Conventionally, the mean sea level has been used as the reference surface for topographic elevations for generations. Regional, national and continental vertical datums were realized using geodetic levelling observations that were constrained to mean sea level as determined by tide gauge measurements. Nowadays, Global Navigation Satellite Systems (GNSS; e.g., GPS, GLONASS, and eventually Galileo) offer an alternative technique to determine elevations. However, these elevations are measured with respect to a reference ellipsoid, which does not have any physical meaning, i.e., water could flow from a lower ellipsoidal height to a higher ellipsoidal height. This is why ellipsoidal heights (h) must be converted to orthometric heights (H) using geoid heights (N): H = h – N. Unfortunately, the geoid does not coincide exactly with the mean sea level because the latter is not an equipotential surface (a level surface). The mean ocean surface has slight hills and valleys similar to land topography, but much smoother. Globally, these hills and valleys range from -2.0 m to +2.0 m with respect to the geoid.
The Sea Surface Topography (SST) or Dynamic Ocean Topography (DOT) is the separation between the geoid and the sea surface. The Sea Surface Topography can be determined by oceanographic and geodetic techniques. The oceanographic estimates of the SST are modeled from the temperature and salinity fields of the oceans. On the other hand, the geodetic estimates of the SST are produced geometrically using tide gauge data that are combined with GNSS observations and a geoid model or combining satellite radar altimetry data (SSH, separation between the ellipsoid and sea surface) and a geoid model (N): SST = SSH – N.
For coastal applications, it might be important to determine heights with respect to the local sea level. In this case, it would require calculating the separation between the mean sea level and the adopted vertical datum. Three (3) procedures are proposed to determine the Sea Surface Topography with respect to CGVD2013 (SSTCGVD2013), allowing height determination with respect to local mean sea level (HMSL):
HMSL = hNAD83(CSRS) – NCGVD2013, NAD83(CSRS) – SSTCGVD2013
where hNAD83(CSRS) is the ellipsoidal height in NAD83(CSRS) and NCGVD2013, NAD83(CSRS) is a CGVD2013 geoid height in NAD83(CSRS).
Procedure 1: SSTCGVD2013 Model
NRCan is investigating the feasibility to develop a data grid allowing stakeholders to interpolate the separation between the vertical datum (geoid) and the mean sea level along the Canadian coast and in open sea. The SSTCGVD2013 grid would be estimated from GPS measurements, levelling observations, tide gauge data and radar satellite altimetry data. Figure 1 shows a preliminary model of the mean Sea Surface Topography with respect to CGVD2013 (W0 = 62,636,856.0 m2s-2) for the oceans surrounding North America. The circles and stars show location of Canadian and American tide gauges, respectively.
NRCan is also looking into distributing a digital table containing the Sea Surface Topography at a series of tide gauges across Canada. It will allow a quick estimate of the separation between the mean sea level and the Canadian geodetic vertical datum. Table 1 shows preliminary estimates of SSTCGVD2013 at four selected tide gauges in Canada.
Procedure 2: GNSS survey at a tide gauge
Local SSTCGVD2013 can also be determined by conducting a GNSS survey on reference markers at a tide gauge. Tide gauge data and information about the tidal reference markers are available from Integrated Science Data Management (ISDM), Fisheries and Oceans Canada. The web site provides monthly mean sea levels above chart datum (Z0) and elevations of the reference markers above the chart datum (HCD).
The SSTCGVD2013 can be determined as follows:
SSTCGVD2013 = hNAD83(CSRS) – NCGVD2013, NAD83(CSRS) – HCD + Z0
where hNAD83(CSRS) is the ellipsoidal height in NAD83(CSRS), NCGVD2013, NAD83(CSRS) is the CGVD2013 geoid height in NAD83(CSRS), HCD is the elevation of the station above the chart datum and Z0 is the separation between the mean water level and chart datum. Figure 2 illustrates the relation between the different vertical datums (ellipsoid, geoid (CGVD2013), mean sea level, chart datum and CGVD28), allowing determination of the separation between a vertical datum and mean sea level.
Procedure 3: Levelling of low and high tides
An approximate procedure for estimating the local separation between mean sea level and the vertical datum (SSTCGVD2013) is to measure by spirit levelling technique the height difference between the low and high tides. The height difference must be tied to a common benchmark with a known ellipsoidal height (h). Figure 3 illustrates the procedure.
The SSTCGVD2013 can be determined as follows:
SSTCGVD2013 = hNAD83(CSRS) – NCGVD2013, NAD83(CSRS) – (ΔHHighTide + ΔHLowTide)/2.0
where ΔHHighTide is the height difference between the benchmark and high tide and ΔHLowTide is the height difference between the same benchmark and the low tide.