1 of 33

The Canadian Geodetic Vertical Datum of 2013

Canadian Institute of Geomatics – Ottawa Branch29 April 2014

Marc VéronneauCanadian Geodetic Survey, Surveyor General

Branch

2 of 33

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

3 of 33

Canadian Spatial Reference System (CSRS)

NAD27

CGVD28

NAD83

NAVD 88

NAD83(CSRS)NAD83(CSRS)Velocity models

CGG2013

Horizontal network (f, l)

Vertical network (H)

3-D Geometric frame (f, l, h)

Adopted in U.S.A.,but not in Canada

4-D Geometric frame(f, l, h, t)

Dynamic coordinates

4-D Geometric frameGeopotential frame (f, l, h, H = h – N, t)

NAD83(CSRS)Velocity models

DirectTransformationITRF96

CGVD2013

4 of 33

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

Orthometric height determination by two techniques: levelling and combination of GPS measurements and a geoid model.

5 of 33

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

6 of 33

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

GOCE

WHY Height Modernisation in Canada?

GRACE

GRAV-D

7 of 33

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

A

Backsightreading BS

Foresight reading FS

Backsigh

t rod

B

Levelling

DH = BS - FS Foresight rod

DH

8 of 33

CGVD28: Levelling networks

Original constraints for Canada’s mainland

Examples of later constraints

Vancouver

Prince Rupert

Rouses Point

Pointe-au-Père

Halifax

Yarmouth

1906-1928 1929-1939 1940-1965 1966-1971 1972-1981 1982-1989 1990-2007

~ 90 000 benchmarks

?

9 of 33

Levelling surveys over the years in Canada

1906-1928 1929-1939 1940-1965

1966-1971

1972-1981 1982-2012

10 of 33

Earth surface

Atlantic Ocean(near Halifax)

(near Vancouver)

St-Lawrence River(Pointe-au-Père)

CGVD28

WHAT are the error sources in CGVD28?

NAVD 88

+36 cm

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

NAVD 88 (not adopted in Canada): Significant east-west systematic error (~1 m)

of unknown sources in Canada (in the US too)

-140 cm

Pacific Ocean

Level surface wrt MSL in Vancouver

Level surface wrt MSL in Halifax

11 of 33

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

12 of 33

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

Canadian tide gauges American tide gauges

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

Sea Surface Topography

13 of 33

Ellipsoidal height and Orthometric height

Ellipsoidal heights

Orthometric heights

Heights are traditionally referred to mean sea level (BM, DEM, Topo maps).

Orthometric heights are consistent with the direction of water flow.

Sept-IlesPortneuf

Sept-Iles

Baie-Comeau

Rimouski

Gros-Cacouna

St-Joseph-de-la-Rive

Ste-Anne-des-Monts

St-Francois

Slope of the Saint-Lawrence River between Portneuf and Sept-Iles

GPS ellipsoidal heights require conversion to orthometric heights (heights above mean sea level) using a geoid model.

14 of 33

Canadian Gravimetric Geoid of 2013 (CGG2013)

GRACE (2002 - ) GOCE (2009 – 2013) Land & ship gravity Altimetry DEM

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)

15 of 33

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

1 53 7 9

67% confidence (1 s)

Unit: cm11

Accuracy of the geoid model (CGG2013)

16 of 33

WHAT is the difference between CGVD2013 and the mean sea level?

Terrain

Geoid (CGVD2013)

Mean Sea Level

-39 cm

17 cm

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 numberCoordinates 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 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

Vancouver

HalifaxMean Sea Level

17 of 33

WHAT is the difference between CGVD2013 and CGVD28?

CGVD2013

CGVD28

Vancouver

Distance (km)

St John’s -37 cmHalifax -64 cmCharlottetown -32 cmFredericton -54 cmMontréal -36 cmToronto -42 cmWinnipeg -37 cmRegina -38 cmEdmonton -04 cmBanff +55 cmVancouver +15 cmWhitehorse +34 cmYellowknife -26 cmTuktoyaktuk -32 cm

Approximate valuesHCGVD2013 – HCGVD28

Diff

ere

nce

(m)

Halifax

Banff

Regina

Thunder Bay

MontréalWindsor

CGVD28(HTv2.0) – CGVD2013(CGG2010)

18 of 33

WHAT is the difference for Ontario?

HCGVD2013 – HCGVD28

Conversion CGVD28-CGVD20131. GPS on BM

2. Published elevations at BMs

3. HTv2.0 - CGG2013 (image on the left)

19 of 33

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 of 33

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

Vertical velocity (Glacial Isostatic Adjustment)

21 of 33

Height: 101.61 mPrecision: ± 0.01 mEpoch: 2013.2Type of height: OrthometricHeight system: CGVD2013Height frame: CGG2013

H = 23.126 ± 0.007 m CGVD2013(CGG2013) Epoch 2013.2

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., 2012.75)

HHeight: 91.256 mPrecision: ± 0.007 mEpoch: 2013.2Type of height: Ellipsoidal (geodetic)Height system: NAD83Height frame: CSRS (version if available)

h = 23.126 ± 0.007 m NAD83(CSRS) Epoch 2013.2 h

Geoid Height: -10.354 mPrecision: ± 0.015 mEpoch: StaticModel: CGG2013Frame: NAD83(CSRS)

N = -10.354 ± 0.015 m CGG2013, NAD83(CSRS)

N

22 of 33

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 of 33

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).

SUMMARY

24 of 33

General concepts: Datum

Datum Reference point or surface against which position measurements are

made

Vertical Datum Reference for measuring the elevations of points

TerrainH

H

Datum

H H

The vertical datum should have physical meaning in order to i.e. properly manage water.

25 of 33

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.

26 of 33

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)

?

27 of 33

General concepts: Types of height

W0

W1

W4

W3

W2

W5

W0 = Geoid

Wi = Equipotential surfaces

Hd1 = (W4 – W0)/g45

North South

W4 = Lake surface

Hd1 = Hd

2

H1 = (W4 – W0)/g1

Eart

h’s

Lake

Hd2 = (W4 – W0)/g45

Dynamic Height (Hd)

Q1

Q2

P1

P2

Orthometric height (H)

H2 = (W4 – W0)/g2

H1 < H2 -

-

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.

surfa

ce

Ellipsoid

Ellipsoidal height (h)

h1 > h2

28 of 33

Gravity is the vertical gradient of potential (W)

General concepts: Relation between heights, potential and gravity

H

Wg

W = 90 m2/s2

W = 80 m2/s2

W = 70 m2/s2

W = 60 m2/s2

W = 90 m2/s2

W = 70 m2/s2

W = 50 m2/s2

W = 30 m2/s2

W = 80 m2/s2

W = 60 m2/s2

W = 40 m2/s2

g

WWH

p 0

g1 g2<

29 of 33

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)

g

geoid

g g

The water drop stays in place

30 of 33

h NAD83(CSRS)

ITRF origin

NAD83(CSRS) origin

~2.2 m

Earth’s surfaceh ITRF

Note: WGS84 has the same origin as ITRF

Geoid

N ITRF

N NAD83(CSRS)

General concepts: Geometric reference frames (NAD83(CSRS), ITRF, WGS84)

Ellipsoid(e.g. GRS80)

Ellipsoid(GRS80)

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.

H

H = h – N

31 of 33

Ellipsoid

W0

W1

W2

ht0 ht1

H = 0

Wi: Equipotential surface

W0: Equipotential surface (datum)

Ht1= 1

Ht1= -1DW

DW

gt0gt1

DW

DW

General concepts: Mass and potential

A

B C

0x 2x

32 of 33

EllipsoidGeoid

Sphere

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

Continent

Ocean

Semi-major axis: aSe

mi-m

inor

axi

s: b

General concepts: The real Earth

33 of 33

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

QUESTIONS?