Question 7 of 7: Brief Definitions

Question 7: Brief Definitions (20 marks — 2 each)

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 / Find. Concise, accurate two-to-three-sentence definitions of ten geodetic terms.

(a) Meridian convergence. Meridian convergence \(\gamma\) is the angle at a point between grid north (parallel to the projection’s central meridian) and true (geodetic) north; it arises because the meridians converge toward the pole while the grid lines stay parallel. To first order \(\gamma \approx \Delta\lambda\,\sin\varphi\), so it is zero on the central meridian and grows with latitude and with longitude difference — reaching about \(3^\circ\sin 49^\circ \approx 2.3^\circ\) at a UTM zone edge in southern Canada. It must be applied to convert a geodetic azimuth to a grid bearing.

(b) Tissot’s indicatrix. Tissot’s indicatrix is the small ellipse into which an infinitesimal circle on the ellipsoid is mapped by a projection; its shape, size and orientation reveal the projection’s local distortion. A circular indicatrix means the projection is conformal at that point (angles preserved); an ellipse of unit area means it is equal-area. It is the standard graphical tool for visualizing scale, angular and area distortion across a map.

(c) Inertial reference coordinate system. An inertial (celestial) coordinate system is one that is non-rotating and non-accelerating with respect to distant matter, in which Newton’s laws hold without fictitious forces. In geodesy it is realized by the directions to extragalactic radio sources (the ICRF), and satellite orbits are naturally described in it. It is the frame against which the Earth’s rotation, precession and nutation are referred.

(d) Apparent coordinate system. Apparent (star) coordinates are the celestial coordinates of a body as actually seen by an observer at a given epoch, after the mean catalogue place has been corrected for precession, nutation, annual aberration and parallax. They give the true observed direction at the instant of observation. Astronomic azimuth and latitude determinations use the apparent places of stars.

(e) Geopotential number. The geopotential number \(C\) of a point is the difference in gravity potential between the geoid and the level surface through the point, \(C = W_0 - W_P = \int g\,dn\) (obtained from levelled height differences weighted by gravity). It is expressed in geopotential units (1 g.p.u. \(= 10\ \text{m}^2\,\text{s}^{-2}\)) and is the rigorous, path-independent measure of “height” in the gravity field. Orthometric, normal and dynamic heights are all derived from \(C\) by dividing by an appropriate gravity value.

(f) Helmert orthometric height. The Helmert orthometric height is the orthometric height \(H = C/\bar{g}\) in which the mean gravity \(\bar{g}\) along the plumb line is approximated by Helmert’s formula, \(\bar{g} = g + 0.0424\,H\) (gal, with \(H\) in km) — i.e. surface gravity corrected by half the Poincaré–Prey (free-air + Bouguer) reduction. It is the height system realized in CGVD2013 (and in NAVD88), whereas the older CGVD28 used normal-orthometric heights. Its small error comes from approximating the true mean gravity inside the topography.

(g) RINEX. RINEX (Receiver INdependent EXchange format) is the standard ASCII text format for exchanging raw GNSS data — carrier-phase, pseudorange and Doppler observations plus the broadcast navigation message — independently of the receiver manufacturer. It lets data from different receivers be processed together in any post-processing or PPP software and is the format in which files are submitted to services such as CSRS-PPP. Standard file types include observation and navigation files.

(h) Conformal map. A conformal (orthomorphic) map projection preserves angles locally: at every point the scale factor is the same in all directions, so infinitesimally small shapes are reproduced without distortion (Tissot’s indicatrix is a circle). Transverse Mercator (UTM, MTM) and Lambert Conformal Conic are conformal, which is why they are standard for surveying and navigation. The price is that areas are distorted.

(i) Canadian Base Network (CBN). The CBN is a national framework of about 160 high-stability, forced-centring pillar monuments across Canada, repeatedly observed with GNSS observed to tie the country rigorously into NAD83(CSRS)/ITRF. Together with the continuously operating CACS stations it realizes and maintains the Canadian Spatial Reference System, providing the control to which lower-order surveys connect. Its stations, typically a few hundred kilometres apart, densify the active-control framework.

(j) IERS. The International Earth Rotation and Reference Systems Service is the body responsible for maintaining the international celestial (ICRF) and terrestrial (ITRF) reference frames and the Earth-orientation parameters (polar motion, UT1−UTC, precession–nutation offsets) that connect them. It also announces leap seconds. Its products are the global backbone to which national frames such as NAD83(CSRS) are tied.