The implementation of a new vertical datum for Canada will require the development of procedures and tools for the conversion of heights back and forth between CGVD28 and the new datum.
Officially, the orthometric height of a benchmark will be determined by:
HNew Datum = hRF - NRF, New Datum,
where HNew Datum is the orthometric height in the new vertical datum, hRF is the ellipsoidal height and NRF, New Datum is the geoid height. The geoid height will be determined from the geoid model realizing the new vertical datum for Canada. The ellipsoidal and geoid heights must be in the same reference frame (RF), either NAD83(CSRS) or IRTF.
Even though the new vertical datum for Canada will be realized by geoid modelling, benchmarks observed by geodetic levelling technique over the last 90 years will be given orthometric heights in the new vertical datum by readjusting the Canadian levelling networks. These adjustments will be constrained to a series of stations of the Canadian Active Control System (CACS) and Canadian Base Network (CBN), where the ellipsoidal heights are known accurately (sub-cm accuracy). The constraints are not determined yet, but they will be required to remove systematic errors that accumulate over long distances in the Canadian levelling networks. However, these constraints will not hamper the high precision of the local height differences.
In order to understand properly height conversion, it is important to be familiar these two statements:
- The relative precision of CGVD28 is generally within a few centimetres locally; and
- The distortion in CGVD28 is at the national scale.
The local precision of a few centimetres may represent an area with a radius of 15 to 20 km while preliminary results indicate that the national distortion ranges from -35 cm in Halifax (NS) to 75 cm in Banff (AB), representing about a one-metre distortion. Thus, the conversion of heights for municipal or local projects between CGVD28 and the new datum will consist generally to add a constant value (β):
HNew Datum = HCGVD28 + β,
where HCGVD28 is a normal orthometric height in CGVD28.
Figure 1 [JPEG, 135.2 kb, 1113 X 816, notice] and Figure 2 [JPEG, 123.7 kb, 1092 X 820, notice] show the bias between CGVD28 and Jan06 for the cities of Hamilton and Edmonton, respectively. Jan06 is a preliminary minimum constrained adjusted of the federal first-order levelling data. It does not represent the future vertical datum for Canada. However, this adjustment is used regularly for the validation of geoid models in Canada.
In addition, the Jan06 adjustment allows the identification of a few blunders and discontinuities in CGVD28. For example, Figure 3a [JPEG, 122.8 kb, 1243 X 821, notice] shows a large blunder for a CGVD28 height at a benchmark (Station # 906001) near Edmonton. This blunder is confirmed by GPS observations (Figure 3b [JPEG, 122.8 kb, 1243 X 821, notice]). The orthometric heights derived from GPS and CGG2005 geoid model in the vicinity of Edmonton (including 906001) matches well with the orthometric heights of Jan06. Blunders can be easily corrected in CGVD28; however, the discontinuities would require new GPS or levelling surveys to confirm the source of the problem. A few examples of discontinuities are shown below.
- Figure 4 [JPEG, 56.6 kb, 793 X 826, notice] shows a discontinuity along a levelling line near Dauphin Lake in Manitoba. The levelling observation used in CGVD28 between stations 81M170 and 81M169 has the opposite sign as the field book value. This error produces a 17 cm discontinuity. The question is: Was the sign of the observation reversed voluntarily, but not indicated in any records?
- Figure 5 [JPEG, 85.3 kb, 965 X 824, notice] shows a 12 cm discontinuity (-51 cm vs -39 cm) near the Alberta and Saskatchewan border.
- Figure 6 [JPEG, 81.4 kb, 962 X 841, notice] shows two other discontinuities near the Alberta and Saskatchewan border between new (1990) and old (1928) levelling lines.
- Finally, Figure 7 [JPEG, 70.7 kb, 959 X 840, notice] shows a discontinuity in Sept-Iles (24 cm). The old levelling line has no more ties with the newer line along the St-Lawrence River. The benchmarks on the old levelling line that are common with the new levelling line were “floated” because they are designated as unstable.
The discontinuities in the levelling network render the realization of a conversion tool more complex because it does not conform to the first statement mentioned above.
In the next section, we describe three procedures to convert back and forth normal orthometric heights in CGVD28 and orthometric height in the new datum for Canada.
1.0 GPS surveys at benchmarks (vertical control stations)
Stakeholders can determine their own conversion by conducting accurate GPS surveys at a series of benchmarks in the area of interest. It is important that the ellipsoidal heights and the geoid heights be in the same reference frame. The reference frame (RF) can be either NAD83(CSRS) or ITRF. WGS84 is compatible with ITRF reference frame.
The conversion (β) can be determined as followed:
β = (hRF - NRF) - HOld Datum
where hRF is the ellipsoidal height observed by GPS and NRF is the geoid height interpolated from the model. The Old Datum can be CGVD28 or any local datums.
Naturally, the disadvantage of this approach is the necessity to collect data in the field. On the other hand, it allows the conversion of any local datums to the new vertical datum for Canada. It also allows the validation of the NRCan's National Height Conversion grid (see Procedure C).
It is recommended to conduct GPS surveys at a minimum of three benchmarks to assure local stability.
2.0 Benchmarks Information
NRCan and provincial and territorial geodetic agencies will disseminate the height of benchmarks in CGVD28 and in the new datum. This will allow stakeholders to estimate the separation between the two datums in their working area. This procedure does not require the needs to conduct GPS surveys to determine the local conversion. However, the new orthometric heights may not reflect the actual heights of the benchmarks if these benchmarks are unstable.
Thus, the conversion can be simply determined by:
β = HNew datum - HCGVD28
where HNew datum is the orthometric height in the new datum while HCGVD28 is the CGVD28 height as published by geodetic agencies.
Stakeholders should download height information from a series of benchmarks to assure that the local conversion corresponds approximately to a bias. If the area is larger it might require a planar conversion (bias and tilt).
3.0 The National Height Conversion tool
A third procedure is to use NRCan's national height conversion (NHC) tool, which will be developed when the geoid model realizing the new vertical datum will be made available. This tool will be a software providing easy and fast interpolation from a grid containing separation between CGVD28 and the new datum. This will be the most efficient approach because it will not require field operations or downloading a series of benchmarks in the region of interest.
The conversion grid will be generated from the difference between CGVD28 heights and the new orthometric heights as determined at each benchmark by the re-adjustment of the levelling networks.
Orthometric height in the new datum can be determined as followed when using the NHC software:
HNew Datum = HCGVD28 + β(φ,λ),
where β(φ, λ) is the interpolate conversion value from the grid file at latitude φ and longitude λ.
On the down side, the accuracy of the conversion tool might be poor in remote regions. Even though benchmarks are quite dense along a levelling line (one benchmark every ~2 km), levelling lines are quite sparse outside populated areas. Thus, the conversion tool might not be reliable or even available between sparse levelling lines. Furthermore, the conversion tool will be given with respect to the latest CGVD28 available from NRCan. These values may not necessarily correspond to the height values in your own databases.
Some sparse sectors could be improved by adding provincial levelling data. However, these data may be difficult to integrate into the federal network and may create more discontinuities in the national height conversion tool.