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. Three site/spec factors that set how densely a terrain must be sampled.
Find. The direction and reason of each factor's effect on the interval.
(a) Terrain roughness. Rougher terrain contains higher spatial frequencies (short-wavelength undulations), so a finer sampling interval is required to capture them—by a Nyquist argument the interval must be at most half the wavelength of the smallest feature to be resolved. Over smooth terrain the interval can be coarse without loss, so roughness and interval are inversely related.
(b) Required surface accuracy. Higher accuracy demands a smaller interval, because interpolation error grows with sample spacing: between samples the surface is approximated (linearly, in a TIN), and the departure of the true surface from that approximation scales with the spacing and the local curvature. Tightening the accuracy specification therefore forces denser sampling (at higher cost).
(c) Terrain slope. Steeper and more variable slopes carry larger elevation change per unit distance and often sharper curvature, so a finer interval is needed to keep the vertical interpolation error within tolerance; a given planimetric error also maps into a larger height error on steep ground. Gentle, uniform slopes tolerate a coarser interval. Efficient practice therefore uses adaptive/progressive sampling—dense where rough or steep, sparse where flat.
