1. Marc Véronneau Canadian Geodetic Survey, Surveyor General Branch
The Canadian Geodetic Vertical Datum of Canadian Institute of Geomatics – Ottawa Branch 29 April 2014
Marc Véronneau
Canadian Geodetic Survey, Surveyor General Branch

2. 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 … 7
WHAT - Canadian Geodetic Vertical Datum of … 11
WHAT - Impact, Velocity, Labelling and Tools … 19
SUMMARY … 23
General concepts (optional) … 24
I will first outline what the height modernisation project is about. Then we will move into an explanation of the current height system CGVD28 and introduce CGVD2013, the new height system. We will then emphasize that ours is a dynamic planet with changing heights. The final three slides will discuss height labelling, briefly go over the tools available and a short summary of the main points to take away from this presentation.

3. Canadian Spatial Reference System (CSRS)
Horizontal network (f, l)
4-D Geometric frame
Geopotential frame
(f, l, h, H = h – N, t)
NAD27
NAD83
4-D Geometric frame
(f, l, h, t)
Dynamic coordinates
NAD83(CSRS)
Velocity models
CGG2013
NAD83(CSRS)
Velocity models
Direct
Transformation
ITRF96
NAD83(CSRS)
3-D Geometric frame
(f, l, h)
CGVD2013
Vertical network (H)
CGVD28
NAVD 88
Adopted in U.S.A.,
but not in Canada

4. WHAT is Canada’s Height Modernisation?
It is the establishment of a new vertical datum for Canada that is integrated within the CSRS
The Canadian Geodetic Vertical Datum of 2013 (CGVD2013)
Released in November 2013
It replaces the Canadian Geodetic Vertical Datum of 1928 (CGVD28)
Adopted in 1935 by an Order in Council
Three important changes:
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
What is height modernisation? Height modernisation is the release of a new vertical datum for Canada. There are three important changes with this new datum. The first is a new definition (from mean sea level to an equipotential surface). The second is a new realization method (from levelling data to gravity data) and a new dissemination approach (from published elevations of benchmarks to a geoid model). Most importantly, it is compatible with Global Navigation Satellite Systems (GNSS) such as GPS and with satellite altimetry.
Orthometric height determination by two techniques: levelling and combination of GPS measurements and a geoid model.

5. 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.
The levelling technique has well served Canada over the last century in realizing a precise vertical datum. The method has barely changed other than instrumentation improvements and new techniques such as motorized levelling and digital instruments. It still requires measuring the height difference between two graduated roads that are about 100-m apart making levelling a costly technique and prone to systematic errors when leap-frogging over thousands of kilometres.
Area of Europe (which includes western Russia) : 10,180,000 km2
Area of Canada : km2
Area of Germany: km2 (fitting 28 times within Canada)
Population density Europe: 72.5 /km2
Population density Canada: 3.41 /km2
Population density Germany: 225 /km2
Motorized Levelling

6. 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.
GPS
GRAV-D
On the other hand, space based positioning has revolutionized geodesy and surveying in general. We have multiple satellite systems in space allowing accurate positioning, and, more recently, NASA and the European Space Agency (ESA) launched dedicated satellite missions to measure Earth’s gravity field to unprecedented accuracy, allowing a more accurate determination of the geoid.
GRACE
GOCE

7. 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-au-Père, 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
On the screen is a summary of the CGVD28 height system. It is a vertical datum defined by tidal (mean sea level) gauges in Yarmouth, Halifax, Pointe-au-Pere, Vancouver and Prince-Rupert. There is also a height in Rouses Point, New York. Its realisation is levelling based (as depicted by the drawing), with multiple local adjustments over the years since the general least-squares adjustment in They are normal-orthometric heights, which means they are NOT compatible with the geoid.
Backsight
reading BS
Foresight reading FS
Backsight rod B
Levelling
DH = BS - FS
Foresight rod DH A

8. CGVD28: Levelling networks?
~ benchmarks
Prince Rupert
One of the main inconveniences with CGVD28 is its incomplete national coverage. CGVD28 is basically only accessible in Southern Canada. In the northern part of the country, there is either no levelling lines or sparse distribution. Over the years, more than benchmarks have been installed across Canada on some 160,000 kilometres of levelling lines, but a large number of these only covers a fraction of the Canadian landmass. Today, many of these benchmarks are destroyed or could be considered unstable.
Geodetic levelling is a procedure that is very inefficient and costly when maintaining a datum for a country as large as Canada.
*** Canada conducted some 245,000 km of levelling over the years; that represents crossing Germany from North to South 280 times.
Pointe-au-Père
Vancouver
Halifax
Rouses Point
Yarmouth
Original constraints
for Canada’s mainland
Examples of later constraints

9. Levelling surveys over the years in Canada
Natural Ressources has stopped maintaining and extending the federal first-order levelling networks. As can be seen in the graph on the screen, geodetic survey has not conducted any levelling surveys over the last 10 years.

10. WHAT are the error sources in 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
Earth surface
St-Lawrence River
Pacific Ocean
(Pointe-au-Père)
(near Vancouver)
Atlantic Ocean
Level surface wrt MSL in Vancouver
(near Halifax)
CGVD28
Won’t spend too much time on this slide, but I at least wanted to represent some of the main discrepancies that can be observed. It shows a cross-cut of Canada along the east-west direction. The red dots indicate the initial constraints in CGVD28 on the Atlantic, St-Lawrence river and the Pacific. The blue line represents CGVD28 which assumes that oceans are at the same equipotential surface. As we can see, this is in fact not the case. In the U.S, our American colleagues reference their heights with respect to NAVD88.
+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)

11. 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
As a comparison, here is a summary of the CGVD2013 height system. In this case, we are looking at a purely gravimetric (or geoid) model. This equipotential surface has the specific potential value of this big number. It is the result of a US-Canada agreement between the geodetic survey division and the US national geodetic survey. It essentially represents the best global mean sea level potential. Its realisation will be implemented using the geoid model CGG2013 and will be purely an orthometric type of height. We can see from the graphic that we will now be able to recover orthometric heights from GPS ellipsoidal heights using this geoid model anywhere in Canada.

12. WHAT is the definition of CGVD2013?
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
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.
It also corresponds to the current convention adopted by the International Earth Rotation and Reference Systems Service (IERS) and International Astronomical Union (IAU).
Canada’s recommended definition for a World Height System
This image shows the Mean Sea Surface Topography (or the height of the mean ocean surface above the geoid). The blue colour indicates low water while red colour indicated high water. We can see clearly see the cold Labrador current and the warm Gulf Stream.
The potential defining the new datum was done in collaboration between Canada and USA. Note that the US is not moving to a new modern datum until 2022.
Sea Surface Topography
Canadian tide gauges
American tide gauges

13. Ellipsoidal height and Orthometric height
GPS ellipsoidal heights require conversion to orthometric heights (heights above mean sea level) using a geoid model.
Heights are traditionally referred to mean sea level (BM, DEM, Topo maps).
Orthometric heights are consistent with the direction of water flow.
Sept-Iles
Ste-Anne-des-Monts
Baie-Comeau
Slope of the Saint-Lawrence River between Portneuf and Sept-Iles
Rimouski
Gros-Cacouna
Ellipsoidal heights
St-Joseph-de-la-Rive
St-Francois
Orthometric heights
Portneuf
Sept-Iles

14. 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:
(l = 333 km-222 km)
Reference frames
ITRF2008 and NAD83(CSRS)
GRACE ( )
GOCE (2009 – 2013)
Land & ship gravity
Altimetry
DEM

15. 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 9 11
67% confidence (1 s)

16. 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 (W0 = 62,636,856.0 m2s-2).
Location
Gauge number
Coordinates
Observation period
SSTCGVD2013 (m)
Lat.
Lon.
From To
Halifax
490
44.67
-63.58
12/1992
11/2011
-0.39
Rimouski
2985
48.48
-68.51
-0.30
Vancouver
7795
49.34
0.17
Churchill
5010
58.77
-94.18
01/1993
12/2012
-0.22
Tuktoyaktuk
6485
69.44
08/2003
12/2011
-0.36
It is important to recognize that this agreed potential surface between the US and Canada lays BELOW the coastal Pacific sea level by 17cm and above the coastal Atlantic sea level by 39cm. This means the eastern coastline in the area of Halifax would have a negative elevation while Vancouver would have a positive elevation. Be aware that these are preliminary values based on the CGG2010 geoid model.
Terrain
Mean Sea Level
Vancouver
17 cm
Geoid (CGVD2013)
-39 cm
Halifax
Mean Sea Level

17. WHAT is the difference between CGVD2013 and CGVD28?
CGVD28(HTv2.0) – CGVD2013(CGG2010)
Approximate values
HCGVD2013 – HCGVD28
St John’s cm
Halifax cm
Charlottetown -32 cm
Fredericton cm
Montréal cm
Toronto cm
Winnipeg cm
Regina cm
Edmonton cm
Banff cm
Vancouver +15 cm
Whitehorse +34 cm
Yellowknife cm
Tuktoyaktuk cm
So what is the change Canada-wide between CGVD28 and CGVD2013? The graph depicts the difference between CGVD28 and CGVD The changes range from -65 to + 50cm across the Canadian landmass. The largest changes will be occurring in the Maritimes where the new datum will be higher by 65cm, meaning lower elevations for the region, and the Rocky Mountains where the datum will be lower by 50 cm, meaning higher elevations. The table to the right shows the change in elevation in the new vertical datum for different locations across Canada.
Banff
CGVD2013
Vancouver
Thunder Bay
Difference (m)
Regina
CGVD28
Halifax
Windsor
Montréal
Distance (km)

18. WHAT is the difference for Ontario?
Conversion CGVD28-CGVD2013
GPS on BM
Published elevations at BMs
HTv CGG2013 (image on the left)
HCGVD2013 – HCGVD28

19. 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.

20. Vertical velocity (Glacial Isostatic Adjustment)
Vertical velocity of the terrain (GPS)
Vertical velocity of the geoid (GRACE)
Colour scale: -14 mm/a to 14 mm/a
Colour scale: -1.4 mm/a to 1.4 mm/a

21. Labelling Heights
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., ) H N
Height: m
Precision: ± 0.01 m
Epoch:
Type of height: Orthometric
Height system: CGVD2013
Height frame: CGG2013
H = ± m CGVD2013(CGG2013) Epoch
Geoid Height: m
Precision: ± m
Epoch: Static
Model: CGG2013
Frame: NAD83(CSRS)
N = ± m CGG2013, NAD83(CSRS) h
Due to this reason (amongst others), height labelling becomes an important aspect of coordinates information. A tag for a height can include five attributes: the type of height, height reference system, the reference frame, the precision and the epoch. The format of the label will vary according to the technique used to determine height. The example here shows a complete tag for a modernized height determined by GNSS where the attributes are the reference system (CGVD2013), reference frame (CGG2013), precision and epoch.
Height: m
Precision: ± m
Epoch:
Type of height: Ellipsoidal (geodetic)
Height system: NAD83
Height frame: CSRS (version if available)
h = ± m NAD83(CSRS) Epoch

22. 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.

23. 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 The common datum is defined by W0 = 62,636,856.0 m2/s2 (adopted definition of CGVD2013).
To summarize, NRCan will release a new vertical datum in November 2013 that will be called the Canadian Geodetic Vertical Datum of 2013 (CGVD2013) that will be realized by a geoid model compatible with GNSS positioning technique. It must be stressed that CGVD28 will continue to co-exist during the transition period, but that NRCan will no longer maintain the levelling networks. This is not the end of spirit levelling for most construction and surveying projects. The difference between the CGVD2013 and CGVD28 will range between -65 centimetres and 55 centimetres. Also, we can summarize the three main reason for the new national datum. The first one is cost. In addition to being error cumulative; the cost of spirit levelling on long distances across Canada is time consuming and unaffordable. The second is access. Even if traditional spirit levelling would continue to be affordable, all the non urban and areas far from main roads and railway areas would continue to be virtually impossible to access in CGVD1928 (especially in the NORTH and High Arctic where many natural resources development is taking place). The third is technology. We need to better use the space-based technology that GPS and GNSS offers and will offer in the future to access a geoid based vertical datum.

24. General concepts: Datum
Reference point or surface against which position measurements are made
Vertical Datum
Reference for measuring the elevations of points
Terrain H H H H
The vertical datum can be any surfaces, but it is preferable that it is a level surface in order for height to make sense.
Datum
The vertical datum should have physical meaning in order to i.e. properly manage water.

25. General concepts: Reference system and Reference frame
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.
The system is like a plan for a house and the frame is the actual house.

26. 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)
The geodetic datum is purely geometric. You do not have to worry about gravity, potential and sea level, but the geodetic heights (also called ellipsoidal heights) do not have any physical meaning. See example

27. General concepts: Types of height
W0 = Geoid
surface W5
Wi = Equipotential surfaces
W4 = Lake surface P2
Earth’s W4 P1
South
North W3
Ellipsoid
Lake W2 W1 Q1 W0 Q2
Dynamic
Height (Hd)
Orthometric
height (H)
Ellipsoidal
height (h) -
gi is the mean gravity along the plumb line between Qi and Pi.
Hd1 = Hd2
H1 < H2
h1 > h2 -
As the lake is in the northern hemisphere, g1 is larger than g2 because gravity increases towards the pole.
Hd1 = (W4 – W0)/g45
H1 = (W4 – W0)/g1 -
Hd2 = (W4 – W0)/g45
H2 = (W4 – W0)/g2

28. General concepts: Relation between heights, potential and gravity
Gravity is the vertical gradient of potential (W)
W = 60 m2/s2
W = 30 m2/s2
W = 40 m2/s2
W = 70 m2/s2
W = 50 m2/s2
W = 60 m2/s2
This slide is only to show you that heights, potential and gravity are related. Gravity is the vertical gradient of potential as show by the equation this simply means gravity changes according to the rate of change of the potential over a distance. The faster the potential change, the stronger is the gravity as shown by the image to the right.
The equation of gravity can be turned around to express Height in function to potential and gravity.
Height is potential divided by gravity.
W = 80 m2/s2
W = 70 m2/s2
W = 80 m2/s2
W = 90 m2/s2
W = 90 m2/s2 g1
< g2

29. What is the Geoid? geoid g g g
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 geoid is an equipotential surface; it is a particular equipotential surface; it is the equipotential surface representing best, …
So the Earth does not have the shape of a sphere or an ellipsoidal but of a geoid. The geoid is the actual shape of the Earth. It is also a global vertical datum from which heights can be measured.
The physical properties of an equipotential surface are that gravity is always perpendicular to it, that it is a level surface and I could also add that equipotential surfaces never intersect.
This undulating line is an equipotential meaning that it is level and the drop of water will not slide in the dip.
The water drop stays in place
geoid g g g

30. 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
H = h – N
Geoid
Ellipsoid(GRS80)
So the geoid is potential, but we prefer to express in terms of a distance with respect to an ellipsoid. The separation between the ellipsoid and the geoid is the geoid height express by Capital N (ondulation du geoide en francais). Naturally, the ellipsoid need to be define within a geometric frame such as NAD83(CSRS), ITRF or WGS84. Since GPS provide you a height above the ellipsoid (express by small h) and a geoid model provides you geoid heights, By subtracting these two terms you can the orthometric Height (Capital H). Now just to confuse you, the geoid height will change if you work in a different reference frame. As the International Terrestrial Reference frame does not have the same origin as NAD83(CSRS), we have that the geoid heights and the ellipsoidal heights change but the same basic equation apply to provide you the same orthometric height (H). The orthometric height is independent to the geometric reference frame. Thus, the GPS heights and the geoid model must be in the same reference height to determine properly the orthometric height.
NAD83(CSRS) origin
N NAD83(CSRS)
N ITRF
~2.2 m
Note: WGS84 has the same origin as ITRF
ITRF origin

31. General concepts: Mass and potential
Wi: Equipotential surface
W0: Equipotential surface (datum) W2 DW DW W1 DW
H = 0 A
Ht1= -1 DW W0 B
Ht1= 1 C
ht0
ht1
Ellipsoid
gt0
gt1
This is a simple exercise to explain the relation between potential, gravity and height 0x 2x

32. General concepts: The real Earth
Continent
Ocean
Ellipsoid (GRS80)
a: 6,378,137 m
b: 6,356, m
a-b: 21, m
Everest: 8848 m
N max.: 100 m
SST max.: 2 m
Semi-minor axis: b
Semi-major axis: a
If a = 1 m
b: m
a-b: 3.35 mm
Everest: mm
N max: mm
SST max: 0.3 mm
This slide is only to put thing into perspective.
Sphere
Geoid
Ellipsoid

33. QUESTIONS? NRCan Contacts: General information:
Philippe Lamothe
Marc Véronneau
Jianliang Huang
General information:
Web:
Phone:  
Fax:  
For more information on height modernisation, you can contact Philippe Lamothe at Information Management and Client Services or directly Marc Véronneau or Dr. Jianliang Huang. General information on height modernisation can also be found on our website. Thank you.