The Problem with NAD27

- By Bill Strange, NGS (Ret.)

NAD 27 cannot, in the future, serve as a useful basis for expressing positional information in the context of GIS and surveying. This is true because NAD 27 is incapable of supporting the accuracy and three dimensional (3D) capabilities of modern positioning technology, i.e. GPS and GPS georeferenced remote sensing, such as aerial photogrammetry and LIDAR. That NAD 27 coordinates play a role in digital data applications today stems from the fact that much existing hard copy positional information (i.e. USGS quad maps and State Plane coordinate data) was based on NAD 27 and the initial digitization of this information produced NAD 27 coordinates. However, conversion of the digitized coordinate data from NAD 27 coordinates to NAD 83 coordinates is a simple process using existing software. An important point is that this conversion software, not only transforms NAD 27 coordinates to NAD 83 coordinates, but, at the same time, removes much of the error present in the original NAD 27 coordinates.

The problem with using NAD 27 coordinates, and the advantages in using NAD 83 coordinates, shows up in three contexts: (1) in the ability to fully utilize the coordinate accuracy capabilities provided by GPS, (2) in the need for compatibility between coordinate information in data bases and autonomous, real-time, positioning using GPS, and (3) in the need for effective handling of 3D coordinate information that can be provided by modern measurement systems.

  1. ACCURACY CONSIDERATIONS

    To determine the coordinates of points of interest to them users depend, directly or indirectly, upon reference stations whose coordinates have been provided by a national geodetic organization such as the National Geodetic Survey (NGS). The coordinates obtained by users can be no more accurate relative to a datum than the coordinates of these reference stations.

    The errors in reference station horizontal coordinates relative to the NAD 27 coordinate axes can be tens of feet. Thus, stating coordinate accuracies relative to the NAD 27 datum axes is not very useful. Instead, NAD 27 coordinate accuracy is given in terms of the accuracy of the differential positions between stations, expressed as an accuracy proportional to station separation, eg 1:10,000, 1:20,000, 1:50,000, 1:100,000. For two stations 10 miles apart these positional accuracies translate into differential positional accuracies of about 5, 2.5, 1, and .5 foot respectively.

    On the other hand, NGS provides, GPS-derived, 3D, NAD 83 coordinates of HARN and CORS reference stations, whose accuracy, relative to the NAD83 coordinate axes, and relative to one another (regardless of station separation) is in the range of 0.05 to 0.10 feet. GPS positioning is capable of providing users with similar coordinate accuracy for their stations. Thus, while NAD 83 is capable of supporting the full accuracy of GPS positioning regardless of station separation; NAD 27 can not support such accuracy even for stations only10 miles apart.

    To retain the use of NAD 27 in conjunction with GPS measurements it is necessary to introduce error into the GPS results and distort them so that they will agree with the errors in the existing NAD 27 coordinates. The obvious alternative is to convert the existing NAD 27 coordinates to NAD 83 coordinates. With digital coordinate information this is can be readily done using existing coordinate transformation software such as NADCON and CORPSCON. A powerful advantage of proceeding in this way is that these programs do more than simply transform from one coordinate system (NAD 27) to another (NAD 83). At the same time, they remove most of the error in the original NAD 27 coordinates due to reference station coordinate error.

    Neither GIS nor surveying can afford to throw away the accuracy capabilities provided by GPS in order to cling to an outmoded datum. Experience has shown that, as greater levels of accuracy become economically available, applications exist that make use of this fact. Indeed, we are moving toward the inclusion of survey accuracy in the Cadastral layer of GISs, as this happens NAD 83 will be absolutely required, NAD 27 cannot support such accuracy.

  2. COMPATIBILITY WITH GPS AUTONOMOUS POSITIONING

    By autonomous GPS positioning is meant positioning using a single GPS receiver, with coordinates determined within the receiver in real time. Such positioning involves using the information broadcast by the GPS satellites, either alone, or in conjunction with "correctors" broadcast by GPS reference stations. We are rapidly headed toward the situation where autonomous GPS receivers, costing a few hundred dollars and available to the general public, will provide coordinate accuracies of no worse than 2 to 5 feet. More expensive autonomous receivers will allow positioning professionals to achieve accuracies at the 0.1 to 1.0 foot level. Over time the accuracy of both types of autonomous GPS receivers will increase.

    A major application based on such receivers will be the relating of a user's receiver location to the location of existing entities whose coordinates have been previously determined and placed in digital data bases. An example would be an emergency 911 application where the objective would be to "navigate" an emergency vehicle to a particular address. The initial coordinates computed by the vehicles' GPS autonomous receiver will be NAD 83 coordinates. If NAD 27 coordinates are contained in a digital data base as NAD 27 coordinates, they can differ from the NAD 83 coordinates by over 300 feet. Thus, mixing coordinates relative to the two datums will introduce unacceptable error. One could argue that one set of coordinates could be converted to the other's datum for comparison. This is, of course, possible, but it is an approach that is rife with the potential for error, and would seem to be highly undesirable in a 911 context. There are many other potential applications of autonomous positioning requiring compatibility with data base coordinates. Examples are positioning a backhoe in relation to buried utilities and positioning a snowplow relative to a road when plowing deep snow and navigating to the location of a survey monument.

    With respect to the general public, I would not want to be someone at any level of government trying to explain to John Q. Citizen why I was using a 75 year old reference system that was causing me to provide him with positions that were 300 feet different from the positions of his GPS receiver, when his positions are accurate relative to the currently accepted national reference system to within 3 feet.

  3. THREE DIMENSIONS

    GPS, and GPS georeferenced aerial topography and LIDAR, can provide 3D coordinate information, height as well as horizontal coordinates. NAD 83 directly supports 3D coordinate information. Moreover, with NAD 83 coordinates it is possible for NGS to provide geoid heights that convert GPS derived NAD 83 ellipsoid heights to sea level (orthometric heights) that are needed for most applications. NAD 27 can only be used as a datum for providing horizontal position. If horizontal coordinates, initially obtained by a 3D measurement system as NAD 83 coordinates, are converted to NAD 27 coordinates (with their accuracy degraded), it will still be necessary to retain NAD 83 as the basis for expressing ellipsoid height, thus requiring dual datums to be used in the data bases that are maintained.

    DATUMS, COORDINATES, AND TRANSFORMATIONS

    The information below is designed to give a brief summary of how NAD 27 and NAD 83 were defined by the National Geodetic Survey (NGS) and its predessesor organization the United States Coast & Geodetic Survey (USC&GS), how the coordinates of reference stations relative to these datums were derived, and the nature of the computer programs developed to allow users to convert NAD 27 horizontal coordinates to NAD 83 horizontal coordinates.

    WHAT IS A GEODETIC DATUM?

    Computing the coordinates of points on the Earth's surface requires a reference framework, known as a geodetic datum, as a basis for computation. A geodetic datum consists of a set of three dimensional (3D) coordinate axes (x,y,z), whose origin is within a few hundred meters of the center of mass of the Earth, and a reference ellipsoid that is an ellipsoid of revolution. Only two datums have been used in North America since 1927 to provide the basis for computing horizontal positions, the North American Datum of 1927 (NAD 27) and the North American Datum of 1983 (NAD 83). NAD 27 was the official datum of the United States from 1927 until it was replaced in 1986 (not 1983) by NAD 83.

    A national geodetic organization such as NGS or USC&GS has two primary jobs, to define a national datum and to realize that datum. Defining a datum consists of (1) specifying the origin and orientation of the datum's coordinate axes relative to the Earth and (2) specifying the the size and shape of the reference ellipsoid to be used. The reference ellipsoid is assumed to have a specific geometric relationship to the datum axes. Thus, defining the geometry of the axes also defines the location of the reference ellipsoid relative to the Earth. Realizing a datum is geodetic jargon for computing and making available the coordinates of a network of reference stations relative to the defined datum. This allows users to determine the coordinates of points of interest to them by, directly or indirectly, differentially positioning their points relative to one or more of these reference stations.

    DEFINING NAD 27 AND NAD 83

    Specifying the origin and orientation of datum axes relative to the Earth was done quite differently for NAD 27 and for NAD 83. With NAD 27 this was accomplished by (1) specifying the coordinates of a single monumented station in Kansas, Meades Ranch, (2) specifying the geodetic azimuth from Meades Ranch to a nearby station, and (3) imposing the condition that the z axis be parallel to the mean rotation axis of the Earth. With NAD 83 the origin of axes was defined to be the center of mass of the Earth as determined from the analysis of the orbits of artificial satellites. Axes orientation was based on the optical observations of stars at stations across the country. With NAD 27 the axes origin is several hundred feet from the currently accepted location of the center of mass, with NAD 83 the origin is about 6 feet from the center of mass. The actual location of the center of mass is currently known to within a few centimeters.

    The size and shape of the reference ellipsoid was, in both cases, defined by specifying the lengths of its major and minor axes. Most commonly these lengths are not stated directly. Rather, what is given is the semi major axis, a, and a term referred to as the flattening, f, where f = (a-b)/a and b is the semi minor axis. In the case of NAD 27, a and f were chosen so that, taken in conjunction with the definition of the axes origin and orientation, they cause the surface of the reference ellipsoid to, on the average, coincide with the geoid (mean sea level) across the United States. In the case of NAD 83 a and f were chosen to give a best fit of the reference ellipsoid to the geoid (mean sea level) for the Earth as a whole. The reference ellipsoid used for NAD 27 was the Clarke ellipsoid of 1866, that of NAD 83 the the Geodetic Reference System of 1980 (GRS 80 ) ellipsoid. The two reference ellipsoids had different values of a and f.

    REALIZING THE DATUMS (COORDINATE DETERMINATION)

    In discussing reference station coordinates provided by geodetic organizations it is important to understand the difference between how they are computed using conventional observations of angles, distances, and azimuths and how they are computed using space system observations. When using conventional observations what is actually computed are the latitudes and longitudes of the projections of the monumented reference stations onto the reference ellipsoid being used. The conventional observations are first "reduced to the ellipsoid" using approximate ellipsoid height information and then computations "on the ellipsoid" are carried out. Because a projection point lies on the reference ellipsoid (its ellipsoid height is zero), computing its latitude and longitude gives its 3D position.

    The latitude and longitude of a projection point are the same as those of the associated surface reference station. Thus, in computing the latitude and longitude of the projection point one has also obtained the latitude and longitude of the reference station. It is in this sense that the horizontal coordinates of reference stations can be said to have been obtained from conventional observations. This holds for reference station horizontal coordinates obtained relative to both NAD 27 and NAD 83. One should keep in mind that the three dimensional coordinates for the surface reference stations are not computed in this case, and that the x,y,z coordinates for the reference station and its projection will usually be quite different. Also a point of special significance is that the distance between two reference stations, which can lie well above the reference ellipsoid, can be quite different from the distance between their projection points on the ellipsoid.

    With space system observations, such as GPS, satellite Doppler, and VLBI, the situation is quite different. Using these space system observations the 3D coordinates of the surface reference stations are computed directly in the form of x,y,z coordinate without making use of the reference ellipsoid. They are then converted to ellipsoidal coordinates (latitude, longitude, and ellipsoid height) in order to separate horizontal position from height for practical application.

    Realization of the datum, ie determination of reference station coordinates, was also achieved differently for the two datums. With NAD 27 the initial determination of reference station coordinates involved holding fixed the coordinates of Meades Ranch and the azimuth from Meades Ranch to an adjacent station while adjusting observations of angles, distances, and azimuths across the country to obtain latitudes and longitudes (horizontal coordinates) of other monumented reference stations relative to Meades Ranch and thus relative to the NAD 27 coordinate axes. The primary reference station network across the country was felt to have a coordinate accuracy relative to the NAD 27 axes that was proportional to its distance from Meades Ranch and was of a magnitude of 1:100,000. Since stations could be well over a thousand miles from Meades Ranch, this implied these primary reference stations could have coordinate errors relative to the datum axes of more than 60 feet. Indeed, it has been demonstrated that errors of tens of feet relative to the datum axes exist in NAD 27 coordinates.

    Additional reference stations with NAD 27 coordinates were established by connecting them to the primary reference stations. The proportional accuracy of the positions of these additional reference stations stations, relative to the primary reference stations, was normally in the range of 1:10,000 to 1:50.000. The error in the coordinates of these stations relative to the NAD 27 coordinate axes was, therefore, greater than that of the primary reference stations to which they were connected.

    The existence of these large errors relative to the NAD 27 coordinate axes did not cause a major problem for users because, with conventional surveying methods, users were only interested in the accuracy of their differential coordinates relative to the reference stations in their immediate area not relative to the NAD 27 coordinate axes. Since the proportional accuracy achieved by users was normally less than the proportional accuracy of the reference stations, the coordinates of the local reference stations could be held fixed in adjusting the users' observations to obtain coordinates for their stations that were compatible with the reference station coordinates in their immediate area. As additional reference stations were added to the original NAD 27 reference network, the coordinates of the original stations obtained in the initial adjustment, barring evidence of a substantial error, were held fixed while adjusting observations being used to position the new reference stations. Thus the addition of new observations did not necessarily improve the accuracy of the existing reference station coordinates.

    In the initial NAD 83 reference station adjustment there were three types of reference stations involved: (1) more than two hundred thousand stations based on conventional ground based observations (most of which had been part of the NAD 27 reference station network), (2) about six hundred satellite Doppler stations, and (3) a little more than a dozen stations whose differential positions had been determined very accurately using a space technique known as Very Long Baseline Interferometry (VLBI). At the completion of the initial NAD 83 reference station adjustment, the conventional stations had horizontal coordinates (latitudes and longitudes) whose accuracy relative to the NAD 83 coordinate axes was almost always better than 5 feet. The Doppler stations had 3D coordinates accurate at about 3 feet in all coordinates. The small number of VLBI stations had 3D coordinates accurate at about the 0.1 foot level relative to the NAD 83 coordinate axes.

    Almost as soon as the initial NAD 83 reference station coordinate determination was completed (in 1986, not 1983 as the name would imply) GPS positioning began to become available to users. As a result, beginning in 1987, NGS, in conjunction with various groups in states, set out to use GPS to make available statewide networks of reference stations that had 3D NAD 83 coordinates, with horizontal coordinates much more accurate than the conventional reference station coordinates from the original NAD 83 adjustment. This was accomplished by connecting the new reference stations to the VLBI stations included in the initial NAD 83 reference station coordinate determination.

    These new reference stations were the stations of the High Accuracy Reference Networks (HARNs) that were established on a state-by-state basis over about a ten-year period beginning in 1987. As the GPS technology matured during this period, the accuracy of the HARN station coordinates became progressively better. Except for the very first state, Tennessee, whose HARN was established when GPS technology was in its infancy (it has been redone), the horizontal coordinates (latitude and longitude) of HARN stations were, from the beginning, normally accurate to better than 5 cm (0.17 feet) relative to the NAD 83 coordinate axes and by the end of the ten years were accurate to better than 3 cm (0.1 foot). Initially, vertical coordinates were usually accurate to within 0.4 foot. By the end of the HARN effort they were almost always accurate to better than 0.2 foot.

    When establishing a HARN within a state a number of HARN stations had been placed at existing conventional stations that were included in the initial NAD 83 reference station network. Then, holding fixed the GPS derived HARN coordinates for these stations, the conventional observations in the state were readjusted to give improved NAD 83 horizontal coordinates for all of the conventionally established reference stations in that state. In the vast majority of cases the readjusted NAD 83 coordinates for the conventional reference stations were then accurate to better than 1 foot.

    The most recent step by NGS in providing reference stations is the Continuously Operating Reference Station (CORS) network of GPS stations. These are reference stations where there are permanently located GPS receivers from which NGS makes available GPS observations. Three dimensional coordinates are computed by NGS for these reference stations on a daily basis to continuously monitor their position at about the 0.03 foot accuracy level relative to the NAD 83 coordinate axes and, therefore, relative to one another. NGS is currently involved in reobserving the HARNs to, as nearly as possible, bring their coordinate accuracy up to that of the CORS stations.

    TRANSFORMING BETWEEN DATUMS

    In 1986, after NAD 83 became the official datum for the United States, there was a need to provide users with the ability to transform the NAD 27 horizontal coordinates of their stations, which were not included in the NAD 83 adjustment by NGS, to NAD 83 coordinates. To provide this capability NGS used the coordinate information from the more than 100,000 reference stations which had both NAD 27 and NAD 83 coordinates available. The differences between NAD 27 and NAD 83 latitudes and longitudes at these stations were used to estimate gridded sets of (NAD 83 -NAD27) latitude and longitude differences. These gridded differences (ie transformation values) were then incorporated into a computer program, together with a simple routine to interpolate between grid points to any given position. This program, known as NADCON is available, free, from NGS. To transform NAD 27 coordinates of a point to NAD 83 coordinates all that is required of a user is to input the NAD 27 latitude and longitude of a point to NADCON. The program then computes and provides the NAD 83 latitude and longitude of the point.

    Because much NAD 27 information, particularly survey information, is in the form of State Plane (SP) coordinates rather than latitude and longitude, the U.S. Army Corps of Engineers added a front and back end to NADCON that allows a user to input NAD 27 coordinates as SP coordinates and get out answers as NAD 83 SP coordinates when using NADCON to convert between datums. Their program is known as CORPSCON.

    Note that the transformation performed using NADCON or CORPSCON does three things: (1) it accounts for the difference in origin and orientation of the coordinate axes of the two datums (2) it accounts for the difference in the size and shape of the two ellipsoids and (3) it removes the error introduced into the users NAD 27 coordinates due to the errors relative to the NAD 27 coordinate axes of the reference stations to which the users stations are connected. The error remaining in the transformed NAD 83 coordinates has two primary components: the original error in connecting the user's station to the reference stations and the error in the NAD 83 coordinates of the reference stations that were used to obtain the gridded transformation values. The second error is usually less than 1 foot. So the accuracy of the transformed coordinates relative to the NAD coordinate axes is in most cases primarily the accuracy with which the users points were originally connected to the reference station(s) used

    After using the HARN station coordinates to get improved NAD 83 coordinates for the conventionally positioned reference stations in a state, NGS went back and recomputed the gridded NAD 27 to NAD 83 coordinate differences being used in NADCON based on the improved NAD 83 coordinates of the conventional reference stations. Because the NAD 83 reference station coordinates were now more accurate, the gridded coordinate differences now gave more accurate NAD 83 coordinates for the transformed coordinates at users' stations.

Bill Strange, Ret.
National Geodetic Survey
December 2001

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