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REFERENCE SYSTEMS

Modern Terrestrial Reference Systems (Part 1)

Dr. Richard A. Snay and Dr. Tomás Soler

urveyors, GIS/LIS pro f e s s i o n a l s , S engineers, cartographers, and oth- ers who work in America face the challenge of dealing with at least three different 3D terrestrial reference systems. For many legal activities, these people express positional coordinates in the ref- erence system known as the North Amer- ican Datum of 1983 (NAD 83). Alterna- tively, they often favor using the of 1984 (WGS 84) for various practical positioning activities in- volving the Global Positioning System (GPS), or they find the International Ter- restrial Reference System (ITRS) more suitable for achieving superior positional accuracy. While these three reference systems differ from one another only slightly in concept, they differ significant- ly in how they have been realized, where the realization of a particular reference system is called a “reference frame”. A particular reference frame is usually es- Figure 1 tablished by designating positions and velocities for several identifiable points. To date there have been several realiza- the fourth step addresses the question of ence systems—NAD 83, WGS 84, and tions of each of these three reference sys- how Earth’s gravity field contributes to ITRS—has been accordingly defined in tems, as institutions have systematically the notion of position, and especially that concept. They differ, however, as we revised positions and velocities from time of height. We shall be concerned here shall soon discuss, in their realizations; to time to keep pace with how evolving with only the first three steps, thus focus- that is, in how the and orienta- technology has improved positioning ac- ing on the geometric aspects involved in tion of their respective cartesian axes curacy. Here, we review the evolution of defining a ref e r ence system. have been physically materialized as well these reference frames, and we discuss For the first step, most scientists in- as their respective concepts of distance. transforming positions between different volved in defining modern reference sys- Unfortunately, what initially appears to reference frames. Finally, we address tems agree that the origin of the 3D carte- be a simple geometric procedure is com- some practical considerations for accu- sian system should be located at Earth’s plicated by Earth’s dynamic behavior. For rate positioning and discuss plans for a center of mass (geocenter); also that the example, Earth’s center of mass is mov- new NAD 83 realization. cartesian system’s z-axis should pass ing relative to Earth’s . Also, there through the conventional definition of are variations of Earth’s rotation rate as Defining a Reference System the , or more precisely, the In- well as motions of Earth’s rotation axis The modern approach to defining a ternational Reference Pole (IRP) as de- both with respect to space (precession 3D terrestrial ref e r ence system may be di- fined by the International Earth Rotation and nutation) and to Earth’s surface (po- vided into four steps. The first step links Service (IERS), an international organiza- lar motion). Moreover, points on the the axes of a 3D cartesian coordinate sys- tion established in 1988 and headquar- earth’s crust are moving relative to one tem to a configuration of physically meas- tered in Paris, France. The x-axis should another as a result of , urable on or within the earth. As go through the point of zero earthquakes, volcanic/magmatic activity, a result, the location and orientation of located on the plane of the conventional postglacial rebound, people’s extraction the three coordinate axes are defined. , which is also defined by the of underground fluids, solid Earth tides, The second step relates the concept of IERS. The going through this ocean loading, and several other geo- distance to physically measurable quanti- point is located very close to the meridi- physical phenomena. Modern terres t r i a l ties whereby a unit of length is intro- an of Greenwich although the two are ref e r ence systems, hence, need to ac- duced. The third step introduces an aux- not coincident. The y-axis forms a right- count for these motions. One option is to iliary geometric surface that approx i m a t e s handed coordinate frame with the x- and relate the cartesian axes to the locations the size and shape of the earth. Finally, z-axes. Indeed, each of the three refer- of selected points measured at a particu-

COPYRIGHT PROFESSIONAL SURVEYOR • December 1999 • All Rights Reserved 1 REFERENCE SYSTEMS

lar instant of time (epoch). This alternative is noted b, which approximates the dis- soid adopted by the IERS. Corre s p o n d- generally used when dealing with the motion tance from the geocenter to the North ing values of a and f a re presented in of the earth’s rotational axis and with the mo- Pole. The value of b is about 0.3% the table below. tions associated with plate tectonics. Other shorter than a. The fact that a is Given values for a and b (or f) , types of motion (for example, subsidence) are longer than b is a consequence of the people can convert 3D cartesian coor- accounted for by fixing the cartesian axes to fo r ce imparted by Earth’s rot a t i o n dinates—x, y, z— into the curvilinear some temporal average of the locations for se- causing our home planet to bulge coordinates—, longitude, and lected points. As we shall see, a fundamental outward around its equator. Often, in- ellipsoidal height—and vice versa. di ff e r ence among the various ref e r ence frames stead of b, the ’s , These curvilinear coordinates embody a involves how they address the motion associ- f = (a - b)/a , is used. certain intuitive appeal in specifying lo- ated with plate tectonics. D i ff e rent have been cations on and near the earth’s surf a c e , For the second step, scientists concerne d adopted for the diff e rent re f e re n c e as they relate to our innate sense of the with defining up-to-date terrestrial ref e re n c e systems. NAD 83 uses the same el- horizontal and vertical . systems agree that the unit of length, the me- lipsoid as the Geodetic Refere n c e ter or “”, corresponds to the length of System of 1980 which was adopted DR. RICHARD A. SNAY is Manager of the path traveled by light in a vacuum during a by the International Association of National Continuously Operating Refer- time interval of exactly 1/299,792,458 seconds. . WGS 84 uses an ellipsoid ence Station (CORS) program and a geo- This solves the problem of relating the con- adopted by the National Imagery desist with the National Geodetic Survey. cept of distance to a physically measurable and Mapping Agency (NIMA, for- DR. TOM Á S SOL E R , is Chief, Global Position- quantity in theory, but not in realization. Each merly the Defense Mapping ing System Branch, Spatial Reference Sys- of the various ref e r ence frames associated Agency), and ITRS uses an ellip- tems Division, National Geodetic Survey. with NAD 83, WGS 84, and ITRS relies on a distinct set of measurements that were per- Reference System Semi-major axis, m Flattening, unitless fo r med using one or more of several widely NAD 83 6,378,137.0 1/298.257222101 di ff e r ent types of instruments and techniques, WGS 84 6,378,137.0 1/298.257223563 among the most rep r esentative: GPS, electro- optical distance measuring instrumentation, ITRS 6,378,136.49 1/298.25645 Doppler positioning, very long base- line interfe r ometry (VLBI), and satellite laser ranging (SLR). While each measurement type had been calibrated to fit the definition of a meter as best as possible, the observations, nevertheless, contain uncertainties. Conse- quently, the “” of any particular ref e re n c e frame is somewhat less than perfect. In partic- ul a r , when old classical terrestrial frames are co m p a r ed with modern “space-age” frames, scale errors at the part-per-million (ppm) level may often be detected. Because of rec e n t technological advances in the measurement of time and, consequently, distance, scale diffe r - ences between modern frames are now ap- pr oaching the part-per-billion (ppb) level. For the third step, the earth’s surface is ap- pr oximated in size and shape by the geometric su r face that is formed by rotating an about its smaller axis (Figure 1). The generat- ed surface is termed an “ellipsoid of rev o l u - tion” or simply ellipsoid. The ellipsoid’s geo- metric center should be located at the origin of the 3D cartesian system, and its axis of radial symmetry (semi-minor axis) should coincide with the cartesian z-axis of the selected terres - trial ref e r ence frame. The size and shape of the rotated ellipse may be completely specified us- ing two parameters: the length of its semi-ma- jor axis, usually denoted a, which approx i - mates the distance from the geocenter to a point on the equator (approximately 6,378 km); and the length of the semi-minor axis, de-

2 COPYRIGHT PROFESSIONAL SURVEYOR • December 1999 • All Rights Reserved