model and a reference ellipsoid. Deviations range from a high of 75 meters (colored red, over New Guinea) to a low of 104 meters (colored purple, in the Indian Ocean).
National Geodetic Survey, n. d.

The geographic coordinate system of latitude and longitude coordinates provides a means to define positions on a sphere. Inaccuracies that are unacceptable for some applications creep in, however, when we confront the Earth's "actual" irregular shape, which is called the geoid. Furthermore, the calculations of angles and distance that surveyors and others need to perform routinely are cumbersome with spherical coordinates.

That consideration, along with the need to depict the Earth on flat pieces of paper, compels us to transform the globe into a plane, and to specify locations in plane coordinates instead of spherical coordinates. The set of mathematical transformations by which spherical locations are converted to locations on a plane--called map projections--all lead inevitably to one or another form of inaccuracy.

All this is trouble enough, but we encounter even more difficulties when we seek to define "vertical" positions (elevations) in addition to "horizontal" positions. Perhaps it goes without saying that an elevation is the height of a location above some datum, such as mean sea level. Unfortunately, to be suitable for precise positioning, a datum must correspond closely with the Earth's actual shape. Which brings us back again to the problem of the geoid.

We will consider these issues in greater depth in Chapter 2. For now, suffice it to say that geographic data are unique in having to represent phenomena that are distributed on a continuous and nearly spherical surface.