1COPYRIGHT PROFESSIONAL SURVEYOR • December 1999 • All Rights Reserved

urveyors, GIS/LIS pro f e s s i o n a l s ,engineers, cartographers, and oth-

ers who work in North America face thechallenge of dealing with at least threedifferent 3D terrestrial reference systems.For many legal activities, these peopleexpress 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 WorldGeodetic System of 1984 (WGS 84) forvarious practical positioning activities in-volving the Global Positioning System(GPS), or they find the International Ter-restrial Reference System (ITRS) moresuitable for achieving superior positionalaccuracy. While these three referencesystems differ from one another onlyslightly in concept, they differ significant-ly in how they have been realized, wherethe realization of a particular referencesystem is called a “reference frame”. Aparticular reference frame is usually es-tablished by designating positions andvelocities for several identifiable points.To date there have been several realiza-tions of each of these three reference sys-tems, as institutions have systematicallyrevised positions and velocities from timeto time to keep pace with how evolvingtechnology has improved positioning ac-curacy. Here, we review the evolution ofthese reference frames, and we discusstransforming positions between differentreference frames. Finally, we addresssome practical considerations for accu-rate positioning and discuss plans for anew NAD 83 realization.

Defining a Reference System

The modern approach to defining a3D terrestrial re f e rence system may be di-vided into four steps. The first step linksthe axes of a 3D cartesian coordinate sys-tem to a configuration of physically meas-urable locations on or within the earth. Asa result, the location and orientation ofthe three coordinate axes are defined.The second step relates the concept ofdistance to physically measurable quanti-ties whereby a unit of length is intro-duced. The third step introduces an aux-iliary geometric surface that appro x i m a t e sthe size and shape of the earth. Finally,

the fourth step addresses the question ofhow Earth’s gravity field contributes tothe notion of position, and especially thatof height. We shall be concerned herewith only the first three steps, thus focus-ing on the geometric aspects involved indefining a re f e rence system.

For the first step, most scientists in-volved in defining modern reference sys-tems agree that the origin of the 3D carte-sian system should be located at Earth’scenter of mass (geocenter); also that thecartesian system’s z-axis should passthrough the conventional definition ofthe North Pole, or more precisely, the In-ternational Reference Pole (IRP) as de-fined by the International Earth RotationService (IERS), an international organiza-tion established in 1988 and headquar-tered in Paris, France. The x-axis shouldgo through the point of zero longitudelocated on the plane of the conventionalequator, which is also defined by theIERS. The meridian going through thispoint is located very close to the meridi-an of Greenwich although the two arenot coincident. The y-axis forms a right-handed coordinate frame with the x- andz-axes. Indeed, each of the three refer-

ence systems—NAD 83, WGS 84, andITRS—has been accordingly defined inconcept. They differ, however, as weshall soon discuss, in their realizations;that is, in how the location and orienta-tion of their respective cartesian axeshave been physically materialized as wellas their respective concepts of distance.Unfortunately, what initially appears tobe a simple geometric procedure is com-plicated by Earth’s dynamic behavior. Forexample, Earth’s center of mass is mov-ing relative to Earth’s surface. Also, thereare variations of Earth’s rotation rate aswell as motions of Earth’s rotation axisboth with respect to space (precessionand nutation) and to Earth’s surface (po-lar motion). Moreover, points on theearth’s crust are moving relative to oneanother as a result of plate tectonics,earthquakes, volcanic/magmatic activity,postglacial rebound, people’s extractionof underground fluids, solid Earth tides,ocean loading, and several other geo-physical phenomena. Modern terre s t r i a lre f e rence systems, hence, need to ac-count for these motions. One option is torelate the cartesian axes to the locationsof selected points measured at a particu-

REFERENCE SYSTEMS

Modern Terrestrial Reference Systems (Part 1)Dr. Richard A. Snay and Dr. Tomás Soler

S

Figure 1

2 COPYRIGHT PROFESSIONAL SURVEYOR • December 1999 • All Rights Reserved

lar instant of time (epoch). This alternative isgenerally used when dealing with the motionof the earth’s rotational axis and with the mo-tions associated with plate tectonics. Othertypes of motion (for example, subsidence) areaccounted for by fixing the cartesian axes tosome temporal average of the locations for se-lected points. As we shall see, a fundamentald i ff e rence among the various re f e rence framesinvolves how they address the motion associ-ated with plate tectonics.

For the second step, scientists concern e dwith defining up-to-date terrestrial re f e re n c esystems agree that the unit of length, the me-ter or “metre”, corresponds to the length ofpath traveled by light in a vacuum during atime interval of exactly 1/299,792,458 seconds.This solves the problem of relating the con-cept of distance to a physically measurablequantity in theory, but not in realization. Eachof the various re f e rence frames associatedwith NAD 83, WGS 84, and ITRS relies on adistinct set of measurements that were per-f o rmed using one or more of several widelyd i ff e rent types of instruments and techniques,among the most re p resentative: GPS, electro -optical distance measuring instrumentation,Doppler satellite positioning, very long base-line interf e rometry (VLBI), and satellite laserranging (SLR). While each measurement typehad been calibrated to fit the definition of ameter as best as possible, the observations,nevertheless, contain uncertainties. Conse-quently, the “scale” of any particular re f e re n c eframe is somewhat less than perfect. In partic-u l a r, when old classical terrestrial frames arec o m p a red with modern “space-age” frames,scale errors at the part-per-million (ppm) levelmay often be detected. Because of re c e n ttechnological advances in the measurement oftime and, consequently, distance, scale diff e r-ences between modern frames are now ap-p roaching the part-per-billion (ppb) level.

For the third step, the earth’s surface is ap-p roximated in size and shape by the geometrics u rface that is formed by rotating an ellipseabout its smaller axis (Figure 1). The generat-ed surface is termed an “ellipsoid of re v o l u-tion” or simply ellipsoid. The ellipsoid’s geo-metric center should be located at the origin ofthe 3D cartesian system, and its axis of radialsymmetry (semi-minor axis) should coincidewith the cartesian z-axis of the selected terre s-trial re f e rence frame. The size and shape of therotated ellipse may be completely specified us-ing two parameters: the length of its semi-ma-jor axis, usually denoted a, which appro x i-mates the distance from the geocenter to apoint on the equator (approximately 6,378km); and the length of the semi-minor axis, de-

noted b, which approximates the dis-tance from the geocenter to the NorthPole. The value of b is about 0.3%shorter than a. The fact that a i slonger than b is a consequence of thef o rce imparted by Earth’s ro t a t i o ncausing our home planet to bulgeoutward around its equator. Often, in-stead of b, the ellipsoid’s flattening, f = (a - b)/ a, is used.

D i ff e rent ellipsoids have beenadopted for the diff e rent re f e re n c esystems. NAD 83 uses the same el-lipsoid as the Geodetic Refere n c eSystem of 1980 which was adoptedby the International Association ofGeodesy. WGS 84 uses an ellipsoidadopted by the National Imageryand Mapping Agency (NIMA, for-merly the Defense MappingAgency), and ITRS uses an ellip-

soid adopted by the IERS. Corre s p o n d-ing values of a and f a re presented inthe table below.

Given values for a and b (or f) ,people can convert 3D cartesian coor-dinates—x, y, z— into the curvilinearcoordinates—latitude, longitude, andellipsoidal height—and vice versa.These curvilinear coordinates embody acertain intuitive appeal in specifying lo-cations on and near the earth’s surf a c e ,as they relate to our innate sense of thehorizontal and vertical dimensions.

DR. RICHARD A. SNAY is Manager of theNational Continuously Operating Refer-ence Station (CORS) program and a geo-desist with the National Geodetic Survey.DR. TO M Á S SO L E R, is Chief, Global Position-ing System Branch, Spatial Reference Sys-tems Division, National Geodetic Survey.

Reference System Semi-major axis, m Flattening, unitless

NAD 83 6,378,137.0 1/298.257222101

WGS 84 6,378,137.0 1/298.257223563

ITRS 6,378,136.49 1/298.25645

REFERENCE SYSTEMS