Coordinate Systems Give Meaning to Spatial Data (Spatial Data and the Science of Measurement) (The 3-D Global Spatial Data Model)

When working with spatial data, assumptions are made about the underlying coordinate system. Since each reader deserves to know at all times “with respect to what,” an attempt is made to be very specific about the underlying coordinate system and whether the spatial data are absolute or relative. As a matter of convention, absolute spatial data are taken to be data with respect to a defined coordinate system, while relative spatial data are taken to be the difference between two absolute values in the same system. A coordinate is an absolute distance with respect to the defined coordinate system, and an azimuth is an absolute direction with respect to the zero reference. Spatial data components are coordinate differences (in the same system) and are used as relative values. An angle, defined as the difference between two directions, is also a relative value. Absolute data are often used to store spatial information, while relative data are more often associated with measurements.

Admitting the use of undefined terms, relying upon prior knowledge, and acknowledging a difference between a reference system and a reference frame, the information presented in this topic is intended to be consistent with current definitions of coordinate systems, such as those described by Soler and Hothem (1988). Three coordinate systems are an integral part of the GSDM.

1.    ECEF: A functional 3-D geocentric coordinate system for spatial data is called the Earth-centered Earth-fixed (ECEF) rectangular Cartesian coordinate system and defined by the National Imagery and Mapping Agency (NIMA; 1997). (See Figure 2.1.) With its origin at the Earth’s center of mass, the X/Y plane is coincident with the Earth’s equator, and the Z-axis is defined by the location of the Conventional Terrestrial Pole (CTP). The X-axis is defined by the arbitrarily fixed location of the Greenwich meridian, and the Y-axis is at longitude 90° east, giving a right-handed coordinate system.


2.    Geodetic: A geodetic coordinate system (Figure 2.2) is used to reference spatial data by geodetic positions on the ellipsoid, a mathematical approximation of the Earth’s surface. Position is defined in the north-south direction by angular units (degrees, minutes, and seconds) of latitude and in the east-west direction by angular units of longitude. Lines of equal latitude are called parallels, and lines of equal longitude are called meridians. The sign convention for latitude is positive north of the equator and negative south of the equator. The sign convention for longitude is positive eastward for a full circle from 0° on the Greenwich meridian to 360° (arriving again on the Greenwich meridian). A west longitude, as commonly used in the western hemisphere, is acceptable and mathematically compatible if used as a negative value.

Geodetic latitude and longitude are 2-D curvilinear coordinates given in angular units. The third dimension, ellipsoid height, in this worldwide coordinate system is the distance above or below the mathematical ellipsoid and is measured in length units, meters being the international standard. With the conceptual separation of horizontal and vertical, this system of geodetic coordinates more closely matches physical reality in a global sense than does the ECEF system and remains very useful for cartographic visualizations. But, the geodetic coordinate system is computationally more complex and more cumbersome to use than rectangular components when working with 3-D spatial data.

Geocentric ECEF Coordinate System

FIGURE 2.1 Geocentric ECEF Coordinate System

3. Local: Local coordinate systems (Figure 2.3) portray the location of spatial data with respect to some user-specified reference and/or origin. A local coordinate system can be defined such that horizontal and vertical relationships are both accurately portrayed and 3-D relationships are preserved. However, many local coordinate systems enjoy true 3-D geometrical integrity only to the extent that a flat Earth can be assumed. If spatial data issues are addressed strictly on a local basis, the error caused by such flat-Earth assumptions can be negligible. However, as one works over larger areas, needs greater precision in small areas, or needs to establish compatibility between local coordinate systems, the flat-Earth model is not adequate for referencing spatial data. But, when used as a component of the GSDM, the local flat-Earth model can support visualization and use of 3-D data without being adversely affected by the underlying curved-Earth distortions. That means local rectangular (flat-Earth) relationships can be utilized in a global environment without compromising the geometrical integrity of spatial data.

Geodetic Coordinate System

FIGURE 2.2 Geodetic Coordinate System

Spatial Data Types

Given descriptions of the geocentric ECEF coordinate system, the geodetic coordinate system, and a local coordinate system, the following spatial data types are listed:

1.    Absolute geocentric X/Y/Z coordinates are perpendicular distances in meter units from the respective axes of an ECEF reference system.

2.    Absolute geodetic coordinates of latitude/longitude/height are derived and computed from ECEF coordinates with respect to some named model (geodetic datum).

3.    Relative geocentric coordinate differences,tmp7f94-28_thumbare obtained  by differencing compatible geocentric X/Y/Z coordinate values.

4.    Relative geodetic coordinate differences,tmp7f94-29_thumbare  obtained as the difference of compatible (common datum) geodetic coordinates.

5.    Relative local coordinate differences,tmp7f94-30_thumbare local components of  a space vector defined by relative geocentric coordinate differences.

6.    Absolute local coordinates, e/n/u, are distances from some origin whose definition may be mathematically sufficient in 3-D, 2-D, or 1-D. Examples are as follows:

• Point-of-beginning (P.O.B.) datum coordinates, as defined.

These derived coordinates enjoy full mathematical definition in 3-D, suffer no loss of geometrical integrity in the GSDM, and serve the local needs of many spatial data users.

Local Coordinate System

FIGURE 2.3 Local Coordinate System

•    Map projection (state plane) coordinates, which are well defined in 2-D with respect to some named origin and geodetic datum.

•    Elevations, which are 1-D distances above or below some named reference equipotential surface. In the past, mean sea level was assumed to be acceptable as a vertical reference, but, due to the difficulty of finding mean sea level precisely, modern vertical datums are referenced to an arbitrary equipotential reference surface (Zilkoski, Richards, and Young 1992).

7. Arbitrary local coordinates may be 1-D (assumed elevations), 2-D (assumed plane coordinates), or 3-D (spatial objects, rectangular coordinates, or assumed elevations and plane coordinates). Although useful in some applications, arbitrary local coordinates are generally not compatible with other local systems and have limited value in the broader context of georeferenc-ing. Many computer graphics and data visualization programs use arbitrary local coordinates.

The GSDM efficiently handles spatial data that fall into categories 1, 3, and 5 (absolute geocentric coordinates, relative geocentric coordinate differences, and relative local coordinate differences). Spatial information is stored most efficiently using digital geocentric coordinates, manipulated most readily using geocentric coordinate differences, and displayed for human visualization and analysis using relative local coordinate differences. Spatial data consisting of geodetic coordinates and geodetic coordinate differences (categories 2 and 4) are useful for cartographic portrayal and, to the extent they can be competently related to category 1, generally are not a problem. Category 6 spatial data (local coordinate differences) can be incorporated into the GSDM if and only if they enjoy full 3-D mathematical definition. Without additional survey measurements, attempts to incorporate category 7 data into the GSDM are not viewed as fruitful. This is where the difference between spatial and geospatial data definitions may become significant.

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