The National Spatial Reference System Readjustment of NAD83

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The National Spatial Reference SystemReadjustment
of NAD83

• Chris Pearson
• October 2005
• Madison

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Datums
Cartesian system X -2691542.5437 m Y
-4301026.4260 m Z 3851926.3688 m

• The datum is the coordinate system that we use to
  locate ourselves on the earth
• Involves the origin and orientation of coordinate
  axes
• Usually the origin is near the center of mass of
  the earth
• one axis intersects the earths surface at the
  intersection of the prime meridian and the
  equator
• and a reference ellipsoid
• Latitude Longitude and height

Lat Lon f 37o 23 26.38035 N l 122o 02
16.62574 W H -5.4083 m
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WGS84, NAD83 and NAD27
NAD27
NAD83-WGS84/ITRF00

Approximately 2 meters
Earth Mass Center
GEOID
WGS84 and NAD83 share the GRS80 ellipsoid but the
origin differs by about 2m NAD27 uses the Clark
ellipsoid of 1866, the origin is 236 m from WGS84
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Tectonic Plate Motions
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WHAT IS ITRF AND HOW IS IT ESTABLISHED

• ITRF stands for International Terrestrial
  Reference Frame
• 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
• Plate tectonics is accommodated by having all
  coordinates change with time.

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Tectonic motions and NAD83

• The earth is divided into tectonic plates in
  relative motion
• most of the US and Canada is on one single plate
• Allowing us to correct positions back to a stable
  North American reference frame
• So plate motions can be ignored
• An the advantage of NAD83

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Adjustment tags

• NAD83 has been readjusted periodically with most
  states having 2 or 3 adjustments
• Each time this happens a small number of points
  are held fixed at the best values available at
  the time
• Each readjustment will cause new coordinators for
  all points in the network.

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Why readjust now

• The current system with individual state
  adjustments can cause problems for projects
  crossing state lines

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Federal Geographic Data Committee

• The new standards require (FGDC 1998)
• Local and network accuracy measures computed by
  random error propagation
• This has been interpreted to mean that the local
  and network accuracies are determined by the mean
  the principal axes of the absolute and relative
  coordinate error ellipses respectively.
• Neither of these quantities can be calculated for
  control points in the North American network
  without a full readjustment

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Network Accuracies

• Network accuracy of a control point
• A value that represents the uncertainty of its
  coordinates with respect to the geodetic datum at
  the 95-percent confidence level
• Datum is considered to be best expressed by the
  Continuous Operating Reference Stations (CORS)
• Network accuracy values at CORS sites are
  considered to be infinitesimal (approach zero)

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Absolute Error ellipses

• Error ellipses area 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
• the size of the principle axes will increase with
  the confidence interval

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Local Accuracies

• Local Accuracy of a control point
• A value that represents the uncertainty of its
  coordinates relative to other directly connected,
  adjacent control points at the 95-percent
  confidence level
• An approximate average of the individual local
  accuracy values between this control point and
  other observed control points used to establish
  its coordinates

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Relative error ellipses

• Relative error ellipses show the error in point 2
  assuming that the position of point 1 is known
  precisely
• So the only error we are considering is in the
  vector between the two points
• Suppose we have two points

X (E2,N2)

• Relative error ellipses represent the errors in
  the relative position between two points
• They can be calculated regardless of whether
  observations between the points or not.

X (E1,N1)
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National Readjustment General Comments

• The CORS will provide the control
• Only GPS projects will participate
• The FBN/CBN Surveys are a key element since these
  are high accuracy (2 cm) surveys that tie the
  HARN to the CORS throughout the contiguous United
  States and provide more accurate values for the
  ellipsoid heights of most HARN stations.
• The required free adjustment analysis of each GPS
  project that contributes to the National Spatial
  Reference System is underway.

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• Continuously Operating Reference Station
• Nationwide network of GPS stations that log data
  every 30 s or better
• Every day all data is combined and processed to
  give a independent estimate of positions
• Can determine velocities and monitor stability by
  looking at time series
• Control for the national readjustment

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FBN/CBN Surveys

• Next highest order of control
• HARN stations
• At least 4 hr of GPS data for each point
• Now called B order stations

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Helmert blocking

• developed 100 years ago by F. R. Helmert
• a technique for breaking up a least squares
  adjustment problem into many smaller adjustments
  which can be reassembled to give the same results
  as if the adjustment was done in a single network
• While other strategies exist for dividing a
  large survey network into manageable sized pieces
  
• the method of Helmert Blocking has the crucial
  advantage of producing
• a set of coordinates that will work together,
• complete covariance matrix relating errors
  between all coordinates in the network

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Helmert Blocks

• Each state will comprise a separate block of data.

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Time-line for National Readjustment Positions
and Ellipsoid Heights

• All new tasks and software completed by 06/2005
• All projects guaranteed to be included in the
  adjustment must be loaded in the database no
  later than 06/2005
• Anticipated completion in 02/2007
• Project Report
• 3 months-February, 2007 through May, 2007

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Post National Readjustment

• A transformation model for classical non-GPS
  stations and GPS stations that were excluded from
  the National Readjustment will be needed
• New adjustment procedures need to be developed
  that incorporate local and network accuracies
• Areas outside the US may need to be readjusted
  (e.g. Hawaii)
• A reference frame maintenance strategy (NAD83,
  ITRF, either or both) needs to be developed

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Projects submitted after June 05

• These will be added to the database using the
  current adjustment for your state
• After the adjustment is complete,
• These projects will be at the head of the queue
  to be added to the new adjustment
• Using a similar procedure to that used now for
  new project submission

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Single block adjustment of FBN
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Estimate of coordinate shift for Illinois

• To estimate the coordinate shift for Illinois I
  started with coordinates for the entire US FBN
• Which were adjusted using the constraints we plan
  to use for the full adjustment
• Compared with the existing NAD83(97) coordinates
  for Illinois

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Implications for GIS

• Comparing the coordinates of marks in NAD83(97)
  with the prototype national adjustment give an
  estimate of the coordinate shifts
• Approximate shifts 0.0150.001m E and
  -0.0030.001 m N
• Or 0.0490.002 ft E and -0.0090.003 ft N
• 0.016 m in the vertical

• 
  IL HARN
  NAD83(NSRS

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NGS Adjustment Team (1986)
NGS Adjustment Team (2005)