18-Geom-B1 Digital Terrain Modelling · December 2015
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format: National Exams, December 2015 — 3 hours, closed book (an approved Casio or Sharp calculator permitted). TWELVE numbered questions constitute a complete paper; each is of varying value and the margin schedule totals 100 marks. Most answers are required in essay format, so clarity and organization are graded. All twelve questions are solved below for completeness.
Reference texts: Li, Zhu & Gold, Digital Terrain Modeling — Principles and Methodology (CRC Press, 2005); Maune (ed.), Digital Elevation Model Technologies and Applications: The DEM Users Manual (2nd ed., ASPRS, 2007); Wilson & Gallant, Terrain Analysis — Principles and Applications (Wiley, 2000); Wolf, Dewitt & Wilkinson, Elements of Photogrammetry with Applications in GIS (4th ed., McGraw-Hill); Natural Resources Canada High-Resolution DEM (HRDEM) and CDEM product specifications. Canadian datums throughout (NAD83(CSRS), CGVD2013).
Note: this December 2015 paper is the same twelve-question essay set as the December 2014 04-Geom-B1 exam, re-ordered and with one definition changed (Q3(e) asks for the contour interval where the 2014 paper asked for the interpolation method). The margin marks are internally consistent this year — every sub-part annotation matches its header weight and the schedule sums to 100.
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. Five terms central to building, describing and portraying a terrain model.
Find. A precise definition of each.
(a) Breaklines. Linear features along which the terrain slope changes abruptly—ridge lines, valley/drainage lines, the tops and toes of banks, road crowns, curbs, retaining walls and shorelines. They are stored as constraints so that interpolation and triangulation are not allowed to cross them, preserving the discontinuity. A hard breakline marks a true slope break (a ditch); a soft breakline enforces a feature edge without a slope change (a mapped boundary).
(b) Spot heights. Discrete, individually measured points of known elevation placed at locally significant locations—summits, depressions (pits), saddles, and other points the grid would otherwise miss. They supplement the systematic samples and anchor the surface at critical morphological points.
(c) Sampling interval. The spacing (ground distance) between adjacent elevation samples—the grid post-spacing or the mean point spacing of an irregular set. It governs the spatial resolution of the model, the smallest terrain feature that can be represented (a Nyquist-type limit), the data volume, and the achievable accuracy.
(d) Elevation data accuracy. The closeness of the modelled heights to their true values, i.e. the vertical accuracy, usually quantified as a root-mean-square error $\text{RMSE}_z$ or, following the ASPRS/NSSDA convention, as a 95%-confidence value ($\text{RMSE}_z\times1.96$ in open terrain). It is a function of the source technique, the sampling interval, the terrain and the interpolation.
(e) Contour interval. The constant vertical distance between successive contour lines used to portray the surface—for example a 1 m, 5 m or 10 m interval. It is chosen from the map scale, the relief and steepness of the ground, and the accuracy of the source data: a small interval reveals more detail but the lines crowd together (and can merge) on steep slopes, while a larger interval is used for steep terrain or small-scale maps. As a guide the interval is kept larger than roughly three to four times the vertical $\text{RMSE}_z$, so that adjacent contours reflect real relief rather than height noise.
