# 1 of 33 The Canadian Geodetic Vertical Datum

- Slides: 33

1 of 33 The Canadian Geodetic Vertical Datum of 2013 Canadian Institute of Geomatics – Ottawa Branch 29 April 2014 Marc Véronneau Canadian Geodetic Survey, Surveyor General Branch

2 of 33 OUTLINE Ø The Canadian Spatial Reference System (CSRS) … 3 Ø WHAT - Canada’s Height Modernization … 4 Ø WHY - Canada’s Height Modernization … 5 Ø WHAT - Canadian Geodetic Vertical Datum of 1928 … 7 Ø WHAT - Canadian Geodetic Vertical Datum of 2013 … 11 Ø WHAT - Impact, Velocity, Labelling and Tools … 19 Ø SUMMARY … 23 Ø General concepts (optional) … 24

3 of 33 Canadian Spatial Reference System (CSRS) Horizontal network (f, l) NAD 27 ITRF 96 4 -D Geometric frame (f, l, h, t) Dynamic coordinates NAD 83 Direct Transformation NAD 83(CSRS) 3 -D Geometric frame (f, l, h) Vertical network (H) CGVD 28 NAVD 88 Adopted in U. S. A. , but not in Canada NAD 83(CSRS) Velocity models 4 -D Geometric frame Geopotential frame (f, l, h, H = h – N, t) NAD 83(CSRS) Velocity models CGG 2013 CGVD 2013

4 of 33 WHAT is Canada’s Height Modernisation? Ø It is the establishment of a new vertical datum for Canada that is integrated within the CSRS ü ü Ø It replaces the Canadian Geodetic Vertical Datum of 1928 (CGVD 28) ü Ø Adopted in 1935 by an Order in Council Three important changes: ü ü ü Ø The Canadian Geodetic Vertical Datum of 2013 (CGVD 2013) 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 CGVD 2013 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? Ø TECHNOLOGY, ACCESS & COST Ø 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 … ü ü ü 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 WHY Height Modernisation in Canada? Ø Modern technology in positioning ü ü ü 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

7 of 33 WHAT is the Canadian Geodetic Vertical Datum of 1928 (CGVD 28)? Name: Canadian Geodetic Vertical Datum of 1928 Abbreviation: CGVD 28 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 DH = BS - FS Backsight rod A Foresight rod Levelling Backsight reading BS Foresight reading FS DH B

8 of 33 CGVD 28: 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

9 of 33 Levelling surveys over the years in Canada 1906 -1928 1929 -1939 1940 -1965 1972 -1981 1966 -1971 1982 -2012

10 of 33 WHAT are the error sources in CGVD 28? Ø CGVD 28: ü Assume that oceans are at a same equipotential surface ü Use entirely gravity values from a mathematical model ü Omit systematic corrections on old levelling data ü Neglect post-glacial rebound ü Accumulation of systematic errors Ea rt hs Pacific Ocean urf ace St-Lawrence River (Pointe-au-Père) (near Vancouver) Level surface wrt MSL in Vancouver Atlantic Ocean (near Halifax) CGVD 28 +36 cm -140 cm NAVD 88 Level surface wrt MSL in Halifax Ø NAVD 88 (not adopted in Canada): ü Significant east-west systematic error (~1 m) of unknown sources in Canada (in the US too)

11 of 33 WHAT is the Canadian Geodetic Vertical Datum of 2013 (CGVD 2013) Name: Canadian Geodetic Vertical Datum of 2013 Abbreviation: CGVD 2013 Type of datum: Gravimetric (geoid) Vertical datum: W 0 = 62, 636, 856. 0 m 2 s-2 Realisation: Geoid model CGG 2013 (NAD 83(CSRS) and ITRF 2008) Type of height : Orthometric

12 of 33 WHAT is the definition of CGVD 2013? Ø CGVD 2013: Conventional equipotential surface (W 0 = 62, 636, 856. 0 m 2/s 2) averaging the coastal mean sea level for North America measured at Canadian and American tide gauges. Ø 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 W 0 = 62, 636, 856. 0 m 2/s 2 Ø 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 Ø Canada’s recommended definition for a World Height System

13 of 33 Ellipsoidal height and Orthometric height Ø GPS ellipsoidal heights require conversion to orthometric heights (heights above mean sea level) using a geoid model. Sept-Iles Ste-Anne-des-Monts Ø Heights are traditionally referred to mean sea level (BM, DEM, Topo maps). Ø 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 eig al h hts soid Ellip St-Joseph-de-la-Rive Orthometric heights St-Francois Portneuf Sept-Iles

14 of 33 Canadian Gravimetric Geoid of 2013 (CGG 2013) Boundaries North: 90° South: 10° West: -170° East: -10° Resolution 2’ x 2’ Satellite model EIGEN-6 C 3 stat (GFZ) Förste et al. , IAG 2013 GOCE (until May 24, 2013) Transition zone Degrees: 120 -180 (l = 333 km-222 km) Reference frames ITRF 2008 and NAD 83(CSRS) GRACE (2002 - ) GOCE (2009 – 2013) Land & ship gravity Altimetry DEM

15 of 33 Accuracy of the geoid model (CGG 2013) Ø The accuracy considers data errors (gravity and DEM), grid resolution, discrepancies between gravity datasets and cut-off of satellite contribution. ü 3 cm or better accuracy over 80% of Canada’s landmass ü Decimeter level in areas with greater topography/mass distribution variability ü Centimeter level relative precision over distances of 100 km or less 1 3 5 7 67% confidence (1 s) 9 11 Unit: cm

16 of 33 WHAT is the difference between CGVD 2013 and the mean sea level? Table 1: Mean Sea Surface Topograpy (SSTCGVD 2013) at five tidal gauges in Canada. These are preliminary values based on CGG 2010 (W 0 = 62, 636, 856. 0 m 2 s-2). Coordinates Observation period Lat. Lon. From To SSTCGVD 2013 (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 Te rra Mean Sea Level 17 cm Vancouver in Geoid (CGVD 2013) -39 cm Halifax Mean Sea Level

17 of 33 WHAT is the difference between CGVD 2013 and CGVD 28? CGVD 28(HTv 2. 0) – CGVD 2013(CGG 2010) Approximate values HCGVD 2013 – HCGVD 28 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 CGVD 2013 Thunder Bay Regina CGVD 28 Distance (km) Windsor Montréal Halifax Difference (m) Banff

18 of 33 WHAT is the difference for Ontario? Ø Conversion CGVD 28 -CGVD 2013 1. 2. 3. GPS on BM Published elevations at BMs HTv 2. 0 - CGG 2013 (image on the left) HCGVD 2013 – HCGVD 28

19 of 33 HOW CGVD 2013 impact heights in Canada? Ø All reference points (benchmarks) will have a new elevation. Ø Natural Resources Canada (NRCan) stopped levelling surveys for the maintenance of the vertical datum. Ø NRCan is NOT maintaining benchmarks by either levelling or GNSS technique. ü However, the levelling networks is readjusted to conform with CGVD 2013 using existing data. ü NRCan is publishing CGVD 28 and CGVD 2013 heights at benchmarks. ü NRCan cannot confirm the actual height of benchmarks in either CGVD 28 or CGVD 2013 (cannot confirm stability of benchmarks). Ø The Canadian Active Control Stations (CACS) and Stations of the Canadian Base Network (CBN) form the federal infrastructure for positioning. ü 250 stations Ø Modern alternative techniques provide height determination. ü NRCan’s Precise Point Positioning (PPP) ü Differential GNSS positioning ü Public and Private Real-Time Kinematic (RTK) positioning Ø Levelling will remain the most efficient technique for most short distance work.

20 of 33 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

21 of 33 Labelling Heights Ø Ø Ø Type of height: Orthometric (H), dynamic (Hd), normal (Hn), ellipsoidal (h), geoid (N) Height Reference System: NAD 83, ITRF, CGVD 28, CGVD 2013, 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: CGVD 2013 Height frame: CGG 2013 H = 23. 126 ± 0. 007 m CGVD 2013(CGG 2013) Epoch 2013. 2 Geoid Height: -10. 354 m Precision: ± 0. 015 m Epoch: Static Model: CGG 2013 Frame: NAD 83(CSRS) Height: 91. 256 m Precision: ± 0. 007 m Epoch: 2013. 2 Type of height: Ellipsoidal (geodetic) Height system: NAD 83 Height frame: CSRS (version if available) N = -10. 354 ± 0. 015 m CGG 2013, NAD 83(CSRS) h = 23. 126 ± 0. 007 m NAD 83(CSRS) Epoch 2013. 2 H h

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 (NAD 83(CSRS) and ITRF)) TRX: Transform coordinates between different geometric reference frames, epochs and coordinate systems.

23 of 33 SUMMARY Ø NRCan released a new vertical datum in November 2013 ü ü Canadian Geodetic Vertical Datum of 2013 (CGVD 2013) Realised by geoid model CGG 2013 (W 0 = 62, 636, 856. 0 m 2/s 2) Compatible with GNSS positioning technique Levelling networks were readjusted using existing data to conform with CGVD 2013 Ø Why a new national vertical datum? ü Cost of conducting levelling surveys at the national scale ü To provide access to the vertical datum all across Canada ü New space-based technologies (GNSS/Gravity) in positioning Ø The difference between CGVD 2013 and CGVD 28 ü Separation ranging from -65 cm and 55 cm at the national scale. Ø 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 W 0 = 62, 636, 856. 0 m 2/s 2 (adopted definition of CGVD 2013).

24 of 33 General concepts: Datum Ø Datum ü Reference point or surface against which position measurements are made Ø Vertical Datum ü Reference for measuring the elevations of points H Terrain H H H Datum Ø 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 Ø Reference System ü Collection of abstract principles ü Definitions, conventions, standards, fundamental parameters Ø Reference frame ü Concrete realisation of the reference system • Levelling (e. g. , CGVD 28, NAVD 88, IGLD 85) • Geoid modelling (e. g. , CGG 2010, EGM 08) Ø A reference system may have several realisations (reference frames) ü New data ü New processing approach Ø 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 Ø Tidal ü ü Sea level at tide gauges Levelling (benchmarks) Advantage: Simple concept Disadvantage: MSL stops at the coast, MSL is not level ? Ø Gravimetric ü ü Potential Geoid model Advantage: Define everywhere Disadvantage: Complex process Ø Geodetic ü ü Ellipsoid Geometric reference frame Advantage: Efficient and precise method Disadvantage: No physical meaning N = f(gsat, gter)

27 of 33 ce General concepts: Types of height rfa W 0 = Geoid P 2 P 1 South North Ellipsoid Lake W 5 W 4 Eart W 4 = Lake surface h’s su Wi = Equipotential surfaces W 3 W 2 W 1 Q 1 Dynamic Height (Hd) Orthometric height (H) Ellipsoidal height (h) Hd 1 = Hd 2 H 1 < H 2 h 1 > h 2 Hd 1 = (W 4 – W 0)/g 45 Hd 2 = (W 4 – W 0)/g 45 H 1 = (W 4 – W 0)/g 1 H = (W – W )/g 2 4 0 2 Q 2 W 0 gi is the mean gravity along the plumb line between Qi and Pi. As the lake is in the northern hemisphere, g 1 is larger than g 2 because gravity increases towards the pole.

28 of 33 General concepts: Relation between heights, potential and gravity Ø Gravity is the vertical gradient of potential (W) W = 60 m 2/s 2 W = 30 m 2/s 2 W = 40 m 2/s 2 W = 70 m 2/s 2 W = 50 m 2/s 2 W = 60 m 2/s 2 W = 80 m 2/s 2 W = 70 m 2/s 2 W = 80 m 2/s 2 W = 90 m 2/s 2 g 1 < W = 90 m 2/s 2 g 2

29 of 33 What is the Geoid? Ø Equipotential surface representing best, in a least-squares sense, the global mean sea level (MSL) ü ü The actual shape of the Earth Vertical datum (W 0) 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

30 of 33 General concepts: Geometric reference frames (NAD 83(CSRS), ITRF, WGS 84) Geodetic (ellipsoidal) heights (h) and geoid heights (N) do not have the same magnitude in the ITRF and NAD 83(CSRS) reference frames because the position of the origin is different. Orthometric heights (H) are independent to the 3 D geometric reference frames. Earth’s surface h ITRF Ellipsoid (e. g. GRS 80) h NAD 83(CSRS) H Geoid H=h–N Ellipsoid(GRS 80) NAD 83(CSRS) origin N ITRF ~2. 2 m ITRF origin N NAD 83(CSRS) Note: WGS 84 has the same origin as ITRF

31 of 33 General concepts: Mass and potential Wi: Equipotential surface W 0: Equipotential surface (datum) W 2 DW DW DW H=0 DW ht 0 W 1 Ht 1= -1 A Ht 1= 1 B C gt 0 0 x W 0 ht 1 Ellipsoid gt 1 2 x

32 of 33 General concepts: The real Earth Continent Semi-minor axis: b Ocean Semi-major axis: a Ellipsoid (GRS 80) 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

33 of 33 QUESTIONS? § NRCan Contacts: § Philippe Lamothe ([email protected] gc. ca) § Marc Véronneau ([email protected] gc. ca) § Jianliang Huang ([email protected] gc. ca) § General information: § § Web: http: //www. geod. nrcan. gc. ca Email: [email protected] nrcan. gc. ca Phone: 1 -613 -995 -4410 Fax: 1 -613 -995 -3215

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