Projections - A Primer of GIS: Fundamental Geographic and Cartographic Concepts - page 80

ferent periods often involves determining if different ellipsoids were used in
collecting data; data from different coordinate systems, even if in the same
area, may also have different ellipsoids.
The Spheroid Model
The spheroid is the simplest model of the earth's surface, using only a single
measurement to approximate the shape of the earth's surface for geographic
information and maps. This measurement is the distance from the hypothet-
ical center of the earth to the surface, or, in geometrical terms, the radius.
The mean earth radius R E is 3,959 miles (6,371.3 km). The spheroid is very
inaccurate and you should only use the spheroid for scales smaller than
1:5,000,000,000. The inaccuracies of this model of the earth's surface are
unapparent at these small scales. It is much easier to calculate the projec-
tions using a spherical model but using the spheroid for projecting geo-
graphic information and making maps for scales larger can lead to grave
inaccuracies.
Putting the Models Together: Demythologizing the Datum
Datum is the term used to refer to the calibration of location measurements
including the vertical references, horizontal references, and particular pro-
jections or versions of a projections—for example, the North American
Datum 1927 or the North American Datum 1983. Datums constitute one of
the most confounding aspects of working with projections for many geo-
graphic information and map users. This term simply specifies the model of
the shape of the earth at a particular point in time and often for a particular
area—for example, North America, Europe, or Australia. A horizontal datum
is often the basis for determining an ellipsoid used in a projection for a coor-
dinate system (see Chapter 5). A datum can be used with different projec-
tions—for example, the North American Datum 1927 is used with both the
Lambert and the transverse Mercator projections. For geographic informa-
tion users, datums are references to a set of parameters needed for measur-
ing locations and the basis for projections. Because there are many parame-
ters and the mathematics for transforming datums is highly complex, many
people have been stymied by datums. But it is really, for most general pur-
poses, quite simple: the datum refers to a reference surface for making posi-
tional measurements. While most datums in North America are described in
technical guidelines or even laws, theoretically a datum can be defined by
any government agency or private group as it sees fit.
Datums distinguish between horizontal and vertical references and local
and geocentric datums. A datum should (but might not) contain both hori-
zontal and vertical references. Horizontal references are used to measure the
location of positions on the earth and vertical datums are used to measure
the elevation of a position. You can think of a vertical datum as the base level
used in recording elevations or the mean height of tides. All elevations using