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) Polar motion. Polar motion is the small, quasi-periodic wandering of the Earth’s instantaneous rotation axis relative to the crust (relative to a conventional reference pole, the CIP/IRP). Its main components are the ~14-month Chandler wobble and an annual term, with the pole wandering within roughly ±10 m (a few tenths of an arc-second) of its mean position, plus a slow secular drift. It is one of the Earth-orientation parameters, monitored by the IERS (via VLBI/GNSS) and required to relate the terrestrial and celestial frames.

(b) Atomic time. Atomic time is a uniform time scale defined by the frequency of the caesium-133 hyperfine transition (one SI second = 9 192 631 770 cycles). International Atomic Time (TAI) is the weighted average of many atomic clocks and flows at a constant rate, independent of the Earth’s rotation. Coordinated Universal Time (UTC) is derived from TAI but kept within 0.9 s of Earth-rotation time (UT1) by leap seconds; GPS time is a continuous atomic scale offset from TAI by a constant.

(c) Sidereal time. Sidereal time is time measured by the apparent diurnal rotation of the Earth with respect to the stars (the vernal equinox) rather than the Sun; local sidereal time equals the hour angle of the equinox and, numerically, the right ascension of a star on the observer’s meridian. A sidereal day (~23 h 56 m) is about 4 minutes shorter than a solar day because the Earth must turn a little further each day to face the Sun again. It links Earth rotation to the celestial frame and is fundamental to astronomic position and azimuth determination.

(d) GNSS-PPP. Precise Point Positioning determines absolute coordinates with a single dual-frequency GNSS receiver — no local base — by applying precise satellite orbit and clock products (from the IGS or NRCan) and rigorously modelling the ionosphere, troposphere, tides and antenna effects. A RINEX file is submitted to a service such as NRCan’s CSRS-PPP, which returns coordinates directly in NAD83(CSRS) or ITRF at a chosen epoch. Static accuracy reaches the centimetre level after a convergence period of roughly an hour or more (better with longer sessions).

(e) Combined factor. The combined factor (grid factor) is the single multiplier that converts a horizontal ground distance directly to its grid (plane-projection) distance. It is the product of the elevation factor (ground→ellipsoid) and the projection scale factor \(k\) (ellipsoid→grid): \(CF=\dfrac{R}{R+H}\,k\). For example with \(EF=0.9997646\) and \(k=0.99985\), \(CF=0.99961\), so a 1000 m ground line plots as 999.61 m on the grid.

(f) Geodetic datum. A geodetic datum is the set of parameters that defines the position, orientation and scale of a coordinate reference system for the Earth — a reference ellipsoid (size and shape) plus its location and orientation relative to the Earth’s body, and, in modern practice, the epoch and station coordinates/velocities that realize the frame. A horizontal datum (e.g. NAD83(CSRS)) fixes latitude/longitude; a vertical datum (e.g. CGVD2013) fixes heights. It is the agreed foundation to which all coordinates in a region are referred.

(g) Canadian Base Network (CBN). The CBN is a national framework of about 160 high-precision, forced-centring pillar-monumented GNSS control stations (spacing of a few hundred km) 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 passive control to which lower-order surveys connect.

(h) 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 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.

(i) RINEX. RINEX (Receiver INdependent EXchange format) is the standard ASCII 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 submitted to services such as CSRS-PPP.

(j) IGS. The International GNSS Service is a voluntary federation of agencies operating a global network of tracking stations and analysis centres that produce freely available high-precision GNSS products — precise satellite orbits and clocks, Earth-rotation parameters, station coordinates and ionosphere/troposphere models. Its products underpin PPP and the maintenance of the ITRF. It is the civilian backbone of precise global GNSS positioning.