### Height Systems

The height (or elevation) of a point is defined as the vertical distance that separates it from a reference surface. If the reference surface is mean sea level (or geoid), the height is known as orthometric. If the ellipsoid is used as a reference surface, the height is referred to as ellipsoidal or geodetic. Ellipsoidal heights are geometric quantities that are insensitive to the potential of the gravity field. They are obtained by trigonometric levelling or GNSS. In contrast, orthometric heights are referenced to an equipotential surface called geoid, which is consistent with direction of water flow. Heights can be positive or negative depending on whether they are above or below their respective reference surface.

The geoid is a closed and continuous surface that best fits average mean sea level. It is the global reference surface of ‘zero’ orthometric height. Geoid heights are computed using models that combine information about the gravity field, terrain topography and Earth mass density. Knowing geoid heights (or geoid-ellipsoid separation), it is possible to transform GNSS heights to their orthometric equivalent. GNSS heighting can be a more efficient and cost effective way of levelling for many survey applications. Many GNSS receivers and processing software have built-in geoid models and deliver orthometric heights ‘out of the box’. However, global geoid models do not have a consistent accuracy level as the availability of local gravity data and accurate height information can vary greatly in different parts of the world. Therefore, special care should be taken when using global geoid models, as they may have varying accuracy. As orthometric and ellipsoidal heights may differ by up to one hundred metres depending on location in Canada, it is of utmost importance that users be aware of the type of height they are measuring or being provided.

In Canada, NRCan has published six national geoid models over the past 20 years. Each new model is a more accurate representation of the true geoid. Details on these geoids can be accessed at https://webapp.geod.nrcan.gc.ca/geod/data-donnees/geoid.php?locale=en. Practical details about geoid modelling and the public geoid models for Canada can be found at https://www.nrcan.gc.ca/earth-sciences/geomatics/geodetic-reference-systems/9054#_Toc372901508.

### Canadian Geodetic Vertical Datum of 1928 (CGVD28)

The CGVD28 was realized by measuring height differences between benchmarks distributed along Canada’s roads and railways using spirit levelling. Over a period of almost 100 years, lines connecting these benchmarks were formed and anchored to mean sea-level at a few tide gauges along Canada’s Atlantic, Pacific, and Arctic coastlines. The first national scale adjustment of all levelling lines was completed in 1928. This initial network was extended and densified until the end of the century by adding new levelling lines and re-adjusting them to the existing network in a piece-wise fashion. Currently, CGVD28 is accessible at about 80,000 benchmarks of the primary vertical control network, as well as a number of other benchmarks established by provincial agencies. Unfortunately, all these benchmarks are distributed over less than half of Canada’s landmass. To date, no practical or cost-effective means have become available to extend CGVD28 levelling lines to northern Canada and the arctic. While promoting the adoption of CGVD2013, NRCan continues to publish CGVD28 benchmark heights and the hybrid geoid model HTv2.0 to facilitate the comparison of solutions in both systems as gradual transition to the new datum is being encouraged.

### Canadian Geodetic Vertical Datum of 2013 (CGVD2013)

CGVD2013 is now the new reference standard for heights in Canada. CGVD2013 is defined by the equipotential surface which best represents the mean sea level around North America’s coastline. This new vertical datum is realized by the CGG2013 geoid model, which provides the separation between the GRS80 ellipsoid and the selected equipotential surface in the NAD83(CSRS) reference frame.

Unlike CGVD28, which can only be accessed at benchmarks, CGVD2013 is available at any location in Canada, the arctic and along its coastlines. The heights of CGVD28 benchmarks are also published in CGVD2013 following a readjustment of the entire federal first-order levelling network with constraints at a number of integrated CBN stations. In the geoid-based height system, the formal orthometric height of a point is now established by measuring the ellipsoidal height with GNSS and applying the CGVD2013 geoid height. As benchmarks are no longer maintained and have not been observed for several decades, their stability and the accuracy of their assigned heights cannot be confirmed. Therefore, published values should be used with caution mainly to verify whether the new GNSS determination is valid.

As CGG2013 is anchored to NAD83(CSRS) and geoid heights are assumed constant over time, CGVD2013 is considered a static reference. Nevertheless, reference to the 2011.0 epoch is required when transforming ellipsoidal heights between ITRF2008 and NAD83(CSRS) realizations. In general, the precision of CGG2013 varies from a few centimeters to a decimeter from coast to coast. Working in CGVD2013, GNSS and spirit-levelling height differences can be integrated seamlessly with centimeter precision at most spatial scales. For local height surveys that may require millimeter-level of relative precision, spirit-levelling may still be required and GNSS used only to connect to CGVD2013 reference.

More information about height datums can be found at http://www.nrcan.gc.ca/earth-sciences/geomatics/geodetic-reference-systems/9054. A procedure to convert heights between CGVD28 and CGVD2013 is described at https://www.nrcan.gc.ca/earth-sciences/geomatics/geodetic-reference-systems/9054#_Toc372901507.

### International Great Lakes Datum of 1985 (IGLD85)

IGLD85 is a regional vertical datum specially defined for the St-Lawrence Seaway and Great Lakes regions. IGLD85 differs from the CGVD realizations in the sense that it uses dynamic instead of orthometric heights. Dynamic height is most appropriate when working with water levels over a large geographic area as it accounts for the fact that the vertical distance between lines of equal potential is not constant. IGLD85 is based on the North American Vertical Datum adjustment of 1988 (NAVD88)* and has for origin the adopted elevation of the Rimouski water gauge in Quebec. IGLD85 is the realization of the mean water level at a set of master water gauges on the Great Lakes. More details about IGLD85 and NAVD88 can be found at https://www.ngs.noaa.gov/TOOLS/IGLD85/igld85.shtml. IGLD85 and NAVD88 heights can be converted to one another by a utility available at https://www.ngs.noaa.gov/cgi-bin/IGLD85/IGLD85.prl. IGLD85 heights for Canadian benchmarks are available by contacting NRCan.

* NAVD88 was adopted as the official vertical datum in the National Spatial Reference System (NSRS) for the conterminous United States and Alaska in 1993. It is a tidal datum defined by the mean water level at the tide gauge in Rimouski, Québec, propagated over land using geodetic levelling. The vertical datum is accessible at benchmarks. NAVD88 heights are Helmert orthometric. Although Canada did not adopt NAVD88, heights in this system are available on a subset of stations of the Canadian levelling network.