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The Canadian Geodetic Vertical Datum of 2013
Canadian Institute of Geomatics – Ottawa Branch
29 April 2014
Marc Véronneau
Canadian Geodetic Survey, Surveyor General Branch
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OUTLINE

The Canadian Spatial Reference System (CSRS)
… 3

WHAT - Canada’s Height Modernization
… 4

WHY - Canada’s Height Modernization
… 5

WHAT - Canadian Geodetic Vertical Datum of 1928
… 7

WHAT - Canadian Geodetic Vertical Datum of 2013
… 11

WHAT - Impact, Velocity, Labelling and Tools
… 19

SUMMARY
… 23

General concepts (optional)
… 24
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Canadian Spatial Reference System (CSRS)
Horizontal network (f, l)
NAD27
ITRF96
4-D Geometric frame
(f, l, h, t)
Dynamic coordinates
NAD83
Direct
Transformation
NAD83(CSRS)
3-D Geometric frame
(f, l, h)
Vertical network (H)
CGVD28
NAVD 88
Adopted in U.S.A.,
but not in Canada
NAD83(CSRS)
Velocity models
4-D Geometric frame
Geopotential frame
(f, l, h, H = h – N, t)
NAD83(CSRS)
Velocity models
CGG2013
CGVD2013
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WHAT is Canada’s Height Modernisation?

It is the establishment of a new vertical
datum for Canada that is integrated
within the CSRS



It replaces the Canadian Geodetic
Vertical Datum of 1928 (CGVD28)


Adopted in 1935 by an Order in Council
Three important changes:




The Canadian Geodetic Vertical Datum
of 2013 (CGVD2013)
Released in November 2013
New definition: from mean sea level at
specific tide gauges to an equipotential
surface
New realisation: from adjusting levelling
data to integrating gravity data
New access: from benchmarks to a
geoid model
CGVD2013 is compatible with Global
Navigation Satellite Systems (GNSS)
such as GPS
Orthometric height determination by two techniques:
levelling and combination of GPS measurements and a
geoid model.
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WHY Height Modernisation in Canada?

TECHNOLOGY, ACCESS & COST

Levelling is a precise technique that
served Canada well over the last 100
years to realise and maintain a vertical
datum, but for a country as wide as
Canada …



It is prone to the accumulation of
systematic errors over long distances;
It does not provide a national coverage
(BMs only along major roads and
railways);
It is a costly and time-consuming
technique.
Motorized Levelling
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WHY Height Modernisation in Canada?

Modern technology in positioning





GNSS positioning is now mature and has
gained widespread adoption by users.
It is a cost efficient technique in
determining precise heights everywhere in
Canada.
Satellite gravity missions offer
unprecedented precision in the
determination of the long and middle
wavelength components of the geoid.
A geoid model realizes an accurate and
homogeneous vertical reference surface
all across Canada (land, lakes and
oceans).
Our U.S. partners contributed GRAV-D
data in the Great Lakes region.
GRACE
GOCE
GPS
GRAV-D
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WHAT is the Canadian Geodetic Vertical Datum of 1928
(CGVD28)?
Name:
Canadian Geodetic Vertical Datum of 1928
Abbreviation:
CGVD28
Type of datum:
Tidal (Mean sea level)
Vertical datum:
Mean sea level at tide gauges in Yarmouth, Halifax, Pointe-auPère, Vancouver and Prince-Rupert, and a height in Rouses
Point, NY.
Realisation:
Levelling (benchmarks). Multiple local adjustments over the years
since the general least-squares adjustment in 1928.
Type of height:
Normal-orthometric
DH = BS - FS
Backsight
rod
A
Foresight
rod
Levelling
Backsight
reading BS
Foresight reading FS
DH
B
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CGVD28: Levelling networks
?
~ 90 000 benchmarks
Prince Rupert
Pointe-au-Père
Vancouver
Halifax
Rouses Point
1906-1928
1929-1939
1940-1965
1966-1971
Original constraints
for Canada’s mainland
1972-1981
1982-1989
Examples of later constraints
Yarmouth
1990-2007
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Levelling surveys over the years in Canada
1906-1928
1929-1939
1940-1965
1972-1981
1966-1971
1982-2012
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WHAT are the error sources in CGVD28?
 CGVD28:
 Assume that oceans are at a same equipotential surface
 Use entirely gravity values from a mathematical model
 Omit systematic corrections on old levelling data
 Neglect post-glacial rebound
 Accumulation of systematic errors
St-Lawrence River
(Pointe-au-Père)
Pacific Ocean
(near Vancouver)
Atlantic Ocean
Level surface wrt MSL in Vancouver
(near Halifax)
CGVD28
+36 cm
-140 cm
Level surface wrt MSL in Halifax
NAVD 88
 NAVD 88 (not adopted in Canada):
 Significant east-west systematic error (~1 m) of
unknown sources in Canada (in the US too)
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WHAT is the Canadian Geodetic Vertical Datum of 2013
(CGVD2013)
Name:
Canadian Geodetic Vertical Datum of 2013
Abbreviation:
CGVD2013
Type of datum:
Gravimetric (geoid)
Vertical datum:
W0 = 62,636,856.0 m2s-2
Realisation:
Geoid model CGG2013 (NAD83(CSRS) and ITRF2008)
Type of height :
Orthometric
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WHAT is the definition of CGVD2013?
 CGVD2013: Conventional equipotential surface (W0 =
62,636,856.0 m2/s2) averaging the coastal mean sea level
for North America measured at Canadian and American
tide gauges.
 U.S. NGS and NRCan’s
GSD signed an
agreement (16 April
2012) to realize and
maintain a common
vertical datum for USA
and Canada defined by
W0 = 62,636,856.0 m2/s2
 It also corresponds to
the current convention
adopted by the International
Earth Rotation and Reference
Systems Service (IERS) and
International Astronomical Union
(IAU).
Sea Surface Topography
Canadian tide gauges
American tide gauges
 Canada’s recommended
definition for a World
Height System
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Ellipsoidal height and Orthometric height
 GPS ellipsoidal heights require conversion to orthometric heights (heights
above mean sea level) using a geoid model.
Sept-Iles
Ste-Anne-des-Monts
 Heights are traditionally referred to
mean sea level (BM, DEM, Topo maps).
 Orthometric heights are consistent with
the direction of water flow.
Baie-Comeau
Slope of the Saint-Lawrence River
between Portneuf and Sept-Iles
Rimouski
Gros-Cacouna
St-Joseph-de-la-Rive
Orthometric heights
St-Francois
Portneuf
Sept-Iles
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Canadian Gravimetric Geoid of 2013 (CGG2013)
Boundaries
North: 90°
South: 10°
West: -170°
East: -10°
Resolution
2’ x 2’
Satellite model
EIGEN-6C3stat (GFZ)
Förste et al., IAG 2013
GOCE (until May 24, 2013)
Transition zone
Degrees: 120-180
(l = 333 km-222 km)
Reference frames
ITRF2008 and NAD83(CSRS)
GRACE (2002 - )
GOCE (2009 – 2013)
Land & ship gravity
Altimetry
DEM
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Accuracy of the geoid model (CGG2013)
 The accuracy considers data
errors (gravity and DEM), grid
resolution, discrepancies
between gravity datasets and
cut-off of satellite contribution.
 3 cm or better accuracy over
80% of Canada’s landmass
 Decimeter level in areas with
greater topography/mass
distribution variability
 Centimeter level relative
precision over distances of 100
km or less
Unit: cm
1
3
5
7
67% confidence (1 s)
9
11
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WHAT is the difference between CGVD2013 and the
mean sea level?
Table 1: Mean Sea Surface Topograpy (SSTCGVD2013) at five tidal gauges in Canada. These are preliminary values
based on CGG2010 (W 0 = 62,636,856.0 m2s-2).
Coordinates
Observation period
Lat.
Lon.
From
To
SSTCGVD2013
(m)
490
44.67
-63.58
12/1992
11/2011
-0.39
Rimouski
2985
48.48
-68.51
12/1992
11/2011
-0.30
Vancouver
7795
49.34
-123.25
12/1992
11/2011
0.17
Churchill
5010
58.77
-94.18
01/1993
12/2012
-0.22
Tuktoyaktuk
6485
69.44
-132.99
08/2003
12/2011
-0.36
Location
Gauge number
Halifax
Mean Sea Level
17 cm
Vancouver
Geoid (CGVD2013)
-39 cm
Halifax
Mean Sea Level
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WHAT is the difference between CGVD2013 and CGVD28?
CGVD28(HTv2.0) – CGVD2013(CGG2010)
Approximate values
HCGVD2013 – HCGVD28
St John’s
-37 cm
Halifax
-64 cm
Charlottetown -32 cm
Fredericton
-54 cm
Montréal
-36 cm
Toronto
-42 cm
Winnipeg
-37 cm
Regina
-38 cm
Edmonton
-04 cm
Banff
+55 cm
Vancouver
+15 cm
Whitehorse +34 cm
Yellowknife
-26 cm
Tuktoyaktuk -32 cm
Vancouver
CGVD2013
Thunder Bay
Regina
CGVD28
Distance (km)
Windsor
Montréal
Halifax
Difference (m)
Banff
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WHAT is the difference for Ontario?
 Conversion CGVD28-CGVD2013
1.
2.
3.
GPS on BM
Published elevations at BMs
HTv2.0 - CGG2013 (image on the left)
HCGVD2013 – HCGVD28
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HOW CGVD2013 impact heights in Canada?
 All reference points (benchmarks) will have a new elevation.
 Natural Resources Canada (NRCan) stopped levelling surveys for the
maintenance of the vertical datum.
 NRCan is NOT maintaining benchmarks by either levelling or GNSS technique.
 However, the levelling networks is readjusted to conform with CGVD2013 using existing data.
 NRCan is publishing CGVD28 and CGVD2013 heights at benchmarks.
 NRCan cannot confirm the actual height of benchmarks in either CGVD28 or CGVD2013 (cannot
confirm stability of benchmarks).
 The Canadian Active Control Stations (CACS) and Stations of the Canadian
Base Network (CBN) form the federal infrastructure for positioning.
 250 stations
 Modern alternative techniques provide height determination.
 NRCan’s Precise Point Positioning (PPP)
 Differential GNSS positioning
 Public and Private Real-Time Kinematic (RTK) positioning
 Levelling will remain the most efficient technique for most short distance work.
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Vertical velocity (Glacial Isostatic Adjustment)
Vertical velocity of the terrain (GPS)
Colour scale: -14 mm/a to 14 mm/a
Vertical velocity of the geoid (GRACE)
Colour scale: -1.4 mm/a to 1.4 mm/a
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Labelling Heights


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Type of height: Orthometric (H), dynamic (Hd), normal (Hn), ellipsoidal (h), geoid (N)
Height Reference System: NAD83, ITRF, CGVD28, CGVD2013, NAVD 88
Height Reference Frame: CSRS v., geoid model
Precision (e.g., ± 0.05 m)
Epoch (e.g., 2012.75)
N
Height: 101.61 m
Precision: ± 0.01 m
Epoch: 2013.2
Type of height: Orthometric
Height system: CGVD2013
Height frame: CGG2013
H = 23.126 ± 0.007 m CGVD2013(CGG2013) Epoch 2013.2
Geoid Height: -10.354 m
Precision: ± 0.015 m
Epoch: Static
Model: CGG2013
Frame: NAD83(CSRS)
Height: 91.256 m
Precision: ± 0.007 m
Epoch: 2013.2
Type of height: Ellipsoidal (geodetic)
Height system: NAD83
Height frame: CSRS (version if available)
N = -10.354 ± 0.015 m
CGG2013, NAD83(CSRS)
h = 23.126 ± 0.007 m NAD83(CSRS) Epoch 2013.2
H
h
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Tools available for Height Modernisation
Precise Point Positioning (PPP): Process GPS RINEX
files to provide coordinates (latitude, longitude,
ellipsoidal height and orthometric height)
GPS-H: Convert ellipsoidal heights to orthometric
heights (makes use of any geoid models, works with
different types of coordinate systems (geographic, UTM,
MTM and Cartesian), and different geometric reference
frames (NAD83(CSRS) and ITRF))
TRX: Transform coordinates between different geometric
reference frames, epochs and coordinate systems.
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SUMMARY
 NRCan released a new vertical datum in November 2013




Canadian Geodetic Vertical Datum of 2013 (CGVD2013)
Realised by geoid model CGG2013 (W0 = 62,636,856.0 m2/s2)
Compatible with GNSS positioning technique
Levelling networks were readjusted using existing data to conform with
CGVD2013
 Why a new national vertical datum?
 Cost of conducting levelling surveys at the national scale
 To provide access to the vertical datum all across Canada
 New space-based technologies (GNSS/Gravity) in positioning
 The difference between CGVD2013 and CGVD28
 Separation ranging from -65 cm and 55 cm at the national scale.
 US and Canada signed an agreement for the realisation of a unique
height reference system between the two country by 2022. The
common datum is defined by W0 = 62,636,856.0 m2/s2 (adopted
definition of CGVD2013).
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General concepts: Datum
 Datum
 Reference point or surface against which position measurements are
made
 Vertical Datum
 Reference for measuring the elevations of points
H
Terrain
H
H
H
Datum
 The vertical datum should have physical meaning in order to i.e.
properly manage water.
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General concepts: Reference system and Reference frame
 Reference System
 Collection of abstract principles
 Definitions, conventions, standards, fundamental parameters
 Reference frame
 Concrete realisation of the reference system
• Levelling (e.g., CGVD28, NAVD88, IGLD85)
• Geoid modelling (e.g., CGG2010, EGM08)
 A reference system may have several realisations (reference frames)
 New data
 New processing approach
 A new reference frame is generally an improvement (more accurate)
with respect to the previous frame.
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General concepts: Types of vertical datum
 Tidal




Sea level at tide gauges
Levelling (benchmarks)
Advantage: Simple concept
Disadvantage: MSL stops at the coast, MSL is not level
?
 Gravimetric




Potential
Geoid model
Advantage: Define everywhere
Disadvantage: Complex process
 Geodetic




Ellipsoid
Geometric reference frame
Advantage: Efficient and precise method
Disadvantage: No physical meaning
N = f(gsat, gter)
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General concepts: Types of height
W0 = Geoid
W5
Wi = Equipotential surfaces
W4 = Lake surface
P2
P1
South
North
W4
W3
Lake
W2
W1
Q1
Q2
Dynamic
Height (Hd)
Orthometric
height (H)
Ellipsoidal
height (h)
Hd1 = Hd2
H1 < H2
h1 > h2
Hd1 = (W4 – W0)/g45
Hd2 = (W4 – W0)/g45
H1 = (W4 – W0)/g1
H = (W – W )/g2
4
0
2
W0
gi is the mean gravity along the plumb
line between Qi and Pi.
As the lake is in the northern hemisphere,
g1 is larger than g2 because gravity
increases towards the pole.
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General concepts: Relation between heights, potential
and gravity
 Gravity is the vertical gradient of potential (W)
W = 60 m2/s2
g
W = 30 m2/s2
W
H
W = 40 m2/s2
W = 70 m2/s2
W = 50 m2/s2
W = 60 m2/s2
W = 80 m2/s2
Wp  W 0
H
g
W = 70 m2/s2
W = 80 m2/s2
W = 90 m2/s2
g1
<
W = 90 m2/s2
g2
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What is the Geoid?
 Equipotential surface representing best, in a least-squares sense,
the global mean sea level (MSL)




The actual shape of the Earth
Vertical datum (W0)
Gravity is perpendicular (vertical) to the geoid
Water stays at rest on the geoid (a level surface)
The water drop
stays in place
g
geoid
g
g
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General concepts: Geometric reference frames
(NAD83(CSRS), ITRF, WGS84)
Geodetic (ellipsoidal)
heights (h) and geoid
heights (N) do not have the
same magnitude in the ITRF
and NAD83(CSRS)
reference frames because
the position of the origin is
different. Orthometric
heights (H) are independent
to the 3D geometric
reference frames.
Earth’s surface
h ITRF
Ellipsoid
(e.g. GRS80)
h NAD83(CSRS)
H
Geoid
H=h–N
Ellipsoid(GRS80)
NAD83(CSRS) origin
N ITRF
ITRF origin
N NAD83(CSRS)
Note: WGS84 has the same origin as ITRF
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General concepts: Mass and potential
Wi: Equipotential surface
W0: Equipotential surface (datum)
W2
DW
DW
W1
DW
DW
H=0
ht0
Ht1= -1
A
Ht1= 1
B
C
W0
ht1
Ellipsoid
gt0
0x
gt1
2x
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General concepts: The real Earth
Continent
Semi-minor axis: b
Ocean
Semi-major axis: a
Ellipsoid (GRS80)
a: 6,378,137 m
b: 6,356,752.3141 m
a-b: 21,384.6859 m
Everest: 8848 m
N max.: 100 m
SST max.: 2 m
If a = 1 m
b: 0.996647 m
a-b: 3.35 mm
Everest: 1.387 mm
N max: 0.016 mm
SST max: 0.3 mm
Sphere
Geoid
Ellipsoid
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QUESTIONS?

NRCan Contacts:
 Philippe Lamothe (phlamoth@nrcan.gc.ca)
 Marc Véronneau (marcv@nrcan.gc.ca)
 Jianliang Huang (jianhuan@nrcan.gc.ca)

General information:




Web: http://www.geod.nrcan.gc.ca
Email: information@geod.nrcan.gc.ca
Phone: 1-613-995-4410
Fax: 1-613-995-3215