Evolution of NAD 83 in the United States:Journey from 2D toward 4D

Richard A. Snay1

Abstract: In 1986, Canada, Greenland, and the United States adopted the North American Datum of 1983 (NAD 83) to replace the NorthAmerican Datum of 1927 as their official spatial reference system for geometric positioning. The rigor of the original NAD 83 realizationbenefited from the extensive use of electronic distance measuring instrumentation and from the use of both TRANSIT Doppler observationsand very long baseline interferometry observations. However, the original NAD 83 realization predated the widespread use of the global po-sitioning system and the use of continuously operating reference stations. Consequently, NAD 83 has evolved significantly in the United Statessince 1986 to embrace these technological advances, as well as to accommodate improvements in the understanding of crustal motion. Thispaper traces this evolution from what started as essentially a two-dimensional (2D) reference frame and has been progressing toward afour-dimensional (4D) frame. In anticipation of future geodetic advances, the U.S. National Geodetic Survey is planning to replace NAD 83about a decade from now with a newer, more geocentric spatial reference system for geometric positioning. DOI: 10.1061/(ASCE)SU.1943-5428.0000083. © 2012 American Society of Civil Engineers.

CE Database subject headings: History; Datum; Transformations; Geodetic surveys; North America.

Author keywords: History; Datum transformations; Dynamic datums; Crustal deformation; NAD 83.

Introduction

In 1986 a group of institutions representing Canada, Greenland, andthe United States of America adopted the North American Datum of1983 (NAD 83) as their official spatial reference system for geo-metric positioning (Schwarz 1989). The National Geodetic Survey(NGS), an office of the U.S. National Oceanic and AtmosphericAdministration, represented the United States, where the first NAD83 realization is referred to as NAD 83 (1986). NAD 83 replaced theNorth AmericanDatum of 1927 (NAD27), and the NGS has alreadyexpressed its intention to replace NAD 83 about a decade fromnow with a newer geometric reference system (NGS 2010). Dracup(1989) provides a history of horizontal geodetic control in theUnitedStates prior to the adoption of NAD 83. Craymer (2006) discussesthe evolution of NAD 83 in Canada since its adoption in 1986.

Here, the term reference system pertains to an abstract collectionof principles, fundamental parameters, and specifications for quan-titatively describing the positions of points in space and how thesepositions vary over time, whereas the term reference frame pertainsto the materialization or realization of such a system. Traditionally,a reference frame consists of a network of reference stations on theground with adopted positional coordinates (and sometimes veloc-ities), which may be used to help determine coordinates for otherlocations. NAD 83 is a reference system, whereas NAD 83 (1986) isjust one of many reference frames associated with NAD 83.

Modern geometric reference systems are intended to provide afoundation for measuring geodetic latitude, longitude, and ellipsoid

height, and how these three coordinates vary over time. NAD 27provided a foundation for measuring only geodetic latitude and lon-gitude; therefore, it is considered a horizontal datum. NAD 27 wasestablished using triangulation data together with 112 taped baselinelengths to provide scale and 175 astronomic azimuths to provideorientation. The origin of NAD 27 was established by prescribingspecific values for both the geodetic latitude and longitude of thereference station inKansas known asMeades Ranch—a point locatednear the geographic center of the conterminous United States(CONUS).

In 1927, theUnitedStates’ horizontal reference network containedapproximately 25,000 reference stations. By 1983, this network hadexpanded to include approximately 272,000 reference stations.NAD 27 served the nation well until electronic distance measuring(EDM) instrumentation came into widespread usage in the 1960s.EDM instrumentation enabled surveyors and others to measurebaseline lengths with relative ease and with an accuracy of a fewparts per million (ppm). With the existing triangulation network,geodesists often had to propagate a taped baseline length more than100 km via the laws of trigonometry and geometry to compute thedistance of a baseline connecting a pair of NAD 27 reference sta-tions. The distance of this same baseline could be measured muchmore accurately with EDM instrumentation. As such, EDM resultsexposed significant regional and local distortions among NAD 27coordinates for reference stations. In some cases, the relative errorbetween the NAD 27 coordinates of two separate reference stationsexceeded 1 m.

The 1960s also witnessed the dawning of yet another innovativetechnology for measuring positional coordinates; namely, the use ofartificial earth-orbiting satellites. In particular, the U.S. Navy’sTRANSIT Doppler constellation of satellites enabled its users tomeasure the three-dimensional (3D) coordinates of a point relative tothe earth’s center ofmass (hereafter referred to as the geocenter) witha precision of approximately 1 m. An earth-based receiver did so bytracking the Doppler shifts of satellite-transmitted radio signals. Thereceiver needed to collect data at a reference station for at least one

1Retired; formerly, National Geodetic Survey, 9505 Aspenwood Ct.,Montgomery Village, MD 20886. E-mail: rssnay@aol.com

Note. This manuscript was submitted on November 22, 2011; approvedon January 30, 2012; published online onFebruary1, 2012.Discussion periodopen until April 1, 2013; separate discussions must be submitted for in-dividual papers. This paper is part of the Journal of Surveying Engineering,Vol. 138, No. 4, November 1, 2012. ©ASCE, ISSN 0733-9453/2012/4-161e171/$25.00.

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week to achieve such meter-level precision. TRANSIT technologymay seem quite outdated compared with today’s global navigationsatellite system (GNSS) technology; however, TRANSIT Dopplerresults were popular back in the 1960s and 1970s. TRANSIT en-abled geodesists to measure all three spatial dimensions simulta-neously and in an absolute sense; that is, relative to the geocenterrather than to some arbitrary point such as a reference station locatedinKansas. This facilitated various countries, if they so desired, to usethe geocenter as a common origin for their respective referencesystems. The U.S. Department of Defense (DoD) employedTRANSIT Doppler observations extensively for establishing theoriginal realization of theWorldGeodetic Systemof 1984 (WGS84)(True 2004). Indeed, the NGS and DoD collaborated to make theoriginal NAD 83 coordinates and the original WGS 84 coordinatesconsistent with each other in the sense that both sets of coordinatesare referred to the same origin and share the same orientation andscale. Only a submillimeter difference in the semimajor axis of thechosen reference ellipsoid differentiates the original NAD 83coordinates from the original WGS 84 coordinates in a systematicway.

It was both EDM and TRANSIT Doppler that provided the im-petus for replacing NAD 27 with NAD 83. The NGS, in collabo-ration with other institutions, performed numerous very highaccuracy trilateration surveys with EDM instrumentation and posi-tioned 612 reference stations with TRANSIT Doppler observationsprior to establishing the geocentric NAD 83 reference system. Fig. 1

illustrates the magnitudes of the two-dimensional (2D) coordinateshifts associatedwith the transition fromNAD27 toNAD83 (1986).The NGS developed the NADCON software (Dewhurst 1990),which enables users to convert betweenNAD27 andNAD83 (1986)positional coordinates. AlthoughNAD83 started as 3D in scope, theNGS adopted only horizontal coordinates (geodetic latitude andlongitude) for over 99% of the approximately 272,000 United Statesreference stations that were involved in its first realization. This firstrealization did include a few global positioning system (GPS)observations; however, this first realization occurred before GPSblossomed into the technology that has helped to make the verticaldimension economically accessible.

GPS Changes Everything

Just before the NGS adopted NAD 83 (1986), the agency beganusing GPS, instead of triangulation and/or trilateration, for hori-zontal positioning. In the 1980s, surveyors, hydrologists, and otherusers of vertical positions somewhat overlooked GPS results be-cause they required orthometric heights rather than ellipsoid heights.As shown inFig. 2, an orthometric height, denoted asH, at a locationquantifies the distance along the curved plumb line (through thatlocation) above or below the geoid, an equipotential surface ap-proximating mean sea level. Orthometric heights depend on theearth’s gravity field, and these heights are traditionally measured

Fig. 1. Magnitude of shifts from NAD 27 horizontal coordinates to NAD 83 (1986) horizontal coordinates

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using tide gauges, spirit leveling, and surface gravity (observed ormodeled). Ellipsoid heights, denoted as h, are geometric heightsrelative to an abstract mathematical surface (the ellipsoid) and caneasily be obtained with GPS data. Compared with ellipsoid heights,orthometric heights better reflect what direction water will flowbecause they better address the influence of the earth’s gravitationalfield. The attitude toward using GPS to measure heights graduallyevolved as the NGS and other institutions developed improvedmodels for determining the height of the geoid relative to the el-lipsoid, denoted as N, for specific geographic regions. The threeheights are related by the approximation,H� heN. These improvedmodels for determining N enabled converting ellipsoid heights intoorthometric heights with greater and greater accuracy. Moreover,practitioners canmeasure ellipsoid heightsmuchmore economicallywith GPS than they can measure orthometric heights with spiritleveling, except over short distances.

As GPS matured, so did other space-age geodetic technologies;in particular, very long baseline interferometry (VLBI) and satellitelaser ranging (SLR). VLBI accurately measures the coordinate dif-ferences defining a 3D vector between two antennas that are si-multaneously receiving radio signals from extragalactic sources,such as quasars. VLBI is especially useful for measuring the earth’sorientation in space and for providing scale to geodetic networks.SLR accurately measures the distance from a laser source on theearth to a reflector located on an orbiting satellite. SLR is like usingan EDM instrument on steroids. SLR is especially useful formeasuring the location of the geocenter and for providing scale togeodetic networks.

Within a few years after 1986, both GPS and SLRmeasurementsallowed geodesists to locate the geocenter with a precision of a fewcentimeters. In doing so, these technologies revealed that the geo-center adopted for both NAD 83 (1986) and the original WGS 84realization is displaced by more than 2 m from the true geocenter.Similarly, GPS, SLR, and VLBI revealed that the orientation of theNAD 83 (1986) Cartesian axes is misaligned by over 0.03 arcsecrelative to the orientation associated with current versions of the

International Terrestrial Reference Frame (ITRF), and that the NAD83 (1986) scale differs by approximately 0.0871 ppm from the truedefinition of ameter. These discrepancies caused significant concernas the use of highly accurate GPS measurements proliferated. Inparticular, starting with Tennessee in 1989, each state—in collab-oration with the NGS and various other institutions—used GPStechnology to establish a statewide or regional reference frame thatwas to be consistent with NAD 83. The corresponding networks ofGPS reference stations were originally called high-precision geo-detic networks. Currently, they are referred to as high-accuracyreference networks (HARNs) (Strange and Love 1991). This lattername follows because relative coordinate accuracies among HARNreference stations are better than 1 ppm, whereas relative coordinateaccuracies among the pre-existing reference stationswere nominallyonly 10 ppm.

For defining these statewide/regional reference frames, the NGSretained the location of the geocenter and the orientation of the 3DCartesian axes that had been derived in 1986 from TRANSITDoppler observations. However, the NGS opted to introduce a newscale that would be consistent with the scale of the 1989 ITRF(ITRF89). The resulting scale change, equal to 20.0871 ppm, al-tered the existing NAD 83 latitudes and longitudes insignificantly;however, it systematically decreased all NAD83 ellipsoid heights byabout 0.56 m (5 0.08713 1026R, where R denotes the radius of theearth). Nevertheless, this change to a more accurate scale facilitatedthe migration toward using GPS technology for deriving accurateheights. This second realization is referred to as NAD 83 (HARN).However, it should be kept in mind that this second realization isactually a collection of almost 50 statewide or regional realizationsthat were formulated individually over a period of several years(1989e1997) with each new statewide/regional realization beingadjusted to fit those that adjoined it. In actuality, each statewide/regional realization was given a name like NAD 83 (xxxx), wherexxxx corresponds either to the year when the associated HARNGPSsurvey was performed or to the year when the related GPS mea-surements were adjusted to obtain coordinates for the reference

Fig. 2. Relationship between orthometric height, ellipsoid height, and geoid height

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stations at which the GPS measurements were performed. Thechoice between these two years was made in accordance with thewishes of representatives from the associated state/region. The NGSthen readjusted all the relevant triangulation/trilateration data in thestate/region to obtain NAD83 (HARN) coordinates for the referencestations that had been established solely by these classical obser-vations. The NADCON software (Dewhurst 1990) enables users toconvert between NAD 83 (1986) and NAD 83 (HARN) horizontalcoordinates.

In the early 1990s, DoD decided to introduce a new WGS 84realization whose origin, orientation, and scale would be identical tothose adopted for the 1991 ITRF (ITRF91). DoD adopted the nameWGS 84 (G730) to identify this second realization of their globalreference system. Here, G stands for GPS because this newer re-alization is based on GPS data rather than TRANSIT Doppler data.The number 730 refers to the GPS week when this frame wasimplemented by DoD’s National Imagery and Mapping Agency(NIMA) [NIMA 2004; National Geospatial-Intelligence Agency(NGIA) 2004]. The first day of GPS Week 730 corresponds toJanuary 2, 1994. From this date onward, NAD 83 coordinates andWGS 84 coordinates have systematically differed bymore than 2m.The DoD has since published three additional realizations: WGS 84(G873), WGS 84(G1150), and WGS 84(G1674). The origin, ori-entation, and scale of each realization are identical to those of anITRF realization: ITRF94, ITRF2000, and ITRF2008, respectively.

NAD 83 Coordinates for Continuously OperatingReference Stations

In 1995, the NGS introduced yet another realization of NAD83 afterthe agency initiated a network of continuously operating referencestations (CORSs) (Snay and Soler 2008). Each CORS includesa high-quality GPS receiver whose data the NGS collects, processes,archives, and disseminates for public use. Geospatial professionals

and others can apply CORS data to position points at which otherGPS data have been collected with centimeter-level accuracy, bothhorizontally and vertically (i.e., ellipsoid heights). The CORSnetwork started with approximately a dozen stations in February1994 and it has since grown to include over 1,800 stations, thanks tomore than 200 organizations that have built and maintained thesestations and have allowed the NGS to provide the associated GPSdata freely to the public. For the past several years, the CORSnetwork has been growing at a rate of approximately 200 newstations per year, and it is continuing to grow. The CORS networkprovides coverage throughout the United States, its territories, anda few foreign countries. Fig. 3 depicts the status of the CORSnetwork as of November 2011. Positional coordinates for the earlyCORSs (approximately 30 stations) were first computed in the 1993ITRF (ITRF93). The NGS then employed a seven-parameter sim-ilarity (Helmert) transformation to convert these coordinates toNAD83. Such a transformation includes three translations, three rotations,and a scale factor (often expressed as a difference from unity). Thevalues for the first six parameters (three translations and threerotations) were estimated so that the ITRF93 positional coordinatesof nine VLBI stations located in the United States would transformas best as possible (in a least-squares sense) to their previouslyadopted NAD 83 (HARN) positional coordinates. These VLBIstations (shown in Fig. 4) were used because they had highly ac-curate coordinates (centimeter level) in both ITRF93 and NAD 83(HARN). The scale factor was constrained to 1.0 in value, orequivalently, the scale difference was constrained to zero in value.The reference frame obtained by applying this transformation toconvert the ITRF93 coordinates for CORSs to the NAD 83 coor-dinates is called NAD 83 (CORS93).

In 1996, the NGS computed the ITRF94 positional coordinates forthe approximately 60 then-existing CORSs. The NGS then convertedthese ITRF94 coordinates to NAD 83 by using a 14-parameter trans-formation. The additional seven parameters correspond to the rates ofchangewith respect to timeof the sevenparameters defining a similarity

Fig. 3.United States CORS network in November 2011 containedmore than 1,800 stations spanning the United States, its territories, and a few foreigncountries

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transformation. These additional seven parameters are needed to ad-dress crustal motion. According to plate tectonic theory, the earth’souter layer is comprised of several crustal plates that move laterally,more or less rigidly, across the earth’s surface. An eighteenth centurySwiss mathematician, Leonard Euler, had proven that the constantmotion of a rigid region across the surface of a sphere can be quantifiedin terms of three parameters; i.e., the rotation rate of the region abouta pole that passes through the geocenter and the (geographic) latitudeand longitude of one of the points at which this pole pierces the earth’ssurface. Hence, these three parameters are known as the Euler pole for

the region. The international geodetic community has addressed platemotion by defining the ITRF coordinates so that their associatedhorizontal velocities have anaveragevalueof zerowhen integratedoverthe entire surface of the earth. As a result, the North American Platerotates counterclockwise about a Euler pole that pierces the earth’ssurface near Ecuador. As shown in Fig. 5, the reference stations locatedin Florida move essentially westward at approximately 10 mm/yearrelative to ITRF2008. Also, the reference stations located near theCONUS-Canada border move essentially westward at approximately20 mm/year relative to ITRF2008, and the Alaskan reference stations

Fig. 4.VLBI stations involved in developing NAD 83 (1986): all nine United States VLBI stations were also used to define NAD 83 (CORS93); onlyeight of these United States VLBI stations (GOLDSTONEwas excluded) were used to define NAD 83 (CORS94); and all four Canadian VLBI stationsplus eight of the United States VLBI stations (again, GOLDSTONE was excluded) were used to define NAD 83 (CORS96)

Fig. 5. ITRF2008/IGS08 velocities at CORSs: horizontal velocities at points located in stable North America reflect counterclockwise rotation of thistectonic plate about a pole through the geocenter, which pierces the earth’s surface near Ecuador

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moveeven fasterwith respect to ITRF2008.Fig. 5 also presents how thereference stations located within a few-hundred-kilometer-wide zonebetween the Pacific Plate and the North American Plate move in re-sponse to the deformation associatedwith the interaction between thesetectonic plates. As a result of thismotion, theNGSdecided to define theNAD 83 coordinates so that, to the extent possible, they are associatedwith little or no horizontal motion relative to the stable interior of theNorth American Plate. The three parameters defining a Euler pole canequivalently be quantified in terms of the three rotation rates involved ina 14-parameter transformation. Accordingly, in 1996 the NGS usedeightVLBI stations located inwhatwas considered the stable interior ofNorth America to estimate values for the three rotation rates that wouldbest convert (in a least-squares sense) the computed ITRF94 horizontalvelocities of these VLBI stations to zero horizontal velocities (seeFig. 4). The VLBI station known as GOLDSTONE and located inCalifornia was not used because of its anticipated motion relative tostable North America. The NGS also used these same eight VLBIstations to estimate the seven parameters that would best convert theirITRF94 positional coordinates (as computed for January 1, 1996) totheir previously adopted NAD 83 (HARN) coordinates subject to theconstraint that the scale difference equal zero. The other four trans-formation parameters (the three translation rates and the scale differencerate)were eachalso set to zero invalue.The reference frameobtainedbyapplying this transformation to convert the ITRF94 coordinates andvelocities for CORSs to NAD 83 coordinates and velocities is calledNAD 83 (CORS94).

In 1998, the NGS computed the coordinates for the approxi-mately 100 then-existing CORSs relative to ITRF96. However, thistime the NGS collaborated with Canada’s Geodetic Survey Di-vision to derive a 14-parameter transformation from ITRF96 toNAD 83 based on eight VLBI stations in the United States and fourVLBI stations in Canada (Fig. 4) (Craymer et al. 2000). Again, thescale differencewas set equal to zero. The resulting reference frameis called NAD 83 (CORS96) in the United States. The seven rate-of-change parameters for the transformation from ITRF96 to NAD83 (CORS96) were constrained in value such that the threetranslation rates are each zero, the scale-difference rate is zero, andthe three rotation rates equal the corresponding rotation rates for theNorth American tectonic plate relative to the no-net-rotation(NNR) NUVEL-1A model (DeMets et al. 1994). This model isbased on various geophysical data types that help quantify howeach major tectonic plate moves. The model was further con-strained by the condition that the average horizontal velocity of thecollection of all points located on the earth’s surface is equal to zero.The international geodetic community had adopted thisNNR model in establishing ITRF96 (Boucher et al. 1998). Thetransformation’s three rotation rates were set equal to the NNR-NUVEL-1A rotation rates for North America so that mostlocations in stable North America would experience little, if any,horizontal motion relative to NAD 83 (CORS96). Tectonicallydeforming states—such as California, Oregon, Washington, andAlaska—still need to cope with horizontal motion relative to NAD83 (CORS96).

In 2002, the NGS computed the ITRF2000 coordinates for theapproximately 350 then-existing CORSs. The NGS then used aninternationally adopted 14-parameter transformation from ITRF2000to ITRF96 in compositionwith the previously derived transformationfrom ITRF96 to NAD 83 (CORS96) to define a transformation fromITRF2000 to NAD 83 (CORS96) (Soler and Snay 2004). The NGSused this latter transformation to convert the ITRF2000 coordinatesfor all existing CORSs to the corresponding NAD 83 (CORS96)coordinates. Because these new NAD 83 (CORS96) coordinatesdiffer (usually by less than a couple of centimeters) from the pre-vious NAD 83 (CORS96) coordinates that had been obtained by

transforming the computed ITRF96 CORS coordinates, these newcoordinates actually represent a new realization of NAD 83. How-ever, this subtle point of nomenclature was inadvertently notaddressed, and the name NAD 83 (CORS96) was used for the newrealization aswell, without the occurrence of any noticeable impact toNAD 83 users.

In 2011, the NGS computed coordinates for approximately1,000 then-existing CORSs relative to IGS08, which is a referenceframe adopted by the International GNSS Service (IGS) and basedupon a modification to ITRF2008 to incorporate newer calibrationresults forGNSS antennas (Rebischung et al. 2011). The NGS thenused an internationally adopted 14-parameter transformation fromIGS08 to ITRF96 in composition with the previously derivedtransformation from ITRF96 to NAD 83 (CORS96) to forma transformation from IGS08 to NAD 83 (CORS96) (Pearson andSnay 2012). The NGS used this latter transformation to convert thenew IGS08 coordinates for all the then-existing CORSs to a newNAD 83 realization called NAD 83 (2011) Epoch 2010.00 (seewww.geodesy.noaa.gov/CORS/coords.shtml). The expressionEpoch 2010.00 is included in the name to explicitly denote thatadopted positional coordinates for each reference station refer tothe station’s location on January 1, 2010 (or 2010.00 in decimalyears). For previous NAD 83 realizations, the reference epoch (orreference date) associated with the realization could only be foundin pertinent metadata. The concept of a reference epoch isaddressed further in the subsequent section.

As a result of how the NAD 83 (2011) coordinates were com-puted, the nominal 14-parameter transformation between the NAD83 (2011) coordinates and NAD 83 (CORS96) coordinates (whenreferring to the same epoch) is the identity function. Nevertheless,the NAD 83 (2011) coordinates for an individual CORS most likelydiffer from their corresponding NAD 83 (CORS96) coordinates(even when referring to the same epoch) because the 2011 compu-tations incorporated approximately nine more years of GPS datathan the 2002 computations and greatly improved metadata. Also,the corresponding coordinates differ because the 2011 computationsused more modern techniques than did the 2002 computations foraddressing several physical phenomena that affect GPS accuracy,including the use of the following:• Absolute (rather than relative) calibrations of GPS antennas

(Schmid et al. 2007);• Newer models for tropospheric delay (Boehm et al. 2006, 2007);• Newer models for ocean tide loading (Scherneck 1991; Letellier

2004; Petit and Luzum 2011); and• Newer models for the solar radiation pressure on GPS satellites

(Beutler et al. 1994).

Addressing Crustal Motion

As its name implies, a CORS collects GPS data every few seconds,24 h per day, 7 days per week, and week after week. Thus, it is the-oretically possible to compute new CORS coordinates every fewseconds, although NGS operationally computes 3D positionalcoordinates for CORSs only once per day. The NGS uses the col-lection of daily CORS coordinates to generate time series of weeklyCORS coordinates. After spanning several years, these time series ofweekly coordinates have been used to estimate 3DCORS velocities.Hence, the CORS network serves as the foundation for NAD 83becoming more fully four-dimensional (4D). The capability to es-timate accurate velocities is radically different fromwhat is possiblewith passive reference stations; that is, reference stations to whichpeople and instruments are deployed episodically to observe thegeodetic data needed to compute their positional coordinates. As

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a result, geodetic data at most passive reference stations have beenobserved only every few decades, except in locations of extremecrustal motion, such as in the vicinity of California’s San AndreasFault. Even then, geodetic observations at these stations weretypically performed only once per year.

To support the original NAD 83 adjustment, Snay et al. (1987)developed a set of numerical horizontal crustal motion models forseveral tectonically active areas of the United States (California andparts of Alaska, Hawaii, and Nevada) to estimate horizontalvelocities in these regions. The NGS used these models to convertthe geodetic data observed in these regions from their original valuesto values that would have been measured had these observationsbeen performed on December 31, 1983. The NAD 83 adjustment of1986 used these time-homogenized observations rather than theactual observations in computing the positional coordinates in theseregions. As a result, the NAD 83 (1986) positional coordinatescorrespond to a reference epoch of December 31, 1983. Todetermine the corresponding coordinates for a reference station atsome other epoch, how the station moved between December 31,1983, and this other epoch needs to be known. To this end, the NGSdeveloped the Horizontal Time-Dependent Positioning (HTDP)software in 1992. TheNGShas since updatedHTDP every fewyears

(Snay 1999; Pearson and Snay 2007; Pearson et al. 2010; Pearsonand Snay 2012). HTDP incorporates numerical models for bothhorizontal crustal velocities throughout the United States and forthe 3D displacements associated with major (magnitude . 6.0)earthquakes that have occurred in theUnited States since 1934. Fig. 6presents the NAD 83 horizontal velocities for western CONUS asgiven by HTDP. HTDP may also be used to transform the coor-dinates between reference frames that move relative to one another.TheNGS is currently developing a vertical crustal velocitymodel forall of CONUS, and the agency plans to replace HTDP in 2014 witha utility for transforming coordinates across time and betweenreference frames, which will address vertical crustal motion as wellas horizontal crustal motion.

On the other hand, CORS velocities are estimated every fewyears directly fromCORSdatawhen possible; that is, it usually takesat least 3 years of GPS data before a CORS velocity can be estimatedwith sufficient precision (∼1.0 mm/year). Until sufficient data havebecome available, NGS uses HTDP to estimate a CORS’ horizontalvelocity and assumes that its vertical velocity is 0.0 mm/year.Consequently, the NGS has always published 3D velocities foreach CORS along with the corresponding 3D positional coordinatesfor an adopted reference epoch.

Fig. 6. Horizontal velocities in western CONUS relative to NAD 83 (2011) as estimated using HTDP

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Upgrading Coordinates for PassiveReference Stations

Around 1995, while HARN surveys were still in progress in manystates, the NGS realized GPS technology had improved so dramati-cally that differential ellipsoid heights among a collection of referencestations could then be measured with an accuracy of a few centi-meters. To achieve this accuracy, the NGS prescribed multiple 6-hobserving sessions, each involving the simultaneous occupation oftwo or more reference stations such that each reference station wasoccupied on at least two different days. The two occupations wereused to check for coordinate repeatability and thus help to identifyblunders and systematic errors in the observations. The improvedGPS results realized since 1995 were in part a result of the following:• GPS having attained full operational capability, thereby ensuring

that at least 24 satellites would be operational at all times;• The development of GPS receivers that experience considerably

fewer cycle slips compared with earlier GPS receivers; and• Accurate GPS satellite ephemerides having become available

from the IGS.Thus, the NGS decided to collaborate with each state and other

institutions to resurvey each HARN starting in 1997. Also, theNGS encouraged other organizations to perform additional GPSsurveys throughout the country in order to densify the spatialcoverage provided by the HARN reference stations. For the HARNresurveys and for many of these other GPS surveys, the NGS andits partners made a concerted effort to deploy GPS receivers at asmany leveling benchmarks as feasible in order to obtain accurateellipsoid heights at these points where orthometric heights hadpreviously been derived relative to the North American VerticalDatum of 1988 (NAVD 88) through the use of leveling data. [Forinformation about NAVD 88 see Zilkoski et al. (1992).] Thecollection of differences between the NAD83 ellipsoid heights andthe NAVD 88 orthometric heights could then serve to help develophybrid geoid models for converting NAD 83 ellipsoid heightsmeasured at other points into correspondingNAVD 88 orthometricheights. The qualifier, hybrid, is used to distinguish this modelfrom a gravimetric geoid model. The geoid, theoretically, iscomputable from gravimetric sources only; however, a hybridgeoid adds the further component of known systematic errorsexisting in the associated datums. For example, the NAD 83 origindiffers in location from the true geocenter by more than 2 m and theNAVD88 reference surface of zero elevation deviates in both a biasand a cross-country tilt from mean sea level. The NGS has de-veloped several hybrid geoid models over the years, starting withGEOID96, which was adopted in 1996 (Milbert and Smith 1996).The current hybrid geoid model, called GEOID12A, was adoptedin 2012. Information about geoid-related activities at the NGSmaybe found at www.geodesy.noaa.gov/GEOID/.

The HARN resurveys were completed by 2005. Then, the NGSembarked on performing a simultaneous least-squares adjustment ofall HARN data together with data from approximately 3,500 addi-tional GPS surveys (Pursell and Potterfield 2008). For this adjust-ment, the NGS constrained the CORS coordinates to their computedNAD83 (CORS96) values. This adjustment produced consistent 3Dcoordinates for approximately 70,000 passive reference stations thathad been surveyed using GPS technology. The resulting referenceframe is called NAD 83 (NSRS2007). By design, it approximatesNAD 83 (CORS96).

Within a year after the NAD 83 (2011) coordinates becameavailable for CORSs, the NGS computed new coordinates for theapproximately 70,000 passive reference stations that have NAD 83(NSRS2007) coordinates, as well as for the approximately 10,000

passive reference stations that have been newly surveyed since2005. The computational process involved a least-squares adjust-ment with the coordinates of approximately 1,000 CORSs con-strained to their NAD 83 (2011) values at a reference epoch of2010.00. The reference frame for the new passive reference stationcoordinates is also called NAD 83 (2011) Epoch 2010.00 in order tonot differentiate by name the frame of these coordinates from theframe of the CORS coordinates.

NAD 83 Realizations for Other Tectonic Plates

As mentioned previously, NAD 83 (CORS96) was defined so thatpoints located in the stable part of the North American Plate wouldexperience little, if any, horizontal motion relative to this refer-ence frame. However, points located in U.S. states and territorieson Pacific islands are moving as much as 8 cm/year relative toNAD 83 (CORS96) because they lie on either the Pacific Plate orthe Mariana Plate. Consequently, and to support the surveyingandmapping activities on these latter two tectonic plates, the NGSintroduced two new realizations of NAD 83 in 2003 (Snay 2003).In particular, the NGS introduced NAD 83 (PACP00) for islandson the Pacific Plate, such as the Hawaiian Islands, Marshall Is-lands, and American Samoa. In addition, the NGS introducedNAD 83 (MARP00) for islands on the Mariana Plate, such asGuam, Rota, Saipan, and Tinian. Each of these two referenceframes is defined in terms of a 14-parameter transformation fromITRF2000. The first seven parameters (three translations, threerotations, and the scale difference) are the same for each. The NGSused 11 VLBI stations and three CORSs that had adopted posi-tional coordinates in both ITRF2000 and NAD 83 (HARN) toestimate the three translations and the three rotations that besttransformed the ITRF2000 coordinates to the correspondingNAD83(HARN) coordinates at Epoch 1993.62 (August 14, 1993). Thescale difference was constrained to equal zero. The significance ofEpoch 1993.62 is that it corresponds in time to the midpoint of anextensive GPS survey performed by the NGS to update positionalcoordinates for points located on several Pacific islands. The threetranslation rates and the scale difference rate are all zero in valuefor each transformation. Thus, the two transformations differ onlyin their values of their three rotation rates. For the transformationdefining NAD 83 (PACP00), the three rotation rates were esti-mated such that points residing on the stable part of the PacificPlate would experience little, if any, horizontal motion. For thetransformation defining NAD 83 (MARP00), the three rotationrates were estimated such that points residing on the stable partof the Mariana Plate would experience little, if any, horizontalmotion.

Now that the NGS has adopted NAD 83 (2011) Epoch 2010.00 toreplace NAD 83 (CORS96) Epoch 2002.00 for points located inCONUS, Alaska, Puerto Rico, and the American Virgin Islands, theNGS has also adopted NAD 83 (PA11) Epoch 2010.00 to replaceNAD 83 (PACP00) Epoch 1993.62 for islands on the Pacific Plate.The NAD 83 (PA11) coordinates are based on the IGS08 coordinatesand velocities for CORSs located on the Pacific Plate. The IGS08coordinates usually refer to Epoch 2005.00. TheNGS used the IGS08velocities for the points in question to estimate the correspondingIGS08 coordinates for Epoch 2010.00. Then, the NGS used aninternationally adopted 14-parameter transformation from IGS08 toITRF2000, in composition with its adopted transformation fromITRF2000 to NAD 83 (PACP00), to transform these IGS08 (Epoch2010.00) coordinates to the NAD 83 (PA11) (Epoch 2010.00) coor-dinates. In a similar manner, the NGS also adopted NAD 83(MA11)Epoch 2010.00 to replace the NAD 83 (MARP00) Epoch 1993.62

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Table 1. Summary of the Evolution of NAD 83

Year Event Significance

1986 NGS adopted NAD 83 (1986) coordinates for ∼272,000United States passive reference stations. Canada andGreenland also adopted NAD 83 coordinates for their passivereference stations. The NAD 83 developers collaborated withDoD so that NAD 83 and WGS 84 (TRANSIT) sharea common origin, orientation, and scale.

Replaced NAD 27 with a geocentric reference system that is free of meter-level distortions.

1989 NGS collaborated with the state of Tennessee to perform a GPSsurvey to establish the first statewide HARN. NGS subsequentlycollaborated with each of the other 49 states during the periodfrom 1989 to 1997 to establish statewide and regional HARNsthat collectively span the United States. NGS used these surveysto derive new, more precise NAD 83 coordinates for passivereference stations on essentially a state-by-state basis.

Effected a transition from 2D to 3D coordinates. Updated relative horizontalcoordinate accuracies from a nominal value of 10 ppm to a nominal value of1 ppm.

1990 Dewhurst (1990) published a report describingthe NADCON utility.

NADCON enables its users to transform between NAD 27 coordinates andNAD 83 (1986) coordinates, as well as between NAD 83 (1986) coordinatesand NAD 83 (HARN) coordinates.

1992 NGS released the first version of the HTDP software. NGS hassince updated HTDP every few years.

HTDP enables its users to transform horizontal coordinates across time andbetween reference frames.

1994 DoD adopted WGS 84 (G730) to replace WGS 84 (TRANSIT).The WGS 84 (G730) coordinates differ systematically from thecorresponding NAD 83 coordinates by approximately 2 m.

WGS 84 (G730) is based on GPS observations rather than TRANSITDoppler observations, resulting in it being more geocentric, as well as moreaccurate, than WGS 84 (TRANSIT).

1994 NGS installed its first CORS. As of November 2011, the CORSnetwork included more than 1,800 stations collectively spanningthe United States, its territories, and a few foreign countries.

CORSs enable GPS users to position points by deploying as few as oneperson and one GPS receiver.

1995 NGS adopted the NAD 83 (CORS93) coordinates for ∼30 CORSs. Related the NAD 83 coordinates for CORSs directly to their ITRF93coordinates.

1996 NGS adopted the NAD 83 (CORS94) coordinates andvelocities for ∼60 CORSs.

Related NAD 83 coordinates and velocities for CORSs directly to theirITRF94 coordinates and velocities and in such a way that locations in stableNorth America experience little, if any, horizontal motion.

1996 NGS developed the GEOID96 hybrid geoid model. This model wasupdated in 1999 (GEOID99), 2003 (GEOID03), 2006 (GEOID06),2009 (GEOID09), and 2012 (GEOID12A).

These hybrid geoid models enable users to transform between NAD 83ellipsoid heights and NAVD 88 orthometric heights.

1997 NGS initiated a project to resurvey the HARN in each state.The surveys used the latest GPS technology then available. NGS alsoencouraged other institutions to perform additional GPS surveys thatwould yield ellipsoid heights on many benchmarks where NAVD 88orthometric heights were previously measured. The HARN resurveyswere completed by 2005.

Greatly improved the accuracy of NAD 83 ellipsoid heights at many passivereference stations.

1998 NGS adopted NAD 83 (CORS96) coordinates and velocitiesfor ∼100 CORSs. These coordinates and velocities were updated in2002 for ∼350 CORSs.

Related NAD 83 coordinates and velocities for CORSs directly to theirITRF96 coordinates and velocities. Canada also adopted this relationshipbetween NAD 83 and ITRF96.

2003 NGS adopted NAD 83 (PACP00) coordinates for locations on thePacific tectonic plate and NAD 83 (MARP00) coordinates forlocations on the Mariana tectonic plate.

Related NAD83 coordinates on the Pacific Plate or theMariana Plate to theirITRF2000 coordinates and in such a way that the NAD 83 coordinatesexperience little, if any, horizontal motion.

2007 NGS adopted the NAD 83 (NSRS2007) coordinates for ∼70,000passive reference stations located in CONUS and Alaska via anadjustment in which the NAD 83 (CORS96) coordinates forCORSs were held fixed.

Unified the ∼50 statewide/regional HARN reference frames into a singlereference frame that is consistent with NAD 83 (CORS96).

2011 NGS adopted the NAD 83 (2011) Epoch 2010.00 coordinates andvelocities for CORSs located in CONUS, Alaska, and the Caribbean.NGS adopted the NAD 83 (PA11) Epoch 2010.00 coordinates andvelocities for CORSs located on the Pacific tectonic plate and theNAD 83 (MA11) Epoch 2010.00 coordinates and velocities forCORSs located on the Mariana tectonic plate.

Related NAD 83 coordinates and velocities for CORSs to their IGS08coordinates and velocities and in such a way that locations on the NorthAmerican Plate or the Pacific Plate or the Mariana Plate experience little, ifany, horizontal motion relative to NAD 83. Greatly improved the accuracyof CORS coordinates and velocities by applying rigorous models to reducesystematic errors contaminating GPS data.

2012 NGS adopted NAD 83 (2011) Epoch 2010.00 coordinatesfor ∼80,000 passive reference stations located in CONUS andAlaska via an adjustment in which the NAD 83 (2011) coordinatesof the CORSs were held fixed.

Greatly improve the accuracy of the coordinates of the involved passivereference stations.

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coordinates for points residing on the Mariana Plate (for additionaldetails, see Pearson and Snay 2012).

Replacing NAD 83

Asmentioned previously, the NGS is planning to replace NAD 83about a decade from now with a newer reference system (NGS2010). The primary motivation for replacing NAD 83 is totransition to a more geocentric reference system in the UnitedStates. The NGS anticipates that within the next 10 years peoplewill be able to use GNSS technology to obtain geospatialcoordinates for a location with subdecimeter-level accuracy bothinstantaneously and economically. Perhaps this capability willautomatically be built into some future generation of cell phones.These GNSS-derived coordinates would most conveniently beexpressed in a geocentric reference system because such a systemquantifies the orbits of GNSS satellites more directly than anynongeocentric system. Some people may argue that the UnitedStates could continue using the NAD 83 coordinates for speci-fying locations for property boundaries, roads, and other map-worthy features by simply transforming the GNSS-derivedcoordinates to NAD 83. However, it is impractical to expectthat everyone will have convenient access to software that canperform such a transformation. The transformation betweenWGS84 and NAD 83 was historically a concern mostly to geodesists,and it is often coded incorrectly in commercial software. Eventoday, there persists software that treats WGS 84 as equivalentto NAD 83. Rather than risk life and property to suchmisunderstandings, the NGS believes that adopting a geocentricreference system is the best approach.

In addition to replacing NAD 83, the NGS is planning to replaceNAVD 88 (Zilkoski et al. 1992) at the same time, in large partbecause errors in the NAVD 88 orthometric heights exhibit a sys-tematic tilt across CONUS in a direction approximately parallel toa line from Florida (in the southeast) to Washington (in thenorthwest) (NGS 2010). The accumulated error difference betweena NAVD 88 height in Florida and one in Washington exceeds 1 m(Wang et al. 2012). Because the NAD 83 replacement will begeocentric, the NGS can develop a purely gravimetric geoid model,as opposed to a hybrid geoid model, to directly convert ellipsoidheights to orthometric heights in the future.

Finally, in order for it to be more fully 4D, the NAD 83 re-placement will need to be accompanied by more accurate crustalmotion models that address both horizontal and vertical motion.These models will also need to address discontinuities in positionalcoordinates, such as those associated with earthquakes. In addition,they will need to address velocity variations, such as those associ-ated with postseismic deformation, magmatic activity, and varioustypes of crustal loading (tidal, atmospheric, and hydrologic). Insummary, these models will need to enable users of the future ref-erence system to measure the positional coordinates of a location at

one time and easily relate them to corresponding coordinates for thislocation at some other time.

Summary

Table 1 summarizes the contents of this article by chronologicallylisting the major events in the evolution of NAD 83 in the UnitedStates.

Acknowledgments

This paper has benefited from contributions by Bernard Chovitz,Michael Cline, Michael Dennis, David Doyle, Jake Griffiths, JuliePrusky, Jim Ray, Jarir Saleh, Giovanni Sella, Dru Smith, and TomásSoler. The paper also benefited from suggestions from three anon-ymous reviewers. Several figures were prepared with the GeneralMapping Tool software available at http://gmt.soest.hawaii.edu/under the GNU General Public License.

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