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) Nutation of the Earth’s spin axis. Nutation is the small, short-period (periods up to ~18.6 years and shorter) “nodding” oscillation of the Earth’s rotation axis in space, superimposed on the much larger, ~25,800-year precession. It is caused by the periodically varying luni-solar gravitational torques on the equatorial bulge and reaches amplitudes of a about 9 arc-seconds (the principal 18.6-year term, 9.2″). It must be modelled to relate the instantaneous (true) celestial pole to the mean pole.

(b) 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.

(c) 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 apparent places of stars.

(d) 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 m²s⁻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.

(e) 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 NAVD 88), whereas the older CGVD28 used normal-orthometric heights. Its small error comes from approximating the true mean gravity inside the topography.

(f) 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.

(g) Satellite altimetry. Satellite altimetry measures the height of a satellite above the sea (or ice/land) surface by timing a radar (or, for ICESat, laser) pulse’s round trip; combined with the precisely known satellite orbit it yields the height of the reflecting surface relative to the ellipsoid. Over the oceans it maps sea-surface height and, after removing ocean dynamics, the marine geoid. Missions such as TOPEX/Poseidon, Jason and ICESat exemplify the technique.

(h) Canadian Base Network (CBN). The CBN is a national framework of about 160 high-precision, monumented GNSS control stations across Canada, 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 spacing (~200 km) densifies the active-control framework.

(i) 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.

(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.