**National Spatial Reference System Readjustment of NAD83**

Chris Pearson

NGS Geodetic Advisor for Illinois

2300 S. Dirksen Pkwy.

Springfield, IL. 62764

Chris.Pearson@noaa.gov

**Abstract**

The National Geodetic Survey is responsible for the establishment and
maintenance of the National Spatial Reference System (NSRS). As such,
our goal is to maintain a network of stations which are of high enough
accuracy to serve as control for any project undertaken by local
surveyors. In addition, numerous other applications benefit from an
accurate, consistent coordinate system. The NSRS serves as the framework
for those also. As the Global Positioning System (GPS) became
operational in the early 1990's, NGS quickly realized the possible
increased accuracies of the coordinates and undertook a series of GPS
surveys to establish High Accuracy Reference Networks (HARNS) in each
state to serve as the basis for the NSRS. These were completed in 1998.
In addition, by the mid-1990's, the establishment of the network of
Continuously Operating Reference Stations (CORS) was begun which made
even higher accuracies possible. So, in 1998, NGS undertook yet another
series of observations in each state designed to tie the network to the
CORS and to realize the advances in surveying with GPS which allowed
increased accuracies in the height component - long a weak link in the
framework. These surveys are now complete (December 2004). The
availability of this high accuracy data, along with substantial growth
in the NSRS due to the addition of local GPS surveys to the network, has
resulted in a need for a national simultaneous readjustment which
utilizes all these observations. Although NGS has strived to maintain a
consistent network, inevitable discrepancies between surveys and between
states have taken place. Such a readjustment, using all available GPS
data archived in the NGS database, also allows for the computation of
local and network accuracies for each mark. This readjustment is
scheduled to begin in June of 2005 and be completed in February of 2007.

**Introduction**

The readjustment of all GPS survey control in the United States is being
undertaken by the National Geodetic Survey and expected to be completed
by 2007. The adjustment has been developed for two major reasons. The
first of these is a requirement stated in the Federal Geographic Data
Committee (FGDC) Draft Geospatial Positioning Accuracy Standards (FGDC
1998) to develop individual local and network accuracy estimates for
each point in the network. The second purpose for the readjustment is to
resolve inconsistencies between the existing state wide HARN adjustments
and the nationwide CORS system as well as between states. The purpose of
this paper is to update the survey community on the reasons for the
readjustment, the general timeline that the readjustment is expected to
follow and the methodologies that the readjustment will use.

**History of adjustments in NAD83**

NAD83 was implemented in 1986 with a complete readjustment of all
available survey data to establish a uniform set of coordinates for all
points in the network based on an earth centered ellipsoid.
Unfortunately, with the advent of GPS shortly after the completion of
the 1986 adjustment, the local accuracies of points included in this
adjustment were found to be too low to support the new satellite based
techniques. In order to remedy this problem quickly, a series of GPS
surveys called [High Accuracy Reference Networks
(HARNS)](http://www.ngs.noaa.gov/faq.shtml#WhatHARN) were conducted in
each state starting with Wisconsin in 1989 and followed by readjustments
of all survey data available (GPS and classical) in each state. These
surveys and subsequent readjustments produced a set of coordinates with
much improved local accuracies. However, the situation was again
complicated with the establishment of the [Continuously Operating
Reference Stations (CORS) network](http://www.ngs.noaa.gov/CORS/) in the
mid-1990\'s. Once again statewide high accuracy GPS surveys were
conducted in each state to tie the HARN network to the CORS and, in
addition, to take advantage of advances in GPS technology which resulted
in much improved ellipsoid heights. Subsequent statewide readjustments
have also been undertaken as required (including all the GPS data
available in the state only). All these readjustments, only undertaken
on a statewide basis and limited to inconsistencies greater than 5 cm,
have resulted in consistency problems across state lines. In addition,
public demands for greater than 5 cm accuracy in the positions and
heights contributed to NGS's decision to undertake a national
readjustment. The availability of this high accuracy data and the need
to implement the local and network accuracy standards suggested that the
time was right for a new National Readjustment and on September 24,
2003, NGS\'s Executive Steering Committee approved a plan for the
readjustment of horizontal positions and ellipsoid heights for GPS
stations in the contiguous United States. Some of the key points are:

1.  Only GPS will be adjusted. Classical geodetic observations will not
    be included.

2.  The CORS stations will serve as control, ie, CORS positional
    coordinates will be held fixed.

3.  The FBN/CBN surveys are a key element since these are high accuracy
    (2 cm) surveys that tie the traditional geodetic marks from the HARN
    network to the CORS throughout the contiguous United States.

4.  A Helmert Blocking strategy will be used for the adjustment.

5.  Both NAD 83 and ITRF coordinates will be produced and published. The
    former will be designated *NAD 83 (NSRS)*.

6.  User densification projects will be included if observed with GPS,
    tied to the HARN network and submitted prior to the June 1, 2005
    deadline.

7.  Projects submitted after this date will be accepted and loaded into
    the database with a datum tag reflecting the most current HARN
    adjustment available for the state. These projects will be
    readjusted to reflect the new national readjustment as soon as
    possible after its completion in 2007.

8.  Network and local accuracies will be implemented with the
    Readjustment of the National Spatial Reference System (NSRS).

9.  In the event of a delay in software development, testing, and
    implementation of the new network and local accuracies, a
    contingency option was adopted. This option endorses immediate
    statewide GPS readjustments of both horizontal positions and
    ellipsoid heights; local and network accuracies would not be
    produced. (Implementation of this contingency is not currently
    anticipated.)

**Local and Network accuracies**

As noted above, the changes in the way the accuracies of geodetic
positions are published were defined by the FGDC:

> "Local and network accuracy measures computed by random error
> propagation determine the provisional accuracy. In contrast to a
> constrained adjustment where coordinates are obtained by holding fixed
> the datum values of the existing network control, accuracy measures
> are computed by weighting datum values in accordance with the network
> accuracies of the existing network control."

This has been interpreted to mean that the local and network accuracies
are determined by the mean of the principal axes of the absolute and
relative coordinate error ellipses respectively. Unfortunately, as
discussed below, neither of these quantities can be calculated for
control points in the North American network without a full readjustment
of all of the underlying survey data.

Local and network accuracies are two measures which express to what
accuracy the coordinates of a point are known. Network accuracies define
how well the absolute coordinates are known and local accuracy defines
how well the coordinates are defined relative to other points in the
network. These quantities will be computed from error ellipses, which
are graphical representation of errors associated with adjusted
coordinates. They represent the region about the computed position of a
station where there is a particular probability (confidence interval)
that the station is actually located. They are characterized by
orientation and size of the principle axes and the size of the principle
axes will increase with a decrease in confidence. There are two basic
types of error ellipses. Absolute error ellipses represent how well
coordinates are determined relative to the datum and relative error
ellipses represent the errors in the relative position between two
points. They can be calculated from the off diagonal covariance matrix
and can be defined regardless of whether observations exist between the
points or not. Both types of error ellipses are calculated from the
appropriate parts of the coordinate covariance matrix which can be
produced only during a least squares adjustment. Because the covariance
matrix for points within the NGS database is not currently available, a
simultaneous national readjustment is required before local and network
accuracies can be calculated.

In simpler terms, the network accuracy of a control point is a value
that represents the uncertainty of its coordinates with respect to the
geodetic datum at the 95-percent confidence level. Since the datum is
considered to be best expressed by the Continuous Operating Reference
Stations (CORS), which are held fixed during the adjustment, local and
network accuracy values at CORS sites are considered to be infinitesimal
(approach zero). The Local Accuracy of a control point is a value that
represents the uncertainty of its coordinates relative to other directly
connected, adjacent control points at the 95-percent confidence level.
This value represents the relative positional error which surveyors can
expect between survey marks in a locality. It also represents an
approximate average of the individual local accuracy values between this
control point and other observed control points used to establish its
coordinates although, in general, all of the immediately surrounding
stations will not necessarily have been used in the survey which
established the original coordinates. These accuracies will be
implemented with the National Readjustment.

**Helmert Blocking**

Helmert blocking, which was developed a little over 100 years ago by F.
R. Helmert (Helmert 1880) is basically a technique for breaking up a
least squares adjustment problem, which is too large to be managed as a
single computation, into many smaller computational tasks with
potentially large savings in computer storage and CPU requirements.
While several other strategies exist for dividing a large survey network
into manageable sized pieces for adjustment, the method of Helmert
Blocking has the crucial advantage of producing not only a set of
coordinates that will work together, but also a complete covariance
matrix relating errors in each coordinate in the network to every other
coordinate.

Helmert blocking starts by dividing a survey network into a series of
subnets or blocks. The requirements for dividing survey data into blocks
are fairly simple. Each observation must be included in one, and only
one, block. In conventional surveying, each observation can be assigned
to a block fairly arbitrarily, however, in GPS measurements, the
situation is more complex because each simultaneously observed GPS
baseline has in principal, nonzero covariance terms with every other
baseline observed at the same time. If these off diagonal co-variance
terms are preserved, as they are for all sessions processed using the
NGS vector reduction program PAGES and other advanced GPS processing
packages, then all of the baselines observed during a session must be
assigned to a single block rather than being partitioned between blocks.
This occurs because in session processing, all baselines processed from
the GPS phase data from all of the GPS receivers logging at a given time
are in effect a single observation.

Division of survey data into blocks is, perhaps the key step to
developing a successful adjustment using Helmut Blocking. Generally
blocks are based on some criterion such as survey order (for example
FBN/CBN surveys vs 1st order UDN surveys) or geographically (for example
all surveys within an individual state). Within each block, the unknowns
(ie coordinates) are divided into junction unknowns (ie those that have
some observation connection with neighboring partial nets) and inner
unknowns (which have no observation connection outside the block).

For the national readjustment, North America will be divided into a
series of regional blocks with one block per state, one for our
neighbors Canada (and perhaps Mexico and one for the Caribbean data
available from the airport survey there). Each block will include all of
the data GPS based surveys submitted to NGS within these regions with
the exception of data which, due to its timing or quality would not
contribute to the success of the readjustment. Currently 149 Projects
with 9903 stations are not recommended for inclusion. These include:

1.  Many Third Order FAA Projects from 1980's

2.  Some Projects that have no ties to the Network

3.  Original TN HARN (Macrometer Data)

4.  Original Eastern Strain Network Project

Once all the normal equations of each of the blocks have been formed and
adjusted, they are reassembled using the back solution to give a full
homogeneous solution for all coordinates in the network and a full
covariance matrix. The covariance matrix is a very important result as
it provides the method for calculating relative accuracies and thus
satisfying the requirements for reporting accuracies within the FGDC
guidelines.

**Weighting**

One of the most important requirements for the procedure to be
successfully concluded is a uniform set of weights that will reflect the
relative accuracies of the disparate sources of survey data included in
the national readjustment. In order to accomplish this, projects are
adjusted individually, checked for blunders and weights determined for
the horizontal component and the vertical component of the project
observations. Since only GPS data will be included in the adjustment,
the network is reasonably homogeneous, and determining a realistic set
of weights is not considered to be a major problem.

**Datum issues**

The adjustment involves two different datums. The first of these is the
International Terrestrial Reference Frame (ITRF). Its origin is at the
center of mass of the whole Earth, including the oceans and the
atmosphere. The datum is updated periodically each time there is a new
origin, most recently with ITRF2000. The ITRF approximates the NUVEL1
NNR or no net rotation reference frame where plate motions average
globally to zero. Plate tectonic movement is accommodated explicitly by
giving each point a coordinate at a reference epoch and a velocity
vector that reflects the future trajectory of the point with time.

NAD83 is similar to the ITRF datum in that it has the same earth model
(or ellipsoid) and a similar origin (Snay and Soler 2000). However
points that fall on the stable North American Plate (which covers most
of the 48 contiguous states) have coordinates that are fixed in time.
Points in the far west of the United States which lie on the boundary
between the North American and Pacific plates do have velocities that
are provided by the NGS utility HTTP.

Because of the difference in the way plate tectonic velocities are
treated in the two systems, the difference between them is slowly
changing. Transformations between NAD83 and the various ITRF
realizations are periodically updated (Craymer, Milbert and Knudsen
2001)

Coordinates will be produced and published for both NAD83 (NSRS) and
ITRF. At this stage, we plan to conduct the adjustment in NAD83 and use
published transformations to derive values in the ITRF afterward. We
have chosen this methodology because the ITRF requires velocity vectors
for each point, while the NAD83 datum is referenced to the stable part
of North America. Since stable North America moves in the global
reference frame due to plate tectonics, each point in the adjustment
would require a velocity vector to be adjusted in the ITRF. The NGS
utility HTTP can provide the required velocity vector by extrapolating
velocity vectors from areas where measured vectors exist. However since
most of the points in the NSRS network are located on the stable North
American plate, this step is unnecessary if the adjustment is conducted
in the NAD83 datum. HTTP is used for points on the far west of North
America which straddle the divide between the North American and Pacific
plates.

**Policy**

The Readjustment of the NSRS is scheduled to commence in June 2005 and
is scheduled for completion February 10, 2007. Because a Helmert
Blocking strategy will be used, all projects which will participate in
the readjustment must be loaded in the National Geodetic Survey Database
prior to its commencement. Hence, a cutoff date of June 1, 2005 will be
required for submission of all projects to allow for review and loading
in the database. Any project submitted after that date will be loaded in
the database and published but not included in the adjustment.

**Conclusions**

The readjustment of all horizontal survey control in North America is
being undertaken by the National Geodetic Survey with an anticipated
completion in 2007. This readjustment will have three important results
for surveyors working in the United States. First, all survey points in
North America will have a single adjustment tag in contrast to the
current system of HARN adjustments where most states are adjusted
individually producing a bewildering number of adjustment tags.
Secondly, it will remove any residual differences between NAD83 (CORS)
positions which are produced by the NGS OPUS
(Online Positioning User Service) facility and the various HARN
adjustments used by the various states. Thirdly it will allow
implementation of FGDC standards requiring each station to have
individual estimates of local and network accuracies. Because
implementation of the local and network accuracy standards require an
estimate of the covariance matrix obtained from a simultaneous solution,
the adjustment will be conducted using the Helmert blocking technique.

**References**

M. R. Craymer, D. Milbert, P. Knudsen. Report of the Sub-Commission for
North America IAG Commission X (Global and Regional Geodetic Networks),
(2001) http://www.naref.org/pubs/naref_iag2001report.pdf

Federal Geographic Data Committee FGDC Draft Geospatial Positioning
Accuracy Standards Part 2: Standards for Geodetic Networks
-STD-007.2-1998

Helmert, F. R., Die mathematischen und physikalischen Theorien der
höheren Geodäsie, 1. Teil, Leipzig, 1880.

R. Snay and T. Soler, Reference Systems: Part 2: The Evolution of NAD 83
Professional Surveyor February 2000 Volume 20, Number 2, 16-18

Wolf, H. 1978 Proceedings of the Second International Symposium on
Problems Related to the Redefinition of North American Geodetic
Networks, 319-326