Question 1 of 7: Coordinate Systems, Reference Frames and Datums

Question 1: Coordinate Systems, Reference Frames and Datums (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given. Two realizations of NAD83 in Canadian practice — NAD83(original), the 1986 continental adjustment, and NAD83(CSRS), the modern space-geodetic realization tagged with an epoch — together with the global ITRF used internationally.

Find. (a)(i) the main differences between the two NAD83 versions; (a)(ii) the meaning of “(CSRS+epoch)” and why the epoch matters; (b) the similarities and differences between NAD83(CSRS) and ITRF, with the order of magnitude of any offset.

(a)(i) NAD83(original) vs NAD83(CSRS). NAD83(original) — in Canada the 1986 adjustment, sometimes written NAD83(1986) — was defined largely from terrestrial observations (triangulation, trilateration, traverse) with a limited amount of early Doppler satellite data, and it was held fixed to that 1980s solution. Its internal consistency is only at the metre-to-decimetre level over continental distances, and it carries no rigorous connection to a geocentric, time-dependent global frame. NAD83(CSRS) is the Canadian Spatial Reference System realization: it is defined by high-precision GNSS observations at the Canadian Active Control System (CACS) and Canadian Base Network (CBN) stations, rigorously connected to the ITRF through a published transformation, and internally consistent to a few centimetres with epoch-dependent coordinates. Both versions keep the same NAD83 datum definition — the GRS80 ellipsoid and an origin about 2 m from the true geocentre — so NAD83(CSRS) is not geocentric to the centimetre; what changed is the accuracy of the realization. Because the original adjustment carried network distortions, the same mark’s coordinates differ between the two versions by decimetres, locally approaching a metre, so the versions are not interchangeable without a transformation.

(a)(ii) Meaning of “(CSRS+epoch)” and the importance of epoch. “CSRS” identifies the realization (the Canadian Spatial Reference System, tied to a specific ITRF solution such as ITRF2005 or ITRF2008 through a published transformation). The “epoch” is the reference date, expressed as a decimal year (e.g. 2010.0), at which the published coordinates are valid. Epoch is essential because the Earth’s crust is not rigid: the North American plate moves at roughly 1–2 cm/yr, and additional local motion (glacial isostatic adjustment, subsidence) can add millimetres to centimetres per year. A point’s coordinates therefore change measurably with time. Stating the epoch fixes when the coordinates apply; to combine or compare observations taken at different times one must propagate coordinates from one epoch to another using a crustal-velocity model (e.g. NRCan’s velocity grid). Omitting the epoch makes a centimetre-level coordinate ambiguous.

(b) NAD83(CSRS) vs ITRF. Similarities: both are three-dimensional, Earth-centred Earth-fixed Cartesian (X, Y, Z) / ellipsoidal reference frames realized from space geodesy (GNSS, VLBI, SLR); both are epoch-based and time-dependent; and NAD83(CSRS) is defined through a published 14-parameter (Helmert + rates) transformation from a specific ITRF, so their internal precision is comparable at the centimetre level. Differences: NAD83(CSRS) is attached to the stable interior of the North American plate, so points on that plate appear nearly stationary in it, whereas in ITRF the same points drift at the full plate velocity; and the two frames have different origins and orientations, so coordinates for the same mark differ by roughly 1–2 m in horizontal position (ITRF is geocentric, whereas NAD83(CSRS) keeps the historic NAD83 origin about 2 m from the geocentre), with the discrepancy growing over time at the plate-motion rate if the epoch is not tracked. Practically: use NAD83(CSRS) for Canadian mapping and cadastre; convert to ITRF (with epoch) for global or scientific work.