Conventionally, the mean sea level has been used as the reference surface for topographic elevations and bathymetric depth 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 data.  Nowadays, Global Navigation Satellite Systems (e.g., GPS, GLONASS, and eventually Galileo) offer alternative techniques to determine elevations.  However, these elevations are measured with respect to an 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 one reason why ellipsoidal heights (h) must be converted to orthometric heights (H) using geoid heights (N): H = h – N.  A second reason is to keep heights consistent with existing topographic maps, which have elevations above mean sea level.  Unfortunately, the geoid does not coincide exactly with the mean sea level because the latter is not an equipotential 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.  Because several coastal applications will require relating elevations with respect to mean sea level, it is important to determine the separation between the geoid and mean sea level.

The Sea Surface Topography (SST) is the actual separation between the mean sea level and the geoid, which is here the equipotential surface representing best, in a least-squares sense, the global mean sea level.  Figure 1 [JPEG, 60.8 kb, 632 X 519, notice] and Figure 2 [JPEG, 67.2 kb, 633 X 513, notice] show the actual SST for the north Atlantic as determined by oceanographic and geodetic techniques, respectively.  The former is determined from oceanographic data such as temperature, salinity, permanent ocean patterns, wind-set, etc.  The latter is based on satellite radar altimetry data (SSH) and the CGG2005 geoid model (N):  SST = SSH – N.

[Click on an image thumbnail to view a larger image, notice]

 

Figure 1:  SST from oceanographic technique

Figure 2:  SST from geodetic technique

However, for coastal applications in Canada, it is more important to estimate the separation between the mean seal level and the equipotential surface representing the new vertical datum.  This separation can be expressed by SST_CHRS, where the subscript CHRS stands for Canadian Height Reference System and can be substituted by any specific vertical datums (e.g., CGVD28, NAVD88, CGG2005, ...)  The reference system for the new vertical datum for Canada is the mean water level at the tide gauge in Rimouski, Québec.  Thus, SST_{New Datum} is approximately zero for the coastal region of the Maritimes.  On the other hand, SST_{New Datum} for the region of Vancouver is close to 60 cm.  Figures 3 and 4 show a preliminary model of Sea Surface Topography with respect to CGG2005 geoid model (shifted to represent the Rimouski datum) for the North-East Pacific Ocean and North Atlantic Ocean, respectively.

Three procedures are proposed to estimate the sea surface topography with respect to the vertical datum (SST_CHRS) for Canada.  This will allow the determination of heights above mean sea level (H_MSL):

H_MSL = h_NAD83(CSRS)  – N_NAD83(CSRS)  – SST_CHRS

where h_NAD83(CSRS)  is the NAD83 ellipsoidal height and N_NAD83(CSRS)  is the NAD83 geoid height.

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 SST_CHRS grid will be estimated from GPS measurements, levelling observations, tide gauge information and radar satellite altimetry data.  The software will be available on-line. 

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 MSL and the vertical datum for Canada.  Table 1 shows SST_CHRS at some selected tide gauges in Canada based on CGG2005 geoid model.  These are preliminary data while waiting for the new geoid model that will include gravity data from the GOCE satellite mission and define the new vertical datum for Canada.

Table 1: Sample set of mean Sea Surface topography (SST_CGG2005) at specific tide gauges across Canada.  These are preliminary values based on CGG2005.

Site Name	Gauge No.	Location		Obs. Period		SSTCGG2005 (m)
		Lat.	Lon.	From	To
Halifax	490	44.667	-63.583	05/1988	04/2007	0.109
Vancouver	7795	49.34	-123.25	05/1988	04/2007	0.551
Tuktoyaktuk	6485	69.44	-132.99	08/2003	10/2006	0.034

Stakeholders can determine local SST_CHRS by conducting a GPS survey on reference markers at a tide gauge. The tide gauge information is available from the Marine Environmental Data Services (MEDS), Fisheries and Oceans Canada under Tide and Water Level (TWL).  The data set includes monthly mean sea level above chart datum (Z₀, see Inventory & Download of TWL digital archives) and elevations of the reference markers above the chart datum (H_CD, see TWL Regional Station Benchmark Database).  The reference markers can be located by the available descriptions and sketches.

The SST_CHRS can be determined as follows:

SST_CHRS = h_NAD83(CSRS) – N_NAD83(CSRS) – H_CD + Z₀

where h_NAD83(CSRS)  is the NAD83 ellipsoidal height, N_NAD83(CSRS)  is the NAD83 geoid height, H_CD is the elevation of the station above the chart datum and Z₀ is the separation between the mean water level and chart datum.

A crude procedure for estimating the local separation between mean sea level and the vertical datum (SST_CHRS) is to measure by spirit levelling technique the height difference between the low and high tides.  These measurements must be tied to a station with a known ellipsoidal height (h).  The approach is illustrated on Figure 4 [JPEG, 104.5 kb, 1267 X 943, notice]. 

The separation SST_CHRS can be determined as follows:

SST_CHRS = h_NAD83(CSRS) – N_NAD83(CSRS) – (Δ H_{High Tide} + Δ H_{Low Tide})/2.0

where Δ H_{High Tide} is the height differences between the reference marker and high tide and Δ H_{Low Tide} is the height difference between the reference marker and the low tide.