Transcript Document

GS 608
Introduction to GPS: Theory and
Applications
Undergraduate and Graduate, 3 credit hours
AU 2001
Department of Civil and Environmental
Engineering and Geodetic Science
Part I
SPATIAL REFRENCE SYSTEMS AND
FRAMES
GS608
References:
http://www.geocities.com/CapeCanaveral/1224/theory/theory.html
(and referenced links)
http://www.colorado.Edu/geography/gcraft/notes/datum/datum_f.html
Now, where in
the world am I?
Local and Global Ellipsoid
 Maps are 2-dimensional abstractions of reality
 As such, they are not located in their “real” geographic
setting
 They are removed from real coordinates
Thus:
 We must have a system for locating objects once they
are depicted on a map, in geographic space
 These systems are called Spatial Reference Systems
 Reference systems
 Abstract (Cartesian)
 Geographical (geometric)
 Earth is projected into 2-dimensional space
 Or, can be viewed in 3-dimensions
Grid can vary from map to map and make
comparison between maps difficult
Sphere as an approximation of the Earth
surface
Geographical coordinates
Latitude, longitude and height above
the sphere (measured along the
normal to the sphere)
Point is located on
the surface of the
reference sphere
• r is a radius of the
reference sphere
approximating the
shape of the Earth
• XYZ triad is placed
at the center of the
sphere
For points with elevation h
above the reference sphere:
x  (r  h) cos cos
y  (r  h) cos sin 
z  (r  h) sin 
 If the triad XYZ is ECEF (Earth-centered and Earthfixed), centered at the center of mass of the reference
sphere with radius r
 And the plane XZ is located in the reference (zero)
meridian plane
 And the plane XY is located in the equatorial plane
 The polar coordinates  and  can be referred to
as geographical (spherical) coordinates, latitude and
longitude.
 Geographical coordinate systems
 Based on spherical shape of the Earth
 Geodetic coordinate systems
 Based on ellipsoidal shape of the Earth
 Varying systems use different reference ellipsoids
(spheroids)
 Ellipsoid is an approximation of the shape of the
Earth: the Earth is an oblate ellipsoid, nearly spherical,
but bulging at the equator.
Terminology confusion with geographic coordinates
3 types of co-ordinates define different perpendiculars:
• astronomical coordinates
physically defined perpendicular, based on the gravity
• geodetic coordinates
mathematically defined perpendicular, based on the reference
surface, specifically ellipsoid, used for large and medium scale
mapping, and in geodesy.
• geographic coordinates
mathematically defined perpendicular, based on the reference
surface, typically spheres, used for small scale mapping
Spherical Coordinates Based on Ellipsoid of
Revolution
• They are consistent from map to map, but making
measurements necessary to use them may be difficult as
• degrees of longitude vary in distance from about 69
miles at the equator to 0 mile at the poles
• Geodetic coordinates are not directly measurable in the
field, they can be observed by astronomical methods and
reduced to the ellipsoid
WGS84
Coordinate Frame Geometry
Coordinate Conversion: Cartesian
X,Y,Z to Geodetic Lat, Lon, h
 Precise (accurate) conversion can be performed
 Iteratively
• direct computation of longitude
• iterate for latitude and height
 Closed formulas (Borkowski, 1989; see the handout, IERS
Conventions, 1996, p.12)
Short Definitions 1/2
Map Projection
A Map Projection defines the mapping from geographic
coordinates on a sphere or the geodetic coordinates on a
spheroid to a plane.
Reference System
Shape, size, position and orientation of a (mathematical)
Reference Surface, (e.g. Sphere or Spheroid). It normally
is defined in a superior, geocentric three-dimensional
coordinate system (for example WGS84, ITRF).
Short Definitions 2/2
Reference Surface
Mathematically (e.g. Sphere or Spheroid) or physically
(Geoid) defined surface to approximate the shape of the
earth for referencing the horizontal and/or vertical
position.
Reference Frame
A set of control points to realize a Reference System.
Geodetic Datum
Traditional Term for Reference System.
Reference Systems: SUMMARY 1/2
• A coordinate system is most commonly referred to as three
mutually perpendicular axes, scale and a specifically defined
origin
• An access to the coordinate system is provided by coordinates
of a set of well defined reference points
• Coordinate system and an ellipsoid create a datum; ellipsoid
must be defined by two parameters (a and f or a and e);
ellipsoid must be oriented in space
• Modern systems, especially these derived from GPS
observations are Earth-centered, Earth-fixed (ECEF)
Reference Systems: SUMMARY 2/2
• Geodetic datum defines the size and shape of the earth and the origin and
orientation of the coordinate systems used to map the earth.
• Numerous different datums have been created and used so far, evolving from
those describing a spherical earth to ellipsoidal models derived by modern
techniques, such as satellite observations
• Modern geodetic datums range from flat-earth models used for plane surveying to
complex, global models, which completely describe the size, shape, orientation,
gravity field, and angular velocity of the earth.
• Potential problems:
• Referencing geodetic coordinates to the wrong datum can result in significant
position errors
• The diversity of datums in use today and the technological advancements that
have made possible global positioning measurements with sub-decimeter accuracies
require careful datum selection and careful conversion between coordinates in
different datums.
• Datums are created by geodesists, while cartography, surveying,
navigation, and astronomy are the end users
• National Imagery and Mapping Agency (NIMA), former Defense
Mapping Agency created WGS84 – World Geodetic Datum 84
• National Geodetic Survey (NGS) created NAD83 – North American
Datum 83
• International Earth Rotation Service (IERS) created ITRFxx, where xx
stands for the reference year at which the frame was (re)established or
(re)computed
• ITRF stands for International Terrestrial Reference Frame
• ITRF coordinates can be expressed in WGS84 at 10 cm level
• Newest ITRF refers to epoch 2000 (ITRF2000)
ITRF200 Reference Frame
What is ITRF ?
• The International Earth Rotation Service (IERS) has been established in
1988 jointly by the International Astronomical Union (IAU) and the
International Union of Geodesy and Geophysics (IUGG). The IERS mission is
to provide to the worldwide scientific and technical community reference
values for Earth orientation parameters and reference realizations of
internationally accepted celestial and terrestrial reference systems
• In the geodetic terminology, a reference frame is a set of points with their
coordinates (in the broad sense) which realize an ideal reference system
• The frames produced by IERS as realizations of ITRS are named
International Terrestrial Reference Frames (ITRF).
• Such frames are all (or a part of) the tracking stations and the related
monuments which constitute the IERS Network, together with coordinates and
their time variations.
ITRF97
• The reference frame definition (origin, scale, orientation and time
evolution) is achieved in such a way that ITRF97 is in the same system as the
ITRF96
• Station velocities are constrained to be the same for all points within each
site;
• ITRF97 positions were estimated at epoch 1997.0;
• Transformation parameters (at epoch 1997.0) and their rates from ITRF97
to each individual solution were also estimated.
• Transformation between ITRF at epoch 1997.0 and other frames:
• Ri represent rotations, D scale change and Ti stands for translation; i=1,2,3
TRANSFORMATION PARAMETERS AND THEIR RATES FROM ITRF94 TO
OTHER FRAMES
---------------------------------------------------------------------------------------------SOLUTION T1 T2 T3
D
R1
R2
R3 EPOCH Ref.
cm cm cm 10-8 .001" .001" .001"
.
.
.
RATES T1 T2 T3
.
.
.
.
D
R1
R2
R3
IERS Tech.
Note #, page
cm/y cm/y cm/y 10-8/y .001"/y .001"/y .001"/y
----------------------------------------------------------------------------------------------
ITRF93
0.6 -0.5 -1.5 0.04 -0.39 0.80 -0.96 88.0
RATES -0.29 0.04 0.08 0.00 -0.11 -0.19 0.05
18 82
ITRF92
0.8 0.2 -0.8 -0.08
0.0
0.0
0.0 88.0 18 80
ITRF91
2.0 1.6 -1.4 0.06
0.0
0.0
0.0 88.0 15 44
ITRF90
1.8 1.2 -3.0 0.09
0.0
0.0
0.0 88.0 12 32
ITRF89
2.3 3.6 -6.8 0.43
0.0
0.0
0.0 88.0
9 29
ITRF88
1.8 0.0 -9.2 0.74
0.1 0.0
0.0 88.0
6 34
X,Y,Z
(Lat, Lon, h) based on the definition of WGS84
ellipsoid
WGS 84 Four Defining
Parameters
Parameter
Notation
Magnitude
Semi-major Axis
a
6378137.0 meters
Reciprocal of Flattening
1/f
298.257223563
Angular Velocity of the Earth
w
7292115.0 x 10 -11 rad sec -1
Earth’s GravitationalConstant GM
3986004.418 x 10 8 m 3 /s 2
(Mass of Earth’s Atmosphere Included)
a and 1/f are the same as in the original definition of WGS 84
World Geodetic System 1984 (WGS 84)
• The original WGS 84 reference frame established in 1987 was
realized through a set of Navy Navigation Satellite System (NNSS) or
TRANSIT (Doppler) station coordinates
• Significant improvements in the realization of the WGS 84 reference
frame have been achieved through the use of the NAVSTAR Global
Positioning System (GPS).
• Currently WGS 84 is realized by the coordinates assigned to the GPS
tracking stations used in the calculation of precise GPS orbits at NIMA
(former DMA).
• NIMA currently utilizes the five globally dispersed Air Force
operational GPS tracking stations augmented by seven tracking stations
operated by NIMA. The coordinates of these tracking stations have
been determined to an absolute accuracy of ±5 cm (1s).
World Geodetic System 1984 (WGS 84)
Using GPS data from the Air Force and NIMA permanent GPS
tracking stations along with data from a number of selected core
stations from the International GPS Service for Geodynamics (IGS),
NIMA estimated refined coordinates for the permanent Air Force and
DMA stations. In this geodetic solution, a subset of selected IGS
station coordinates was held fixed to their IERS Terrestrial Reference
Frame (ITRF) coordinates.
World Geodetic System 1984 (WGS 84)
 Within the past years, the coordinates for the NIMA GPS reference
stations have been refined two times, once in 1994, and again in 1996. The
two sets of self-consistent GPS-realized coordinates (Terrestrial Reference
Frames) derived to date have been designated:
• WGS 84 (G730 or 1994)
• WGS 84 (G873 OR 1997) , where the ’G’ indicates these
coordinates were obtained through GPS techniques and the number
following the ’G’ indicates the GPS week number when these
coordinates were implemented in the NIMA precise GPS ephemeris
estimation process.
 These reference frame enhancements are negligible (less than 30
centimeters) in the context of mapping, charting and enroute navigation.
Therefore, users should consider the WGS 84 reference frame unchanged
for applications involving mapping, charting and enroute navigation.
Differences between WGS 84 (G873) Coordinates and WGS 84 (G730), compared at 1994.0
Station Location NIMA Station Number D East (cm) D North (cm) D Ellipsoid Height (cm)
Air Force Stations
Colorado Springs
85128
0.1
1.3
3.3
Ascension
85129
2.0
4.0
-1.1
Diego Garcia(<2 Mar 97)
85130
-3.3
-8.5
5.2
Kwajalein
85131
4.7
0.3
4.1
Hawaii
85132
0.6
2.6
2.7
Australia
85402
-6.2
-2.7
7.5
Argentina
85403
-1.0
4.1
6.7
England
85404
8.8
7.1
1.1
Bahrain
85405
-4.3
-4.8
-8.1
Ecuador
85406
-2.0
2.5
10.7
US Naval Observatory
85407
39.1
7.8
-3.7
China
85409
31.0
-8.1
-1.5
NIMA Stations
*Coordinates are at the antenna electrical center.
World Geodetic System 1984 (WGS 84)
• The WGS 84 (G730) reference frame was shown to be in agreement,
after the adjustment of a best fitting 7-parameter transformation, with the
ITRF92 at a level approaching 10 cm.
• While similar comparisons of WGS 84 (G873) and ITRF94 reveal
systematic differences no larger than 2 cm (thus WGS 84 and ITRF94
(epoch 1997.0) practically coincide).
• In summary, the refinements which have been made to WGS 84 have
reduced the uncertainty in the coordinates of the reference frame, the
uncertainty of the gravitational model and the uncertainty of the geoid
undulations. They have not changed WGS 84. As a result, the refinements
are most important to the users requiring increased accuracies over
capabilities provided by the previous editions of WGS 84.
World Geodetic System 1984 (WGS 84)
• The global geocentric reference frame and collection of
models known as the World Geodetic System 1984 (WGS 84)
has evolved significantly since its creation in the mid-1980s
primarily due to use of GPS.
• The WGS 84 continues to provide a single, common,
accessible 3-dimensional coordinate system for geospatial data
collected from a broad spectrum of sources.
• Some of this geospatial data exhibits a high degree of
’metric’ fidelity and requires a global reference frame which is
free of any significant distortions or biases. For this reason, a
series of improvements to WGS 84 were developed in the past
several years which served to refine the original version.
Other commonly used spatial reference systems
• North American Datum 1983 (NAD83)
• State Plane Coordinate System (SPCS) based on NAD83
• Universal Transverse Mercator (UTM)
North American Datum (NAD)
NAD27 established in 1927
 defined by ellipsoid that best fit the North American
continent, fixed at Meades Ranch in Kansas
over the years errors and distortions reaching several
meters were revealed
In 1970’s and 1980’s NGS carried out massive readjustment
of the horizontal datum, and redefined the ellipsoid
The results is NAD83 (1986)
 based on earth-centered ellipsoid that best fits the globe
and is more compatible with GPS surveying
 in 1990’s state-based networks readjustment and
densification, accuracy improvement with GPS (HARN and
CORS networks)
NAD 83 Defining Parameters
Parameter
Notation
Semi-major Axis
Reciprocal of Flattening
a
1/f
Magnitude
6378137.0 meters
298.2572221
Datum point – none
Longitude origin – Greenwich meridian
Azimuth orientation – from north
Best fitting – worldwide
X,Y,Z
(Lat, Lon, h) based on the definition of GRS80
ellipsoid
State Plane Coordinate System
 Based on Lambert and Transverse Mercator projections
 Developed in 1930’s and redefined in 1980’s and 90’s
 NAD ellipsoid was projected to the conical (Lambert)
and cylindrical (Transverse Mercator) flat surfaces
Allowed the entire USA to be mapped on a set of flat
surfaces with no more than one foot distortion in every
10,000 feet (maximum scale distortion 1 in 10,000)
 Coordinates used are called easting and northing;
derived from NAD latitude, longitude and ellipsoidal
parameters
Lambert projection
Lambert projection
Transverse Mercator Projection
State Plane Coordinate System
 The scale of the Lambert projection varies from north
to south, thus, it is used in areas mostly extended in the
east-west direction
 Conversely, the Transverse Mercator projection varies
in scale in the east-west direction, making it most suitable
for areas extending north and south
 Both projections retain the shape of the mapped surface
 Each state is usually covered by more than one zone,
which have their own origins – thus, passing the zone
boundary would cause the coordinate jump!
Universal Transverse Mercator, UTM
 Developed by the Department of Defense for military
purpose
 It is a global coordinate system
 Has 60 north-south zones numbered from west to east
beginning at the 180th meridian
 The coordinate origin for each zone is at its central
meridian and the equator
Universal Transverse Mercator
• UTM zone numbers designate 6-degree longitudinal
strips extending from 80 degrees south latitude to 84
degrees north latitude
• UTM zone characters designate 8-degree zones
extending north and south from the equator
• There are special UTM zones between 0 degrees and 36
degrees longitude above 72 degrees latitude, and a
special zone 32 between 56 degrees and 64 degrees north
latitude
UTM Zones
• Each zone has a central meridia. Zone 14, for example,
has a central meridial of 99 degrees west longitude. The
zone extends from 96 to 102 degrees west longitude
• Easting are measured from the central meridian, with a
500 km false easting to insure positive coordinates
• Northing are measured from the equator, with a 10,000
km false northing for positions south of the equator
Ohio State Plane (Lambert projection, two zones)
and UTM Coordinate Zone
Universal Transverse Mercator, UTM
Vertical Datum Definition 1/2
 Horizontal control networks provide positional information (latitude
and longitude) with reference to a mathematical surface called sphere or
spheroid (ellipsoid)
 By contrast, vertical control networks provide elevation with
reference to a surface of constant gravitational potential, called geoid
(approximately mean see level)
• this type of elevation information is called orthometric height
(height above the geoid or mean sea level) determined by spirit
leveling (including gravity measurements and reduction formulas).
 Height information referenced to the ellipsoidal surface is called
ellipsoidal height. This kind of height information is provided by GPS
Height Systems Used in the USA
 Orthometric
 Normal (orthometric normal)
 Dynamic
 Ellipsoidal
Variety of height systems (datums) used requires
careful definition of differences and transformation
among the systems
Vertical Datum Definition 2/2
 Vertical datum is defined by the surface of reference – geoid or
ellipsoid
 An access to the vertical datum is provided by a vertical control
network (similar to the network of reference points furnishing the access
to the horizontal datums)
 Vertical control network is defined as an interconnected system of
bench marks
 Why do we need vertical control network?
• to reduce amount of leveling required for surveying job
• to provide backup for destroyed bench marks
• to assist in monitoring local changes
• to provide a common framework
The height reference that is mostly used in
surveying job is orthometric
 Orthometric height is also commonly
provided on topographic maps
Thus, even though ellipsoidal heights are
much simpler to determine (eg. GPS) we still
need to determine orthometric heights
 - angle between the normal to the ellipsoid and the vertical direction (normal
to the geoid), so-called deflection of the vertical
H – orthometric height
h – ellipsoidal height
h=H+N
N – geoid undulation (computed from geoid model provided by NGS)
Normal to the
ellipsoid

P
H
h
N
Normal to the geoid
(plumb line or vertical)
terrain
geoid
ellipsoid
Orthometric vs Ellipsoidal Height
(Orthometric height)
(computed from a
geoid model)
So, how do we determine orthometric height?
 By spirit leveling
 And gravity observations along the leveling path, or
 Recently -- GPS combined with geoid models (easy!!!) but
not as accurate as spirit leveling + gravity observations
H = h-N
But why do we need gravity observations with spirit leveling?
Because the sum of the measured height differences along the
leveling path between points A and B is not equal to the difference
in orthometric height between points A and B
Why?
Level Surfaces and Plumb Lines 1/2
Equipotential surfaces are not parallel to each other
Level Surfaces and Plumb Lines 2/2
 The level surfaces are, so to speak, horizontal everywhere, they share
the geodetic importance of the plumb line, because they are normal to it
Plumb lines (line of forces, vertical lines) are curved
 Orthometric heights are measured along the curved plumb lines
Equipotential surfaces are rather complicated mathematically and they
are not parallel to each other
 Consequently:
 Orthometric heights are not constant on the equipotential
surface !
 Thus, points on the same level surface would have different
orthometric height !
Spirit leveling
Height differences between the consecutive locations of backward and forward rods
correspond to the local separation between the level surfaces through the bottom of the
rods, measured along the plumb line direction
Orthometric Height vs. Spirit Leveling
C4
dh4
dh3
C3
C2
dh2
dh1
C1
dhi  H
C1, C2, C3, C4 – geopotential numbers corresponding to level (equipotential)
surfaces
dh1, dh2, dh3, dh4 – height difference between the level surfaces (determined
by spirit leveling, path-dependent); their sum is not equal to H !
Because equipotential surfaces are not parallel to each other
Geopotential Numbers 1/3
 The difference in height, dh, measured during each set up of leveling can be
converted to a difference in potential by multiplying dh by the mean value
of gravity, gm, for the set up (along dh).
geopotential difference = gm*dh
 Geopotential number C, or potential difference between the geoid level
W0 and the geopotential surface WP through point P on the Earth surface (see
Figure 2-8), is defined as
P
 gdh  C  W
0
 WP
0
Where g is the gravity value along the leveling path. This formula is used to
compute C when g is measured, and is independent on the path of integration!
Geopotential Numbers 2/3
Since the computation of C is not path-dependent, the geopotential number
can be also expressed as
C = gm*H,
where H is the height above the geoid (mean sea level) and gm represents the
mean value of gravity along H (along the plumb line at point P on Figure 2-8;
see “orthometric height vs. spirit leveling)
 the last relationship justifies the units for C being kgal*meter; it is not used
to determine C!
 Finally:
 Geopotential number is constant for the geopotential (level) surface
 Consequently, geopotential numbers can be used to define height
and are considered a natural measure for height
REMEMBER: Orthometric heights are not constant on the equipotential
surface !
 Observed difference in height depends on leveling route
 Points on the same level surface have different orthometric heights
Local normal (plumb line direction) to
equipotential (level) surfaces
dhup
P1
dhdown
P2
S3
H1
Reference surface (geoid)
H2
S2
S1
Orthometric height measured
along the plumb line
direction
DH = H1-H2  dhup + dhdown  0
No direct geometrical
relation between the
results of leveling and
orthometric heights
What then, if not orthometric height, is directly obtained
by leveling?
 If gravity is also measured, then geopotential numbers, C
(defined by the integral formula shown earlier), result from
leveling
 Thus, leveling combined with gravity measurements
furnishes potential difference, that is, physical quantities
 Consequently, orthometric height are considered as
quantities derived from potential differences
 Thus, leveling without gravity measurements introduces
error (for short lines might be neglected) to orthometric height
Geopotential Numbers 3/3
Let’s summarize:
The sum of leveled height differences between two pints, A and B, on the
Earth surface will not equal to the difference in the orthometric heights HA
and HB
The difference in height, dh, measured during each set up of leveling
depends on the route taken, as level (equipotential) surfaces are not parallel
to each other
 Consequently, based on the leveling and gravity measurements
 the geopotential numbers are initially estimated (using the integral
formula introduced earlier), based on the leveling and gravity
measurements along the leveling path
 geopotential numbers can then be converted to heights (orthometric,
normal or dynamic – see definitions below) if gravity value along the
plumb line through surface point P is known
Height = C/gravity
Height Systems 1/5
 In order to convert the results of leveling to orthometric heights we need
gravity inside the earth (along the plumb line)
 since we cannot measure it directly, as the reference surface lies within
the Earth, beneath the point, we use special formulas to compute the mean
value of gravity, along the plumb line, based on the surface gravity
measured at point P
reduction formulas used to compute the mean gravity, gm, based on
gravity measured at point P on the Earth surface lead to:
 Orthometric height, (H = C/gm) or
 The reduction formula used to compute mean gravity, based on normal
gravity at point P on the Earth surface leads to:
 Normal (also called normal orthometric) height, (H* = C/ m )
Where  is so-called normal gravity (model) corresponding to the gravity
field of an ellipsoid of reference (Earth best fitting ellipsoid), and subscript
“m” stands for “mean”
Height Systems 2/5
 We can also define dynamic heights
 use normal gravity, 45, defined on the ellipsoid at 45 degree
latitude, (HD = C/ 45)
Note: term “normal gravity” always refers to the gravity defined for
the reference ellipsoid, while “gravity” relates to geoid or Earth itself
Height Systems 3/5
Sometimes, instead of formulas provided above (involving C), it is
convenient to use correction terms and apply them to the sum of
leveled height differences:
 Consequently, the measured elevation difference has to be
corrected using so-called orthometric correction to obtain
orthometric height (height above the geoid)
Max orthometric correction is about 15 cm per 1 km of
measured height difference
 Or, the measured elevation difference has to be corrected using
so-called dynamic correction to obtain dynamic height (no
geometric meaning and factual reference surface; defined
mathematically)
 Or, normal correction is used to derive normal heights
 All corrections need gravity information along the leveling path
(equivalent to computation of C based on gravity observations!)
Height Systems 4/5
 Dynamic heights are constant for the level surface, and have no
geometric meaning
 Orthometric height
differs for points on the same level surface because the level
surfaces are not parallel. This gives rise to the well-known paradoxes
of “water flowing uphill”
 measured along the curved plumb line with respect to geoid level
 Normal height of point P on earth surface is a geometric height above
the reference ellipsoid of the point Q on the plumb line of P such as normal
gravity potential and Q is the same as actual gravity potential at P.
 measured along the normal plumb line (“normal” refers to the line
of force direction in the gravity field of the reference ellipsoid
(model))
 All above types of heights are derived from geopotential numbers
Height Systems 5/5
A disadvantage of orthometric and normal heights is that
neither indicates the direction of flow of water. Only dynamic
heights possess this property.
That is, two points with identical dynamic heights are on the
same equipotential surface of the actual gravity field, and water
will not flow from one to the other point.
Two points with identical orthometric heights lie on different
equipotential surfaces and water will flow from one point to
the other, even though they have the same orthometric height
The last statement holds for normal heights, although due to
the smoothness of the normal gravity field, the effect is not as
severe
Vertical Datums: NGVD 29 and NAVD 88
 NGVD 29 – National Geodetic Vertical Datum of 1929
• defined by heights of 26 tidal stations in US and Canada
• uses normal orthometric height (based on normal gravity formula)
 NAVD 88 – North American Vertical Datum of 1988
• defined by one height (Father Point/Rimouski, Quebec, Canada)
• 585,000 permanent bench marks
• uses Helmert orthometric height (based on Helmert gravity formula)
• removed systematic errors and blunders present in the earlier datum
• orthometric height compatible with GPS-derived height using geoid
model
• improved set of heights on single vertical datum for North America
Vertical Datums: NGVD 29 and NAVD 88
 Difference between NGVD 29 and NAVD 88
• ranges between – 40 cm to 150 cm
• in Alaska between 94 and 240 cm
• in most stable areas the difference stays around 1 cm
• accuracy of datum conversion is 1-2 cm, may exceed 2.5 cm
• transformation procedures and software provided by NGS
(www.ngs.noaa.gov)
International Great Lake Datum (IGLD)
1985
 IGLD 85
• replaced earlier IGLD 1955
• defined by one height (Father Point/Rimouski, Quebec, Canada)
• uses dynamic height (based on normal gravity at 45 degrees latitude)
• virtually identical to NAVD 88 but published in dynamic heights!
Vertical Datums
 Use of proper vertical datum (reference surface) is very
important
 Never mix vertical datums as ellipsoid – geoid separation can
reach 100 m!
 Geoid undulation, N, is provided by models (high accuracy,
few centimeters in the most recent model) developed by the
National Geodetic Survey (NGS) and published on their web
page
www.ngs.noaa.gov
So, in order to derive the height above the see level (H) with
GPS observations – determine the ellipsoidal height (h) with
GPS and apply the geoid undulation (N) according to the
formula H = h - N