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 closely related but distinct digital representations of height data over a landscape.
Find. The defining difference of each of DTM, DEM and DSM.
(a) Digital Terrain Model (DTM). A DTM is a digital representation of the bare-earth topographic surface—the ground with all buildings and vegetation removed—together with the morphological information that describes its shape. In addition to a set of elevations it carries structural terrain elements such as breaklines, ridge and drainage (form) lines, spot heights at peaks, pits and saddles, and sometimes coded surface types. It is therefore the richest of the three: a structured surface model from which slope, aspect, contours and drainage can be derived faithfully because the discontinuities of the terrain are explicitly stored.
(b) Digital Elevation Model (DEM). A DEM is the simplest form: a bare-earth surface stored as elevation only, almost always as a regular raster grid of height posts at a fixed spacing (a $Z$ value per cell, referenced by row/column). It contains no explicit breaklines or feature coding—just the height field—so it is essentially a DTM stripped down to a gridded elevation array. In many texts “DEM” is used as the umbrella term, but strictly it denotes the gridded bare-earth heights.
(c) Digital Surface Model (DSM). A DSM represents the top reflective surface of the landscape as sensed—the first return—so it includes above-ground objects: building roofs, tree canopy, bridges and other features. It is what a Lidar first-return or an image-matching correlator measures directly before any filtering. The essential contrast is: DSM = ground plus everything on it; DEM = bare-earth heights on a grid; DTM = bare-earth surface enriched with terrain structure. A DEM/DTM is produced from a DSM by filtering out the non-ground points.
