Spatial data are created by measurement, and no measurement is perfect. In a simple case, a distance is determined by direct comparison of some unknown length with a standard such as a ruler, steel tape, or wavelength. Whether the distance is horizontal or vertical is a condition noted by the person recording the observation. More often, however, spatial data are obtained as the result of an indirect measurement in which one or more spatial data components are computed from the observations, as is the case when a slope distance is resolved into its horizontal and vertical components. In other cases, some physical quantity is observed and a distance is computed using known mathematical relationships (a model). An example is computing a distance from a voltage, which represents the phase shift of a sine wave signal in an electronic distance-measuring (EDM) instrument. Restating, spatial data measurements may be the result of a direct comparison, or, more often, they are computed indirectly from observations of various fundamental physical quantities.
Fundamental Physical Constants Are Held Exact
Fundamental physical quantities as expressed in the International System (SI) are as follows:
Length: meter
Time: second
Mass: kilogram
Current: ampere
Temperature: Kelvin
Luminous intensity: candela
Amount of substance: mole
Derived physical quantities include the following (there are others—see Nelson 1999):
Frequency: hertz
Force: newton
Pressure: pascal
Energy: joule
Power: watt
Electric charge: coulomb
Electric potential: volt
Plane angle: radian
Solid angle: steradian
Measurements Contain Errors
Spatial data are created by measurement of some combination of physical quantities, and those measurements are used in models that relate the observed quantity to a physical distance (spatial data) relative to one of the three coordinate systems listed earlier. The accuracy of such spatial data is dependent upon (1) the quality and sufficiency of the measurements, (2) the appropriateness of the models used to compute the spatial data components, and (3) error propagation computations. The GSDM accommodates all three considerations.
