Continuous Vertical Datum for Canadian Waters (CVDCW)

When navigating a ship the number one objective is to not sink the ship. To achieve this, it of course helps if the ship does not run into anything above or below the water surface but it is not always possible to see submerged objects coming up in time to navigate around them and so the navigator of a ship will refer to a chart in order to avoid obstacles. These charts contain 2 pieces of information, the horizontal position of features, and their associated depth in relationship to what is called the chart datum. 
Chart datum is defined in Canada as the Lower Low Water, Large Tide (LLWLT) which is to say that the depth is relative to the yearly average of the predicted lowest water level for a 19 year lunar cycle based on observations from tide gauges. The water depths are then determined through bathymetric surveys in relation to these tide gauges. With the advent of GNSS the ocean mapping community saw the advantage to perform their surveys in relationship to the ellipsoid and then linking these heights to the tide gauges, this in turn lead the Canadian Hydrographic Service (CHS) to create a seperation model (SEP) between the chart datum and the ellipsoid by measuring the separation with GNSS on the tide gauges.
Of course the ocean system is dynamic, meaning that the water levels measured at a tide gauge are only relevant to those waters nearby (less than 10 km) as water levels are not a linear function of distance. This is due to different factors that change over time such as the chemical composition of the water, the currents, etc.. This creates a problem as it would be unrealistic to have a complete network of permanent tide gauges covering the entire Canadian coastline (stretching over 200,000 km it is the longest in the world) and re-survey these waters, tieing them into the tide gauges.
And so in 2010 the CHS and the Canadian Geodetic Survey (CGS) to examine the possibility of creating a model that would represent the continuously changing water levels which would be called the Continuous Vertical Datum for Canadian Waters. Such a model will aid in defining; coastlines, inter-tidal zones, maritime boundaries, marine cadastres, claims to sovereignty. As well as serving as a baseline for sea level rise & related climate change adaptation strategies, and improve coastal infrastructure maintenance & development.
To get an idea of just how complex such a model is, the input data for the model includes; the Canadian Gravimetric Geoid of 2013 (CGG2013), GNSS observations, Satellite Altimetry, Water Level Observations, Ocean Models, and Coastline Surveys.
As you are starting to gather by now, this is an extremely complex project that encompasses the most challenging of problems over multiple fields and disciplines. Aka a perfect topic for the Geodesy Corner and I look forward to exploring this further in the weeks to come.
Adapted from:
Catherine Robin, Shannon Nudds, Phillip MacAulay, Andre Godin, Bodo De Lange Boom & Jason Bartlett (2016) Hydrographic Vertical Seperation Surfaces (HyVSEPs) for the Tidal Waters of Canada. Marine Geodesy, 39:2, 195-222, DIO:10.1080/01490419.2016.1160011

Right-Handed/Left-Handed Rules

For any kind of vector mathematics it is common to find cases in which you want to find a vector that is perpendicular to two other vectors, e.x. current/magnetic field/force, the moment of force (the cross-product of two force vectors), coordinates, etc.. We know from linear algebra that we can calculate this perpendicular vector by taking the cross-product of the two vectors. The problem is that the cross product can yield an answer with two possible orientations depending on the order of the vectors within the cross-product equation.

To establish a way of properly orientating the vectors we can use the mnemonic of the right-handed or left-handed rule. This is where you ‘assign’ your thumb as the the third vector, or ‘Z’, your fingers as the first vector, or ‘X’, and then your palm is pointed in the direction of the second vector, or ‘Y’.

Left handed rule.png

Left-Handed Rule

Right handed rule.png

Right-Handed Rule


Describing a Coordinate System

One of the fundamentals of any spatial project is establishing a coordinate system to describe the data. This coordinate system allows us to pass our data along to another person and they are able to understand it, or enter the data into a computer system to process the data.

A coordinate system is described by an origin, the orientation of three axes, and the parameters of which describe the position. (Krakiwsky and Wells, 1971)

the origin.pngThe origin of a system is an arbitrary point of which all measurements will be in relation to, this point is often a stable, non-moving, point at the center or corner of the measurements. The origin must be a clearly defined point so that it maybe related to other coordinate systems, for example, we describe the origin of a geocentric system as being the center of mass of the earth.

The Tertiary Axis.pngOften the next part of the coordinate system we describe is the tertiary axis. In most topocentric terrestrial coordinate systems we define this as being inline with the plumb-line, i.e. the direction of gravity at that point, at the point of origin with the positive direction being in the zenith direction though it could run in the nadir direction. In some cases it is to our advantage to define the axis in terms of a primary pole which is an axis of symmetry for the system. Often for geocentric systems we assign the primary pole as the spin axis of the earth.

Primary Plane.pngAfter the tertiary axis is defined we may set the primary plane as a plane that contains the origin and is perpendicular to the tertiary axis. Often for geocentric systems the primary plane is often the equator. Contained within the primary plane is the primary axis, and the secondary axis. 

Secondary Plane.pngWe can establish the primary axis through defining a secondary plane which is a plane that is perpendicular to the primary plane and contains the origin as well as another point, whether it be of interest or an arbitrary point. The intersection of the primary and secondary planes is then the primary axis with the values running positive in the direction of the defining point, this axis is also sometimes referred to as the secondary pole. For most earth systems Greenwich, UK, is the arbitrary point used to define the secondary plane.

Secondary Axis.pngThe secondary axis is then defined as a line that runs perpendicular to the primary and tertiary axes. The direction of this axis is defined by the right/left-handed orientation. Figure (V) uses the left-handed rule.

The parameters that describe a system will be covered more in-depth in a later post.

References/Further Reading:

Great Britain. (1965). Admiralty manual of Hydrographic Surveying. London. England: Hydrographer of the Navy. Vol I

Krakiwsky, E. J., & Wells (1971). Coordinate Systems in Geodesy. Fredericton, N.B: Dept. of Surveying Engineering, University of New Brunswick.

Vaníček, P., & Krakiwsky, E. J. (1986). Geodesy: the concepts. Amsterdam: North Holland.